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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)
Boris
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  • Maybe useful : Ian Rumfitt, [The Boundary Stones of Thought: An Essay in the Philosophy of Logic](https://books.google.it/books?id=R_EkBwAAQBAJ&pg=PR13), Oxford University Press (2015). – Mauro ALLEGRANZA Mar 14 '17 at 15:29
  • Neil Tennant, [Anti-realism and Logic: Truth as Eternal](https://books.google.it/books?id=xgFHc_P62SoC) (1987). – Mauro ALLEGRANZA Mar 14 '17 at 15:44
  • Maybe also parts of Heinrich Wansing (editor), [Dag Prawitz on Proofs and Meaning](https://books.google.it/books?id=GfObBQAAQBAJ&printsec=frontcover), Springer (2015) – Mauro ALLEGRANZA Mar 14 '17 at 15:44
  • Hilary Putnam ["Is Logic Empirical?"](http://www.socsci.uci.edu/~dmalamen/courses/prob-determ/Putnam.pdf), (also goes under the tile "The Logic of Quantum Mechanics") – Alexander S King Mar 31 '17 at 23:13

2 Answers2

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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.

gonzo
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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](http://iml.univ-mrs.fr/~girard/TS2.pdf) 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 01 '17 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 01 '17 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 02 '17 at 00:31
  • 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 02 '17 at 00:32
  • 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 02 '17 at 10:02
  • @Boris Eng Maybe the most efficient way to express it in this context is to say that realism essentially posits that there is a "fact of the matter as to whether or not P [is true]", whereas anti realism posits that there is not. Essentially, the question is whether or not our experiences (claims/beliefs etc) are factual/true turns on whether or not they correspond to, are in agreement with, the world/reality. It then occurred to critical thinkers that this is unknowable, because one can only "compare" one experience/belief with another experience/belief. – gonzo Apr 03 '17 at 00:59
  • So the concept "truth", long a metaphysical notion, was "deflated" and came to be known as an epistemic notion -- it became equated with the notion of "warranted assertability". Beliefs/concepts/vocabularies became "instrumental" -- the question ceased to be whether they are "true" or "false", since we can never "know" this with certainty, but, like any instrument or "tool" [ vis "conceptual toolbox"] whether or not they "work" - assist one in anticipating/predicting. Bear in mind, I have outlined this is all very broadly, very simplistically. – gonzo Apr 03 '17 at 01:11
  • Do you also have references for Kant and Carnap (as you suggested in your answer) ? – Boris Apr 05 '17 at 11:30
  • @Boris Eng Wow. Been decades since I read anything by either of them. As for Kant, maybe just start with the First Citique. Carnap: Read Quine’s "Carnap and Logical Truth," and if you still hunger for his POV, his own "The Elimination of Metaphysics through the Logical Analysis of Language" and "Empiricism, Semantics and Ontology." – gonzo Apr 06 '17 at 00:10
  • By "First Critique" do you mean his "Critique of Pure Reason" ? And I know that the Tractatus and Philosophical Investigations are well-known and important but why do you recommend Wittgenstein's Blue and Brown books and "On Certainty" after these ? – Boris Apr 06 '17 at 15:15
  • Yes re the Critique of Pure Reason. As for Witt: Because Certainty and Blue/Brown explicate, flesh out, the ideas introduced in the Investigations. But again, I do not know what you are up to. It may be, for instance, if what you want to do is simply put to "use" the ideas in order, say, to cope with the world, and have little patience with "contemplating" them/their geneology, then stick to the blue and brown books and skip the rest of W's opus. – gonzo Apr 06 '17 at 17:43
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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.

Frank Hubeny
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