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Canute
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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?
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?
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