It is often said that metaphysical questions are undecidable but not so often explained what this word means in a metaphysical context.

I'm wondering whether a mathematician would class metaphysical questions as undecidable, or whether philosophers are rather sloppy in the use of this word.

  1. Where philosophers use the word 'undecidable' for metaphysical antinomies but do not define its meaning what would you naturally assume they mean?
  2. Where they do define it, how do they usually do so?

I have my own views on this but I'm wondering if I'm misjudging the way people read this word in philosophy. If so, my own use of it may need to change.

  • 2
    No, they aren't using it in the way mathematicians use that word. But that doesn't mean philosophers are necessarily being sloppy. Mathematics has its own kind of language-game, and no one except mathematicians use the words mathematicians use in the same way. It's not as though mathematicians have some kind of final say on what words mean. For example, many recipes for pastries direct the chef to arrange the pastry material into a lattice. Mathematicians use 'lattice' in a rigorously defined way. Has the recipe writer been sloppy? No, they've conveyed precisely what they meant to convey. Commented Feb 15, 2020 at 22:33
  • 3
    It would help to see a specific context where "undecidable" is used. The uses I can think of refer to roughly the same thing as metaphysical claims being untestable, unverifiable and unfalsifiable, unanswerable in principle, etc. In mathematics decidability is relativized to a formal system and does not concern reality, here it is meant in a more absolute and real sense.
    – Conifold
    Commented Feb 15, 2020 at 23:44
  • See Carnap and metaphysics : the critique on metaphysics is that (most of) its problems are meaningless; thus they cannot have a "solution": they are "fake" questions without answer. This is not the same sense of "undecidable" used in mathematics and logic. Undecidable statements/problems in modern logic are perfectly meaningful question in the language of the relevant theory. Commented Feb 16, 2020 at 8:51
  • @Conifold - Any of Kant's antinomies or Russell's 'problems' would do as an example. If your answer is that philosophers may often equate 'undecidable' with 'untestable, unverifiable and unfalsifiable' then they must get in a hell of a muddle. Are not most philosophers more careful than this? You may be right,and they are not, in which case your comment/answer is helpful and quite surprising to me. .
    – user20253
    Commented Feb 16, 2020 at 12:57
  • @MauroALLEGRANZA - Thanks. I get that some people think that such questions are meaningless, but I'm asking about those like Kant who think they are undecidable.
    – user20253
    Commented Feb 16, 2020 at 13:00

1 Answer 1


I conjecture two possibilities.

Incapable of rational resolution due to equality of evidence or argument for and against

As regards antinomies I would hazard 'incapable of rational resolution'. In an antinomy there are two contradictory hypotheses, theories or claims and each is confirmed by equally cogent evidence or argument. Moreover, the equal confirmation of each hypothesis, etc., is such that no conceivable extra evidence or new argument could tilt the balance in favour of one hypothesis or the other. That, I think, is the sense in which an antinomy is said or supposed to be 'undecidable'.

But it is not to say that there are any such antinomies in philosophy or science. (It's 'highpriori' to suppose that no new argument could resolve an antinomy.)

Consistent with all possible evidence

Metaphysics is not confined to antinomies, of course. Other metaphysical issues are also said by some to be undecidable. Take a claim such as that 'The concrete universal determines its own particularisation', which is what the late 19th-century Oxford Idealists such as Bernard Bosanquet said (M.B.Foster, 'The Concrete Universal: Cook Wilson and Bosanquet', Mind, Vol. 40, No. 157 (Jan., 1931), pp. 1-22: 1). This certainly looks like a metaphysical claim; and it sits within the complex metaphysical system of (Oxford) Absolute Idealism.

However, what evidence could one deploy to prove or defend it? Put another way and with acknowledgement to William James: How would the world be different if it were false? Since we can't say or even begin to answer this question, we can designate it as 'undecidable'. That is, if we do not take the different path of saying that it is meaningless.

  • +1 Nice answer. I especially like "It's 'highpriori' to suppose that no new argument could resolve an antinomy." Some things that were previously metaphysical speculation can now be answered with some degree of confidence (at least based on a straightforward realist reading of highly confirmed scientific theories). I can imagine folks centuries ago declaring questions about whether the universe had a beginning, whether determinism is true or not, where complex life came from, whether there are atomic building blocks, etc. as being undecidable in principle. Science has a way of surprising us! Commented Feb 15, 2020 at 21:05
  • Thanks for comment. I had in fact very much the scientific reshaping of our concepts in mind. Appreciated - Geoffrey
    – Geoffrey Thomas
    Commented Feb 15, 2020 at 21:13
  • +1 also. It seems the word is generally given one of these two meanings in philosophy. They don;t exhaust the possibilities but I asked what folks usually mean by 'undecidable' and this seems to be it.
    – user20253
    Commented Feb 16, 2020 at 12:38
  • @AdamSharpe - I intended not to do any arguing back here but... If you think science can answer any of the questions you mention then I'd suggest you've misunderstood science. These questions have always belonged in metaphysics and always will. Science certainly surprises us at times but not by answering metaphysical questions. The methodology is not suitable. No question that was 'previously metaphysical' has been anwered by science. We needn't argue about this since there are no examples of such questions being answered by science.
    – user20253
    Commented Feb 16, 2020 at 12:49
  • Adam - What I meant was that some antinomies, e.g. of space and time, disappear when (courtesy of science) our concepts of space and time change.
    – Geoffrey Thomas
    Commented Feb 16, 2020 at 13:16

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