Is Haskell Curry's unconventional way of defining True(x) incorrect?

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I tend to ask questions that do not have existing answers in any book. The above question is a very difficult question that has no answer in any book. It is not an opinion based question it is a question with an objective analytical answer.

Whenever I ask very difficult questions people react as if I made a mistake on the basis of their own lack of understanding.


3 Answers 3


The reason your question attracted downvotes is already explained here on meta and in the comments:

  1. The title question has nothing to do with the body of the question

  2. The body of the question mixes a quote by Curry, something about mere points of views and something about truth and provability. The three have nothing inherently to do with each other, yet you completely fail to provide a line of thought linking them.

  3. The question about Gödel/Tarski has been repeatedly addressed, pointing out that they apply to most useful formal systems and there being no reason for changing these because truth is not as useful a category in mathematics as you may think. It basically is just one category among many, formed the same way.

  4. You claiming that the question (which one? Title or body?) had an "objective analytical answer" already shows that there is no genuine question and you will not accept anything but what agrees with your (marginal) view. This is the very opposite of objectivity.

  5. The question is not difficult at all. It is just a bad fit here for the reasons stated. That's all.

  • I addressed your points (1) & (2) & (4) as a separate answer because a reply did not give me enough room or proper formatting. I addressed your point (3) In the same way for the same reason. Feedback on these two answers will allow me to address your point (5) more effectively.
    – polcott
    May 11, 2020 at 17:27
  • "The title question has nothing to do with the body of the question." Yes it does as I carefully explained in my other answer show below. Three high ranking members including you indicated that they didn't believe such as notion as "correct" existed.
    – polcott
    May 12, 2020 at 20:46

Reply to Philip Klöcking point (3) "truth is not as useful a category in mathematics as you may think. It basically is just one category among many, formed the same way."

The notion of truth is very important as the foundational of truth conditional semantics.

Truth-conditional semantics is an approach to semantics of natural language that sees meaning (or at least the meaning of assertions) as being the same as, or reducible to, their truth conditions. This approach to semantics is principally associated with Donald Davidson, and attempts to carry out for the semantics of natural language what Tarski's semantic theory of truth achieves for the semantics of logic.[1] https://en.wikipedia.org/wiki/Truth-conditional_semantics

My independent area of research involves the mathematics of natural language semantics based on Truth-conditional semantics, thus having a correct foundation is crucial.

  • 2
    Even if this may be your pet theory, there is nothing inherently mathematical about it and it is not warranted by Curry's quote in any sense, as the comment thread on Math.SE increasingly shows. I said it once and will say it again: The foundationalism you envision has been tried time and again and is, philosophically, a dead horse. Nuff said.
    – Philip Klöcking Mod
    May 11, 2020 at 21:33
  • "philosophically, a dead horse" How so? What objective basis do you have for this assertion?
    – polcott
    May 11, 2020 at 21:47
  • 2
    Gettier cases, empirical validation of language and understanding being holistic, Wittgensteinian incommensurability, the fact that objects in the world are not themselves conceptually structured...as I said: Quine, Sellars, Davidson, Rorty, Putnam. Serious epistemology since the early 1960s, basically. One last reading suggestion: Limits of Realism by Tim Buttons. He even has a nice analytic part where he shows the logical structure of all arguments mentioned
    – Philip Klöcking Mod
    May 11, 2020 at 21:50
  • @PhilipKlöcking All of those are outside of the bounds of analytical knowledge and sound deductive logical inference. The nature of reality is a whole other can-of-worms outside of the scope of the nature of analytical knowledge. When we stick to expressions of language that can be verified as true entirely on the basis of their semantic meaning every undecidable decision problem can be understood to only be undecidable on the basis of its inherent incoherence.
    – polcott
    May 11, 2020 at 22:03
  • 1
    For there being verification entirely based on semantics you will need a set of basic beliefs. Foundationalism is the branch of analytical philosophy which tries to establish exactly that. The whole branch is only about analytical knowledge and logical inference. But without basic beliefs, there's nothing to infer from
    – Philip Klöcking Mod
    May 11, 2020 at 22:06
  • @PhilipKlöcking This doesn't really seem like any sort of belief, it seems more like a mutually self-defining semantic tautology encoded as finite strings: >>>Successor(Successor(Successor(0))) = 3 is correct and thus true<<<
    – polcott
    May 11, 2020 at 22:13
  • Concepts (finite strings) are not as well defined, though. Correctness is just as messy as truth there. As soon as you leave the bounds of a pre-defined formal system (something natural language is not) or try to say something about the world (something that is not language), this whole thing collapses like a house of cards. This is why Frege could not succeed with this idea (it's actually 100ish years old).
    – Philip Klöcking Mod
    May 11, 2020 at 22:26
  • @PhilipKlöcking That is why I have been focusing on formalizing natural language semantics. Richard Montague established an excellent foundation and Doug Lenat's team spent 700 labor years manually encoding a tiny portion of this. With a breakthrough in the formalized notion of truth I would have credibility to carry on Doug Lenat's work and automate the process of encoding formalized knowledge.
    – polcott
    May 11, 2020 at 22:33
  • 1
    No matter how many labour hours went into it, it shows a lack of understanding of the nature of natural language beyond logical particles. Maybe interesting, maybe a nice exercise for computer scientists, but ultimately a waste of time since language without equivocation is not a natural language. That being said, it is questionable that anyone is able to nail down the truth conditions of "having the sensation of a red triangle" or "feeling a bit sad". They are either tautological (meaningless) or nonsensical (appealing to things that cannot be known).
    – Philip Klöcking Mod
    May 11, 2020 at 22:44
  • @PhilipKlöcking I myself am simplifying the problem of the nature of truth by only examining the analytical portion. A software system that is a fully functional human mind would not be able have this constraint. Yet by limiting my focus on the analytical portion I may be able to gain substantial credibility by showing that the only reason any undecidable decision problem is undecidable is because of previously undiscovered inherent incoherence.
    – polcott
    May 11, 2020 at 22:54
  • @PhilipKlöcking Try an imagine the simplifying assumption of just the set of analytical knowledge, those expressions of language that are known to be true entirely based on their semantic meaning. No undecidable decision problem has any of the limitations that you refer to and yet they remain undecidable. They are only undecidable because they are incoherent.
    – polcott
    May 12, 2020 at 0:03

Reply to Philip Klöcking points (1) & (2) & (4) Is Haskell Curry's unconventional way of defining True(x) incorrect?

(a) "Incorrect" in what sense? One is free to define words however they wish. ...
"truth is provability" is quite a conventional stance for intuitionists that Curry was sympathetic to. – Conifold

(b) the quote ... is an argument showing implications of a certain line of thought. Philip Klöcking

(c) (From Math SE) H.Curry was a "formalist" ... Thus, he is simply saying that the true statements of a theory are the statements provable in the theory. – Mauro ALLEGRANZA

Correct in the sense that: Successor(Successor(Successor(0))) = 3 is correct and thus true and Successor(Successor(Successor(0))) = 7 is incorrect and thus untrue. polcott

(The Math SE version) Is Haskell Curry's unconventional way of defining True(x) incorrect?

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