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The concept of anti-realism in logic seems to be an interesting and growing idea.

I'm looking for references (papers, books, authors...) regarding the debate between realism and anti-realism but especially related to logic and mostly on the anti-realism side but the defense of realism or the criticism of anti-realism are, indeed, accepted.

For instance, I'm interested in the ideas exposed in The Realism-Antirealism Debate in the Age of Alternative Logics but realism-oriented.

It seems that Anti-Realism has a link with substructural logic (see : Radical Anti-Realism and substructural logics)

As far as I know the main current programs are :

  • The proof-theoretic semantics (M.Dummett, D.Prawitz)
  • Transcendental Syntax (JY.Girard)
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Looking at your profile before answering, this is a very tough question. The perennial realism/anti-realism debate essentially boils down to whether and how language (formerly -- pre 20th Century -- thoughts/experience) hook up to things/objects -- whether they be chairs, numbers or theorems. Given your level of logical, but not philosophical (ontology v. metaphisics v. epistemology), sophistication, and not knowing what you want to do with the knowledge/distinction, I would say start maybe with some light CS Pierce semiotics (though Kant and Carnap would also be likely starting points), then Quine (maybe Truth by Convention and On What There Is), Wittgenstein's Tractatus (first), then the Investigations (after reading about how it came to be that evolved/devolved (depending upon your tribe/camp) from the T to the I (which strikes me as precisely describing your state/dilemma), then read either the Blue and Brown Books and/or On Certainty. Then go to Hillary Putnam, maybe his Rethinking Mathematical Necessity, from his Words and Life collection of essays. (go here for a great essay with a priceless bibliography that is roughly on point: https://www.princeton.edu/~jburgess/Quine2.doc) Bon Appetit.

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  • "and not knowing what you want to do with the knowledge/distinction" I don't really know either. I just came across Linear Logic and Girard's Transcendental Syntax from Computer Science. It was really confusing for a computer scientist but I wanted to understand more about these ideas and I learned that it was linked to what we call anti-realism.
    – Boris
    Apr 1, 2017 at 23:52
  • Why do you think one should read Wittgenstein's Tractatus before the Investigations ? And why do you recommend reading the Blue and Brown books after these ? I once saw someone recommending to read the latter first.
    – Boris
    Apr 1, 2017 at 23:54
  • @Boris Eng As I said before, it depends on what you're doing. What you're up to. A logician you are, but do you have a taste for, or are you allergic to, traditional philosophy? Is coherence and ability to anticipate/predict enough for you, or do you find it interesting to think about if and (if so) how your ideas/thoughts/experiences/sentences/knowledge/theorems somehow "correspond" to the world/reality that you appear to inhabit?
    – gonzo
    Apr 2, 2017 at 0:31
  • The change of mind that occurred in Wittgenstein's prescient brain over the decades between the Tractatus and the Investigations are quite amazing in that it is emblematic of what was going on, and what was soon to be, in philosophy -- how things hang together in the broadest sense. W. Sellars. In fact, whereas the young Wittgenstein believed that with the Tractatus he had answered all of the questions traditional philosophy had grappled with for centuries, many say that traditional philosophy died (was made superfluous) by the Investigations.
    – gonzo
    Apr 2, 2017 at 0:32
  • I don't think I'm allergic to traditional philosophy. I think it may be necessary to really understand the current ideas. What do you mean by the ability to anticipate and predict ? I find it interesting to understand how things "corresponds" (or not) to "reality". Maybe some introductions to basic concepts woud be useful. I came to all these ideas a bit by accident without a strong background in philosophy.
    – Boris
    Apr 2, 2017 at 10:02
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This answer will focus on two references that may be useful to understand the issues dividing realism and anti-realism.

Rather than looking at this from the perspective of logic it may be more useful to see it from the perspective of various metaphysical disputes such as platonism in mathematics versus intuitionism, realism of the physical world versus phenomenalism, or realism of past or future events versus neutralism. One may take different realist/anti-realist views with respect to each of these classes of statements.

In all of these the logical issue is over acceptance of bivalence with respect to the specific class of statements. Realism would like to claim that each statement in a specific class of statements is either true or false. Anti-realism would deny this.

  1. For a view favorable to anti-realism see Michael Dummett's The Logical Basis of Metaphysics, 1991, Harvard University Press. Dummett discusses realism and anti-realism from the perspective of various metaphysical disputes.

  2. Focusing on the metaphysical dispute from all sides surrounding mathematics, see the collection of essays edited by Paul Benacerraf and Hilary Putnam, Philosophy of mathematics: Selected readings, Second Edition, 1983, Cambridge University Press. This collection contains Dummett's essay "The philosophical basis of intuitionistic logic" as well as essays by Brouwer and Heyting and others taking logicist and formalist (realist) positions.

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