Why Are Metaphysical Questions Undecidable?

[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
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And assuming bivalence, and possibly other things I haven't realized.
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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.
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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.

 

[quantumdude]

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]

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.

 

[Royce]

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?

 

[Royce]

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]

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]

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?

 

[Canute]

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]

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?

 

[Canute]

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 criticize them for not applying the same standards of reasoning to materialism).

 

[Royce]

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?