View Full Version : A Meta-Metaphysical Question
My question is - why are metaphysical questions undecidable?
Don't feel obliged to read any more of this before answering, it's a bit long, but I wanted to put the question in some sort of context and so focus any discussion, and also see what objections are made to my thoughts on the issues.
Metaphysical questions are defined as coming ‘after’ Physics, or as having answers that lie ‘beyond’ Nature. Now, if such questions were simply beyond the reach of science to answer then we could argue that the existence and intractability of these questions is evidence for the inadequacy of the scientific method, the falsity of the ‘scientific view’, or the incoherence of the beliefs of many scientists. This is not an uncommon argument.
However metaphysical questions are not simply undecidable in this sense. They are undecidable in a formal mathematical sense. That is, all reasonable answers to a metaphysical question give rise to contradictions within the formal systems of reasoning that give rise to the question. That is to say, metaphysical questions cannot be decided within the system of reasoning used by the person who is asking the question. This is for the same reasons that ‘Gödel-sentences’ cannot be decided within the formal systems in which they arise.
What this means is that if it were found to be the case that either answer to a metaphysical question were true or false then this would contradict our reason and call into question our whole notion of logic and illogic, consistency and inconsistency. It would mean that the explanation of our existence contradicts our reason. This presents us with a stark choice of view. Either we must conclude that metaphysical questions are formally undecidable or that the true explanation for the existence of our universe contradicts reason.
This dilemma can be illustrated by looking at the question ‘did the universe arise from something or nothing?’ This is a pretty simple question, and it appears to be a perfectly reasonable and meaningful one. On the surface there seems no reason why it should be undecidable in principle.
Yet it is. This simple little question has baffled thinkers for millenia. Both answers to it give rise to logical contradictions, so neither answer can be correct according to common sense. No reasonable answer to it is given anywhere in western metaphysics or the scientific literature. It is such an impossible question that some philosophers have argued that it's not a question at all.
It doesn’t take much analysis to uncover the paradoxes that appear if we try to answer this question by deductive reasoning. If the universe arose from something that existed already then clearly this just begs the question. What did this ‘something that already existed’ itself arise from, something or nothing? And if spacetime comes into existence with this universe, as most scientists seem to believe, then how can something have existed ‘before’ this universe? In what sense can something be said to ‘exist’ if it has no extension in either time or space?
Perhaps some kind of God predated the universe. But if so where did He, She or It appear from? To appeal to a divine miracle begs the question again. Why isn’t there just nothing at all?
Perhaps philosophical idealism is true, in which case consciousness is fundamental and we are all figments of our own imagination. But this doesn’t help. Whose imagination is doing this imagining? If, as in Berkeley’s idealism, to be is to be perceived and to perceive is to be, then it is not possible for the perceiver to exist before the perceived, nor for the perceived to exist before the perceiver, nor possible for them to come into existence at the same time except by coincidence. And what did this perceiving or perceived entity arise from?
Does ex nihilo creation make sense? Cosmologist Alan Guth has conjectured that it might be possible, and even necessary, to devise a theory of how the universe comes into being from nothing. However, and perhaps this is a just matter of opinion, there seems to be an air of desperation about the idea, and I can't help feeling that any such theory would be bound to contradict reason at some point, mine anyway.
It’s hopeless. Metaphysical questions are always questions about ultimate reality, what it is that lies outside the cave, behind the world of appearances, and they have no reasonable answers. There are no exceptions to this rule for this is how we define 'metaphysical questions'.
I’ve run through all this before asking my question because sometimes metaphysical questions are thought to be simply undecidable by physics, when in fact they are undecidable in a much stronger sense than this. One of the most secure pieces of knowledge about reality that we have is that metaphysical questions, questions about what is ultimately real or ultimately true, have no reasonable answers, cannot be answered without causing logical contradictions.
The situation we find ourselves in is one in which either the existence of the universe contradicts reason, or all questions about what is ultimate and fundamental, ‘ultimate reality’ if you like, are undecidable by reason. If this is the case then there seem to be only three possible views as to why this might be the case.
The first possiblility, or possible view, is that it is not true to say that we and our universe arise from something or nothing. In this view the universe arises from ‘something’ undefinable that cannot be properly characterised as being either something or nothing, and the 'something-nothing' question, and other such questions about reality, embody false assumptions and therefore cannot be answered non-contradictorily.
The second possibility is that the true explanation for the existence of ourselves and our universe makes complete sense, is perfectly reasonable, is self-consistent in a formal mathematical sense, but that for some reason it does not appear to be so to human beings. Equivalently, the explanation is logically consistent, but in a way that is beyond the ability of human reasoning to understand.
The third possibility is that we and our universe exist for reasons that would, if we knew them, contradict our reason. This seems unlikely to me, but I notice that respected science-writer Paul Davies speculates on this possibility in his book 'The Mind of God'.
To me these seem to be the only three possibilities, and all explanations of the universe seem in the end to rest on one of these three views. However, I'm sure not everyone will agree (I hope not anyway).
My question is then, (and sorry for the length of it), why are metaphysical questions undecidable? And would you agree that the three answers to it I've outlined above are the only possibilities?
Iacchus32
Nov28-04, 09:54 PM
Is it possible that there's another dimension, more akin to the realm of thought (http://www.physicsforums.com/showthread.php?t=49670) let's say, which gave rise to the material dimension?
I'd say very possible. But why would this make metaphysical questions undecidable?
By the way, sorry about the ridiculously long question. I can see now that I wrote far too much, but I can't get back to it to delete any of it. Is there a time limit on edits?
"If the conclusion is absurd and the logic is correct then the premises must be re-examined." The obvious logical answer is that at least one or our assumed premises must be wrong. IMHO the most likely candidates are that the universe must have a beginning, must have arisen at all much less from something or from nothing. The other is that the universe is all that there is.
If there is an "Ultimate Reality" of which the universe is part then the Ultimate reality must either have arisen or be eternal. This again begs the question as you said; so, if there must be an answer then the answer must be that something is eternal. As hard as that is to except it is more logical or reasonable than something haven arisen spontaneously without reason or cause from nothing.
To answer your question, I would say that all reasonable metaphysical questions have reasonable answers; but, as they are metaphysical questions so are the answers; that is, outside of or beyond physics.
It is not reasonable to expect a physical answer that can be empirically tested and proven to a metaphysical question. Nor is it reasonable to apply physical, scientific methodology to a metaphysical question.
I fully realize that this is not a satisfactory answer to most physicalist; but, would one reasonable use mechanical or carpentry tools to bake a cake? Physics, science and logic are after all only tools that we use to learn, know and reason. They, like all tools, are useless even harmful when misapplied.
When asking metaphysical questions we must expect, look for and accept metaphysical answers. This is perfectly logical, reasonable and acceptable to me. This is, however, totally illogical, unreasonable and unacceptable to most physicalist. This says something about physicalist but I will refrain from saying any more as I do not want to start that old fight again.
I agree with a lot of that. But I feel you've slightly dodged the question. Certainly there can be no scientific answers to metaphysical questions (not unless we decide to redefine science anyway) but why are there no answers at all? This is why I wrote so much at the start, to get away from the idea that questions about reality are simply beyond science. That isn't too hard to live with, but the situation is worse than that. Why is it that, according to reason, it is impossible for any answer to these questions to ever be given?
Why is it that, according to reason, it is impossible for any answer to these questions to ever be given?
You will have to define what you mean by reason. If you mean formal logical reasoning then the answer to your question is that most of the questions do not lend themselves to formal logical reasoning as there is no inductive or deductive proofs. That is why it is metaphysics.
There is no way that the existence of anything can be proven empirically in metaphysics because there is no empirical reasoning in metaphysics. If there is empirical reasoning then it is physics. Logic can be used but can only be used if we make assumptions that can not be proved.
In other words, to answer your question directly, if there are proven answers it isn't metaphysics. If it is metaphysics then there are no provable or reasonable answers without prior unprovable assumptions.
It is the nature of the beast, a built in catch 22. If there are reasonable answers it ain't metaphysics. If there are no reasonable answers then it is metaphysics.
The wonderful thing about metaphysics is that it is an area of pure speculation. We are free to make assumptions of any sort and go from there and there is no end, no conclusion, no restrictions and no rules. Given the beginning assumptions we should use the rules of reason and logic but that doesn't mean that there is any satisfactory conclusion to be made or even possible. If you want answers stick with mathematics or formal logic. Even physics has more questions than answers and the boundary between physics and metaphysics is blurring more and more the more we learn.
selfAdjoint
Nov30-04, 09:48 AM
Metaphysical questions have traditionally been about either being or knowledge. Those which are about knowledge risk the trap of self reference, which could lead to undecidability in the formal sense (but I am not aware of any proof that this is so). Questions about being turn on individual definitions of being, which is vague, and entails the definition of non-being, which is even more vague than being. So I don't think philosophers' sayings about being can be anything more than an art form.
Why is it that, according to reason, it is impossible for any answer to these questions to ever be given?
The human brain may never be able to understand and answer metaphysical questions because it is bi-polar in its nature of thinking. It can only take a measurement from a position of analyzing opposite ends, based on an unchanging set of laws. Why we may never know where the universe came from, what matter is made of, or what is the mind matter relationship is, demands the question, is there something outside of physical systems? There may be but as long as it is inside of a body, analyzing the outside, we will not know what it really is, nor know the answers to which it is related. If there is a after life maybe this non-physical being will be able to analyze a holistic metaphysical existence and know those answers.
You will have to define what you mean by reason. If you mean formal logical reasoning then the answer to your question is that most of the questions do not lend themselves to formal logical reasoning as there is no inductive or deductive proofs. That is why it is metaphysics.
Yes, that is what I mean by 'reason'.
It seems true that these questions do not lend themselves to inductive or deductive solutions, the question is why this is so.
There is no way that the existence of anything can be proven empirically in metaphysics because there is no empirical reasoning in metaphysics. If there is empirical reasoning then it is physics.
It's not correct to say that metaphysics is not empirical. The facts about the world that we know empirically are the basis for metaphysical speculation, and so are all the facts of physics. One cannot speculate metaphysically without the knowledge gained through ones sense, and it would be odd to ignore the empirically confirmed findings of physicists. These days most philosophers are pretty knowledgable about physics, they have to be.
Logic can be used but can only be used if we make assumptions that can not be proved.
Yes, there is no other form of formal logic but the construction of systems based on unproven assumptions. But you seem to be saying that formal logic cannot be used in metaphysics, which I cannot agree with. It is formal logic that tells us that metaphysical questions are undecidable.
In other words, to answer your question directly, if there are proven answers it isn't metaphysics. If it is metaphysics then there are no provable or reasonable answers without prior unprovable assumptions.
I agree that there are no provable or reasonable answers to these questions, whether or not we make assumptions. Metaphysical questions just do not have reasonable answers. But my question was not about whether this is so, but why.
The wonderful thing about metaphysics is that it is an area of pure speculation. We are free to make assumptions of any sort and go from there and there is no end, no conclusion, no restrictions and no rules.
Here I very much disagree. Doing metaphysics isn't an excuse to give up rationality.
Given the beginning assumptions we should use the rules of reason and logic but that doesn't mean that there is any satisfactory conclusion to be made or even possible.
Yes, but why not? The questions are simple enough, why can't they be answered? For example, if materialism is true (is the case) then why can't we falsify idealism. What is it about 'reality' that prohibits us from deciding these quetions one way or the other, even if only in principle. Whether we can prove things one way or the other is not the point here. These questions cannot be answered even hypothetically without contradiction.
If you want answers stick with mathematics or formal logic. Even physics has more questions than answers and the boundary between physics and metaphysics is blurring more and more the more we learn.
Yes, I have no intention of giving up formal logic, and see no need to. I would say that formal logic suggests that metaphysical questions cannot be answered because none of their answers are correct, not because there's something logically inconsistent about our existence.
It seems true that these questions do not lend themselves to inductive or deductive solutions, the question is why this is so.
They do, as I said. It is just that the premises and/or conclusions are not acceptable to most, primarily because the premises are speculative, subjective and not provable. For example: The universe is eternal or had a beginning. We cannot prove either way but once we accept that it had a beginning we can argue what that beginning was, the Big Bang or Created.
In ether case it had to come from somewhere or something or from nothing.
Somewhere or some hing brings another questions of where that something came from etc. This is no answer so that leaves the choice of either the universe is eternal or that from which it came is eternal. That is a valid reasonable conclusion and an answer. Is it acceptable? Most would say, no.
Yet it is a reasonable logical answer reached by reason and logic once a speculative premise is agreed upon for the sake of the argument. It is a classical method of deductive reasoning via reductio ad absurdum.
It's not correct to say that metaphysics is not empirical. The facts about the world that we know empirically are the basis for metaphysical speculation, and so are all the facts of physics. One cannot speculate metaphysically without the knowledge gained through ones sense, and it would be odd to ignore the empirically confirmed findings of physicists. These days most philosophers are pretty knowledgeable about physics, they have to be.
The word "empirical" mean to experience, measure or test. Most metaphysical questions cannot be measured or tested. That leaves experience. I and others report that we have personally experienced God in our lives. It is consistent, reproducible, verifiable, and supported by similar claims from many others. That is empirical evidence that God exists and is active in our lives. Is this scientific proof? Do you accept this as proof of the existence of God? No, of course not. Nor would (or did) I unless and until I experienced it myself. That is metaphysics. The question of the existence of God is as metaphysical as it get. We have evidence that is consistent, verifiable, reproduce able and substantiated but it is not acceptable scientific proof. Why? Because that kind of experience is not considered empirical or scientific. It is meta physical. Yet it is as I said a metaphysical answer to a metaphysical question.
Yes, there is no other form of formal logic but the construction of systems based on unproven assumptions. But you seem to be saying that formal logic cannot be used in metaphysics, which I cannot agree with. It is formal logic that tells us that metaphysical questions are undecidable.
No, I am not saying that at all. I am saying just the opposite; however, regardless of the quality of the logic or reasoning it is neither acceptable to most nor is is scientific because it is a metaphysical answer to a metaphysical question regardless of the validity of the process or conclusion because the premises must be by their very nature metaphysical speculation and therefore unprovable.
I agree that there are no provable or reasonable answers to these questions, whether or not we make assumptions. Metaphysical questions just do not have reasonable answers. But my question was not about whether this is so, but why.
I do not agree with any of this statement; nor; is is what I said in my previous or this post. Just the opposite is true in my opinion. All metaphysical questions have reasonable metaphysical answers They just don't have reasonable scientific, physical answers. Why? BECAUSE THEY AIN'T SCIENTIFIC, PHYSICAL QUESTIONS! Do you get reasonable mathematical answers when answering a logic question? No. Why? Because logic isn't mathematics.
Here I very much disagree. Doing metaphysics isn't an excuse to give up rationality.
No it isn't and I never said it was. It is a reason (not excuse) to think outside the very limited scientific box. If is isn't science, then how does one ask these questions at all unless one delves into the metaphysical? Once we have dove in why do you insist one looking for nice neat wrapped up in the the box scientific answers? All the answers are right there all around you and perfectly reasonable and acceptable withing the realm of metaphysics which is an important part of our reality whether you like it or not. If it were not real then and rational then how could you ask a real rational question about it in the first place?
Yes, but why not? The questions are simple enough, why can't they be answered? For example, if materialism is true (is the case) then why can't we falsify idealism.
Answer your own question using logic. If we cannot falsify idealism them idealism must be real. If idealism is real then materialism cannot be all there is, cannot be all inclusive and therefore must not be the case, the whole case and nothing but the case. If Idealism and Materialism are real then they both must be part of reality. Simple!
What is it about 'reality' that prohibits us from deciding these questions one way or the other, even if only in principle. Whether we can prove things one way or the other is not the point here. These questions cannot be answered even hypothetically without contradiction.
There is no contradiction. The material world, universe exists. This cannot be denied. The non-material, subjective, ideal, metaphysical world also exists. This too cannot be denied. Intent, purpose, feeling, awareness and consciousness exist, are real, cannot be denied and cannot be completely satisfactorily explained by pure materialism. Where Materialism make its fatal flaw is that it maintains that materialism is all inclusive to the exclusion of everything else. Nothing that is not material or of the material world exists or can be real. This in itself is a contradiction because Materialism is an idea, a philosophy that is purely subjective. The contradiction is contained within Materialism itself not between the material and ideal realms of reality. They are both parts of the one reality and not mutually exclusive at all but merely different aspects of the same, the one reality.
Yes, I have no intention of giving up formal logic, and see no need to. I would say that formal logic suggests that metaphysical questions cannot be answered because none of their answers are correct, not because there's something logically inconsistent about our existence.
This is not correct. I would say that formal logic (itself an ideal concept) suggests that metaphysical questions cannot give material answerers because it isn't a material subject. There is nothing inconsistent about our existence or about all of reality. It is just that there is more to reality than the physical, material and Materialism.
But we do know that everything came from or was caused by a/the eternal universal mind by whatever name or term you choose to use. Is it still metaphysics? Yes because our empirical evidence though overwhelming is not deemed scientific, material empirical evidence and therefore is not physical but metaphysical. Go figure. Oh well, so much for the mythical open, inquisitive, scientific mind.
Remember back in the good old days when the world was flat and the earth was motionless at the center of the universe. We used to burn, hang and torture open minded inquisitive scientist. We must have got all of them, huh? Or at least taught them a lesson.
Of course now our scientist figuratively do the same thing to all of those who think outside of their neat little boxes and text books. I guess we have nobody to blame but ourselves.
selfAdjoint
Dec1-04, 07:28 PM
This is silly. Scientists have defined their enterprize to be based on objective checkable evidence; nullius in verbo. To slam them for not accepting your subjective, uncheckable evidence is like critcising a horse for not being a cow.
Scientists are truly open minded as a culture for things that can be checked (pace Kuhn, who distorts history to make his points). If the scientists gave up this voluntary restriction on the evidence they will take seriously, then they wouldn't be any better than the wooly dreamers and charlatans who have infested the world since the stone age, and produced nothing that can be generally used.
RingoKid
Dec1-04, 07:43 PM
I'm sure I posted an answer here along the lines of it is not undecideable, we just can't reach consensus on an answer.
Subjective interpretations would have you make up your own answers and be happy with them cos they are right for you as when it comes right down to it all there is is YOU.
So what happened to my posts ???
Tom Mattson
Dec1-04, 08:01 PM
So what happened to my posts ???
I deleted your posts because they were off-topic. You are using a colloquial definition of the word "undecidable", when Canute explained exactly what he meant by the term in his opening post:
However metaphysical questions are not simply undecidable in this sense. They are undecidable in a formal mathematical sense. That is, all reasonable answers to a metaphysical question give rise to contradictions within the formal systems of reasoning that give rise to the question. That is to say, metaphysical questions cannot be decided within the system of reasoning used by the person who is asking the question. This is for the same reasons that ‘Gödel-sentences’ cannot be decided within the formal systems in which they arise.
RingoKid
Dec1-04, 08:33 PM
well actuallyTom
However metaphysical questions are not simply undecidable in this sense.
The implication is there are 2 definitions of the sense in which he framed his question. In line with that my answer is perfectly on point.
I think it is an assumption on his part that there is no answer. Just because he doesn't have an answer doesn't mean the rest of us don't.
RingoKid
Dec1-04, 08:44 PM
...perhaps he should define what the term undecidable means or seeing as how you obviously have a handle on it's meaning then maybe you could enlighten me
I can't seem to find an accurate definiton let alone a colloquial one...
Tom Mattson
Dec1-04, 08:44 PM
However metaphysical questions are not simply undecidable in this sense.
The implication is there are 2 definitions of the sense in which he framed his question. In line with that my answer is perfectly on point.
Yes, and your responses don't refer to either definition. By one definition of "undecidable", he is saying that the answers to metaphysical questions cannot be decisively found because they cannot be found scientifically. But that's not what the thread is about. This thread is about formal undecidability, as that undecidability referred to in Goedel's theorem. Your answer is not "on point" with this at all.
I think it is an assumption on his part that there is no answer. Just because he doesn't have an answer doesn't mean the rest of us don't.
It isn't an assumption on his part. It's not a matter of opinion, it's a matter of logic.
I repeat my previous statement: Let's stay on topic, please.
Tom Mattson
Dec1-04, 08:48 PM
...perhaps he should define what the term undecidable means or seeing as how you obviously have a handle on it's meaning then maybe you could enlighten me
He did say what he meant by it. I quoted the passage.
If you are still unclear, then read this page, and follow the links therein:
Undecidable, from MathWorld (http://mathworld.wolfram.com/Undecidable.html)
That's what he's talking about.
RingoKid
Dec1-04, 08:52 PM
OK then...
how about the system of reasoning and logic aren't all they are cracked up to be and one should be reluctant to rely on them solely to provide answers that cater for everybody.
I don't think they are "undecideable" . I think it is Canute that is undecided about his answers as the reasoning he is using is faulty.
RingoKid
Dec1-04, 08:53 PM
BTW thanks for the definition...
Tom Mattson
Dec1-04, 08:56 PM
how about the system of reasoning and logic aren't all they are cracked up to be and one should be reluctant to rely on them solely to provide answers that cater for everybody.
So you're attacking first order logic now? On what basis?
I don't think they are "undecideable" . I think it is Canute that is undecided about his answers as the reasoning he is using is faulty.
:rofl:
So basically your response is, "You're wrong because your reasoning is wrong," without a word of explanation.
That's not philosophy, and if you keep up this line of "argumentation", then you needn't wonder where your posts have disappeared to, because I am going to delete them.
Tom Mattson
Dec1-04, 11:10 PM
There is no contradiction. The material world, universe exists. This cannot be denied. The non-material, subjective, ideal, metaphysical world also exists. This too cannot be denied.
But this is not consistent with the antecedent condition set forth by Canute. He said that if materialism is true, then idealism remains unfalsifiable. Materialism doesn't allow for what you describe here. Materialism says that knowledge of the physical state of existents is the only knowledge that there is. So if such a thing is true, then why is idealism not falsifiable, even in principle?
This is silly. Scientists have defined their enterprize to be based on objective checkable evidence; nullius in verbo. To slam them for not accepting your subjective, uncheckable evidence is like critcising a horse for not being a cow.
Yes it is. It was meant to be satire, you know funny; but, failed miserably. I was out of sorts when I posted it and couldn't resisted taking a jab at materialist and scientist in general. I apologize and would rathe see that part of the post deleted.
Scientists are truly open minded as a culture for things that can be checked (pace Kuhn, who distorts history to make his points). If the scientists gave up this voluntary restriction on the evidence they will take seriously, then they wouldn't be any better than the wooly dreamers and charlatans who have infested the world since the stone age, and produced nothing that can be generally used.
Scientist are people and some people are open minded and some are not. It often take ten years or so before a new theory is accepted whether fully supported by evidence and fully substantiated or not. It is often a bitter and dirty fight. Sometime this is a good thing some time not so good. People hate change and hate to see their life long work go into the trash can. I can understand that but expect more from scientists who pride themselves for being so open minded. This is my problem not theirs I guess.
They do, as I said. It is just that the premises and/or conclusions are not acceptable to most, primarily because the premises are speculative, subjective and not provable. For example: The universe is eternal or had a beginning. We cannot prove either way but once we accept that it had a beginning we can argue what that beginning was, the Big Bang or Created.
In either case it had to come from somewhere or something or from nothing.
But this is precisely the problem. These three answers are not reasonable. If one of them was reasonable then philosophers would have realised this long ago. Instead the question is deemed undecidable, in other words it has no reasonable answer.
Somewhere or something brings another questions of where that something came from etc. This is no answer so that leaves the choice of either the universe is eternal or that from which it came is eternal. That is a valid reasonable conclusion and an answer. Is it acceptable? Most would say, no.
Exactly.
Yet it is a reasonable logical answer reached by reason and logic once a speculative premise is agreed upon for the sake of the argument. It is a classical method of deductive reasoning via reductio ad absurdum.
I'm not sure what premise you are referring to here. But in any case this line of reasoning ends up showing that the idea of the universe arising from something that has existed eternally is either absurd or simply begs the question.
Most metaphysical questions cannot be measured or tested.
Not sure what you mean here.
That leaves experience. I and others report that we have personally experienced God in our lives. It is consistent, reproducible, verifiable, and supported by similar claims from many others. That is empirical evidence that God exists and is active in our lives. Is this scientific proof? Do you accept this as proof of the existence of God? No, of course not. Nor would (or did) I unless and until I experienced it myself. That is metaphysics. The question of the existence of God is as metaphysical as it get.
I agree that if one reasons about the existence of God then one is doing metaphysics. However if one experiences God directly this is not metaphysics, it is revelation. I have no problem with the idea of revelation through direct experience. But that doesn't address my original question.
We have evidence that is consistent, verifiable, reproduce able and substantiated but it is not acceptable scientific proof. Why? Because that kind of experience is not considered empirical or scientific. It is meta physical. Yet it is as I said a metaphysical answer to a metaphysical question.
I feel this is a confusing use of the term 'metaphysical', but I see what you mean. However the issue here is a little more subtle than this. I completely agree with you that metaphysical questions can only be dealt with by transcending metaphysics, but this does not alter the fact that these questions are undecidable. That is, through experience one may discover why metaphysical questions are undecidable, but one cannot decide them by any method.
it is neither acceptable to most nor is is scientific because it is a metaphysical answer to a metaphysical question regardless of the validity of the process or conclusion because the premises must be by their very nature metaphysical speculation and therefore unprovable.
But you have not yet given an answer to any metaphysical question, scientific or not. Asserting that God exists does nothing at all to address such questions. Even if He does exist the questions remain. This is why A. N. Whitehead characterised Christianity as 'a religion in search of a metaphysic'.
All metaphysical questions have reasonable metaphysical answers
I don't think you'll find any philosophers who agree with you. It is the lack of reasonable answers to such questions makes them undecidable.
They just don't have reasonable scientific, physical answers. Why? BECAUSE THEY AIN'T SCIENTIFIC, PHYSICAL QUESTIONS!
They have no reasonable answers, scientific or not. I feel that you're missing this important point.
No it isn't and I never said it was. It is a reason (not excuse) to think outside the very limited scientific box. If is isn't science, then how does one ask these questions at all unless one delves into the metaphysical? Once we have dove in why do you insist one looking for nice neat wrapped up in the the box scientific answers?
I was trying to avoid getting into a anti-science thing here. One cannot blame science for not being able to answer metaphysical questions when nobody at all can answer them.
If we cannot falsify idealism them idealism must be real. If idealism is real then materialism cannot be all there is, cannot be all inclusive and therefore must not be the case, the whole case and nothing but the case. If Idealism and Materialism are real then they both must be part of reality. Simple!
I can't follow your argument here. Philosophical idealism is also unverifiable, but it doesn't follow from this that idealism is not the case. A thing isn't true just because we cannot show that it's false.
There is no contradiction. The material world, universe exists. This cannot be denied.
Don't count on it. Many people assert that in the final analysis it's an illusion.
Where Materialism make its fatal flaw is that it maintains that materialism is all inclusive to the exclusion of everything else. Nothing that is not material or of the material world exists or can be real. This in itself is a contradiction because Materialism is an idea, a philosophy that is purely subjective.
Yes, materialism is a metaphysical doctrine. As such it gives rise to contradictions, just like most forms of idealism. It is not, and never will be, a testable scientific theory.
This is not correct. I would say that formal logic (itself an ideal concept) suggests that metaphysical questions cannot give material answerers because it isn't a material subject. There is nothing inconsistent about our existence or about all of reality. It is just that there is more to reality than the physical, material and Materialism.
Perhaps. But again you are criticising science for its limits, when it precisely those limits that makes science do-able. I agree that science cannot explain the existence of the physical universe or consciousness. But how does this help explain why metaphysical questions are undecidable?
But this is not consistent with the antecedent condition set forth by Canute. He said that if materialism is true, then idealism remains unfalsifiable. Materialism doesn't allow for what you describe here. Materialism says that knowledge of the physical state of existents is the only knowledge that there is. So if such a thing is true, then why is idealism not falsifiable, even in principle?
Yes, Tom of course you are right if materialism is true and idealism remains unfalsifiablethen there is a contradiction.
However, if a statement contains a contradiction or is self contrdictory then the statement itself cannot be true.
If the statement is not true then both of the premises cannot be true.
idealism is unfalsifiable is true.
Therefore Materialism as stated must be false.
"Materialism says that knowledge of the physical state of existents is the only knowledge that there is."
Knowledge is subjective, non-material
If the non-material can exist is one form it can logically exist in principle in another form.
The Materialistic statement cannot logically deny its own existence.
If it is true then it is possible for idealism to be true.
There is no contradiction because Materialism as stated is false.
Practically speaking it is obvious and cannot be denied that the material universe exists and is real. It also cannot be denied that knowledge exists and is real. It is the tenet of materialism that one and only one form of knowledge can exits. Materialism is all inclusive and excludes the possibility of anything else existing. Therefore if materialism is true and idealism is unfalsifiable then either idealism is materialistic knowledge or Materialism is false. Take your choice. There can be no contradiction.
Metaphysical questions have traditionally been about either being or knowledge. Those which are about knowledge risk the trap of self reference, which could lead to undecidability in the formal sense (but I am not aware of any proof that this is so). Questions about being turn on individual definitions of being, which is vague, and entails the definition of non-being, which is even more vague than being. So I don't think philosophers' sayings about being can be anything more than an art form.
I'm not sure that you're right about this, but there's probably more than one way of looking at it. To me metaphysics does not deal with Being, but with beings, which is a rather different thing. This was Heideggers view, and I wish I could express myself like he could on this. His lecture 'What is Metaphysics', which is online here and there, is worth a read.
It seems true that metaphysical questions nearly always raise epistemilogical issues, but as questions they are not generally about knowledge. If we ask 'is materialism the case' then this is very nearly a scientific question. It does raise questions about what is knowable, but the question in itself is about cosmology. It's a simple question really, and in principle at least one would expect it to be decidable. It is true that immediately one attempts to decide it one becomes enmired in questions of how we know things and what we can know, but the question itself is not about knowledge.
Tom - thanks for the stuff about undecidability. I should have been more clear about this at the start.
Iacchus32
Dec2-04, 08:41 AM
But this is not consistent with the antecedent condition set forth by Canute. He said that if materialism is true, then idealism remains unfalsifiable. Materialism doesn't allow for what you describe here. Materialism says that knowledge of the physical state of existents is the only knowledge that there is. So if such a thing is true, then why is idealism not falsifiable, even in principle?No, I don't believe that's what he said at all. Indeed, it sounded very much like he was inquiring as to why this should be true. Which of course is not the same thing.
No, I don't believe that's what he said at all. Indeed, it sounded very much like he was inquiring as to why this should be true. Which of course is not the same thing.
You're right, that isn't quite what I wrote. However Tom's version is better in a way. If materialism is true then we will never be able to know it, because however hard we try we will never be able to show that idealism is false.
This entails that science will never be able to explain what matter is made out of, which is what is the case according to most philosophers, western and eastern. In western philosophy this conclusion is reached by all those who attempt to solve the old 'problem of attributes', of what it is that underlies the observable attributes of 'physical' objects. There is no reasonable answer. It is a metaphysical question, not just beyond science but beyond reason.
Our reason tells us that the question is a fair one, for surely there must be something that exists that is fundamental. But what do we mean by 'exists'. The term implies physical attributes like extension, size, location and so on. Does it make sense to say that matter is made out of something that has the properties of matter? This would be to say that matter is made out of matter. But does it make sense to say that matter is made out of something that isn't matter but that exists?
Yet the alternative is that matter is made out of nothing, and this is no better. All the answers contradict reason, and the question is deemed 'metaphysical'. We can prove that it cannot be decided. Inevitably it is impossible to give a consistent and complete explanation of what matter is made out of, never mind consciousness.
But idealism (of anything like Berkeley's kind anyway) is unfalsifiable whether or not materialism is true. It is unfalsifiable according to everybody's reason, not just those who make materialist assumptions. When we try to construct a logically consistent 'Explanation of Everything that Exists' that is predicated on the idea that either mind or matter is fundamental, we find that it cannot be done, for according to our reason it wouldn't make sense. So it's a metaphysical question.
I suspect that that philosophical materialism is also unfalsifiable, but I've never seen this argued anywhere, so maybe I'm wrong.
P.S. Philosophical Idealism is unfalsifiable because the question 'is philosophical idealism false?' is undecidable. Whether this is because idealism is not entirely false or a consequence of the way we reason is a matter of opinion. Philosophers are divided, and it may well be both.
Iacchus32
Dec2-04, 11:17 AM
You're right, that isn't quite what I wrote. However Tom's version is better in a way. If materialism is true then we will never be able to know it, because however hard we try we will never be able to show that idealism is false. But are you sure this isn't just a way of dismissing it and washing your hands of it entirely? Of course this is my own opinion here. :smile: Surely we can't be left with the possibility that something stems from nothing can we?
This entails that science will never be able to explain what matter is made out of, which is what is the case according to most philosophers, western and eastern. In western philosophy this conclusion is reached by all those who attempt to solve the old 'problem of attributes', of what it is that underlies the observable attributes of 'physical' objects. There is no reasonable answer. It is a metaphysical question, not just beyond science but beyond reason. So, was there in fact nothing before the Big Bang? Or, nothing in the physical sense? While the fact is we are all here which, to me can only suggest one thing, that the material does extend from the immaterial, which must have existed prior to the Big Bang. In which case I think we have to ask, what is this immaterial realm that we're speaking of? And what, if any, is the difference between it and the realm of our thoughts? ... which of course is abstract and metaphysical.
Tom Mattson
Dec2-04, 02:55 PM
No, I don't believe that's what he said at all. Indeed, it sounded very much like he was inquiring as to why this should be true. Which of course is not the same thing.
Nope. He specifically put it in the form of a conditional.
Tom Mattson
Dec2-04, 03:01 PM
However, if a statement contains a contradiction or is self contrdictory then the statement itself cannot be true.
What Canute is talking about here are propositions that are undecidable. So the thing on the table right now are precisely those propositions about which you cannot say whether or not they "cannot be true", in the context of the formal system in which they are derived.
If the statement is not true then both of the premises cannot be true.
idealism is unfalsifiable is true.
Therefore Materialism as stated must be false.
Again, you are assuming decidability. This is the very thing under discussion!
There can be no contradiction.
I agree that there is no contradiction to reality, but I don't think that that is what this thread is about. This thread is about the conceptual tools that are used to analyze reality, and the question, "Why, to what extent, and in what capacity do those tools break down?"
The way I understand Canute's posts, that is the central question here, and what you are saying doesn't seem to address it.
Tom Mattson
Dec2-04, 03:04 PM
You're right, that isn't quite what I wrote.
I didn't mean to misrepresent. Here's the bit I was referring to.
For example, if materialism is true (is the case) then why can't we falsify idealism. What is it about 'reality' that prohibits us from deciding these quetions one way or the other, even if only in principle. Whether we can prove things one way or the other is not the point here. These questions cannot be answered even hypothetically without contradiction.
I thought I had interpreted it as you meant it. :confused:
But are you sure this isn't just a way of dismissing it and washing your hands of it entirely? Of course this is my own opinion here. :smile: Surely we can't be left with the possibility that something stems from nothing can we?
Very little of what I've said so far is just my opinion. In fact I meant to steer clear of my opinions completely. All I have meant to do so far is outline the situation we are in regarding metaphysical questions.
We are very confronted with the idea that something stems from nothing. I don't believe it makes sense, but as I said earlier, at least one respected cosmologist is hoping for a theory of ex nihilo creation. But we are not forced to accept ex nihilo creation. The problem is that it makes no more and no less sense than the other candidates for a logically consistent explanation of the existence of the universe. This is the defining characteristic of metaphysical questions.
By the way, the fact that these questions are undecidable does not necessarily mean that there is anything irrational about the explanation of existence, but it does suggest that there are assumptions hidden in these questions which makes them unanswerable as they stand.
So, was there in fact nothing before the Big Bang? Or, nothing in the physical sense? While the fact is we are all here which, to me can only suggest one thing, that the material does extend from the immaterial, which must have existed prior to the Big Bang. In which case I think we have to ask, what is this immaterial realm that we're speaking of? And what, if any, is the difference between it and the realm of our thoughts? ... which of course is abstract and metaphysical.
Yep, this where one ends up, with immateriality. But the trouble is that in itself this doesn't solve the problem. Even if we say that the universe arises from 'something' that is immaterial the question of why we cannot reach this conclusion by reason remains. After all, if it made sense that the material world had immaterial origins then the question of its origins, while it would still be metaphysical, would not be formally undecidable. It would just be scientifically untestable, which is a different thing.
I didn't mean to misrepresent. Here's the bit I was referring to...I thought I had interpreted it as you meant it. :confused:
Your interpretation was fine by me, but I didn't originally mean to say that if materialism is true then this would imply the unfalsifiability of idealism. Idealism is unfalsifiable whether or not materialism is true. I linked them simply because it is the unfalsifiability of idealism that allows us to know that we cannot construct a proof of materialism. However I can see that the sentence can read in the way you did. It's not an important point. You didn't really misrepresent, and I agree with everything you've posted so far.
Iacchus32
Dec2-04, 06:43 PM
Yep, this where one ends up, with immateriality. But the trouble is that in itself this doesn't solve the problem. Even if we say that the universe arises from 'something' that is immaterial the question of why we cannot reach this conclusion by reason remains. After all, if it made sense that the material world had immaterial origins then the question of its origins, while it would still be metaphysical, would not be formally undecidable. It would just be scientifically untestable, which is a different thing.And yet the fact is we're here, so something must have happened in order to bring that about. So, what else could we conclude then, except that the immaterial is another dimension, and perhaps we should try to examine it in that respect? ... i.e., how one dimension has an effect upon another. Perhaps we can begin with our very own thinking process which, no doubt entails the immaterial (as well as the metaphysical) housed within the material. Isn't this in fact what we're looking for? Indeed, maybe it all boils down to our ability to think and, reason about things? In fact, how would we know anything, without the ability to do this?
So what is the truth (not to say it doesn't exist) without a mind which is capable of recognizing it? Whereas at what point does the mind recognize it ... within this immaterial dimension we're speaking about here? Certainly the recognition of truth is not external is it? ... albeit what we recognize may be external or, for that matter internal.
loseyourname
Dec2-04, 09:19 PM
Yes, Tom of course you are right if materialism is true and idealism remains unfalsifiablethen there is a contradiction.
That isn't true. If materialism and idealism were both true, then we would have a contradiction. There are many unfalsifiable hypotheses, and their existence does not contradict the truth of reality.
For instance, take Descartes' hypothesis about the evil demon. That hypothesis is unfalsiable. That doesn't mean the contradictory hypothesis that objective reality exists cannot be true. Or take Last Thursdayism, the hypothesis that the universe was created last Thursday with our memories and physical records of history already in place. That hypothesis is unfalsifiable, but that doesn't mean the hypothesis that history did happen cannot be true.
A contradiction is defined (in this case) as two hypotheses that are inconsistent with one another both being true. Not one being true and the other being unfalsifiable.
honestrosewater
Dec3-04, 05:37 AM
Since my question is shorter than the explanation of its relevance to the topic, and if the answer is yes, the question is irrelevant, I'll just ask my question.
Can (logical) implication prove (physical) causation?
And yet the fact is we're here, so something must have happened in order to bring that about. So, what else could we conclude then, except that the immaterial is another dimension, and perhaps we should try to examine it in that respect? ... etc...
What you say is interesting and raises some relevant issues. However I'm not going to respond here because if we start trying to answer these questions the discussion will head off into metaphysics. I'll stick to asking why metaphysical questions exist for the moment, which is a different kind of question.
That isn't true. If materialism and idealism were both true, then we would have a contradiction. There are many unfalsifiable hypotheses, and their existence does not contradict the truth of reality.
This may be a misunderstanding. Nobody is suggesting that materialism and idealism can both be true, or that the unfalsifiability of idealism is a logical contradiction.
Honestrosewater - Your question deserves a thread of its own. It's a minefield. I don't know the arguments at all well but Pietre Abelard, the twelfth century Parisian teacher of logic and theology, asserted that for p to entail q the impossibility of (p and not-q) is not enough. In addition p must also require that q be the case. So even logical implication is a difficult issue, and certainly one cannot ever show that p requires q to be the case if p and q are physical events. All we can do is infer that it does and hope not to meet any exceptions.
honestrosewater
Dec3-04, 08:31 AM
I hesitated joining this discussion because I have tried to understand decidability, but haven't found a precise explanation. (I did just start a thread about it, so hopefully I will understand soon.) If my ignorance ends up wasting your time, I'm sorry, but, on the possibility I might have a partial answer to your question, I'll continue.
for p to entail q the impossibility of (p and not-q) is not enough. In addition p must also require that q be the case.
Okay, assuming the impossibility of (p and not-q) is enough...
certainly one cannot ever show that p requires q to be the case if p and q are physical events. All we can do is infer that it does and hope not to meet any exceptions.
Assuming
1) logic is the only tool by which metaphysical questions can be proven,
2) logic cannot prove causal relationships, and
3) to prove any metaphysical question, one must prove causal relationships,
metaphysical questions cannot be proven.
By "causal relationships", I mean physical, causal relationships. I am certainly not certain 3 is true, but the other two are apparently being assumed in this thread.
___
I know the difference between an argument's validity and truth. I am saying that, well, I don't know how else to say what I'm saying :rolleyes:
___
And assuming bivalence, and possibly other things I haven't realized.
___
Now I understand why the posts here tend to be long.
A: Metaphysical truths can be logically proven.
B: Physical, causal relationships can be logically proven.
A \Rightarrow B, \\ \neg B, \\ \bot \neg A
Of course, perhaps
\neg (A \Rightarrow B)
I don't know.
___
Last edit, promise o:)
That is, if you are trying to use logic to prove
A caused the universe,
B caused time,
C causes consciousness,
etc. you are trying to do the impossible, as they involve establishing physical, causal relationships. You are trying to use logic to do what logic cannot: make physical observations.
Note: I am not convinced my argument is flawless, in fact I suspect it may be.
It is a confusing topic, that's for sure. I was going to post an official definition of 'undecidable' but I also can't find one. I suspect Tom can give one, but I'll have an informal go at it.
If a proposition is undecidable it means that according to the axioms of the system containing that proposition it cannot be the case that the proposition is true or false. If it were true or false it would contradict those axioms.
The example often given is the 'Liar paradox', in which a native of Crete asserts that all Cretans are liars. If the assertion is true it is false, and if is false it is true. Similarly, a 'Goedel-sentence' is a sentence which says of itself that it is not a theorem of the system in which it appears. In formal system T it would take the form 'This well-formed sentence is not a theorem of T'. Such a question can only be decided from outside T, by extending (or abandoning) the axioms of T. A more practical example might be the twin primes conjecture, which is thought by many mathematicians to be undecidable within set theory.
I don't dare say much more than this because these are treacherous waters for non-mathematicians, but there's plenty online if you search under Goedel (spelt properly, which I can't figure out how to do here).
Assuming
1) logic is the only tool by which metaphysical questions can be proven,
This is probably a rather an inexact way of putting it since 'proven' is ambiguous. Undecidable questions cannot be decided by formal logic, and metaphysical questions are undecidable. There is no tool at all for deciding them. This entails that they have to be transcended rather than decided, by somehow leaving the logical system being used to ask them.
In 'The Name of the Rose' Umberto Ecco gives the novice the words "Further, since I had been with my master I had become aware, and was to become even more aware in the days that followed, that logic could be especially useful when you entered it then left it." I suspect that metaphysical questions and the incompleteness theorem were what the author had in mind here.
2) logic cannot prove causal relationships,
This seems to be the conclusion of most philsophers.
and
3) to prove any metaphysical question, one must prove causal relationships,
metaphysical questions cannot be proven.
Again, it would be better to use the word 'decidable' rather than provable. But I don't understand quite what you're saying. Can you clarify how you are linking causality and metaphysical questions?
honestrosewater
Dec3-04, 11:02 AM
I was going to post an official definition of 'undecidable' but I also can't find one.
Grime explained it :biggrin:
Goedel (spelt properly, which I can't figure out how to do here).
Hope no one minds this brief aside:
PF uses ISO-8859-1 encoding. Here's a list of codes for characters http://www.htmlhelp.com/reference/charset/.
The code for the character you want is 246. To get the character to appear, just type:
& #246;
without the space (obviously if I wrote it correctly, it would display ö instead of the code). Er, you don't have to put it in quotes either.
Can you clarify how you are linking causality and metaphysical questions?
Maybe, but it will take some time to expand and refine. I'll post it ASAP.
Iacchus32
Dec3-04, 02:21 PM
The example often given is the 'Liar paradox', in which a native of Crete asserts that all Cretans are liars. If the assertion is true it is false, and if is false it is true.Everybody lies. Now, whether they lie 100% of the time is another story ... So much for your "Liar's paradox." Or, what if we were to say this? ... "The truth exists in all things, even in the lie, otherwise how would you know the truth about the lie?" It sounds to me like classic dualism. You can't have all of one or, all of the other, but a combination of both. In which case there is no paradox.
While I think the same thing can be said with respect to materialism versus immaterialism. It's dualistic. There's no paradox when you understand that both exist and, how they relate to each other.
loseyourname
Dec3-04, 02:23 PM
This may be a misunderstanding. Nobody is suggesting that materialism and idealism can both be true, or that the unfalsifiability of idealism is a logical contradiction.
Iacchus suggested that materialism being true and idealism being unfalsifiable is a contradiction; that is, materialism cannot be true because idealism is unfalsifiable, and Tom agreed. I'll give Tom the benefit of the doubt and assume he didn't read correctly, but obviously that argument is invalid.
Iacchus32
Dec3-04, 02:47 PM
What you say is interesting and raises some relevant issues. However I'm not going to respond here because if we start trying to answer these questions the discussion will head off into metaphysics. I'll stick to asking why metaphysical questions exist for the moment, which is a different kind of question.No, actually it is a metaphysical question. :wink: But I understand what you're saying.
Tom Mattson
Dec3-04, 02:59 PM
that is, materialism cannot be true because idealism is unfalsifiable, and Tom agreed.
No, I didn't agree. I never took a position on it one way or the other.
Tom Mattson
Dec3-04, 03:00 PM
Everybody lies. Now, whether they lie 100% of the time is another story ... So much for your "Liar's paradox."
You're missing the point. The Liar's paradox isn't about Cretans and it isn't about liars. It's about self-reference, which is pertinent to decidability.
Iacchus32
Dec3-04, 03:18 PM
You're missing the point. The Liar's paradox isn't about Cretans and it isn't about liars. It's about self-reference, which is pertinent to decidability.How can there be a reference to anything without contrast? For example, if you had all of one thing and that's all there is, how would you know it was there, unless something was set in contrast to it?
Tom Mattson
Dec3-04, 03:22 PM
How can there be a reference to anything without contrast? For example, if you had all of one thing and that's all there is, how would you know it was there, unless something was set in contrast to it?
The contrast is implicit in the paradox itself. If we strip the Liar's paradox down to its bare bones, it amounts to the following sentence:
This sentence is false.
This is an undecidable proposition, because it is self referential. The very same quantifier ("this") that results in the self reference is the quantifier that provides the implicit contrast. When we say "this sentence", we mean "this sentence, from the set of all sentences".
There is your contrast: We are talking about one sentence to the exclusion of all the others.
Iacchus32
Dec3-04, 03:33 PM
The contrast is implicit in the paradox itself. If we strip the Liar's paradox down to its bare bones, it amounts to the following sentence:
This sentence is false.
This is an undecidable proposition, because it is self referential. The very same quantifier ("this") that results in the self reference is the quantifier that provides the implicit contrast. When we say "this sentence", we mean "this sentence, from the set of all sentences".
There is your contrast: We are talking about one sentence to the exclusion of all the others.The sentence is totally ambiguous. So why does it make it a paradox?
loseyourname
Dec3-04, 03:40 PM
No, I didn't agree. I never took a position on it one way or the other.
Sorry, it was actually Royce that took the position, and said "Tom, you're right, if idealism is unfalsifiable then materialism can't be true." I took that to mean that you had said if idealism is unfalsifiable then materialism can't be true. Guess not.
Tom Mattson
Dec3-04, 03:44 PM
The sentence is totally ambiguous. So why does it make it a paradox?
Uhhh....because it's totally ambiguous!
A paradox is a statement to which it is not possible to assign a truth value.
Iacchus32
Dec3-04, 04:28 PM
Uhhh....because it's totally ambiguous!
A paradox is a statement to which it is not possible to assign a truth value.And yet just because something is ambiguous doesn't mean it contradicts itself does it? Isn't that how you define a paradox? Also, when you bring up "liar," it's misleading -- hence the apparent paradox -- because a liar is somebody who's been known to lie, not somebody who is an abject liar. In fact, one of the best ways to lie is to speak the truth (to conceal your intentions), and if that doesn't sound like a contradiction!
Tom Mattson
Dec3-04, 04:34 PM
And yet just because something is ambiguous doesn't mean it contradicts itself does it? Isn't that how you define a paradox?
I already explained what a paradox is. It is ambiguous in the sense that it defies the assignment of a truth value.
Also, when you bring up "liar," it's misleading -- hence the apparent paradox -- because a liar is somebody who's been known to lie, not somebody who is an abject liar.
It's not misleading at all. You are getting hung up on an irrelevant detail. The liar paradox is a standard exercise in Philosophy 101, and when people use it they expect that the reader has had some exposure to it. But if that's what you think, then fine. Go with the "stripped down" version ("This sentence is false") if you prefer.
In fact, one of the best ways to lie is to speak the truth (to conceal your intentions), and if that doesn't sound like a contradiction!
This has nothing to do with anything in this thread.
Iacchus32
Dec3-04, 04:42 PM
It's not misleading at all. You are getting hung up on an irrelevant detail. The liar paradox is a standard exercise in Philosophy 101, and when people use it they expect that the reader has had some exposure to it. But if that's what you think, then fine. Go with the "stripped down" version ("This sentence is false") if you prefer. Well all I'm saying is, is it really a paradox or, are we just playing with mirrors here? By the way, do you believe there is such a thing as a true paradox? I personally don't. But I guess you would have to be a dualist in order to believe that.
Tom Mattson
Dec3-04, 04:48 PM
Well all I'm saying is, is it really a paradox or, are we just playing with mirrors here?
Yes, it's a paradox. Look at the definition of paradox, and see for yourself that the self-referential sentence I wrote fits that defintion. It's easy.
By the way, do you believe there is such a thing as a true paradox? I personally don't.
No, because by definition paradoxes cannot be "true".
Iacchus32
Dec3-04, 05:09 PM
Yes, it's a paradox. Look at the definition of paradox, and see for yourself that the self-referential sentence I wrote fits that defintion. It's easy.I can see that it's self-referential, yes. But I still don't see how it contradicts itself which, is how my dictionary defines paradox.
Tom Mattson
Dec3-04, 05:13 PM
I can see that it's self-referential, yes. But I still don't see how it contradicts itself which, is how my dictionary defines paradox.
When I assert:
P: This sentence is false.
I am putting it forth as a truth. Thus, when I assert that it is the case that P is true, then I assert the case that the the sentence is false.
This implies that the sentence is not true! So now we have that it is not the case that P is true, or that it is not the case that the sentence is false. So now we are back to the sentence being true, and the whole vicious circle starts over again and never stops.
Since it is not possible to assign a truth value to the sentence, it contradicts itself. It is both true and false, or neither if you prefer.
When I assert:
P: This sentence is false.
I am putting it forth as a truth. Thus, when I assert that it is the case that P is true, then I assert the case that the the sentence is false.
This implies that the sentence is not true! So now we have that it is not the case that P is true, or that it is not the case that the sentence is false. So now we are back to the sentence being true, and the whole vicious circle starts over again and never stops.
Of course, that would never work because you would want to see proof supporting that either P is true or false or the sentence supplying your statement is true or false. Otherwise all it is is fuzzy logic.
Sorry, it was actually Royce that took the position, and said "Tom, you're right, if idealism is unfalsifiable then materialism can't be true." I took that to mean that you had said if idealism is unfalsifiable then materialism can't be true. Guess not.
Neither Tom nor I took any position on either. We were using the statement that Canute made:
For example, if materialism is true (is the case) then why can't we falsify idealism. What is it about 'reality' that prohibits us from deciding these questions one way or the other, even if only in principle. Whether we can prove things one way or the other is not the point here. These questions cannot be answered even hypothetically without contradiction.
as an example. Given that the statement is true then there is a contradiction. This was Canute's point here. I maintained that the statement couldn't be true if it contains a contradiction, and pointed out the logic of my position. Essentially the reason that the question is undecidable or unfalsifiable is that the original question or in this case statement is flawed, false. In this case I pointed out that Materialism cannot be the case and why I thought that way. It could have been that "idealism is unfalsifiable." is the false statement but I have no way of addressing that one way or the other.
Tom Mattson
Dec3-04, 06:14 PM
Of course, that would never work because you would want to see proof supporting that either P is true or false or the sentence supplying your statement is true or false.
You're missing the point, which is that the sentence is neither true nor false under any circumstances. Its truth implies its falsity, and vice versa.
Otherwise all it is is fuzzy logic.
No, it is not fuzzy logic. This is a paradox within plain vanilla two-valued Aristotelian logic.
loseyourname
Dec3-04, 06:24 PM
In this case I pointed out that Materialism cannot be the case and why I thought that way. It could have been that "idealism is unfalsifiable." is the false statement but I have no way of addressing that one way or the other.
Okay, but you said this:
Yes, Tom of course you are right if materialism is true and idealism remains unfalsifiable then there is a contradiction.
That isn't true. The unfalsifiability of idealism holds no implications whatsoever to the truth of materialism. I posted several examples of unfalsifiable hypotheses that run contrary to known truths without contradiction.
Back to Canute's original question:
My question is - why are metaphysical questions undecidable?
To try to get this thread back on topic which i think is important and far from settled. It may be itself undecidable.
Canute, what I was trying to say is that the questions are not undecidable.
Reason and logic can and do come up with conclusions, decisions and answers.
However, they only have meaning in metaphysics.
Within materialism and the science the answers are meaningless, indeterminate and undecidable. The answers are not acceptable.
For instance my conclusion that the universe or Whatever brought it about must be eternal is not an acceptable scientific answer, you did not accept it either, and therefore it was no answer at all rendering the question again undecidable. But again, why?
I tried to point out that they were outside the limits of materialism and science. These limits are necessary and not a shortcoming. Science and the Scientific Method can only deal with the material universe. That is what it was designed to do. The metaphysical questions and answers are by definition outside, beyond, physics.
Science rules supreme within space-time and cause-effect.
Metaphysics lies outside of space-time and cause-effect.
This what I am saying is the answer to your why?
Okay, but you said this:
Yes, Tom, of course you are right, if and idealism remains unfalsifiable then there is a contradiction.
That isn't true. The falsifiability of idealism holds no implications whatsoever to the truth of materialism. I posted several examples of unfalsifiable hypotheses that run contrary to known truths without contradiction.
Again you are missing the point the statement is a logical statement, the logical operative words are if and and.
IF it is the case that:materialism is true
AND idealism remains unfalsifiable.
Under these given conditions and only these given conditions if follows that....
loseyourname
Dec3-04, 06:54 PM
Again you are missing the point the statement is a logical statement, the logical operative words are if and and.
IF it is the case that:materialism is true
AND idealism remains unfalsifiable.
Under these given conditions and only these given conditions if follows that....
It follows that materialism is true and idealism is unfalsifiable. Nothing else follows. Maybe I am missing the point, because it seems to me that you are saying materialism cannot be true if idealism is unfalsifiable. That isn't the case. Materialism cannot be true if idealism is true. Materialism can still be true if idealism is unfalsifiable.
Iacchus32
Dec4-04, 06:43 AM
After all, if it made sense that the material world had immaterial origins then the question of its origins, while it would still be metaphysical, would not be formally undecidable. It would just be scientifically untestable, which is a different thing.Well, maybe this is what I'm suggesting though?
I'll try to clear up a misunderstanding. When I said 'If materialism is true then why is idealism unfalsifiable' I did not mean to imply that idealism is unfalsifiable because materialism is true. Not did I mean to say that idealism is only unfalsifiable if one assumes that materialism is true. Idealism is unfalsifiable full stop, whether or not materialism is true, and there is no logical contradiction between materialism being true and idealism being unfalsifiable.
The sentence wasn't incorrect but maybe it was ambiguous. Put more clearly the question is - if materialism is true then why is it impossible to verify its truth by reason or by observation. It could also be - if idealism is false then why is it impossible to falsify it?
Canute, what I was trying to say is that the questions are not undecidable. Reason and logic can and do come up with conclusions, decisions and answers. However, they only have meaning in metaphysics.
But there are no conclusions, decisions and answers in metaphysics. The questions are undecidable. We know this by logic and reason, the conclusions, decisions and answers give rise to contradictions, and we can infer it from the fact that nobody has ever decided one of them.
materialism and the science the answers are meaningless, indeterminate and undecidable. The answers are not acceptable.
They are not acceptable to philosophers either. If we assume that idealism is true this gives rise to the same kind of logical contradictions as the assumption that materialism is true. (By 'contradiction' I mean that if either materialism or idealism is true this would contradict our reason).
For instance my conclusion that the universe or Whatever brought it about must be eternal is not an acceptable scientific answer, you did not accept it either, and therefore it was no answer at all rendering the question again undecidable. But again, why?
No, it is not the unscientific-ness of this answer that makes the question of origins undecidable. It is the unreasonableness of all the answers.
I tried to point out that they were outside the limits of materialism and science. These limits are necessary and not a shortcoming. Science and the Scientific Method can only deal with the material universe. That is what it was designed to do. The metaphysical questions and answers are by definition outside, beyond, physics.
Yes they are beyond physics, but they are also beyond reason. Philosophers are no more able to answer them than physicists. This is why some philosophers have argued that such questions are meaningless. However we know that questions can be perfectly meaningful ('well-formed') and yet be undecidable, so undecidability is not in itself enough to render a question meaningless.
Science rules supreme within space-time and cause-effect.
Metaphysics lies outside of space-time and cause-effect.
I think I see what you mean, but let's forget about the differences between science and metaphysics. It's not relevant here. When a person asks a metaphysical question, whoever they are, whether they are Einstein or the Buddha, they find it cannot be decided in a formally consistent manner. Nobody has ever claimed to have decided one, not successfully anyway.
Don't you think that to say that metaphysical questions are undecidable because they're metaphysical is to rather beg the question?
Originally Posted by Canute
After all, if it made sense that the material world had immaterial origins then the question of its origins, while it would still be metaphysical, would not be formally undecidable. It would just be scientifically untestable, which is a different thing.
Well, maybe this is what I'm suggesting though?
It's a reasonable suggestion, but it can be shown to be untrue. Idealism, which implies immaterial origins for the universe, is not just scientifically untestable. As a cosmological doctrine, in the form it takes within western philosophy, it is logically inconsistent. This is why scientists, who are not all narrow-minded or dogmatic, cannot really be criticised for not adopting it. (Although one might criticise them for not applying the same standards of reasoning to materialism).
The question then is; "Why are all metaphysical questions undecidable?" period, as a stand alone question having nothing to do with materialism or physicalism. They are undecidable even within the framework of metaphysics using formal logic and reasoning. This statement is supported by the fact that there has never been a complete and satisfactory answer in over 3 thousand years of thinking and reasoning by thousands of thinkers. Is this correct so far?
Iacchus32
Dec4-04, 03:07 PM
It's a reasonable suggestion, but it can be shown to be untrue. Idealism, which implies immaterial origins for the universe, is not just scientifically untestable. As a cosmological doctrine, in the form it takes within western philosophy, it is logically inconsistent. This is why scientists, who are not all narrow-minded or dogmatic, cannot really be criticised for not adopting it. (Although one might criticise them for not applying the same standards of reasoning to materialism).Well, it suggests that either can only be falsifiable when set in contrast to the other. We can't deny that the physical world exists. And yet, the only way we can truly acknowledge it is internally. Which, is why I propose dualism. How do we acknowledge the truth without a brain ... or, the mind which resides therein?
The question then is; "Why are all metaphysical questions undecidable?" period, as a stand alone question having nothing to do with materialism or physicalism. They are undecidable even within the framework of metaphysics using formal logic and reasoning. This statement is supported by the fact that there has never been a complete and satisfactory answer in over 3 thousand years of thinking and reasoning by thousands of thinkers. Is this correct so far?
Damn it, why didn't I just say that at the start? Sorry for muddling the issues by being so longwinded. Yes, this is correct as far as I'm concerned, and I should have said it as concisely and clearly as you have.
I mentioned materialism and idealism alongside asking the question because it seemed to me that many people overlook the significance of the undecidability of metaphysical questions. This undecidability means that according to reason the philosophical doctrine of materialism contradicts reason, just as does the doctrine of idealism, for it is precisely this fact that makes the question of which of them is true or false undecidable in the first place. I thought it would stir up a more interesting debate if l said this along with asking the question. In hindsight I can see that all it was derail the discussion. My apologies.
As you say, the question is simply 'Why are metaphysical questions undecidable?'
Alternatively, to make it sound less like just another pointless 'philosophical' question, it could asked as 'What is it about the universe that makes it impossible to construct a formally consistent explanation of its existence?
Iacchus32
If a proposition is unfalsifiable it's unfalsifiable. It's nothing to do with setting it in contrast with anything. Also, although we cannot deny that the physical world exists in some sense, as you say, we can still wonder in what sense it does, whether it is an epiphenomenon of mind, whether it is made out of something material, and so on.
Despite considerable research there is no evidence yet showing that our consciousness resides in our brains. Rather, it seems to have no extension at all. I must say my consciousness feels for most of the time as if it is somewhere right behind my eyes, but this is just how it seems to me, not scientific evidence of its location.
Iacchus32
Dec5-04, 04:50 PM
Iacchus32
If a proposition is unfalsifiable it's unfalsifiable. So it sounds like both materialism and idealism are unfalsifialble, which is to say self-referential? ... unless, as I suggest, you understand them in context with each other.
It's nothing to do with setting it in contrast with anything. Also, although we cannot deny that the physical world exists in some sense, as you say, we can still wonder in what sense it does, whether it is an epiphenomenon of mind, whether it is made out of something material, and so on. The thing is you can't have an inside without an outside, and that's the only difference between materialism and idealism as far as I'm concerned. Materialism represents the outward manifestation of reality, as determined through the five senses, whereas idealism correpsonds to the inner-experience which is alive and well and perceives that outer-reality. So, we can hoot and holler all we want about the existence of materialism, and yet we don't actually know outside of we perceive of it. In which case the two are wholly contingent upon each other.
Damn it, why didn't I just say that at the start? Sorry for muddling the issues by being so longwinded.
LOL, No apology necessary. It served your purpose and got the discussion started. I felt like a fool when I finally realized what you where asking after 3-4 days of talking about the wrong thing.
I am glad to read that physical-ism or Materialism suffers from the same plight.
I have long contended that Materialism is flawed and incomplete.
As you say, the question is simply 'Why are metaphysical questions undecidable?'
Alternatively, to make it sound less like just another pointless 'philosophical' question, it could asked as 'What is it about the universe that makes it impossible to construct a formally consistent explanation of its existence?
Ans: Obviously we are missing something or leaving out something basic
and crucial to the question. I want to answer God or the Universal
Conscious; but I think that it is more fundamental than that. I think that
it has to do with reality itself in that we are mired in it, within it, and
Trying to get a bird's eye(God's eye) view of it while we are stuck
here on the bottom like a fish swimming in the bottom of a murky pool
trying to learn about not just the water itself but what lies above it too.
We are looking at reality upside down. As the material universe is the medium in which we live and all that we can know with any certainty we look at it first as all there is and secondly as the ultimate cause and ultimate effect.
I think that this is wrong. The material universe is the effect, the result of the non-material reality. IMHO this means subject/mental realm as well as the so called spiritual realm. It is all one reality and all realms or aspects of reality are real but there is an hierarchy of at least cause and effect. This is why so many say that the material universe and our lives within it are in reality an illusion. It is not an illusion but the impression that it is the Ultimate Reality and all the rest is not really real but just subjective, spiritual hogwash is an illusion.
This leads me to believe that the questions being undecidable is because we are asking them from an illusional, invalid, viewpoint.
I have no solution but to try asking them from another viewpoint or mind set.
Example: Ask what it is about consciousness that allows or make the material to come into existence?
I know this is no answer for you; but as I am in way over my head now it is the best that I can do. After all it took this long just to figure out what the hell the question was! :blushing:
Royce
I'd go along with most of your post. I suppose that the question becomes 'what other perspective?'
So it sounds like both materialism and idealism are unfalsifialble, which is to say self-referential? ... unless, as I suggest, you understand them in context with each other.
I don't see that. In what way does understanding them 'in context with each other' change anything? I roughly agree about the inside outside thing. It raises the question of what perspective we should adopt on the question if both the view from the inside and the view from the outside are wrong.
Iacchus32
Dec6-04, 08:11 PM
I don't see that. In what way does understanding them 'in context with each other' change anything? I roughly agree about the inside outside thing. It raises the question of what perspective we should adopt on the question if both the view from the inside and the view from the outside are wrong.How do you know what black is unless you contrast it with white? Of course in that respect, here's what looks to be an interesting paradox (http://web.mit.edu/persci/people/adelson/checkershadow_illusion.html). Which is amazing when you click on "the proof."
As you say, the question is simply 'Why are metaphysical questions undecidable?'
In what sense? From what I vaguely remember, the undecidability really has to do with a recursive algorithm that cannot spit out “yes” or “no” as its output, given an infinity of instances at its input. The famous Halting Problem on a Universal Turing machine (UTM) illustrates the issue (there’s no general UTM that accepts an algorithm (i.e. another UTM) and can tell with a “yes” or “no” answer whether the given UTM will halt (i.e. recursively solve a problem)). If you’re dealing with only problem instance, e.g. find a solution to Fermat’s conjecture, the problem is actually considered to be decidable. Godel’s truths belong to this “decidable” category, the single instance problems. The implication of the incompleteness theorem is not that there are statements that don’t have a “yes or no” answer, the implication is that there are statements that are true, but you don’t know which ones, since there’s no algorithm to prove them to be true. But they can be proved from a meta system. So, what I’m asking is are you aware of some metaphysical statements that are true, but we can’t prove them with our logic, or that the metaphysical statements in general don’t have a yes-no answer? If the former, then it’s either a tautology, since you’re reiterating the incompleteness theorem and merely mentioning that metaphysical statements are part of the system; or, you’re assigning the ontological status to metaphysical statements as being G statements but I don’t see on what grounds.
If you mean metaphysical statements don’t have a yes-no answer, then I don’t see how you differentiate metaphysical and physical from a formal point of view. After all, just like logic, the inability to resolve a problem recursively is demonstrated with variables, not parameters. The Turing machine doesn’t care whether the input variable is metaphysical or not, it cares about halting. So, why do you care whether it’s metaphysical or not? For example, I don’t see what’s undecidable in the latter sense about, let’s say, “my consciousness is undetectable froth that floats on top of my brain”. It’s perfectly decidable, yet metaphysical, isn’t it?
Alternatively, to make it sound less like just another pointless 'philosophical' question, it could asked as 'What is it about the universe that makes it impossible to construct a formally consistent explanation of its existence?
Either that, or our explanatory system is weak and ill-formed. Now, I’m nowhere even close to the position of criticizing Godel’s incompleteness theorem, and I do realize that to do so, you’d have to put the whole number theory upside down, but still. I’m a big fan of Godel, but I always wondered: did he discover something inherently profound about the Universe, or simply showed that our formal system is weak to explain itself. The history is filled with examples of the latter. Newton didn’t have strong mathematics to describe his theory, so he invented his own! Newton’s description of reality was considered to be so firm for a couple of centuries that to question it was unthinkable. Well, we all know what Einstein did to it. My point is that through the history, both physics and math have not been discovered a priori. They have to make sense, and if they don’t, they are modified and expanded. What makes you think there won’t be Einstein in logic (even though Godel has already been considered to be one) who will change our formal system and the next you know we can fulfill Hilbert’s wish – to reduce everything to mathematical axioms and provable theorems. :tongue2:
Pavel.
. I think that it has to do with reality itself in that we are mired in it, within it, and Trying to get a bird's eye(God's eye) view of it while we are stuck here on the bottom like a fish swimming in the bottom of a murky pool trying to learn about not just the water itself but what lies above it too.
We are looking at reality upside down. As the material universe is the medium in which we live and all that we can know with any certainty we look at it first as all there is and secondly as the ultimate cause and ultimate effect.
Your claim is a bird's eye view, isn't it? :smile: Isn't it subject to the same criticism as Kant's noumenon?
honestrosewater
Dec6-04, 10:34 PM
Can someone give an example of a metaphysical question (MQ) so we can analyze its form?
Do all MQs have the same form?
Do all MQs share a combination of (non)reflexive, (non)symmetric, or (non)transitive relations/operators?
Iacchus32
Dec7-04, 01:55 AM
Can someone give an example of a metaphysical question (MQ) so we can analyze its form?
Do all MQs have the same form?
Do all MQs share a combination of (non)reflexive, (non)symmetric, or (non)transitive relations/operators?If we understood that the truth is evidenced within, then every question becomes a metaphysical question. Why? Because it doesn't pertain to the physical world, but only to what we perceive of it. This is my whole point by the way. :wink: We can't separate the metaphysical from the physical, because our consciousness (that which observes the physical) resides within the metaphysical reality of the mind.
In what sense? From what I vaguely remember, the undecidability really has to do with a recursive algorithm ... SNIP.... If you’re dealing with only problem instance, e.g. find a solution to Fermat’s conjecture, the problem is actually considered to be decidable. Godel’s truths belong to this “decidable” category, the single instance problems.
The implication of the incompleteness theorem is not that there are statements that don’t have a “yes or no” answer, the implication is that there are statements that are true, but you don’t know which ones, since there’s no algorithm to prove them to be true. But they can be proved from a meta system.
Great post. Just to be clear, I agree so far.
So, what I’m asking is are you aware of some metaphysical statements that are true, but we can’t prove them with our logic, or that the metaphysical statements in general don’t have a yes-no answer? If the former, then it’s either a tautology, since you’re reiterating the incompleteness theorem and merely mentioning that metaphysical statements are part of the system; or, you’re assigning the ontological status to metaphysical statements as being G statements but I don’t see on what grounds.
Yes, I'm surprised nobody picked me up on that earlier. It is my opinion that they are G-sentences, undecidable within any formally consistent system of reasoning, but it would take a few thousand words to attempt a proof, and I don't know whether I could make it stick.
However given the ongoing failure of analytical philosophers to decide these questions there is some evidence on my side. This is not a proof of it of course. However all the answers to these questions give rise to contradicitions, and that does seem to clinch it. Mathematician George Spencer-Brown sees our attempts to answer them as the same kind of iterative process as that which is used in the trembler circuits of an electric bell. If you say materialism is true (input) then you conclude that it must be false (output) so then you assume that idealism is true (input) only to find that it cannot be (output) and thus we do round and around for all eternity.
If you mean metaphysical statements don’t have a yes-no answer, then I don’t see how you differentiate metaphysical and physical from a formal point of view.
Well, in a way I'm saying that metaphysical question have only yes-no answers and that this is the whole problem with them. I'm not saying that metaphysical questions are undecidable just because they're metaphysical, (while I do think that it does follow I haven't tried to argue it). They are undecidable because they have no non-contradictory answers, and metaphysical because they are about what is ultimately real or ultimately true or false, and ultimates and absolutes lie beyond our senses, beyond science and beyond formal reasoning. This is Kant's transcendent reality I suppose, which requires us to transcend metaphysics to understand it.
After all, just like logic, the inability to resolve a problem recursively is demonstrated with variables, not parameters. The Turing machine doesn’t care whether the input variable is metaphysical or not, it cares about halting. So, why do you care whether it’s metaphysical or not? For example, I don’t see what’s undecidable in the latter sense about, let’s say, “my consciousness is undetectable froth that floats on top of my brain”. It’s perfectly decidable, yet metaphysical, isn’t it?
Clearly there are an infinite number of undecidable questions which are not metaphysical, but I believe that all metaphysical questions (if they are well-formed within the system) are undecidable. This partly because of the way we define 'metaphysical', and also because in my opinion what is ultimate cannot be represented by true and false theorems within any formal system. (The Tao cannot be named etc).
More controversially, or perhaps I should say even more controversially, I would argue that fundamental questions about consciousness are both metaphysical and undecidable. Again, a proof would take me long time, but the evidence is on my side.
Now, I’m nowhere even close to the position of criticizing Godel’s incompleteness theorem, and I do realize that to do so, you’d have to put the whole number theory upside down, but still. I’m a big fan of Godel, but I always wondered: did he discover something inherently profound about the Universe, or simply showed that our formal system is weak to explain itself.
A good question. Personally I believe that the incompleteness theorem holds for all sentient beings in all possible universes, and that it is inevitable that absolute truths cannot be derived from assumptions. I couldn't prove it, but I feel it's already been proved.
Also I'd say it is true for ontological reasons. In other words all the reasonable answers to metaphysical questions are wrong because such questions are based on a false assumption about reality. These are questions about the meta-system which gives rise to the formal system we call the universe, and they can only be resolved or understood (but not decided) from the meta-system, by transcending the system.
What makes you think there won’t be Einstein in logic (even though Godel has already been considered to be one) who will change our formal system and the next you know we can fulfill Hilbert’s wish – to reduce everything to mathematical axioms and provable theorems. :tongue2:
Funnily enough I believe this can be done. But only by creating a formal system which has a (formally) undecidable axiom its heart (one that is formally acknowledged to be undecidable), and which embodies (apparent) contradictions. This is the epistemilogical structure of Buddhism, Taoism, and so on. That would be a daunting topic to get into. However, roughly speaking, it's very similar to the epistemilogical sytem used in QM, in which the question of whether a wavicle is a particle or a wave is undecidable, and two complementary/contradictory formal systems arise as a result, one in which they are waves, one in which they are particles.
On this it's worth noting that undecidable metaphysical questions do not arise in these doctrines. No Buddhist or Taoist batted an eyelid when Goedel produced his proof. What he proved is what they've been asserting for millenia.
If we understood that the truth is evidenced within, then every question becomes a metaphysical question. Why? Because it doesn't pertain to the physical world, but only to what we perceive of it. This is my whole point by the way. :wink: We can't separate the metaphysical from the physical, because our consciousness (that which observes the physical) resides within the metaphysical reality of the mind.
That seems true. I've got a good quote somewhere from a respectable physicist arguing that we cannot do physics without doing metaphysics, but I've mislaid it. I'll post it if I find it. However, I'm not sure it's right to say that scientific questions are metaphysical.
Although come to think of it I suppose this is ultimately the reason why science can never provide absolute proof of any of its theories. But I haven't really thought this through.
Honestrosewater
The trouble with these questions is that they can be asked in different ways. Thus the question 'why does anything exist' is pretty much the same as 'did the universe arise from something or nothing'. But they can all be asked in such a way as to force us to choose between alternative and opposite answers, and it is questions in this form that are most relevant here. Perhaps we could use that one as a test case - did the universe arise from something or nothing? Alternatively - is matter made out of something or nothing?
Sho'Nuff
Dec7-04, 04:52 PM
I'm still digging trough the discussion in this post but I want to see if I got it right so far since my english is a bit lagging behind...help me out here...
A metaphysical question is a question that can have multiple answers aquired with reason but the best answer cannot be decided upon though reason.
This is because none of the answers are either falsifiable of verifiable.
Did I get it ????
Your claim is a bird's eye view, isn't it? :smile: Isn't it subject to the same criticism as Kant's noumenon?
As it is attempting to look from the sky down into the pool, then yes its a bird's eye view. from the ideal to the material rather than just the material.
If I knew what a Kant's noumenon was and the criticism that it is subject to, I might me able to answer that. I am at best a lay philosopher. Its been 30 years since I read any Kant and then it was in a intro philosophy class.
As it is attempting to look from the sky down into the pool, then yes its a bird's eye view. from the ideal to the material rather than just the material.
If I knew what a Kant's noumenon was and the criticism that it is subject to, I might me able to answer that. I am at best a lay philosopher. Its been 30 years since I read any Kant and then it was in a intro philosophy class.
No big deal, I'm not a pro either, I just happen to know about it because it is the kind of stuff I love learning. :smile:
Seems like you didn't understand my pick on you though. Briefly, Kant proposed that reality has a different form or structure than what we perceive it to be. Our knowledge of the world or what we perceive is phenomena. The real stuff is noumena. We can never know the true nature of noumenon because our perception of it is "distorted" by our senses and mind. This is an oversimplified version but you get the idea. The obvious criticism of this is that Kant makes an observation about the system from the outside the system and he has no epistemological right to do so. In other words, if you claim that your perception distorts truth about reality, then your own claim is a distorted view of reality, it’s phenomenon. You trapped yourself. It’s the same fallacy the determinists commit when then say “my thoughts are determined”…..
Similarly, you claimed we’re fish at the bottom of the pool trying to have a bird’s eye view. That very claim seems to be quite a bird’s eye view. But if you’re fish, you can’t make it. You’re assuming an outsider position, a bird, if you will, look down and say “oh, we’re fish” and then jump right back in. I don’t think you can do that unless you show you can fly. :smile: Anyway, I was not trying to start a debate about it, that was just an observation….
It is my opinion that they are G-sentences, undecidable within any formally consistent system of reasoning, but it would take a few thousand words to attempt a proof, and I don't know whether I could make it stick.
Heh, I'm in the same boat, in a sense that what I stated is also my opinion and that it'd take a few thousand words to attempt a proof, even though I believe I know how to proceed with it. I'm not saying you're wrong, and I believe your sources have a lot of merit. I'm just stating there's some inconsistency with my understanding of Godel and I wanted to contribute to this discussion to keep it more informative and detailed.
I hope we're going to avoid coding natural language into binary strings here but, as I said in my early post, I don't believe the metaphysical statements presented here are undecidable. Let me take another shot, but this time in a little more detail.
How did Godel prove incompleteness? He mapped natural language to an axiomatic arithmetic system. He then translated, I believe, a version of Liar’s paradox – “this statement is not provable” or “the statement on the other side of the page is not true….” into this arithmetic system. He thus produced a mathematical version of the Liar paradox. Note, it’s the same kind of contradictory paradox you’re referring to when discussing materialism. The translation is a statement G that says “G is not provable”. So, you have If G is provable, it is not provable, a contradiction. However, if G says it is not provable and it really is not provable, then G is true, but not provable. The first choice makes the system inconsistent, that’s not what we want, so logicians settled for the second choice. The proof is quite interesting and not that complicated but requires focus, in case you haven't indulged yourself yet. Anyhow, the bottom line is the Liar paradox is translatable into a finite formal language, and thus into a finite binary string that can be accepted or rejected by a Turing machine! Let me give you an analogy. Nobody proved Golbach’s conjecture (every even number above 2 is a sum of two primes). However, I can say, let’s define number P as 67 if Golbach’s conjecture is true, and P is 97 if the conjecture is false. We know the number exists, we just don’t know which one it is! Similarly, I can feed the conjecture into 2 Turing machines, one that accepts all input, the other one that rejects. One if them might have the solution, but we don’t know which one. That’s Godel’s G statement. Note that the conjecture, just like the paradox can be coded into a finite binary string. This class of statements is considered to be decidable!
Now, consider the famous Halting problem – is there a general algorithm that can determine if a Turing machine will halt on a given input. Think about it, the general algorithm is a Universal Turing Machine (UTM) that accepts as its input a pair of strings – one is the Turing machine to be tested, the other - that machine’s input binary string. But there is an infinity of the input binary strings and Turing machines. So, the input to the UTM is an infinite set of strings, meaning there’s no effective way to determine if the UTM will halt or not. If you changed the problem to a specific pair of strings, not general, the problem would be decidable. Well, it depends on the nature of the input string to the machine under test. If it’s infinite, like in your infinite regress with causality example, the situation gets convoluted, at least for me, because you start dealing with countable infinity, Cantor set and the whole continuity problem. And speaking of which, here’s another good example of undecidable statement – the continuity hypothesis (uncountable infinity of real numbers “between” a pair of rational numbers, which in their turn form a countable infinity line). Godel proved that the assertion of the hypothesis is consistent with an axiomatic set theory. In fact, I think he made it an axiom, but then Cohen came along and proved that the negation of the hypothesis is also consistent with the set theory. So, now you have truth and negation of the same statement consistent within the same axiomatic system! This is not the same assertion and negation of idealism because it’s unfalsifiable. If translated into formal language, I’m certain the negation will be inconsistent with its assertion, but please don’t make me do it, it’ll be quite a home work. :smile:
Funnily enough I believe this can be done. But only by creating a formal system which has a (formally) undecidable axiom its heart (one that is formally acknowledged to be undecidable), and which embodies (apparent) contradictions. This is the epistemilogical structure of Buddhism, Taoism, and so on.
But are you sure such system will be consistent? I'm not familiar with Buddhist and Tao epistemological structure, they have a consistent system?
However, roughly speaking, it's very similar to the epistemilogical sytem used in QM, in which the question of whether a wavicle is a particle or a wave is undecidable, and two complementary/contradictory formal systems arise as a result, one in which they are waves, one in which they are particles.
Somehow I considered QM simply to show that waves and particles are not mutually exclusive but there's really no undecidability about it. The only other thing I thought was that QM showed to intuitionists that a number can exist even if there is no way to construct it, until you prove it, just like the position of an electron is unknown, until you look. If anything, there's an existence of possible physical worlds, but without corresponding formal systems accompanying each one of them. That's how I view it, but to be quite honest, I'm not that sure about it, as I havent given it too much thought :smile: What's the general consensus among the logicians?
Pavel.
Iacchus32
Dec8-04, 01:29 AM
Our knowledge of the world or what we perceive is phenomena. The real stuff is noumena. We can never know the true nature of noumenon because our perception of it is "distorted" by our senses and mind. This is an oversimplified version but you get the idea. The obvious criticism of this is that Kant makes an observation about the system from the outside the system and he has no epistemological right to do so. In other words, if you claim that your perception distorts truth about reality, then your own claim is a distorted view of reality, it’s phenomenon. You trapped yourself.And yet in not knowing you know. So at least you know that much about reality overall. Which, in fact is what Kant is saying isn't he? ... Reality, in all its absoluteness -- yes -- must be greater than what I perceive of it. Why is that so difficult to understand?
honestrosewater
Dec8-04, 02:59 AM
And yet in not knowing you know. So at least you know that much about reality overall. Which, in fact is what Kant is saying isn't he? ... Reality, in all its absoluteness -- yes -- must be greater than what I perceive of it. Why is that so difficult to understand?
"Noumena exists independently of phenomena." Isn't that statement undecidable in a phenomenal system?
Pavel- Thanks for those explanations. Well, thanks to everyone, but those were especially nice :smile:
Did the universe arise from something or nothing?
I suspect we can answer this question by making one statement and analyzing the relation:
Nothing caused something.
Substituting "$" for "caused", the cause relation:
N $ S
1) Is $ reflexive? (Can A cause A?)
2) Is $ symmetric? (Is it true that if A caused B, then B caused A?)
3) Is $ transitive? (Is it true that if A caused B, and B caused C, then A caused C?)
Does anyone think this approach could be productive?
___
Okay, I should add a few thoughts. There seem to be similarities between physical causation and mathematical order (>). Mathematical order also seems to be at work in other questions, esp. about god. As in, can an omnipotent being limit its own power? Do you see a connection between this and something like "for all x in A, there exists some y in A such that y > x." Of course, because > is not reflexive, y cannot exist (it is never true that y > y). But if you change > to \geq then y can exist. Well, I could have phrased that example better, those are just some rambling thoughts, and I have reached no conclusions yet. :redface:
Iacchus32
Dec8-04, 06:56 AM
"Noumena exists independently of phenomena." Isn't that statement undecidable in a phenomenal system?Yes, but does phenomena give rise to itself? No. Even an illusion needs something tangible to prop it up ... unless of course everything was an illusion to begin with, but then again that's not possible, because even an illusion is something (tangibly based) compared to nothing.
honestrosewater
Dec8-04, 06:58 AM
A metaphysical question is a question that can have multiple answers aquired with reason but the best answer cannot be decided upon though reason.
This is because none of the answers are either falsifiable of verifiable.
Did I get it ????
Yes, that is being assumed by some, but they have yet to prove it :wink:
Someone could argue that it depends on how you ask the question and in what system you ask the question. Canute and Pavel said they think that metaphysical questions are G(ödel) statements (or sentences). I couldn't find much info, but it seems G statements are defined as being undecidable in their system (the system in which they appear). C&P seem to use them to apply to all systems. I'm not sure what is common practice. I imagine if you can prove that all sufficiently complex, consistent formal systems contain G statements, you have a shot at proving that all G statements have certain properties in common, regardless of their system. Perhaps that is precisely what you are proving, I don't know, I can't think that quickly. Perhaps this is precisely how Gödel's proof proceeded. Perhaps someone can enlighten us.
____
http://homepages.which.net/~gk.sherman/baaaaab.htm explains briefly the steps of the proof.
http://home.ddc.net/ygg/etext/godel/godel3.htm the horse's mouth ;)
A metaphysical question is a question that can have multiple answers aquired with reason but the best answer cannot be decided upon though reason.
This is because none of the answers are either falsifiable of verifiable.
Did I get it ????
Sort of, but not quite. Officially (my dictionary) metaphysical questions are questions about what lies 'beyond nature' and beyond ordinary knowledge or experience.
Such questions cannot be answered by reason because the reasonable answers to them are inconsistent with the formal rules of the system of logic in which they are asked. In other words, the question 'Is matter made out of something or nothing' cannot be answered because the only available 'reasonable' answers are something or nothing, and both give rise to logical contradictions (neither answer makes sense to someone asking the question who reasons that these are the only two possible answers).
So this question is metaphysical in that it is about what is ultimately true or false (which puts it beyond science) and undecidable in that neither answer makes sense (which puts it beyond the system of formal reasoning that was used to construct the question).
As it appears that all formal systems of reasoning about reality give rise to undecidable metaphysical questions we can say that undecidable metaphysical questions are beyond reason, rather than just beyond some particular system of reasoning. (I would say this is an error, but I won't risk muddling the issues by going into why here).
Briefly, Kant proposed that reality has a different form or structure than what we perceive it to be. Our knowledge of the world or what we perceive is phenomena. The real stuff is noumena. We can never know the true nature of noumenon because our perception of it is "distorted" by our senses and mind. This is an oversimplified version but you get the idea. The obvious criticism of this is that Kant makes an observation about the system from the outside the system and he has no epistemological right to do so. In other words, if you claim that your perception distorts truth about reality, then your own claim is a distorted view of reality, it’s phenomenon. You trapped yourself. It’s the same fallacy the determinists commit when then say “my thoughts are determined”…..
I read Kant the other way around, as making a comment about what is ouitside the system from within the system. This is logically allowable since it is in the nature of formal systems that they have a meta-system outside themselves. In other words we can formally infer a metasystem without having to actually get out of the system, epistemilogically speaking.
Iow, Kant argued that there was a meta-system not knowable through our senses or by reason ('transcendent' reality), and this seems allowable to me since it seems logically inevitable. I suspect Kant would not have been suprised by Godel's theorem.
Also, I only half agree about the noumenal. It's true that we cannot trancend the system to confirm Kant's assertion by observation or reason. But it is perfectly possible, in principle at least, to transcend it non-conceptually, by direct experience of that transcendent reality. It seems relevant to mention that Buddhism is sometimes characterised as 'the view from nowhere'.
No big deal, I'm not a pro either, I just happen to know about it because it is the kind of stuff I love learning. :smile:
Seems like you didn't understand my pick on you though. Briefly, Kant proposed that reality has a different form or structure than what we perceive it to be. Our knowledge of the world or what we perceive is phenomena. The real stuff is noumena. We can never know the true nature of noumenon because our perception of it is "distorted" by our senses and mind. This is an oversimplified version but you get the idea. The obvious criticism of this is that Kant makes an observation about the system from the outside the system and he has no epistemological right to do so. In other words, if you claim that your perception distorts truth about reality, then your own claim is a distorted view of reality, it’s phenomenon. You trapped yourself. It’s the same fallacy the determinists commit when then say “my thoughts are determined”…..
Well I don't and never have agreed with everything Kants said, especially the above. It may be just the words that he(you) used that we misinterpret. What I am saying and have been saying for some time here is that; if our view
of reality is distorted it is because we limit our view to the physical objective universe and ignore or dismiss the rest of reality, the subjective, mental and spiritual (for want of better words) and that we look at the physical as the cause of our reality whereas it is IMO the effect, hence up-side-down.
Similarly, you claimed we’re fish at the bottom of the pool trying to have a bird’s eye view. That very claim seems to be quite a bird’s eye view. But if you’re fish, you can’t make it. You’re assuming an outsider position, a bird, if you will, look down and say “oh, we’re fish” and then jump right back in. I don’t think you can do that unless you show you can fly. :smile: Anyway, I was not trying to start a debate about it, that was just an observation….
Again you are making an invalid assumption, as most physicalist do, that I am talking about an outside viewpoint. This is why I used the analogy that I did. The sky and the bird are all part of our nature the same, one ecology.
There is only one reality. our error is by looking at only one aspect of it and thinking that that is all that there is. How could we, or God for that matter, be outside of reality looking in. If God and we are real then we obviously are in reality.
How did Godel prove incompleteness? He mapped natural language to an axiomatic arithmetic system. He then translated, I believe, a version of Liar’s paradox – “this statement is not provable” or “the statement on the other side of the page is not true….” into this arithmetic system. He thus produced a mathematical version of the Liar paradox. Note, it’s the same kind of contradictory paradox you’re referring to when discussing materialism. The translation is a statement G that says “G is not provable”. So, you have If G is provable, it is not provable, a contradiction. However, if G says it is not provable and it really is not provable, then G is true, but not provable. The first choice makes the system inconsistent, that’s not what we want, so logicians settled for the second choice.
I'm uncomfortable with the term 'provable' here, and would rather use 'decidable'. But I don't disagree with what I think you mean.
The proof is quite interesting and not that complicated but requires focus, in case you haven't indulged yourself yet.
Ha. Not that complicated to you perhaps. I can't follow the mathematics. However it strikes me that G constructed his proof by departing from his formal system of proof and then re-entering it, which is suggestive.
The two para's you wrote on the continuum hypothesis and the Goldbach conjecture seem about right to me. But I'm not sure why they're relevant here. I cite Goedel simply to show that formal axiomatic systems always have metasystems, so that any formally consistent description of the universe must leave something out (must be incomplete - cf. Kant's transcendent reality), and to show that all formal axiomatic systems must contain at least one undecidable question.
But are you sure such system will be consistent? I'm not familiar with Buddhist and Tao epistemological structure, they have a consistent system?
I'm not sure that this is a decidable question. :biggrin: It depends how you look at it. The peculiar epistemilogical structure of Buddhism stems from the undecidability of all questions about what it takes to be ultimately real, what it takes as axiomatic if you like.
Thus, for instance, what is ultimate cannot be characterised as existing or not-existing. Never mind the counterintuitiveness of this for the moment, what it means is that in Buddhism there are two complementary descriptions of reality, one in which what is absolute exists, one in which it doesn't. Each of these explanations is perfectly consistent in themselves, but both are equally true and false, since what is ultimate transcends such distinctions. This applies to all 'dual' properties that might be assigned to what is ultimate. (The problem here is over the definition of 'exist' - there are at least two ways of defining it, so at least two ways of answering the question. Buddhists tend to say what is ultimate is, rather than that it exists, to avoid making a false assertion).
What this entails is that a Buddhist explanation of reality (and those of Taoism, Advaita, mystical Christianity, Sufism etc.) are really two complementary explanations that contradict/complement each other. Each is entirely consistent in itself, but each contradicts the other and neither is complete. This is not some trick to confuse non-believers, and definitely not 'mysticism' in the disparaging sense. It is just the way things are. What is ultimate transcends distinctions and must remain undefined in any formally systematic description of reality. This is why it can only be approached non-conceptually. (Hence the 'Tao that cannot be named', the avowed danger of naming God or 'idolising' him, and the impossibilty of explaining what Buddhists mean by 'emptiness').
I feel too much has been made of the link between Buddhism and QM, but in this epistemilogical sense they are very similar systems of explanation. A wavicle can be consistently explained as a wave, and can be consistently explained as a particle. But neither explanation is complete, for neither explains what a wavicle is, and contradictions are only avoided by keeping the two contradictory/complementary explanations separated. What a wavicle is is neither a wave nor a particle. What ultimate reality is is neither something nor nothing.
On this view any question that asks whether what is ultimate is something or nothing would be undecidable, for it's an improper question, an artefact of dual thinking. It embodies a false assumption, like the question 'have you stopped beating your wife?' It's unanswerable (unless, that is, you have been beating your wife!).
If that doesn't make sense I won't be surprised. It's a very confusing topic to discuss.
honestrosewater
Dec8-04, 11:34 AM
Canute,
That compliment/contradict idea reminds me of 1 and 0. You know, how you have to include that 1 does not = 0 in the field axioms.
I forgot to mention hierarchies are also ordered. When you say "ultimate", do you mean the root(s) of a hierarchy?
Canute,
That compliment/contradict idea reminds me of 1 and 0. You know, how you have to include that 1 does not = 0 in the field axioms.
I forgot to mention hierarchies are also ordered. When you say "ultimate", do you mean the root(s) of a hierarchy?
I'm afraid I don't know what 'field axioms' are. But it sounds like you're saying that 1 has to be defined as ~0 in the same way as we have to define something as ~nothing, thus giving ourselves a cosmological dilemma. Is that it? Yes, by 'ultimate' I do mean the root of a hierarchy. Or alternatively, that without which nothing else would exist.
And yet in not knowing you know. So at least you know that much about reality overall.
Well, yeah, but how coherent is that knowledge? That's the problem. As thinkers, we want to be consistent in how we understand the reality. If my knowledge allows me to believe that I'm a programmed robot and that I can choose at the same time, the knowledge is flawed.
Reality, in all its absoluteness -- yes -- must be greater than what I perceive of it. Why is that so difficult to understand?
I have no difficulty understanding it, I'm having a problem seeing on what grounds you believe there's something else. Why not add green men and the perfect island to the mix as well?
honestrosewater
Dec9-04, 05:26 PM
Canute,
Right. The field axioms define normal addition and multiplication. I think I'm ducking out of this discussion for a while. Have fun :biggrin:
I read Kant the other way around, as making a comment about what is ouitside the system from within the system...
Iow, Kant argued that there was a meta-system not knowable through our senses or by reason ('transcendent' reality)
See, I told you I'm not a pro. That's right, it's the other way around. :smile:
This is logically allowable since it is in the nature of formal systems that they have a meta-system outside themselves. In other words we can formally infer a metasystem without having to actually get out of the system, epistemilogically speaking.
Hmmm, interesting, I'm not sure about it, but I'll keep my mind open. Do you have any reference I can read on how we can infer a meta system that transcends our level of consciousness? See, to me, Godel's meta systems or any other formal systems in arithmetic are within our level of abstraction or complexity, if you will, just like a 2D space is a subset of a 11D space. That's what allows us to transcend them. All Godel did was to prove there are truths that can be proved only from a meta level. There are two assumptions: the system is consistent, and that it's formal. Such system, he proved, is incomplete. You can't assume that about the system on which our consciousness operates. All these post Godel's speculations about the necessity of meta systems that transcend our being are just that - speculations, in my understanding, but I'd be happy to read a good article about the inference of meta systems, ad infinitum? To put it yet in other words, how do you know, that WE are not at the root of the hierarchy? I don't think Godel proves we are not.
On the same note, I have a problem with the classical agnosticism claiming "we can't know if God exists". I don't have a problem if you say "I don't know if He exists". But when you say "can't", that's a heck of a claim! It's a claim about the reality you're claiming you can't know. Kant said the knoweldge of God, or noumena is unknowable, hidden from the scientific inquiry. If it's unknowable, there's no sense in talking about it, you're talking about something you don't know. (isn't that what "talking out of your butt" means?) How much sense is that making?
It's true that we cannot trancend the system to confirm Kant's assertion by observation or reason. But it is perfectly possible, in principle at least, to transcend it non-conceptually, by direct experience of that transcendent reality. It seems relevant to mention that Buddhism is sometimes characterised as 'the view from nowhere'.
I can't comment on that. WIth all due respect, I think that's highly subjective to personal experience, as my transcendental experience can take me in totally different place than yours, if you know what I mean :smile:
Pavel.
Ha. Not that complicated to you perhaps. I can't follow the mathematics. However it strikes me that G constructed his proof by departing from his formal system of proof and then re-entering it, which is suggestive.
Heh, maybe I got that impression because I read a some kind of "Godel for dummies" version, where they pretty much spoon fed you the steps. Seriously though, if you have understanding of predicate calculus and basic number theory, you're good to go. Knowledge of the diagonalization method would be helpful in understanding his mapping of the natural language to an axiomatic system.
I'm not sure where he departs from his system and then reenters it, specifically?
The two para's you wrote on the continuum hypothesis and the Goldbach conjecture seem about right to me. But I'm not sure why they're relevant here.
Ok, I'll try to be brief this time and take yet another, more general approach. I had a debate with my buddy a couple of years ago (which led me to study Godel in more detail) about our logic. I was trying to convince him that we're stuck with a binary logic, we don't have a choice. Speaking about other logics ultimately brings the same question to the table "but is that logic true"? Denying or questioning our fundamental axioms of logic is meaningless, as in doing so, you have no other tool to do it but the very axioms in question..... You get the idea. He was arguing there are propositions that don't have a boolean yes or no answer to them, they're undecidable. I said wait a second, you can't be talking about Godel, because while we can't prove the statement to be true, it's ontological status, if you will, is still true or false, we just don't know which one it is, as there's no mechanical way to prove it. That's why I mentioned Golbach's and Fermat's conjectures. There might not be a computational way to prove or disprove the conjectures, they're still either true or false. Unfortunately for me, my friend taught an Automata and Intro to computation class in college and he was more up to speed. He showed that problems like the two conjectures are actually trivially decidable; when traslated into a formal language, they are recursive and there's a computational way to decide them. Because of a wide acceptance of Church-Turing thesis, any computable function must be computable by a TUring machine, decidability is tested on Turing machines (not physically of course; TM is just an algorithm). That's how they come into play. Both conjectures can be coded into a finite string and recursively solved, but we don't know if the machine will ever halt or not. There's another set of propositions, however, like the continuim hypothesis, which can't be even coded into a recursive language. I mentioned that the Continuim hypothesis was showed to be consistent with the axiomatic set theory by Godel, and not consistent by Cohen. Unlike Godel's G statement, this one is neither true or false. The assertion and the negation of the proposition is consistent within the same formal system. There's no computational way to reduce the problem to a yes or no answer. And that was my point. Paradoxes like The Liar, or examples of contradictions with materialism are examples of Godel's G statements - they're not provable, but they're true (or false). All they're indicating is that we need a meta system to prove them. BUt they're not making this profound claim about the mystery of the Universe. The undecidable statements of the Cont. Hypoth. might, but I was saying that not all metaphisical statements are of that kind, which seemed to be your claim. Besides, I'm not even sure I could agree even if we stayed within the context of G statements. I still don't understand what is unprovable (in a formal sense of course) about the statement "there are ghosts in my house"?
Thanks,
Pavel.
Hmmm, interesting, I'm not sure about it, but I'll keep my mind open. Do you have any reference I can read on how we can infer a meta system that transcends our level of consciousness?
No I afraid I don't. But it seems to me that if every formal axiomatic system has within it theorems which do not have a truth value relative to the axioms of that system, but can be decided from outside the system by extending the axiom-set, then all for every formal axiomatic system there is a metasystem. Does that seem incorrect to you?
See, to me, Godel's meta systems or any other formal systems in arithmetic are within our level of abstraction or complexity, if you will, just like a 2D space is a subset of a 11D space. That's what allows us to transcend them. All Godel did was to prove there are truths that can be proved only from a meta level. There are two assumptions: the system is consistent, and that it's formal. Such system, he proved, is incomplete. You can't assume that about the system on which our consciousness operates.
I'm not asssuming that. I'm assuming that it applies to all possible systems of formal reasoning based on our usual laws of formal logic.
To put it yet in other words, how do you know, that WE are not at the root of the hierarchy? I don't think Godel proves we are not.
But I do think we are at the root of the hierarchy, and feel that Godel proved it. What I'm suggesting is that for any systems of reasoning there is a consciousness within which the system of reasoning exists, and which is capable of deciding questions that cannot be decided within any system of reasoning.
On the same note, I have a problem with the classical agnosticism claiming "we can't know if God exists". I don't have a problem if you say "I don't know if He exists". But when you say "can't", that's a heck of a claim! It's a claim about the reality you're claiming you can't know. Kant said the knoweldge of God, or noumena is unknowable, hidden from the scientific inquiry. If it's unknowable, there's no sense in talking about it, you're talking about something you don't know. (isn't that what "talking out of your butt" means?) How much sense is that making?
Makes sense to me. What is transcendent is certainly hidden from scientific enquiry, since science studies appearances and phenomena. It is also hidden from reason and our senses, as Kant concluded. However he was quite wrong to conclude that the transendent cannot be not be known becuase of this. He showed only that the noumenal and the transcendent has to be known non-conceptually if at all.
WIth all due respect, I think that's highly subjective to personal experience, as my transcendental experience can take me in totally different place than yours, if you know what I mean :smile:
I wasn't really making a claim about my personal experience. I was just saying, if I remember right, that in principle at least it is possible to know things that cannot be known by reason, and thus transcend Kant's notion of the limits to knowing (or Goedel's notion of the limits to deciding) .
Ok, I'll try to be brief this time and take yet another, more general approach. I had a debate with my buddy a couple of years ago (which led me to study Godel in more detail) about our logic. I was trying to convince him that we're stuck with a binary logic, we don't have a choice. Speaking about other logics ultimately brings the same question to the table "but is that logic true"? Denying or questioning our fundamental axioms of logic is meaningless, as in doing so, you have no other tool to do it but the very axioms in question..... You get the idea.
I do get the idea, and I agree. This is the point really, logic has to be transcended in order to attain certain knowledge. All knowledge gained though logic and reason is relative and uncertain. This is no more than Aristotle said when he wrote that 'true knowledge is identical with its object', or words to that effect. Thus knowledge is gained by 'becoming', not by formally logical reasoning. In this Aristotle anticipated Godel.
He was arguing there are propositions that don't have a boolean yes or no answer to them, they're undecidable. I said wait a second, you can't be talking about Godel, because while we can't prove the statement to be true, it's ontological status, if you will, is still true or false, we just don't know which one it is, as there's no mechanical way to prove it.
This is tricky because like you I'm no pro. However in my layman's opinion you've slightly misunderstood Godel. If a statement is undecidable it does not have a truth value within the system. Of course you can say that it does have a truth-value within some other system, but you cannot say that the ontological status of such statements is true or false. If you change your axiom-set in order to demonstrate a proof of the statement's truth or falsity then it is different statement, since you have derived it from a different axiom-set.
That is, the statement in the original system would say 'this statement does not have a truth-value within this system', whereas the new statement would be 'this statement does not have a truth-value within that system', and as such it becomes decidable. A precisely equivalent statement would be undecidable in the new system.
That's why I mentioned Golbach's and Fermat's conjectures. There might not be a computational way to prove or disprove the conjectures, they're still either true or false.
Yes, but this is a pragmatic issue relating to these particular conjectures. We do not yet know whether they are undecidable or not. However we are talking here about statements which we can formally prove are undecidable.
Paradoxes like The Liar, or examples of contradictions with materialism are examples of Godel's G statements - they're not provable, but they're true (or false).
Again I disagree. This is partly for the reasons given above. The statement 'this sentence is not a theorem of T' is not decidable within any formal system T. Both answers give rise to contradictions. It is decidable only by creating a system that encompasses T, but is not T. Let's call this expanded system U. In U we can decide the statement 'this sentence is not a theorem of T', but we still cannot decide one that says 'this sentence is not a theorem of U'. So a statement that says of itself that is not a theorem within any formal axiomatic sytem' is undecidable full stop.
Statements can be decided only be reference to ones axioms, and thus can be only relatively proved. So no statements have the 'ontological status' of being true or false. Statements are derived from axioms, and, as Godel showed, we can never prove that our axioms are self-consistent. In an absolute sense there is no such thing as a logically-demonstrable true or false statement.
On the continuum hypothesis it seems to me that there is a fundamental difference between its undecidability and that of a G-sentence. The C.H. is undecidable because neither its truth or falsity contradicts the axioms of set theory. But for a G-sentence both its truth and falsity do contradict the axioms. The two situations do not seem to be equivalent.
All they're indicating is that we need a meta system to prove them. BUt they're not making this profound claim about the mystery of the Universe.
No, but consider, metaphysical questions have the characteristic that their answers contradict reason. This is why they are undecidable. They have been found to be undecidable in all the systems of reasoning tried out by all western philsophers, however they have chosen to axiomatise their formal reasoning systems. Here it is not a question of extending ones axioms, that has been tried many times with no success.
Because these questions arise in all systems of reasoning they must have the 'ontological status' of being undecidable. If so then it would suggest that their (reasonable) answers are neither true nor false, or rather, they do not have reasonable answers, and the reason for this may be that 'transcendent reality' is non-dual, and thus impossible to represent truthfully within any formal system of reasoning, as Taoists et al assert. Perhaps this cannot be proved, but if it were true it would at least be consistent with the facts, and it would explain why metaphysical questions are undecidable.
The undecidable statements of the Cont. Hypoth. might, but I was saying that not all metaphisical statements are of that kind, which seemed to be your claim.
Not quite. I see the CH as a different case.
Besides, I'm not even sure I could agree even if we stayed within the context of G statements. I still don't understand what is unprovable (in a formal sense of course) about the statement "there are ghosts in my house"?
That doesn't seem undecidable to me either.
Btw I'm finding this discussion very useful, but if my posts are too long just tell me and I'll cut them down.
No I afraid I don't. But it seems to me that if every formal axiomatic system has within it theorems which do not have a truth value relative to the axioms of that system, but can be decided from outside the system by extending the axiom-set, then all for every formal axiomatic system there is a metasystem. Does that seem incorrect to you?
The statement 'this sentence is not a theorem of T' is not decidable within any formal system T. Both answers give rise to contradictions. It is decidable only by creating a system that encompasses T, but is not T. Let's call this expanded system U. In U we can decide the statement 'this sentence is not a theorem of T', but we still cannot decide one that says 'this sentence is not a theorem of U'. So a statement that says of itself that is not a theorem within any formal axiomatic sytem' is undecidable full stop.
100% agree. I’m afraid I didn’t communicate my point well enough then. The above holds true for a formal, as you said, system. But there’s another premise – consistent system. I believe that, because of the undecidable statements like the Continuum Hypothesis, our own system [that we employ in evaluating simple formal arithmetic systems] is not consistent, and far from being formal. Again, as I was trying make this clear, Godel’s statements are formalizable, translatable, or computable, however you want to say it. That is, they’re legitimate true/false statements in our systems, we just can’t prove them to be one way or the other! They are theorems, but not provable by the axioms of the system. However, there’s another class, what I call undecidable, is the statements that can’t be even formalized. Godel would not be able to map such a statement into his arithmetic. The CH is such an example. Another example is determination of halting of any Turing machine on any input (Halting Problem dealing with infinity of instance problems on the input to the UTM)) You can’t even formalize them to determine whether you can prove them or not, whether they’re examples of G statement or not. I believe that is precisely the reason Godel simply made the CH an axiom and showed that it plays well with other axioms, thus preserving the consistency of the system. But that is, of course, the way I see it. So, to continue with your line of thought, I’d like you to demonstrate to me that our system that we use to have this very discourse is consistent and formal, just like an arithmetic system that Godel proved to be incomplete. If you successfully demonstrate it to me, then by Godel's theorem, I’ll completely agree with you – we can infer a meta-system that transcends our own consciousness, or the level of its complexity. I understand it’s not an easy task, so if you can't, we’ll just have to agree on reaching an impasse and leaving it simply as a matter of personal opinion.
See, to me, Godel's meta systems or any other formal systems in arithmetic are within our level of abstraction or complexity, if you will, just like a 2D space is a subset of a 11D space. That's what allows us to transcend them. All Godel did was to prove there are truths that can be proved only from a meta level. There are two assumptions: the system is consistent, and that it's formal. Such system, he proved, is incomplete. You can't assume that about the system on which our consciousness operates.
I'm not asssuming that. I'm assuming that it applies to all possible systems of formal reasoning based on our usual laws of formal logic.
Well, I get an impression you are assuming that all possible systems of formal reasoning based on our usual laws of formal logic are formal and consistent. That’s how you try to infer a meta system with the help of Godel’s theorem. If they are not, then all bets are off, why do you even bring Godel? The incompleteness theorem deals with consistent and formal systems only. That is really important!
But I do think we are at the root of the hierarchy, and feel that Godel proved it. What I'm suggesting is that for any systems of reasoning there is a consciousness within which the system of reasoning exists, and which is capable of deciding questions that cannot be decided within any system of reasoning.
OK, now I’m getting confused. What I meant by the root of the hierarchy is that our consciousness is final, there’s no meta system that transcends it, the one you’re trying to infer. I’m not sure I see what you mean by “there’s a consciousness within a reasoning system..” which contains a reasoning system in itself?? You have a “total” reasoning system containing subreasoning systems? Where do we fall? Am I on the level of total system? Can you please elaborate a little? :smile:
I was just saying, if I remember right, that in principle at least it is possible to know things that cannot be known by reason, and thus transcend Kant's notion of the limits to knowing (or Goedel's notion of the limits to deciding)
See, that’s exactly what I’m talking about. You’re reasoning about things you claim you can’t reason about. How can you assign, even in principle, these properties to an object which is hidden from your reason??? It’s meaningless, don’t you think? It's one thing to try to infer a meta sytem via Godel's theorem (what you're trying to do), but it's totally something else to be assigning properties to it. Or perhaps I'm putting too much of a functional value into your notion of "knowing". Perhaps an example on your part might help
I do get the idea, and I agree. This is the point really, logic has to be transcended in order to attain certain knowledge. All knowledge gained though logic and reason is relative and uncertain.
There you go again, jumping out of the system. If your knowledge gained through logic and reason is relative and uncertain then what about your very claim itself? How did you come to transcend and “see” that our logic and reason is relative and uncertain, what else did you use to come to this conclusion? Please be specific. Because if you used logic and reason, then to believe you, I need to conclude that what you told me is also relative and uncertain. This seems to me like an obvious fallacy, what is it that I don’t understand here?!?!?!
This is tricky because like you I'm no pro. However in my layman's opinion you've slightly misunderstood Godel. If a statement is undecidable it does not have a truth value within the system. Of course you can say that it does have a truth-value within some other system, but you cannot say that the ontological status of such statements is true or false. If you change your axiom-set in order to demonstrate a proof of the statement's truth or falsity then it is different statement, since you have derived it from a different axiom-set.
That is, the statement in the original system would say 'this statement does not have a truth-value within this system', whereas the new statement would be 'this statement does not have a truth-value within that system', and as such it becomes decidable. A precisely equivalent statement would be undecidable in the new system.
I know exactly what you’re saying, but just like you said, I think you misunderstood Godel. I don’t mean to pull some kind of “argument from authority”, but I think you’d change your mind if you went through the proof itself, or at least read a close interpretation of it. There are numbers on the real number line that do exist, yet incomputable! In fact, there’s an uncountable infinity of them. Square root of 2 is an example. There is no recursive way to solve the number. All we can do is brute force it and find more digits in the decimal. But just because we can't mechanically compute it, it doesn't mean it doesn't exist. In fact, it gave a big headache to the Pythagorians because they couldn't express it as a rational number. They knew the number existed (by the Pythagorian theorem) but they couldn't figure out how to compute it. And as far as computational devices are concerned, such as computers and calculators, they use a computable number that is an aproximation to the square root of 2. Anyhow, this was all known way before Godel and if you want to dig in it, read about Canter sets, diagonilization method (mapping rational numbers to real numbers), and of course, the Cont. Hypothesis. Godel mapped the number theory into logical propositions, that’s the genius of his work, and showed that just like there are numbers that can’t be computed, there are statements that can’t be proven. These statements are theorems. In other words, they are true! But you can’t prove them to be true with the axioms given, just like the set theory can’t map to certain numbers with axioms within the set theory. It’s worth repeating that Godel’s statements are theorems, meaning they are true propositions about the system, just like axioms.
Axioms are true by definition, we stipulate them to be true, they’re self evident and atomic truths. We then deduce theorems from them, which are also necessarily true. How do we deduce? By rules of transformation, which are also axioms, they’re stipulated, but they operate on other axioms. (I know you agree so far, I’m reviewing this to make sure we’re still on common grounds here). These explicit definitions make the system formal. Moreover, the axioms have to play well with each other, i.e, not contradict each other, which makes the system consistent. Godel showed, that given consistency and formality of any powerful enough system, there will be theorems in that system that can’t be deduced from the axioms of that system, but those are nevertheless true statements about the system. In order to understand why it’s a theorem, and not some incoherent “square circle”, you really need to look at his proof. He constructs a wff in predicate logic that shows there is a necessary relationship between two numbers but that relationship is not an axiom in the system. Which is also why I disagree with your following comment:
Statements can be decided only be reference to ones axioms, and thus can be only relatively proved. So no statements have the 'ontological status' of being true or false. Statements are derived from axioms, and, as Godel showed, we can never prove that our axioms are self-consistent. In an absolute sense there is no such thing as a logically-demonstrable true or false statement.
So, yes, there is such a thing as a true statement that you can’t prove to be true by the axioms and rules of transformation of a any [powerful enough] formal and consistent system. That is exactly what Godel’s theorem is all about !!!
Yes, but this is a pragmatic issue relating to these particular conjectures. We do not yet know whether they are undecidable or not. However we are talking here about statements which we can formally prove are undecidable.
Again, this is because we mean different things by “undecidable”. I say we don’t know if Goldbach’s conjecture can be proven or not, but we do know it’s either true or false. The class of what I call “undecidable” is the one in which neither true or false status can be assigned to a statement, yet the statement is consistent within our two value logic system. The CH is an example.
On the continuum hypothesis it seems to me that there is a fundamental difference between its undecidability and that of a G-sentence. The C.H. is undecidable because neither its truth or falsity contradicts the axioms of set theory. But for a G-sentence both its truth and falsity do contradict the axioms. The two situations do not seem to be equivalent.
Exactly, and that’s my point. They’re different classes of statements, but you keep calling both of them “undecidable”.
G-sentence’s truth (or falsity) does NOT contradict the axioms. If the statements contradicted them, the system would be inconsistent. Again, that’s how the theorem reads - in a consistent system, there are unprovable truths, which make the system incomplete (you don’t have enough to prove its own truths) If it was your way, it would read “there are statements that render the system inconsistent”! That’s not the case. The G-statements truths or falsities are consistent within a system, and can’t be both true and false at the same time either, like the CH.
Besides, I'm not even sure I could agree even if we stayed within the context of G statements. I still don't understand what is unprovable (in a formal sense of course) about the statement "there are ghosts in my house"?
That doesn't seem undecidable to me either.
Well, but that’s a metaphysical statement, isn’t it? Ghosts in a sense of physically impossible to detect beings that explain what I perceive to be weird behavior of some objects in my house. I thought you suggested that all metaphysical statements are undecidable. But the “there are ghosts in my house” statement is not. What did I miss?
Btw I'm finding this discussion very useful, but if my posts are too long just tell me and I'll cut them down
Ha! I think I just beat your record for the longest post. But seriously, as long we don’t branch off and start talking about 10 different things at the same time, I finid it a productive discussion as well. It seems like we know where we disagree, and that’s a progress! :smile:
Pavel.
I reread my comments after posting them and realized I misspoke in the first section:
I believe that, because of the undecidable statements like the Continuum Hypothesis, our own system [that we employ in evaluating simple formal arithmetic systems] is not consistent, and far from being formal.
duh. I didn’t mean to make the CH an example of a system being inconsistent. In fact, the opposite is true – the CH is an example of the system being consistent, yet the CH itself being neither true or false, hence undecidable. :yuck: I need to think more carefully about examples of our own natural language, but I’m quite certain that, at least as far as formality is concerned, nobody yet translated our own natural language system into a formal language. So, I still stand by the claim that in order to show that our own natural system has a meta system (by the incompleteness theorem), you have to demonstrate that it is formal and consistent! Otherwise, the argument for the meta system that transcends our cosncousness doesn't hold water.
Pavel.
Iacchus32
Dec11-04, 03:24 AM
Again I disagree. This is partly for the reasons given above. The statement 'this sentence is not a theorem of T' is not decidable within any formal system T. Both answers give rise to contradictions. It is decidable only by creating a system that encompasses T, but is not T. Let's call this expanded system U. In U we can decide the statement 'this sentence is not a theorem of T', but we still cannot decide one that says 'this sentence is not a theorem of U'. So a statement that says of itself that is not a theorem within any formal axiomatic sytem' is undecidable full stop. Yes, context is crucial to understanding anything. You take anything out of context then you have a misnomer, which are really all these paradoxes are as far I'm concerned.
loseyourname
Dec11-04, 04:40 AM
I think we're running into the problem here of whether or not there exists any such thing as an absolute, foundational context.
I agree about the need for an absolute context. To me this is the real issue here. If the universe, (by 'universe' I mean everything, the Cosmos if you like) is, as scientists and mathematicians assert, representable symbolically as a formally consistent and complete system of terms and theorems, or let's say as a reasonable and complete 'explanation of everything', then this would contradict the incompleteness theorem. Also, if it is the case that the universe is representable as a formal axiomatic system then the universe has a meta-system, something that must always be beyond reasonable explanation, something that is not in the system at all, but which contains it, or which constitutes its environment. Unless that metasystem exists then the universe cannot be represented as a formal axiomatic system.
There's an interesting essay by Stephen Hawkings online somewhere called 'The End of Physics' in which he ponders this topic. In the end he just ducks the issue.
By 'foundational context' I take you to mean the level at which we actually decide questions. According to Godel there is no such level. We cannot formally prove that the axioms of any formal system (sufficiently complex etc.) are self-consistent. Therefore all questions are ultimately undecidable. Any search for a foundational level leads to an infinite regress of metasystems, each one examing the one before it.
Yet somehow we decide. It seems to me that the fact that we can decide shows that there is more to deciding than a formally logical process. I see this as being true epistemilogically, in that formal logic cannot decide a question completely so that to decide a question is to transcend logic, and true ontologically, in that it tells us something about the mechanistic processes in our brains. If the physical processes in our brain correlate precisely to our conscious processes when we are deciding questions, then either our brain is not operating according to a formally consistent set of deterministic rules, or we are not deciding, we are just guessing.
Pavel
I agree with most of you first few paragraphs, and I think I see what you're saying better now. I think that you're wrong to say that a G-sentence has a truth value in the system, even though we cannot know what it is, but I might be wrong. Either way, it doesn't seem to affect the main issue here.
So, to continue with your line of thought, I’d like you to demonstrate to me that our system that we use to have this very discourse is consistent and formal, just like an arithmetic system that Godel proved to be incomplete. If you successfully demonstrate it to me, then by Godel's theorem, I’ll completely agree with you – we can infer a meta-system that transcends our own consciousness, or the level of its complexity. I understand it’s not an easy task, so if you can't, we’ll just have to agree on reaching an impasse and leaving it simply as a matter of personal opinion.
Hmm. I'm not saying that the language of our discourse or the reasoning behind it is consistent and formal. Rather, I'm saying that if we try to construct a formal and consistent theory, explanation, metaphor, description, account, picture or whatever of the universe then we cannot complete it.
Now this is usually taken to be an epistemilogical issue, some odd quirk of our formal systems of symbols and rules that prevents us from completing them consistently, and which has no implications for the nature of reality. If this is so then we will never be able to fully understand the nature of reality by reason alone. But it could also be an ontological matter. That is, it could be the case that the universe cannot be fully represented by a formally consistent theory, explanation, mataphor, description etc. If this is the case then we still cannot fully understand the nature of the universe by formal reasoning alone.
I am suggesting that we cannot represent the universe symbolically in a formally consistent and complete way for both of these reasons. In other words, I'm saying that to explain the universe completely requires that our explanation has an undefined term in it, a term standing for 'something' about which no question is decidable, a theorem that is not really inside the system. Equivalently a term that refers to something outside of the system. This is the thing that has to be left out of any symbolic representation of the universe. Inevitably formal systems require undefined terms.
Because we cannot conceive of a thing that cannot be defined and about which no question can be decided we cannot even conceive of this 'something'. There is no way that we can conceive of it except by misconceiving it, since a concept is a definiton, and for strictly ontological reasons this ultimate 'something' is indefinable.
This is very roughly the 'non-dual' view of cosmology, in which 'Unicity', the 'Tao', 'emptiness', and so on cannot be defined, represented, conceived, imagined etc. Christian mystics likewise assert that the Godhead must be approached non-conceptually, for it is formless.
Of course I cannot prove that this is the case. If I could demonstrate a formal proof of it then I would have proved that it is not case, for to prove it is the case would require that this ultimate 'something' be symbolised in a manner consistent with two-value logic, which would contradict the proof that it isn't.
However the empirical evidence, for instance the fact that in the opinion of most philsophers there are in principle explanatory gaps in our formally consistent explanations of the origins of the universe, the origins of consciousness and the ontology of matter, and also, crucially, the fact that all questions about what is ultimate (i.e. all metaphysical questions) are undecidable, suggests that it is the most plausible explanation of the existence and nature of the universe.
If it is not the case then it seems to become impossible for us explain why we are unable to construct a reasonable explanation of our existence. We would have to say that this inability was down to some anomaly of our methods of reasoning. But what other method of reasoning is there?
I haven't put that very well. I'm still trying to figure out a straightforward way of saying some of these things. One question worth considering is why, while masters of Advaita, Buddhism, Taoism, etc have long claimed it is possible to know everything, these same masters were completely unsurprised and unruffled by Godel's proof that nothing can be completely known by reason, and that questions (of any kind) can only be answered with certainty from the metasystem. It's what they've been saying for millenia.
Well, I get an impression you are assuming that all possible systems of formal reasoning based on our usual laws of formal logic are formal and consistent.
No I'm not assuming that. As far as our reasoning systems go I'd say that insofar as they are formal (by our usual definition) they obey the rules of Boolean logic (which was designed to model formal reasoning). But whether they are consistent is an empirical question. All we can say is that if our formally reasoned explanation of everything is consistent then it is not complete, and if it is complete then it is not consistent. (Again, note that Buddhists have said for millenia that there is no such thing as a formally consistent and complete account of reality).
That’s how you try to infer a meta system with the help of Godel’s theorem. If they are not, then all bets are off, why do you even bring Godel? The incompleteness theorem deals with consistent and formal systems only. That is really important!
This is a misunderstanding. I'm saying that metaphysical questions are undecidable because it is impossible to represent what is ultimate symbolically, or symbolise it as a true or false theorem within some formal axiomatic system (because such systems are predicated on the idea that all well-formed theorems are either true or false, i.e that all terms can be defined as being this or that).
If I assume that our theories of reality are formal and consistent it is only because I'm assuming that this is the sort of theory that we are trying to construct. If a theory is not formally consistent then yes, all bets are off. But we needn't consider such systems, they are by definition unreasonable and incable of explaining anything.
OK, now I’m getting confused. What I meant by the root of the hierarchy is that our consciousness is final, there’s no meta system that transcends it, the one you’re trying to infer.
No, I'm saying the same, that consciousness is the metasystem.
I’m not sure I see what you mean by “there’s a consciousness within a reasoning system..” which contains a reasoning system in itself?? You have a “total” reasoning system containing subreasoning systems? Where do we fall? Am I on the level of total system? Can you please elaborate a little? :smile:
Yes, I'm ok at elaborating, it's clarifying that I have trouble with. :smile:
I was saying that the only place a reasoning system can exist is in the mind of a sentient being. (I take reasoning to mean something slightly different to computation). So all formal axiomatic systems exist within an encompassing consciousness. Godel proved this by showing that to decide an undecidable question we must appeal to an infinite regress of extended systems, and it follows from this that in the last analysis we have to decide undecidable questions informally, for if there is an infinite regress of systems then there is no point at which a question can be decided formally. Ultimately we have to decide them informally from the metasystem, a.k.a. our consciousness.
See, that’s exactly what I’m talking about. You’re reasoning about things you claim you can’t reason about.
I'm not saying that one cannot reason about it. I'm saying that we can know things which we cannot know by reasoning alone. We can know what a clarinet sounds like, for instance, which is unknowable by reason alone. Direct experience transcends reason. But we can nevertheless reason about the sound of a clarinet.
It's one thing to try to infer a meta sytem via Godel's theorem (what you're trying to do), but it's totally something else to be assigning properties to it. Or perhaps I'm putting too much of a functional value into your notion of "knowing". Perhaps an example on your part might help
No amount of reasoning will enable a person to know what a clarinet sounds like, but this does not mean that we cannot reason about the sound of a clarinet. Equivalently while Lao-Tsu says "The Tao that can be talked is not the eternal Tao", he also says "The Tao must be talked". It is simply necassary to be very careful when doing so not to define the term incorrectly, and to remember that when we discuss what it, say the 'Tao', really is we cannot do it, for it must remain an undefined term. Again, we cannot represent the sound of a clarinet within a formal system, it is an experience, and experiences are incommunicable, indefinable, incommensurable etc. beyond a certain point.
If I remember right the only qualities I'm assigning to what is ultimate, the ultimate metasystem if you like, is one of indefinability and non-duality (no dual properties). I'm also suggesting that this is directly connected to our inability to give a scientific definition of consciousness.
There you go again, jumping out of the system. If your knowledge gained through logic and reason is relative and uncertain then what about your very claim itself? How did you come to transcend and “see” that our logic and reason is relative and uncertain, what else did you use to come to this conclusion? Please be specific.
This isn't quite right IMO. Godel showed that it is possible to prove that all knowledge gained through reasoning is relative and uncertain. However he proved this with certainty. This is possible because what he proved is true of all formal systems in all possible universes. The reason his proof holds is that the proof is not dependent on any particualr set of axioms, but holds for all formal axiomatic systems whatever the axioms. (This is roughly what I meant by saying he went outside of his logical system to construct his proof). So although reason cannot bring certainty, we can be certain by reason that it doesn't. We can be certain because this proof is about reasoning itself, not what we are reasoning about.
To put this another way, the truth or falsity of any statement is dependent on the axioms of the system within which the statement is formed. A true statement in one set of systems will be false in a system differently axiomatised. But a statement that is true independent of any axioms, that is, true in all formal systems, escapes this relativity.
But this isn't the whole answer. Direct experience is the other issue.
INTERLUDE
"In the standard positivist approach to the philosophy of science, physical theories live rent free in a Platonic heaven of ideal mathematical models. That is, a model can be arbitrarily detailed, and can contain an arbitrary amount of information, without affecting the universes they describe. But we are not angels, who view the universe from the outside. Instead we and our models are both part of the universe we are describing. Thus a physical theory is self-referencing, like in Gödel’s theorem. One might therefore expect it to be either inconsistent, or incomplete"
Stephen Hawking
‘Gödel and The End of Physics’
"…since every word in a dictionary is defined in terms of another word… The only way to avoid circular reasoning in a finite language would be to include some undefined terms in the dictionary. Today we must realise that mathematical systems too, must include undefined terms, and seek to include the minimum number necessary for the system to make sense."
Leonard Mlodinow
‘Euclid’s Window’
"When we encounter the Void, we feel that it is primordial emptiness of cosmic proportions and relevance. We become pure consciousness aware of this absolute nothingness; however, at the same time, we have a strange paradoxical sense of its essential fullness. This cosmic vacuum is also a plenum, since nothing seems to be missing in it. While it does not contain in a concrete manifest form, it seems to comprise all of existence in a potential form. In this paradoxical way, we can transcend the usual dichotomy between emptiness and form, or existence and non-existence. However, the possibility of such a resolution cannot be adequately conveyed in words; it has to be experienced to be understood."
Stanislav Grof
The Cosmic Game
State University of New York (1998)
I'm going to miss a chunk of your post out here, because I think it's dealt with in amongst the other issues.
So, yes, there is such a thing as a true statement that you can’t prove to be true by the axioms and rules of transformation of a any [powerful enough] formal and consistent system. That is exactly what Godel’s theorem is all about !!!
Again I'm afraid I disagree. If a statement is undecidable then it does not have a truth-value within the sytem. Of course it has one in some other system, but saying it is true or false in some other system doesn't alter the fact that it is neither true or false in the original system. Similarly, a statement that has a truth-value in one system may be undecidable in some other system. Metaphysical questions have been found to be undecidable in all formal systems, and as such are 'meta-undecidable'. They have not yet been shown to have a truth-value in any formal system whatever the axioms. I would argue strongly that they do not, since they are improper questions, equivalent to one that asks 'Is the moon made out of Chedder or Stilton?'
Again, this is because we mean different things by “undecidable”. I say we don’t know if Goldbach’s conjecture can be proven or not, but we do know it’s either true or false. The class of what I call “undecidable” is the one in which neither true or false status can be assigned to a statement, yet the statement is consistent within our two value logic system. The CH is an example.
Yes, I agree. But this misses out those question which are not of either of these types. This is why I see the CH and Goldbach's conjecture as not directly relevant. When we ask 'Did the universe arise from something or nothing?' it is a question that we can demonstrate formally to have no non-contradictory answer. In other words such questions do contradict our two-value logic system, and we know that they do not have a true or false answer within any formal system of reasoning.
G-sentence’s truth (or falsity) does NOT contradict the axioms.
But surely they do. Isn't it precisely the fact that both answers give rise to contradictions that makes them undecidable? If a G-sentence was found to be true or false within the system this would contradict the axioms of the system (or its rules, which is the same thing).
The G-statements truths or falsities are consistent within a system, and can’t be both true and false at the same time either, like the CH. I'm afraid I still can't you see how you arrive at that conclusion. If the truth or falsity of a G-sentence is consistent with the axioms of the system then it is not a G-sentence.
Well, but that’s a metaphysical statement, isn’t it? Ghosts in a sense of physically impossible to detect beings that explain what I perceive to be weird behavior of some objects in my house. I thought you suggested that all metaphysical statements are undecidable. But the “there are ghosts in my house” statement is not. What did I miss?
I would say that 'Are there ghosts in my house' is not a metaphysical question. In fact, if one believes that ghosts do not exist then it is probably not even a question, for the term 'ghosts' refers to something non-existent. Also, it is a pragmatic matter, for if we can detect the presence of ghosts by means of our senses then ghosts are not metaphysical entities.
Crucially, the answer to the ghost question might be yes or no without contradicting the laws of formal reasoning. But it is not possible to assign a truth value to a metaphysical questions without contradicting those laws. After all, that's why we've never been able to decide any of them.
I hope some of that makes sense. We'll have written a book by the time we've finished (albeit probably an incomprehensible one) :smile:
Regards
Canute
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