- #31
Iacchus32
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Hey it was just an idea. And according to the way everyone is responding, a pretty "abstract one" at that. Hmm...
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Click For Summary
The discussion centers around the nature of reason and its trustworthiness. Participants explore whether reason is merely a construct of human observation, limited by individual perspectives, or if it is an intrinsic aspect of the universe. There are arguments suggesting that logic and reason may be fundamentally flawed, as they rely on unproven axioms and inductive reasoning, making conclusions about reality tentative. The conversation also touches on whether knowledge is inborn or acquired, with some asserting that human reasoning is shaped by both biology and external reality. The interplay between thought and action is emphasized, with the idea that while thoughts can exist independently, concrete actions require thought to manifest. The discussion raises questions about the relationship between abstract ideas and material reality, suggesting that human-created constructs are rooted in abstract thought. Ultimately, the dialogue reflects on the limitations of reason and the complexities of understanding reality through a rational lens.
- #32
wuliheron
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Reason and logic can as useless, counterproductive, and even destructive as anything else.
I would put it more pointedly that they can be less useless, counterproductive, and destructive if other possible approaches are accepted.
Logic is founded on the concept of the absurd, which is a reasonable concept (sic). That is, the absurd and reasonable are like up and down, back and front, inside and out. In turn, these concepts are not merely abstractions, but originate from our emotions and physiology as much as anything.
Descartes said, "I think, therefore I am" but recent neurological evidence is finding more support for the idea of "I Feel, therefore I think." Rational thought then seems likely to emerge from our feelings and affect more so than vice versa. Metaconcepts like absurd and reasonable then likely evolved out of more primitive emotions and still retain those connections, possibly in some kind of Gestalt or contextual manner.
By retaining an accepting attitude and affect we can strengthen that gestalt or connection and broaden its context.
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- #33
Les Sleeth
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Reason can be trusted because it operates in harmony with the ordered aspects of the universe. You can test that by manipulating the external universe in an orderly way, and seeing if you can make things that "work." When they work, your reason has functioned in accordance with reality; when it doesn't, you can reason out why by discovering where you misapplied orderly principles. The feedback proves over and over again (if you are involved in actualizing) that reason can be trusted.
You may assume too much. A child is born, and if emotionally unhampered, knows a priori how to smile and be fascinated. Since joy and interest are part of reality, it seems there is a priori knowledge of reality. Possibly it would be more accurate to say we cannot know anything external to ourselves a priori.
Both points seem true, but maybe the issue is a chicken-egg sort of thing. All humanly-created objects are preceded by reason, yet an idea in this universe would never come to fruition without physical effort.
Nonetheless, I can't see how it can be denied that we can have creative thought without action, but no creative action without thought.
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- #34
drag
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Greetings !
Tom's part about the building was really funny...
wuliheron, you have an interesting point,
but don't we have the criteria of
apparent consequences to compare our basic
abstract ideas to ? You can't fully trust
anything, but I do not see how the apparent
consequenses of our abstract thought justify
an opinion that says something like - "our logic
is merely a function of physiological and
phsycological evolution (biology in other words)
and is not the result of our attempt to grasp
reality". After all, what is the evolutionary
advantage of creatures with thought "frames" that
are disconnected from reality ?
LW Sleeth, interesting points as well.
I'd like to point out that we are complex
biological machines and we are born adapted to
this world. It would be strange to assume that
the adaptations are only regarding our physical
traits - we have complicated brains that are
also adapted to this Universe. For example,
brains of our size could be created with just
the preferable adaptive state to deal primarily
with chess games - like a separate computer program.
Of course, our brains appear to differ from computer
programs because we appear to be able to include
and learn new possibilities but we still have
some basic processing principles "set in".
For example, we can not comprehend the lack of
time or space. Though I'm not certain that's
a fitting example, I think that's probably a
controversial issue some of you may want to discuss.
Live long and prosper.
Tom's part about the building was really funny...
wuliheron, you have an interesting point,
but don't we have the criteria of
apparent consequences to compare our basic
abstract ideas to ? You can't fully trust
anything, but I do not see how the apparent
consequenses of our abstract thought justify
an opinion that says something like - "our logic
is merely a function of physiological and
phsycological evolution (biology in other words)
and is not the result of our attempt to grasp
reality". After all, what is the evolutionary
advantage of creatures with thought "frames" that
are disconnected from reality ?
LW Sleeth, interesting points as well.
I'd like to point out that we are complex
biological machines and we are born adapted to
this world. It would be strange to assume that
the adaptations are only regarding our physical
traits - we have complicated brains that are
also adapted to this Universe. For example,
brains of our size could be created with just
the preferable adaptive state to deal primarily
with chess games - like a separate computer program.
Of course, our brains appear to differ from computer
programs because we appear to be able to include
and learn new possibilities but we still have
some basic processing principles "set in".
For example, we can not comprehend the lack of
time or space. Though I'm not certain that's
a fitting example, I think that's probably a
controversial issue some of you may want to discuss.
Live long and prosper.
- #35
Iacchus32
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The Paradox of Manifestation
So "abstract" is equal to idealism, and "concrete" is equal to materialism. And there you have it, the "paradox of manifestation." The two exist as correlatives and you can't have one without the other.
And yet, if there was no idea (conceived of the mind = essence) in the first place, there would be nothing concrete to "brag about" in the second place. Which is very interesting (credit to Lifegazer), for it suggests our whole notion of material existence is brought about by abstract thought (or, as Tom would say, the application thereof) and, since we all live in the world collectively (or so materialists claim), then we all must be part of the same "collective mind" as a whole ... Only question is, whose mind is it?
So tell me, what's the difference between a concrete idea and a "solid idea?" Say like 1 + 1 = 2? Is this what an axiom is? (I just looked up axiom in the dictionary for the first time by the way.)
In which case let me restate what I said to Tom:
I guess this has something to do with you telling me in the other thread that the "idea of God" was abstract and that nothing would become of it. And yet, what I'm telling you is that this whole world is built upon nothing "but" abstractions. Therefore it all must have begun with a single "axiom" or idea. Based upon the idea of God perhaps?
So you see that's the whole point, because if God does exist, then this becomes the axiom (idea) by which everything (materially) becomes manifest.
Nope nope ... Shunt shunt! ... Nope nope ... Shunt shunt! ... Yeah, I can see the alarms going off already!
So "abstract" is equal to idealism, and "concrete" is equal to materialism. And there you have it, the "paradox of manifestation." The two exist as correlatives and you can't have one without the other.
And yet, if there was no idea (conceived of the mind = essence) in the first place, there would be nothing concrete to "brag about" in the second place. Which is very interesting (credit to Lifegazer), for it suggests our whole notion of material existence is brought about by abstract thought (or, as Tom would say, the application thereof) and, since we all live in the world collectively (or so materialists claim), then we all must be part of the same "collective mind" as a whole ... Only question is, whose mind is it?
So tell me, what's the difference between a concrete idea and a "solid idea?" Say like 1 + 1 = 2? Is this what an axiom is? (I just looked up axiom in the dictionary for the first time by the way.)
In which case let me restate what I said to Tom:
I guess this has something to do with you telling me in the other thread that the "idea of God" was abstract and that nothing would become of it. And yet, what I'm telling you is that this whole world is built upon nothing "but" abstractions. Therefore it all must have begun with a single "axiom" or idea. Based upon the idea of God perhaps?
So you see that's the whole point, because if God does exist, then this becomes the axiom (idea) by which everything (materially) becomes manifest.
Nope nope ... Shunt shunt! ... Nope nope ... Shunt shunt! ... Yeah, I can see the alarms going off already!
- #36
Les Sleeth
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What's "Given"
I am not sure I understand your point, but I think it is that it's not just the ability to feel that is built into us, but also some reasoning ability as well; and that beyond the "test" of trust I gave for reason (which is dependent on external interaction with reality) there should be internal elements that tell us something about reason as well.
That's a very tough question to ponder. I've been trying to remember my first cognitive moments, my first awareness of "me." One I have I don't know if it's a dream or not, but it is such a vivid flash of memory I've always suspected that it's real. The memory is of being held by someone in the delivery room and seeing a woman (my mother I assume) in a prone position, and a dark man with a thick, black moustache. Later in life I asked my mom what her doctor looked like, and she described the man I saw! I have other flashes too, meaningless events, but things I remember as an infant.
Anyway, in terms of my reasoning ability, I don’t remember any thoughts as an infant. I mostly remember being interested, fascinated, happy. It is really difficult to say whether I ever would have learned to reason properly if the external world weren’t there with which to interact. In fact, some of the worst thinkers at this site seem to be those who don’t pay enough attention to external circumstances. I suspect the order of the universe plays an important role in teaching a human how to use the brain. What I find very interesting is that the part of me which needed no “outside” training to be intrigued, happy, fascinated, etc., is still there inside me. And as much as I enjoy using my brain in all the various thinking opportunities of life, I value that “given” inner part even more.
I am not sure I understand your point, but I think it is that it's not just the ability to feel that is built into us, but also some reasoning ability as well; and that beyond the "test" of trust I gave for reason (which is dependent on external interaction with reality) there should be internal elements that tell us something about reason as well.
That's a very tough question to ponder. I've been trying to remember my first cognitive moments, my first awareness of "me." One I have I don't know if it's a dream or not, but it is such a vivid flash of memory I've always suspected that it's real. The memory is of being held by someone in the delivery room and seeing a woman (my mother I assume) in a prone position, and a dark man with a thick, black moustache. Later in life I asked my mom what her doctor looked like, and she described the man I saw! I have other flashes too, meaningless events, but things I remember as an infant.
Anyway, in terms of my reasoning ability, I don’t remember any thoughts as an infant. I mostly remember being interested, fascinated, happy. It is really difficult to say whether I ever would have learned to reason properly if the external world weren’t there with which to interact. In fact, some of the worst thinkers at this site seem to be those who don’t pay enough attention to external circumstances. I suspect the order of the universe plays an important role in teaching a human how to use the brain. What I find very interesting is that the part of me which needed no “outside” training to be intrigued, happy, fascinated, etc., is still there inside me. And as much as I enjoy using my brain in all the various thinking opportunities of life, I value that “given” inner part even more.
- #37
Mentat
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This assumption is false, and is leading you toward a (probably) wrong conclusion. If there is no god, then the universe (and everything within it, obviously) came about without a thought. Action can take place without thought/imagination/planning/conscious awareness/etc...
And this is probably lifegazer's problem too. Let me repeat, a thought is not required, for an action to take place.[/color]
But this conclusion is based on the aforementioned false premise.
- #38
wuliheron
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The hidden assumption in your statement is that merely reacting to nature or reality confirs a survival advantage. For ants it might, but we are much more complex than that. In particular, we are much more adaptable than ants and inhabited every continent on the planet before agraculture was invented. The map is not the territory, but maps are still incredibly useful no matter how far divorced from reality they might be in many respects.
In a very real sense, our specialty is pretense or the suspension of disbelief. Lying is an artform requiring method acting, we immerse ourselves in our suspension of disbelief while still retaining the ability to directly connect to reality if necessary. In order to do this we must first be capable of lying to ourselves.
As children we all play make-believe, but as we grow older we begin to treat our make-believe more seriously and call it fact. Thus we are incredibly adaptable as animals go. Faced with a life or death situation, however, our brains shut down all the pretense and we react with incredible speed.
- #39
Iacchus32
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Are you referring to the possibility that everything we see around us which is man made just sprang up aribitrarily and at random? This is not possible.
If on the other hand, we were to take mankind out of the picture, thus leaving only the natural world, I would say the likelihood of things happening at random are more plausible. Yet even here, everything seems to have its own rhythm, and behaves in accord with its "own season," suggesting that things really don't happen arbitrarily (not as rule).
Whereas with mankind (at least in the west), it's all about "control" over the environment which, requires a tremendous amount of thought and effort.
- #40
quantumdude
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Yes, that's what I meant.
I don't see any chicken-egg issue. A building derives its concreteness from the materials from which it is made, not because a group of men acted on a thought.
Of course, it can't be denied.
- #41
quantumdude
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Not at all. Everyone acknowledges a difference between things in one's personal imagination and things outside of it, even if one does regard the outside world as "in the imagination of god".
You keep repeating this, and I keep acknowledging it.
Please. That is hardly his idea.
You have to be kind of careful here, because a "notion" of anything, including a material world, is abstract. A notion is just a thought. I say "careful" because you are about to try to derive a consequence on the actual world from the notion of it, and I don't think that is warranted.
This is where you go looney, and it is because you have made the jump from "notion of material existence" (which is abstract and in the mind) to "actual material existence" (which is taken as concrete) to conclude that we are all of one mind.
Just from reading your posts, I can assure you that we are not.
You're still confused: I already told you that there is no such thing as a "concrete idea". Mental constructs are not concrete.
That's not an axiom of arithmetic (the axioms are in ring theory), but it is an abstract notion, which is the only thing that is really important to this part of the discussion.
That's a big "if", and it's one that can't be proven, observed, or obtained by introspection. Since those are the only ways I can think of to obtain knowledge, I see no point in contemplating that "if".
- #42
quantumdude
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I'm going to ask that we forget about god in this thread. It really has nothing to do with the topic.
Continuing along this line...
All systems of logic can be put into one of two categories:
1. Deductive
2. Inductive
I explained all this in detail in my Logic Notes thread, but let me give a rundown here.
Deductive Logic
An argument is deductive if its premises necessarily imply[/color] its conclusions. With a mandate to construct such a system of logic, one is led directly to a formal structural language that strongly resembles mathematics. It contains rules for types of inferences that can always be trusted. This should not be misunderstood to mean that deductive logic can be used to derive absolute truths about reality. In fact, deductive logic is completely silent in this regard. It should be understood as follows:
I may not know whether the premises are correct, but I do know for certain that: If the premises are true, then the conclusion must be true.[/color]
That conditional statement expresses the only idea of which we can be confident using only deductive logic. Deductive logic does not contain a procedure for testing the truth or falsity of propositions (except for some propositions about deductive logic, of course).
Inductive Logic
An argument that is not deductively valid is inductive. The premises of an inductive argument provide only partial support for its conclusion, and as such the conclusions of inductive arguments are accepted only tentatively. This may prompt one to ask, "Why bother with inductive logic?" Good question. The answer is that it is impossible to reason about anything that cannot be known a priori without inductive logic. So, the price we pay for inductive reasoning may be the lack of absolute support for the conclusion, but the benefit is that we obtain the ability to say something meaningful about reality.[/color] In other words, inductive logic provides a means to judge the truth or falsity of propositions, but only in a probable (as opposed to absolute) sense.
The discipline of implementing these two kinds of reasoning to learn about reality is called science.
Continuing along this line...
All systems of logic can be put into one of two categories:
1. Deductive
2. Inductive
I explained all this in detail in my Logic Notes thread, but let me give a rundown here.
Deductive Logic
An argument is deductive if its premises necessarily imply[/color] its conclusions. With a mandate to construct such a system of logic, one is led directly to a formal structural language that strongly resembles mathematics. It contains rules for types of inferences that can always be trusted. This should not be misunderstood to mean that deductive logic can be used to derive absolute truths about reality. In fact, deductive logic is completely silent in this regard. It should be understood as follows:
I may not know whether the premises are correct, but I do know for certain that: If the premises are true, then the conclusion must be true.[/color]
That conditional statement expresses the only idea of which we can be confident using only deductive logic. Deductive logic does not contain a procedure for testing the truth or falsity of propositions (except for some propositions about deductive logic, of course).
Inductive Logic
An argument that is not deductively valid is inductive. The premises of an inductive argument provide only partial support for its conclusion, and as such the conclusions of inductive arguments are accepted only tentatively. This may prompt one to ask, "Why bother with inductive logic?" Good question. The answer is that it is impossible to reason about anything that cannot be known a priori without inductive logic. So, the price we pay for inductive reasoning may be the lack of absolute support for the conclusion, but the benefit is that we obtain the ability to say something meaningful about reality.[/color] In other words, inductive logic provides a means to judge the truth or falsity of propositions, but only in a probable (as opposed to absolute) sense.
The discipline of implementing these two kinds of reasoning to learn about reality is called science.
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- #43
wuliheron
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In turn, Tom, the science of logic can be described as both an epistemological and ontological pursuit depending upon the context. Is science or logic discovering reality, creating reality, describing reality, all the above, or none of the above? It just depends upon the context.
Hence, I would dispute your assertions that:
This tautological assertion denies the existence of genuine paradoxes and the indeterminate which can neither be said to be true or false, but whose existence can be logically demonstrated. Therefore I would modify this statement as valid only within the context logic itself and with the assumption that paradoxes and the indeterminate are axiomatically false.
Hence, I would dispute your assertions that:
This tautological assertion denies the existence of genuine paradoxes and the indeterminate which can neither be said to be true or false, but whose existence can be logically demonstrated. Therefore I would modify this statement as valid only within the context logic itself and with the assumption that paradoxes and the indeterminate are axiomatically false.
- #44
quantumdude
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I would say that science describes what we observe. Is that reality? I don't know, but it's the only thing I have access to.
Actually, the above description does allow for the paradoxes of logic. Remember that a paradox is a type of statement to which we cannot assign a truth value. When I say, "If the premises are true..." I am not ruling paradoxes out, I am simply narrowing the scope of the condtional to exclude them.
Note that the scope is also set to exclude false statements, but it does not rule them out, either.
For a complete description of deductive validity, we could say:
When an inference is deductively valid, then
1. If the premises are true, then the conclusion must be true.
2. If at least one of the premises is false, then the conclusion must be false.
3. If at least one of the premises is undecidable (aka paradoxical), then the conclusion is undecidable.
[/color]
- #45
wuliheron
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In other words, it becomes an epistomological or ontological pursuit depending upon the context.
Because a truth value cannot be assigned does not mean paradoxes don't possesses a truth value which classical logic simply cannot determine. Therefore the argument is tautological and the clearest way out of the tautology is to create a new axiom.
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- #46
Iacchus32
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You're the one who brought up the Problem of Other Minds in the other thread, while it was also emphasized (by both you and heusdens I believe) that by sharing our experiences, we can be more conclusive about their actual existence, if in fact we all concluded the same thing. In other words we're speaking about a "collective experience." Whereas what could that possibly mean if we all didn't share the "same ideals?"
Consider "the entity" of the United States government, which rules over the entire nation. Couldn't this be perceived as the "one mind" which consolidates the interests of the entire nation? Or, if we were to say, "We the people of the United States," aren't we referring to a "collective experience" under one "collective mind?" Me thinks so.
- #47
ahrkron
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What argument are you referring to?
I don't see any tautological argument there.
- #48
wuliheron
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The tautology is that the argument Tom put forth that If the premises are true, then the conclusion must be true. is based on the the definition of truth which Aristotle first established using reductio ad absurdum. In other words, using the concept of the absurd Aristotle defined the absurd as definitively false and then went on to declare that everything must be either true or false, which rules out the possibility of genuinely self-referential and self-contradictory paradox to which classical logic cannot assign any truth value.
Actually, I woke up this morning with the solution to this connundrum in my mind. Instead of creating a new axiom to compound the tautology, it is more elegant to take out the word "must" and replace it with a vague conditional term like "may". This also removes the essentially black and white fundamentalist charcter of classical logic and places it the category of paraconsistent logic.
- #49
ahrkron
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No, actually, the statement is independent of how you define "truth".
Also, the statement you are referring to is not an argument, but only one of the three conditions for a deductive argument (that contains the mentioned premises) to be valid.
btw, why do you say that Aristotle defined truth using reduction ad absurdum (sp?)? I do not know much about how (and if) he tried to define "truth". Can you provide a reference?
My impresion is that he may have used reduction ad absurdum in some arguments, but that is much different than defining truth itself.
Also, the very technique of reductio ad absurdum relies on the assumption that, when you have a self-cotradictory statement, it has to come from either a faulty reasoning or a false hypothesis, which means that it rules out contradictions as valid end points of a deductive argument.
I take it you are referring to the definition of validity given by Tom. I don't think this is a good solution, since the concept of validity is extremely helpful as it is. Also, when you use "may" instead of "must", you need to supply a way to decide if it is indeed the case that the resulting conclusion "may" be true, which means you need to have the stronger version anyway.
I don't think it has to do with paraconsistent logic. Maybe with modal logic (in which the "degree of credibility" of statements is added to the description).
- #50
Mentat
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No, no, I wasn't saying that all man-made things were in fact just random occurances. I was merely illustrating the fact that not all actions are thought-out first. Some actions don't require any thought at all.
- #51
Mentat
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Isn't there a paradox, when it comes to deductive logic (as you've defined it)? To say that the acceptance of premises A and B means that you must accept Z, is to create another premise (premise C), which states: If you accept A and B, you must accept Z. But, let's say that I were to accept premise C, what then? Well, there is no premise that says that by accepting A, B, and C I must accept Z, so we make one (premise D): If you accept A, B, and C you must accept Z. However, there is no premise that says that accepting A, B, C, and D means I must accept Z...and so on, and so on, forever.
I guess Deductive Logic still works, but there is that little paradox, isn't there?
- #52
Mentat
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Oops, I see the paradox has already been brought up. Sorry about that.
- #53
drag
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Greetings !
Mentat,
I believe that if you read Tom's second part -
about inductive logic, you'll notice he says
that inductive logic is probable - never
certain.
Tom,
I believe that what wuliheron basicly means,
and I'm referring to your enitial "short"
definition version, is that not only should you
recognize the probable nature of inductive logic,
like you said, but also that you can have different
rules (different types of logic) when it comes
to your discription of deductive logic.
This also means that some things may be true/false/
indeterminate for the same sets of premises.
There should, theoreticly, be no limmit to
the possible range of such approaches.
You actualy remember yourself when you were
born ?! Com'mon !
Live long and prosper.
- #54
Les Sleeth
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I don't know, I could have dreamed it too. My point was that I believe I remember early moments in my life where I wasn't thinking, and that another apparently inborn cognitive part of me was functioning just fine.
- #55
wuliheron
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The statement itself, If the premises are true, then the conclusion must be true, explicitely defines truth as having true premises. Furthermore, it implicitely defines truth as either applying to everything or not being that which is false.
Sorry, I don't have any links to the subject. Aristotle incorporated the Law of the Excluded Middle and the Law of Noncontradiction as the foundations of his logic. Each of these he demonstrated using reductio ad absurdum which can also be derived from both principles.
This was a significant deviation from other logics at the time like that of Heraclitus which either implied everything was ultimately true or in Zeno's case, absurd. All of these logics, however, were ultimately based on the use of reductio ad absurdum. The situation was analogous to a bunch of politicians today arguing that each other's views are more absurd.
Aristotle's logic became the first to take a fundamentalist stance of everything either being true or false. It is widely hailed as the first formal logic, but has been described as a blunt instrument leading to authoritarianism and is not considered very applicable in modern science, but for the time was revolutionary.
No, that is the law of the noncontradiction from which reductio ad absurdum can be derived. Zeno of Elias was the first to highlight the extreme use of reductio ad absurdum in the west. He argued that the universe is indivisible, indestructable, immortal, and unchanging. His famous paradoxes he proposed as proof that his own beliefs that change and motion are impossible are no more absurd than anyone else's beliefs.
You are correct in assuming the classical definition Tom espouses is useful, but today a great deal of attention is focused on creating many valued logics, the simplest of which assert there is truth, falsehood, and the indeterminate, infinite, or synergistic product of truth/falsehood and the most complex being an infinitely valued logic. The more advanced versions are statistical in nature and incorporate nested matricies. Despite any absurdities they may present from a classical view, they have proven incredibly useful for hundreds of years now.
Two valued logics reflect the way the human mind works but Aristotlian logic is built on denial of its own fundamental assertions. What it leaves out is pointedly the more qualitative human attitudes and affects that define words like absurd. For all these reasons and more the science of logic can be described as a pragmatic science of the absurd, but the art of logic is much more.
Oh really, why do you think that?
- #56
quantumdude
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The similarity of experience comes from the facts that:
1. We are looking at the same universe.
2. We are constructed similarly.
No, it couldn't. If you want proof, just ask one senator what another senator is thinking. He won't be able to tell you, I promise.
Me thinks not, for the same reason.
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- #57
ahrkron
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Not even taken by itself,
but remember that the statement was one of three conditions that, if met, define what a deductive argument is:
When an inference is deductively valid, then
1. If the premises are true, then the conclusion must be true.
2. If at least one of the premises is false, then the conclusion must be false.
3. If at least one of the premises is undecidable (aka paradoxical), then the conclusion is undecidable.
What you are doing is similar to the following:
Tom says "a lung doctor is reliable if: 1. when he says you're ok, your lungs are ok, 2. If he says you're bad, there's something wrong with you, ..."
Then you blame Tom for defining "OK" as having to do with the lungs, when his aim was at the concept of "reliability", and he provided no general criteria for the definition of "OK" (truth).
- #58
quantumdude
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OK, I think I see where there could be some confusion. First, the "if...then" is not an argument, but a statement (but that's a minor point). The major point here is that statement is not a tautology[/color]. It only makes sense to refer to statement schema (the skeleton of a statement, expressed in terms of variables) as "tautologies".
The schema for my statement is: p-->q, which is not tautological. It would only be so if p=q, which it does not here (p and q have different subjects).
Like Ahkron, I don't know about the reductio ad absurdum definition of truth, and I also don't see how it is important.
We don't have to stick with Aristotle. Propositional logic does indeed accommodate paradoxes. Statements are either true, false, or undecidable.
No, it does not define truth at all--It defines deductive validity. The definition of truth has do be done separately.
No, it doesn't. Like I said, it simply limits the scope of statements being considered to those statements that are true. It does not rule out undecidable propositions at all. In fact, Goedel's work on undecidable propositions was done in this very same propositional logic, which uses the above definition of deductive validity.
- #59
quantumdude
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Yes, that's it.
Here's what I was thinking. Look at the whole process as a computer program.
The first function is a sorting routine that puts statements in one of three sets. Set 1 is for true statements, Set 2 is for false statements, and set 3 is for undecidable statements. In the sorting function is the definition for "true", "false", and "undecidable". The returned results of the function are sorted statements.
The second function is a function for determining deductive validity. It contains as a definition: If the premises are all from Set 1, then the conclusion must also be from Set 1.. The second function does not know or care how the statements were sorted[/color]; it only cares what Set they are in.
Hopefully it is clear now that:
1. It is not the case that the second function defines truth.
2. It is not the case that the second function rules out Set 3 statements (aka paradoxes).
- #60
wuliheron
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The other way around, I am debating the validity of his assertions on the basis of semantics and emperical evidence. Read the rest of this post for more details.
For me, it is THE point. Whether you view it as an argument or statement of fact depends upon your point of view. Of course if you take the point of view it is a simple statement of fact it supports classical logic, but then it becomes a tautological argument.
Again, you are using dialectical logic to assert the validity of dialectical logic. You are saying that truth is not falsehood and then attempting to use this fundamental assumption to prove that truth must lead to truth using these rules and falsehood must lead to falsehood.
As Kurt Godel proved, any system must be based at least in part on axioms that can only be taken on faith. Hence even logical systems are ultimately based on faith as much as anything else and the roots of this faith can be traced in the west to the pervasive use of reductio ad absurdum in ancient Greece.
Faith in the vague concept of the absurd, in both east and west, is the foundation of all logical systems. In order to prove the validity of the foundations of a particular logic, Godel proved using propositional logic, one must go outside of that particular logic and use something else. Because all systems of logic are based on rules and the natural language concept of the absurd, ultimately semantics and emperical evidence are the only systematic means of varifying their validity.
Because no single logic system has yet been devised that is applicable to all we observe, emperical evidence does not support one logic over another. Nor has any semantic or linguistic approach proven universally applicable either. What we can say, however, is that mathematics, logistics, and linguistics are all converging towards some kind of statistically oriented logic or logics as capable of explaining all we observe at least well enough to narrow our definition of the absurd. In physics, this is known as a Theory of Everything.