Why Are Metaphysical Questions Undecidable?

[quantumdude]

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.

 

[quantumdude]

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.[/color] 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.

 

[Canute]

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. 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.

 

[Canute]

I didn't mean to misrepresent. Here's the bit I was referring to...I thought I had interpreted it as you meant it.

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]

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]

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]

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?

 

[Canute]

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.

 

[Canute]

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]

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
___
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
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.

 

[Canute]

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]

I was going to post an official definition of 'undecidable' but I also can't find one.

Grime explained it

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]

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]

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]

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. But I understand what you're saying.

 

[quantumdude]

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.

 

[quantumdude]

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]

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?

 

[quantumdude]

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]

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]

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.

 

[quantumdude]

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]

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!

 

[quantumdude]

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]

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.

 

[quantumdude]

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]

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.

 

[quantumdude]

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.

 

[Jeebus]

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.

 

[Royce]

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.