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If philosophy is mathematics and mathematics is computation, can I conclude that philosophy is computation? Can we axiomatize philosophy? Can a computer think for us, given the current rise of AI?

I'm taking the formalist point of view. Philosophy is language and language is the manipulation of symbols. So what philosophers do is to find interesting patterns of symbols. If we can formalize tastes, a computerized brute-force search will do the thinking for us.

So is philosophy merely computation?

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  • But philosophy is defining the axioms (principles). And mathematics is not computation, devising theories is not computation. And why philosophy is mathematics?
    – rus9384
    Mar 27, 2018 at 10:38
  • Related: philosophy.stackexchange.com/questions/26760/… philosophy.stackexchange.com/questions/2445/… In short: All attempts of formalising philosophy have failed because natural languages use semantic layers that are beyond syntax and vocabulary.
    – Philip Klöcking ♦
    Mar 27, 2018 at 10:48
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    Philosophy is not math and math is not computation.
    – Mauro ALLEGRANZA
    Mar 27, 2018 at 11:16
  • +1 I think what you are asking is this: If human understanding can be reduced to a program running on a Turing machine (the strong AI position of computers thinking for us), then wouldn't philosophy and math be reduced to computation? Those who assert that philosophy and math are not computation would be rejecting strong AI.
    – Frank Hubeny
    Mar 27, 2018 at 11:49
  • Philosophy isn't math and math isn't computation, so your two premises are false. But IF philo is math and IF math is computation, then philo is computation. That argument is valid but it is not sound. That is, its logical form is correct, but its premises are false.
    – user4894
    Mar 27, 2018 at 23:14

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If philosophy is mathematics and mathematics is computation, can I conclude that philosophy is computation?

Yes.

So is philosophy merely computation?

No because philosophy isn't mathematics and mathematics isn't computation.

Can we axiomatize philosophy?

If you want. Getting philosophers to agree on a set of axioms should be amusing.

Can a computer think for us, given the current rise of AI?

Not currently, no. Maybe one day but we have no timeline that isn't base speculation.

Philosophy is language and language is the manipulation of symbols.

Philosophy isn't language but it definitely uses it.

So what philosophers do is to find interesting patterns of symbols.

That's probably a fair statement.

If we can formalize tastes, a computerized brute-force search will do the thinking for us.

Very unlikely but you'd need to define tastes before this sentence can be rejected absolutely.

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  • +1 However, if you allow the possibility that computers could think for us, that is understand for us, in the future, then philosophy would be computation.
    – Frank Hubeny
    Mar 27, 2018 at 11:11
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    @FrankHubeny No, it would just be a product of a process that involves computation. As it is today. Identifying philosophy with computation would continue to be incorrect.
    – Alex
    Mar 27, 2018 at 11:26
  • What part of philosophy does not involve computation? I guess I am not sure whether you support strong AI or not. I don't think strong AI is true based on Searle's Chinese Room Argument, but I don't know what your position is given your answer to computers possibly thinking for us in the future.
    – Frank Hubeny
    Mar 27, 2018 at 11:58
  • @FrankHubeny The bits that involve memory for example. Searle's Chinese Room is just intellectual slight of hand. It's quite cunning but it says nothing interesting about the possibility, or otherwise, of any form of artificial intelligence.
    – Alex
    Mar 27, 2018 at 13:06
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    @FrankHubeny Do you consider every part of every science to be 'computation', including the observation and the formation of metaphors and hypotheses? Then why would we have any sciences other than math? It works the other way around -- we share a certain part of philosophy, logic and therefore math, and we force it onto all the sciences because that makes it easier for us to share the results. Philosophy that is not even potentially future science, is not even that close to computation.
    – user9166
    Mar 27, 2018 at 22:44
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The key question here is “Can a computer think for us?” This can be reformulated as “Will strong AI ever be realized?” Or, “Can human understanding be reduced to a program running on a Turing machine?”

There are two answers: Yes or No.

If Yes, then a program can produce human understanding. Since philosophy is the result of human understanding, philosophy is merely computation.

If No, then a program cannot produce human understanding. Since philosophy is the result of human understanding, philosophy is not merely computation.

We will need more than assertions to resolve this. On the one hand there are people who assert that philosophy is not computation. On the other there are people who assert that strong AI is possible. One of those assertions is false.

John Searle provided a thought experiment called the Chinese Room Argument that opposed the assertion that strong AI was possible. See “Minds, Brains and Programs” for details. This argument is one justification for the No answer as to whether computers might ever be able to think for us.

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    Link plato.stanford.edu/entries/chinese-room
    – elliot svensson
    Dec 19, 2018 at 16:39
  • @elliotsvensson Yes, Searles's Chinese Room Argument may be evidence that philosophhy is not computation. There;s more to it. Thanks for the link!
    – Frank Hubeny
    Dec 19, 2018 at 18:03
  • "Minds, Brains, and Programs" is one big example of begging the question, and not being consistent when discussing emergent phenomena. Its reasoning is invalid. I can't get into details in a comment, though.
    – David Thornley
    Dec 19, 2018 at 18:07
  • @DavidThornley It is probably best not to argue it in the comments, but perhaps a new question related to it and begging the question would be appropriate unless it has already been asked.
    – Frank Hubeny
    Dec 19, 2018 at 18:10
  • @FrankHubeny A quick search brings up philosophy.stackexchange.com/questions/1091/…, and I've already written an answer in that question.
    – David Thornley
    Dec 19, 2018 at 23:40
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Regarding mathematics~computation, as @rus9384 says in his comment below your question, "...mathematics is not computation, devising theories is not computation." So your premise is ab initio wrong. But it's partly right -- mathematical proofs >>are<< computation, by the Curry-Howard isomorphism, e.g., https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence It's conjuring up axiomatic systems from which theorems are subsequently derived that's not computational (although, as far as I know, nobody's satisfactorily formally defined what that "conjuring up" is). By the way, as per, e.g., https://en.wikipedia.org/wiki/Axiomatic_system a "theory" is "an axiomatic system and all its derived theorems", so @rus9384 should have phrased his comment a little more precisely -- the axiomatic system isn't computational, whereas the derived theorems are.

As far as philosophy~mathematics goes, your "language and symbols" remarks sound like they're coming straight from Carnap, logical positivism, Quine, analytic philosophy, etc, e.g., https://en.wikipedia.org/wiki/Analytic_philosophy So in that particular school of thought, sounds like you're pretty much barking up the right tree.

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  • The definition of theory as in 'Number theory' or 'Function theory' or 'K-theory' is not the same definition used in science. This is just a complete equivocation.
    – user9166
    Mar 27, 2018 at 22:51
  • @jobermark I'm not quite sure what you mean by "equivocation" here. I'm just quoting the definition of "theory" exactly as per that wikipedia link I gave you -- in fact, I just cut-and-pasted the "theory" definition from its leading paragraph. That it's not the scientific definition, where theory refers to some (presumed) external reality, is irrelevant for this question (I think), where the op refers to "mathematics", "computation", "philosophy". Indeed, my browser search of this page shows the first-and-only occurrence of "science" is in your comment (okay, now there are two occurrences).
    – user19423
    Mar 28, 2018 at 1:14
  • 'Theories' in the sense you are using the word are not 'devised'. So the comment you are criticizing does not necessarily have the fault you are attributing to it, there is a second definition of theory, from the opposite side of philosophy, in which the statement makes sense. Why does it matter that I used a word first? You make its presence sound like an insult.
    – user9166
    Mar 28, 2018 at 1:19
  • "devised"? that's another first-occurence. You referring my "conjured up"? Then, yeah, the axiomatic system is indeed "conjured up", e.g., the axioms for Chu Spaces are a complete mental invention (or contingent rather than necessary, if you will). It's the theorems that are subsequently proven that aren't voluntarily devised (in the conjured_up sense), although selecting the "useful" theorems worth proving (from the class of all provably true statements derivable from the axioms) is also contingent, indeed, a "divination" (noun~"devised"?) if you will.
    – user19423
    Mar 28, 2018 at 1:29
  • Not it is not a first occurrence. It is in the comment you are excessively criticising by @rus938. When we get to accusations that are not just pointless but obviously false, I am out.
    – user9166
    Mar 28, 2018 at 16:52

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