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I just finished reading Dialogue Logic, by Erik C. W. Krabbe (Handbook of the History of Logic. Volume 7). Quote:

In one sense of ‘formal’ all dialogue games are formal because they are based on logical rules that pertain to the logical forms of statements. They are also formal in the sense of displaying rigorous procedures. But (...) Lorenzen’s first examples of dialogue games were based on meaningful statements and therefore, in another sense, material.
In his dissertation, Lorenz [Kuno Lorenz, Arithmetik und Logik als Spiele, 1961) wanted to make a precise distinction between logical and factual truth, and for that purpose he introduced formal dialogue games (formale Dialogspiele) to complement the material games (faktische Dialogspiele) [Lorenzen and Lorenz, Dialogische Logik, 1978, pp. 48–50]. Whereas material games operate with statements, formal games operate more abstractly with statemental schemata (formulas). We saw that with Lorenzen’s material dialogues, it was not immediately obvious which strategies would establish that some statement expressed a logical truth instead of a merely factual one. Lorenz tackles this problem from the other side, by using the formal games to define which statemental schemata are logically valid (allgemeingultig).
A dialogue-definite statemental schema is valid iff there is, in the formal game, for P a winning strategy pertaining to that schema [Lorenzen and Lorenz, 1978, p. 53]. If one wishes, one may then say that statements that are substitution instances of a logically valid schema are logically true. (p. 679)

Clarification: A dialogue logic framework presents arguments as disputes between two parties, P (the proponent) and O (the opponent). The argument proceeds according to certain agreed-upon rules that say whose turn it is, what kind of moves the parties can make, what constitues "winning". The first move is always made by P, and it consists of making a statement, stating a thesis. The argument is considered to be won if the one whose move it is has no legal moves anymores. A "dialogue definite" statement is one that allows a dispute to be finalized, i.e. that will always result in a dialogue that is clearly won by one of the players. See also Wikipedia.

The dialogue logic developed by Lorenzen and Lorenz seems to give a particularly elegant way of defining "logical truth", based on a distinction between "formal" and "material" games. But in some sense all logics are formal: they depend on a distinction between "logical form" and "(material, descriptive, empirical) content". This is true, both for Aristotle's syllogistic logic, for instance, and for the modern formal propositional calculus.

Question: What does dialogue logic add to or improve upon this? What makes the dialogic way of drawing the form/content distinction philosophically distinctive compared to other approaches?

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    With its game-theoretic semantics (GTS), in dialogical logic truth is what survives all attacks, so internalized proponent self-justification as a winning strategy is built into the definition of validity, without external models, which is closer to proof-theoretic semantics (PTS)... Commented Apr 13 at 2:30
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    See also Dialogical Logic as well as Gerhard Heinzmann & Gereon Wolters (editors), Paul Lorenzen Mathematician and Logician (Springer, 2021) and Kuno Lorenz, Basic objectives of dialogue logic in historical perspective (Synthese, 2001) Commented Apr 13 at 8:51
  • Game-theoretic semantics replaces the model-theoretic approach of talking about truth under an interpretation with talk of winning a game. As I see it, this does not make the formal/material distinction any easier to characterise. It just replaces truth under all interpretations with existence of a winning strategy. I doubt whether proving the latter is any easier than proving the former. Commented Apr 13 at 23:15
  • @Bumble - It may not be easier to characterize, but presumably quite different and perhaps more clarifying? also perhaps with fewer metaphysical tangles? Commented Apr 14 at 1:09
  • That's an interesting thought. I suppose that provided you believe in the concept of analyticity, there might be some blurred edges between true/analytically true/logically true. But in a game-theoretic setting, analyticity doesn't seem to have any counterpart. Moves are permitted or they are not. So maybe there are some simplifications. Commented Apr 14 at 3:12

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Long comment

I do not think that there is a "technical" distiction here.

See e.g.N. Clerbout, First-Order Dialogical Games and Tableaux (2014): we present a new proof of soundness/completeness of tableaux with respect to dialogical games in Classical First-Order Logic.

This means that the class of logically valid formulas ("logical truths") is the traditional one.

What is peculiar? Lorenz starts from material dialogues contrasted to formal ones.

The distinction is akin to that used usually: we may say that a sentence like "Either snow is white or snow is not white" is a tautology or that a formula (a schema): A or not-A is a tautology.

If we start with the second point of view, we derive the first one (the sentence) as a substitution instance of the formula.

Both share the same logical form: and this is the key issue for formal logic. As you say, the use of schematic letters is due to Aristotle.

In this way, logical form is captured in terms of invariance under substitution. Of course, as observed by Tarski, we have to assume a priori what are the "logical particles" (connectives) that are not subject to substitution.

This, I think, is the gist of the statement above:

one may then say that statements that are substitution instances of a logically valid schema are logically true. (p. 679)

And see Dialogical Logic: Formality:

one of the most salient features of the dialogical framework [is that] the dialogical approach comes with an internal account of elementary propositions in terms of interaction only, without depending on metalogical meaning explanations for the non-logical vocabulary. More prominently, this means that the dialogical account does not rely—contrary to Hintikka’s GTS games—on the model-theoretic approach to meaning for elementary propositions. Hence, just as Lorenz (2001) clearly stated, the dialogical notion of proposition does not assume truth-conditional semantics.

A recent discussion is in Shahid Rahman & Ansten Klev & Nicolas Clerbout, Immanent Reasoning or Equality in Action. A Plaidoyer for the Play Level (2018, Springer) Ch.11.2 The Built-in Opponent and the Neglect of the Play Level.

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    Hm - if dialogue logic can also be used to ground intuitionist logic, then it doesn't seem correct to say that "This means that the class of logically valid formulas ("logical truths") is the traditional one."? Commented Apr 13 at 14:33
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    @mudskipper - ok. But DL starts wit rules like ND or Sequent Calculus: the set of rules used will discriminate between CL vs IL and the corresponsing soundness/completeness theorems will be relative to the appropriate semantics. The issue is difefrent: Sequent Calculus is a more "natural" approach wrt Intutionistic Logic. Commented Apr 13 at 14:42
  • I think the main philosophical issue here is with the justification of how "logical constants" are separated from "non-logical" ones. Tarski wrote he didn't know an objective reason for making this split in any particular way. So it needs to be assumed as "given" (or as arbitrary stipulation). This seems to have become the dominant pov: the split is declared to be arbitrary. But I wonder if this pov itself is generated by ignoring the wider, social/pragmatic context of "logic". (It also kind of obscures what we expect of "logic" or why all the various "logics" would each be a "logic".) Commented Apr 16 at 18:37
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I haven't read Krabbe (or for that matter Lorenz), so keep that in mind. But I think the gist of this is clear. Consider: I can make a simple practical-material statement like "When I shoot this arrow, I will hit the bullseye". I can then make a serious of other practical-material statements about how I will accomplish this (raising the bow just so, pulling the string just so…), which amounts to a kind of logical argument about how one can hit a bullseye with an arrow. Archers have been making arguments like this since prehistory, when they taught other people to shoot; it's a common form of reasoning (what Piaget called 'concrete-operational' reasoning) used to process simple 'facts'.

But then — a couple of millennia later — Newton comes along and gives a mathematical formula that describes the arc of a projectile in a gravitational field. That formula is also a statement, but it is purely formal: not relating to any specific time, place, or object. It's not practical or material; in its pure form it cannot be used for anything, although it can be worked syntactically to produce other purely formal statements (what Piaget called 'formal-operational' reasoning).

But the point here is that Newton's 'statement' can be used as a schema by archers (or artillery men, or football players, or NASA) for other practical-material statements. Such people can use Newton's statement to calculate angles and forces that will improve the success of their specific (concrete-operational) task. And so we can say that Newton's statement is valid because it offers a 'winning strategy' for people who substitute concrete contexts in for the formal symbols.

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  • This is all fine - but it actually is not clear to me how this answers my question whether (or how) dialogue/dialogic logic is really distinctve in regards to "logical formality". I mean: does dialogue logic clarify/resolve/dissolve certain philosophical questions that otherwise (for instance in a model-theoretic approach or other mono-logic approach) might remain unsolvable? Commented Apr 16 at 18:22
  • @mudskipper: The basic problem here (it seems to me) is that formal systems have the concept of 'validity' which allows them to be checked on purely syntactic grounds. But statements with meaning must be evaluated semantically (on the basis of 'fact', not merely on the basis of 'logic'). And so the idea here is to bridge different language games by making abstract schemata that are subject to the rules of logic, but which can be instantiated and applied to more material language games that are subject to factual analysis. Commented Apr 17 at 1:38
  • @mudskipper: All I did was outline how that would look, using newtonian physics as a example: where ancient archers were engaged in a practical-material discourse about how to laugh a projectile, and Newton's theory provided an abstract schemata which could be checked on a purely formal basis. Commented Apr 17 at 1:40
  • I believe I understand all that. Perhaps we're talking past each other a bit here. I'm still mulling over an answer that I might give to my own question - which might clear things up. But it may take a while before I get to that... Commented Apr 17 at 2:26
  • @mudskipper: It's possible I didn't properly understand what you're asking. I'll reread and see if I can get deeper. Commented Apr 17 at 2:58
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There is a way to look at the issue from the direction of truth-conditional pragmatics (Recanati[10]):

This book argues against the traditional understanding of the semantics/pragmatics divide and puts forward a radical alternative. Through half a dozen case studies, it shows that what an utterance says cannot be neatly separated from what the speaker means. In particular, the speaker's meaning endows words with senses that are tailored to the situation of utterance and depart from the conventional meanings carried by the words in isolation. This phenomenon of ‘pragmatic modulation’ must be taken into account in theorizing about semantic content, for it interacts with the grammar-driven process of semantic composition. Because of that interaction, the book argues, the content of a sentence always depends upon the context in which it is used. This claim defines Contextualism, a view which has attracted considerable attention in recent years, and of which the author of this book is one of the main proponents.

So Wittgenstein and Rawls variously distinguish between games and "forms of life"/practices. A "form of life" is a context, so by parity of interpretation, a practice has a context-setting function. There is some talk in action-theoretic logic/reasoning theory of a generic game-cum-practice, "Intendo":

Tamar Schapiro has extended Rawls’s treatment, developing it into a theory of action (Schapiro 2001; she attributes the view to Kant, but again the historical question will not be taken up). On her view, ‘actions’ are just moves in the completely generic practice; that is, ‘action’ is a status within the generic practice in something like the way that ‘move’ is a status within chess. Schapiro does not name the generic practice, but because it will be convenient to have a short way of referring to it, let’s call it ‘Intendo’. Intendo is the game you are playing whenever you do anything at all; ‘agent’ is thus the generic role in the generic game (the analog of ‘player,’ in chess or baseball). Practices specify standards and reasons, and so ‘practical reason’ turns out to be a practice status as well. Intendo consequently determines what forms practical reasons can take, and so patterns of practical inference are to be read off of what turns out to be the theory of action.

For Kant, it is the spontaneity, or proactivity, of understanding and reason that makes so much for their formal usefulness. So in dialogical logic, the pragmatic background for truth conditions, as possible contents, is more vividly displayed than if we were to appeal to some static Platonic/Fregean syntax. Perhaps we must appeal to conventions and intentional objects (where the ability-to-intend is like having a pre-content structure available, able to be "projected onto" contents), but perhaps these are less "unscientific" or "mystical" than otherworldly abstractions.

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    One thing I like about the dialogic approach is that it explicitly conceptualizes "questioning": "asking a question" (or "challenging a statement") is no longer something extraneous, but becomes an integral part of the way "argument" is looked at. It seems that Recanati adds to this that questioning itself is also a form of framing (?) So, the underlying question is how to demarate "neutral, acceptable" questions (from e.g. leading questions). A DL approach does also have something (but not very much (?)) to say about that (and makes me wonder now how Aristotle handled this). Commented Apr 21 at 12:51
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    Another remarkable feature (which might interest you too) is that DL relates the "necessary" force, the "compelling-ness" of logic (deduction) to (or even grounds it in) the rights and duties, the accepted commitments of the participants in a deductive language game. So, logic is grounded in ethics (in a way). Commented Apr 21 at 13:12
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Relevant literature to answer the question (see also @MauroALLEGRANZA's response):

Historical perspective:

I'll try to come back to this to summarize the main points (I'm still studying all this). For now, I'd just want to point out that the dialogical approach to logic has enabled a re-assessment and re-evaluation of Aristotle's logic (especially of its development from the practice of dialectical debate) that shows Aristotle was not the ignoramus who didn't understand logical quantifiers. Marion and Rückert convincingly show that Łukasiewicz' earlier, very influential, disdainful interpretation of Aristotle's logic is based on gross misinterpretation.

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    If you are interested in the question of what it means for logic to be formal, John MacFarlane's PhD thesis is a good read. Commented Apr 21 at 5:32
  • Thanks @Bumble (Dutilh Novaes also referred to that thesis as one of the few focussed studies of this topic). Commented Apr 21 at 12:42

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