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The Realism-Antirealism Debate in the Age of Alternative Logics pp 141–168Cite as

Game Semantics and the Manifestation Thesis

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Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 23))

Abstract

This paper begins with a discussion of the idea of a successor programme to Dummett’s original anti-realist challenge, which should take into account recent developments, e.g., accommodating logical pluralism; I suggest furthermore that one explores a possible contribution from game semantics in the tradition of Lorenzen’s dialogical logic. The purpose of the paper is to examine what could possibly happen to Dummett’s Manifestation Argument within this new programme. After an analysis of the argument, I extract from it a Manifestation Thesis and argue that it fits game semantics, once some basic ideas concerning sense and force in the theory of meaning are reformulated and the second person standpoint is fully taken into account.

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Notes

  1. 1.

    Part of negative reaction Dummett’s ideas encountered can be explained by the fact that ‘model-theoretical’ semantics, which takes truth as its fundamental notion and forms the background to realist theories of meaning that he criticized, had been the dominant paradigm in analytic philosophy until then, and has remained so to this day. In my opinion, his ideas were often misunderstood precisely because his critics did not fully understand the ‘proof-theoretic’ background to his ideas. Dummett was rather clear about this on occasions, e.g., when he compared Frege’s axiomatic approach to logic with Gentzen’s proof-theoretic approach and called the former ‘retrograde’ [28, pp. 432f.], or when he modelled the two aspects of language use that he distinguishes on introduction and elimination rules in Gentzen’s natural deduction system; he goes even as far as to generalize the notion of harmony between these, e.g., in [28, pp. 454–55]. It is worth pointing out, however, that arguments such as the Manifestation Argument, discussed here, aim at a particular conception of truth as ‘recognition-transcendent’, not at the concept of truth itself, hence some amount of confusion.

  2. 2.

    Even if, as I do, one thinks that the adversarial attitude with which the debate had been conducted is mostly out of place. This is also Dummett’s opinion [29, p. 464]. Although an adversarial attitude is essential in philosophy, lest we all settle on conceptions that could have been improved upon had they been correctly challenged in the first place, one ought to approach these issues more in the scientific spirit of inquiry, which was that of the pioneers of analytic philosophy, Frege and Russell, than in a quasi-theological spirit.

  3. 3.

    As W.V. Quine famously called them [66, chap. 6].

  4. 4.

    For this argument, see [66, p. 81].

  5. 5.

    To mention some of the better-known proposals: [6], and the programme of ‘substructural logics of [24, 71, 79]. Lesser known proposals in [67, 75] are closest in spirit to the standpoint assumed in this paper.

  6. 6.

    The expression ‘semantics of interaction’ has the advantage of avoiding some of the inappropriate connotations linked with the concept of ‘game’; it was only introduced recently in [48].

  7. 7.

    So the proposal here is independent from that in [25, 26], further explored in [55, 57] and more closely linked to the ‘substructural’ programme mentioned in footnote 5.

  8. 8.

    As is standardly done since, e.g., Wittgenstein’s Tractatus [90, 5.101]—or in [17, p. 37].

  9. 9.

    As first done Gentzen’s ‘Investigations into Logical Deduction’, § 5.13 [35, p. 80].

  10. 10.

    More precisely put, these are non-collaborative, zero-sum games with perfect information; there are extensions, e.g., to games of imperfect information, or to games of n-persons.

  11. 11.

    With further help from his student Kuno Lorenz, in a series of papers reproduced in [51]. For a short introduction, see [74]; for a textbook, in French, see [33].

  12. 12.

    For one of the first presentations of Hintikka’s game-theoretical semantics, which displays the origin in his thinking about model sets, see [41], up to and including Chapter 3. For a more recent detailed presentation, see [46].

  13. 13.

    In the application of logic to computation and programming language semantics, there are two broad approaches to game semantics, which reflect the approaches to computation as ‘proof normalization’ and ‘proof search’. Game semantics in the style of Lorenzen or Hintikka related more to the later, while developments sparked by [10], such as [1, 3], to be left aside here, relate more to the former. I owe this point to Dale Miller; see [21, § 6].

  14. 14.

    The following are for Lorenzen’s games only and, even then, it is necessary at this informal level to gloss over many issues.

  15. 15.

    One must distinguish here between ‘semantics’, as understood in this minimal sense and ‘model theory’: to provide an account of the meaning of logical particles in terms of a key concept (truth, proof, game) is to provide, in one sense of the expression, a ‘semantics’ for it. (Of course, understood in this minimal sense, semantics need to be supplemented, if only by further ‘structural rules’.) And this is quite independent of the fact that one might elect to use model-theoretical tools in fleshing out this semantics, as Hintikka did, for example. For that reason, in his work, game semantics look more like a carrier for the usual model-theoretic notions than a genuine logic of interaction, as pointed out in [2, p. 43, n. 1]. On the other hand, Jean-Yves Girard is quite explicit about avoiding model theory in his highly innovative approach to logic, which he calls ‘ludics’ [36]. In this paper, there is no need to get into these issues, it suffice for the argument of this paper that one sticks to a minimal definition of semantics as the provision of an account of the meaning of logical particles.

  16. 16.

    The point is only alluded to in [67, p. 379], for a full discussion, see Rahman’s contribution to this volume. For original exchange concerning ‘Tonk’, see [7, 65].

  17. 17.

    Another way to frame the Winning Rule is as follows: the game will be over when the last player cannot move anymore; if dialogue is closed, then proponent wins, if it is open, opponent wins. Here ‘closed’ means that the same formula occurs twice, asserted by O and by P; if not, it is ‘open’.

  18. 18.

    The Formal Rule also introduces asymmetries in the roles of P and O, a fact that has been perceived since [10, p. 185] as a defect. This led to its abandonment within the numerous attempts at giving a game semantics for linear logic, where the above-given particle rules are construed as defining the set of ‘additive’ connectives, while the new ‘multiplicatives’ from linear logic are introduced via a new set of rules (the details in this remark are slightly wrong, but this is not the place for a detailed discussion; the gist is, I think, correct). Instead, the essential work done by the Formal Rule is done by the ‘copy-cat’ strategy. From the Lorenzen standpoint, one might complain that abandoning the Formal Rule brings about some amount of confusion between Lorenzen’s games and more model-theoretic versions. Models are indeed often assumed in game semantics for linear logic, e.g., Japaridze’s arithmetical models in [47]. And it is a consequence of this reintroduction of models at the atomic level in absence of the Formal Rule that games are now won or lost for reasons that are, so to speak, independent of the player’s moves. Furthermore, asymmetries will resurface in the rules given for the ‘multiplicatives’. (I owe these remarks to discussions with Helge Rückert.)

  19. 19.

    This is the approach taken in [67, 75], which is similar in that respect to the programme of ‘substructural logics’, mentioned above in footnote 5.

  20. 20.

    For Hintikka’s arguments against Lorenzen, see, e.g., [41, pp. 80–81], [45, p. 39f], [42, pp. 297–98] or [44, p. 267] for rather poor criticisms of Hintikka from Lorenzen’s standpoint, see [32, pp. 352–53].

  21. 21.

    See Theorem 22 in [68].

  22. 22.

    For other relevant passages, see, e.g., [44, pp. 254, 256].

  23. 23.

    [44, p. 171, n. 34].

  24. 24.

    Defined as follows: ‘one can behave in such a way as to manifest an intention to effect a certain strategy only if the strategy in question is effective’ [87, pp. 304–05].

  25. 25.

    [87, p. 305]. The point is reasserted in [87, p. 176].

  26. 26.

    See [54, pp. 8–9].

  27. 27.

    See [56] for a brief presentation, and earlier papers [53, 54] where I criticized what I perceived as weaknesses in, respectively, Hintikka’s and Lorenzen’s attempts at providing a philosophical basis to their own game semantics.

  28. 28.

    For an overview, see [61]. Pagin has voiced some objections against the ‘social account’ in [60], but his ultimate claim that assertion would have this particularity that it is the only speech act which is non-social seems hardly credible. This is not the place, however, to discuss it. (John MacFarlane has a rejoinder to Pagin’s objections in an unpublished paper entitled ‘What is an Assertion?’.) One should note that, as pointed out in [89, pp. 68–69], we are never in a position to defend all of our assertoric commitments. The point about feasibility raised in the papers quoted in footnote 7 above could therefore be adjusted to fit here.

  29. 29.

    For these games, see also Between Saying and Doing. Towards an Analytical Pragmatism [14, p. 111]. But Brandom’s project in that book is of a different nature and in order to avoid here needless complications, it shall not be taken into account. The expression ‘games of giving and asking for reasons’ comes from Brandom, who often attributes it to Wilfrid Sellars, e.g., at [13, p. 189], but, as far as I know, there is only really one passage that supports this attribution, namely the last sentences of § 36 of Empiricism and the Philosophy of Mind [80, p. 76], where this expression actually does not occur. On the other hand, Dummett came close to framing it when he wrote: ‘The process of learning to make assertions, and to understand those of others, involves learning what grounds, short of conclusive grounds, are regarded as justifying the making of an assertion, and learning also the procedure of asking for, and giving, the grounds on which an assertion is made’ [28, p. 355]. As it turns out, Dummett used the analogy of chess often, even talking about assertions in terms of ‘game’, e.g., at [27, p. 2] or [28, pp. 2, 355], but he did not make the notion central to his semantics. Likewise for Wittgenstein, who describes once, almost en passant, asserting as ‘a move in the language-game’ [91, §22]. Therefore, although it is nice to notice affinities, we should avoid reading too much back into the texts of Wittgenstein, Sellars, and Dummett.

  30. 30.

    See [49].

  31. 31.

    See his appeal to ‘Dummett’s Model’ in [12, pp. 116–18] and [13, pp. 61–63]. Brandom distinguishes, however, his inferentialism from the sort of ‘assertibilism’ one finds in Dummett by distinguishing two kinds of normative statuses, ‘commitment’ and ‘entitlement’, where Dummett would have only one, ‘being assertible’. (See [13, p. 188]) The interaction between these gives rise to an incompatibility semantics based on the fact that ‘two assertible contents are incompatible in case commitment to one precludes entitlement to the other’ [13, p. 194]. This is not the place for further discussion, but one reason one would need to be careful here is simply the fact that details of this incompatibility semantics are worked in a series of appendices to Chapter 5 of Between Saying and Doing, the result being that ‘any standard incompatibility relation has a logic whose non-modal vocabulary behaves classically’ [14, p. 139]. This would prima facie be a problem for someone looking forward to developing a framework for pluralism.

  32. 32.

    A remark at [12, p. 599] leads me to believe that Brandom was taking his lead from Davidson’s ‘triangulation’—see, e.g., [23, pp. 117–21, 128–29, 202–03, 212–13]—which requires only two speakers. This is related to but different from what is called here the ‘I-Thou’ perspective. A set of tangential issues avoided here is raised by Davidson’s claims that triangulation is necessary [23, pp. 128–29] and sufficient [23, p. 105] for the emergence of thought.

  33. 33.

    [39, p. 163].

  34. 34.

    A reply to Habermas along those lines is found in [77], especially pp. 56–57. Indeed, Brandom considers that there is no ‘globally privileged’ perspective, including that of the community [12, pp. 599–600], while Habermas’ objection stems from the very fact that he considers the community’s perspective as privileged: it is for this reason that he misconstrues Brandom as advocating a form of ‘methodological individualism’ [39, p. 165].

  35. 35.

    [39, p. 163].

  36. 36.

    I am aware that this issue between Brandom and Habermas is more complex, since Habermas is discussing here Brandom’s peculiar understanding of the de re/de dicto distinction, while I keep here to the discussion of logical connectives.

  37. 37.

    It would be worthwhile to investigate further the connections here with Davidson’s ‘triangulation’ (see footnote 32) and in another direction with Sebastian Rödl’s elaboration of the second person standpoint in [73]. One point especially worth exploring is the essential symmetry of the first and second person standpoints, as opposed to the asymmetries of the first and third person standpoints. This essential symmetry is argued for by Collingwood in a splendid passage at [18, pp. 248–49], which was quoted with approval by Davidson [23, p. 219]. This symmetry is, I think, fully cashed out in game semantics by the rule for negation and the possibility to exchange roles.

  38. 38.

    Validity is here understood in the strict logical sense, not in reference to Habermas’ wider notion. For more on Habermas’ theory see footnote 62 below.

  39. 39.

    Sophist 263e; trans. White. For further passages, see Theaetetus 189e–190a and Philebus 38c–39a.

  40. 40.

    The idea behind this interpretation of Plato’s famous saying, I owe to [19, p. 35]. For a similar reading, see [62, pp. 30–33].

  41. 41.

    Posterior Analytics, I, 10, 76b 24–27, trans. Mure.

  42. 42.

    Here too, see [62, pp. 36–41]. It is fitting to note here how nicely Aristotle’s syllogistic can be expressed within a natural deduction framework, as opposed to an axiomatic one. See [20, 84].

  43. 43.

    Indeed, since Lorenzen was a ‘monist’, he believed that his dialogical games would justify intuitionistic logic and this led in his ‘Erlangen School’ for a search for an equivalence theorem between proofs in Gentzen’s natural deduction system for intuitionistic logic and strategies for winning dialogues, and a very ‘bureaucratic’ proof was given in [31]. See [32] for a readable overview. At all events, a perhaps more convincing argument here would use the fact that game semantics also opens the door to games with n-players, as in, e.g., [2].

  44. 44.

    See, e.g., [43, pp. 151, 156, 174].

  45. 45.

    For criticisms, see [53].

  46. 46.

    See also [67, p. 379].

  47. 47.

    I owe this to Helge Rückert, in a paper given at the Université de Nancy, November 2008.

  48. 48.

    Or summarily dismissed, as in [87, p. 314, n. 6].

  49. 49.

    E.g., at [29, p. 84], where Hintikka’s game semantics is misconstrued as a species of falsificationism.

  50. 50.

    See [69, p. 381] and [67, p. 366], where the same line of thought is also pursued.

  51. 51.

    In the sense of ‘proposition’ one finds in [17, p. 27], i.e., a proposition is the meaning of a sentence. This is usually meant to be identical with Frege’s Gedanken, but the notions will diverge sensibly here, as the point is to rethink what ‘proposition’ might mean. In his paper, Ranta discusses Hintikka games, not Lorenzen’s, and his idea paves the way to a suitable reinterpretation of them in type-theoretical terms. But his idea of ‘propositions as games’ is independent of these issues.

  52. 52.

    That ‘inner process’ need not be an ‘inner psychological mechanism’ of the sort Dummett rejects in [29, p. 37]. The point is fully to adopt the dialogical ‘I-Thou’ standpoint for which ‘know how’ is first and foremost of a social practice.

  53. 53.

    One could also refer here to Wittgenstein’s objections in [91, §§ 185–242], properly understood.

  54. 54.

    The point is rather standard, see, e.g., [64, p. 291] and [81, p. 337].

  55. 55.

    [72, pp. 28–29].

  56. 56.

    This argument was about inferences but a similar one could be made for particle rules, so it is open to us to conceive of the introduction of rules for the logical particles as ‘making explicit’ moves already current in a given practice, such as the regimented practice of ‘dialectical games’ in Ancient Greece and ‘obligationes’ in the Medieval Ages. (For a game semantic approach to the latter, see [30, part 4].)

  57. 57.

    Republic 534b–d; trans. Grube.

  58. 58.

    For details about this characterization of ‘dialectical games’ and the elenchus along those lines, see [16]. Note that there is a reference, en passant, to the Socratic elenchus in [12, p. 178], which shows that the ideas put forth here are not far from Brandom’s thinking.

  59. 59.

    For this reading of Republic 534b–d, see [5, pp. 283–84]. Of course, the underlying reading of Plato here is very controversial, it certainly has nothing to do with what is peddled as ‘Platonism’ in the philosophy of logic and mathematics since the early twentieth century but, again, this is not the place for this sort of debate.

  60. 60.

    This is, of course, only a suggestion; the set of such rules would need to be worked out more precisely. Ranta has an initial proposal for such rules in [69, pp. 388 ff.]—in fact, the rule (R) is a variant of one of his rules—but see also his point of departure [85].

  61. 61.

    [27, p. 2].

  62. 62.

    [28, p. 298]. On the Continental side, Jürgen Habermas developed an ‘universal pragmatics’ on the basis that a communication is defined as action oriented towards reaching (mutual) understanding. Follows from this what is broadly similar to Dummett’s dictum: ‘The speaker must have the intention of communicating a true proposition (or propositional content […]) so that the hearer can share the knowledge of the speaker’ [38, p. 22]. In doing so, the speaker raises a ‘validity claim’ (Geltungsanspruch). (For clarification of that notion, see [40].) This means that the speaker is committed to providing reasons for the ‘acceptability’ of his claim, so: ‘We understand a speech act when we know the kinds of reasons that a speaker could provide in order to convince a hearer that he is entitled in the given circumstances to claim validity for his utterance—in short, when we know what makes it acceptable. A speaker, with a validity claim, appeals to a reservoir of potential reasons that he could produce in support of the claim’ [38, pp. 232–33]. Habermas’ standpoint is thus close, but does not corresponds exactly to Dummett’s or Brandom’s, it is more like a generalization of it, that embeds it into a larger theory of social action. At all events, it is quite clear, e.g., from [38, pp. 231–32], that it was inspired by Dummett’s, and not surprising that Habermas reacted so positively to Brandom’s Making it Explicit, see [39, chap. 3].

  63. 63.

    There is also a tangential debate concerning Dummett’s mention of ‘conventions’, since he is generally taken as having fallen foul of a famous argument by Donald Davidson in ‘Communication and Convention’ [22, pp. 265–80]. (Pagin also picks on Dummett’s dictum(s) in [60, pp. 2–3].) Davidson also rejects in his paper the analogy between language and game, which is central here [22, pp. 267–68]. His critique of the analogy consists in the claim that ‘linguistic behaviour’ does not exhibit a combination of these features of games: (a) people who play want to win, (b) winning is wholly defined by the rules, (c) ‘winning can be, and often is an end in itself’ [22, p. 267]. He actually concedes partly (b) and provides an obscure Gricean argument concerning (a), that need not be addressed here (as it involves concepts such as ‘representing oneself as wanting to win’ that are not relevant here). Finally, he claims that ‘speaking the truth, in the sense of uttering a true sentence, is never an end in itself’ [22, p. 268]. One should note in reply that Davidson was careful enough not to write something like ‘winning is always an end in itself’, because that would be false; he did not notice that this fact undermined his argument: that speaking the truth is not an end in itself is not contradicting the fact that for some games winning can be an end in itself. The use of the metaphor of games in this paper presupposes that winning is not an end in itself. Indeed, there are many reasons to look at the rule (R) above as involving winning in the assertion game as not being an end in itself. To take only one example, to suppose that O loses to P several plays of, say, a dialectical game, for A, this may convince O that P was correct in asserting A, so that O might not only refrain from further challenges and endorse A. Furthermore, Davidson seems not to have realized that Dummett’s point remains even when the analogy does not hold: one needs an account of what it is that a speaker aims at when ‘asserting A’ for one’s semantic account to be complete.

  64. 64.

    Shieh’s reformulation of Dummett’s dictum, as follows, comes rather close to the position advocated here: ‘To be taken as making an assertion, a speaker must acknowledge that the statement she is making is subject to assessment as correct or incorrect, by reference to what she would count as justifying it’ [82, p. 51].

  65. 65.

    [29, p. 464].

  66. 66.

    See [58, 59], and, on the anti-realist side [88]. The first two are soundly criticized in [82] for the quasi-behaviouristic construal of the manifestation argument (see footnote 85 below), which is neither really compelling, nor faithful to Dummett. (The latter’s formulations are admittedly often ambiguous, given the context in which they were written, permeated as it was by Quine’s philosophy.) But it turns Dummett into some sort of easily refutable old-style ‘epistemological foundationalist’.

  67. 67.

    [29, p. 46].

  68. 68.

    Despite his best efforts, Shieh concludes [83] on a sceptical note.

  69. 69.

    [27, p. 225].

  70. 70.

    [27, p. 216], [63, p. 4].

  71. 71.

    [27, p. 216].

  72. 72.

    See [27, pp. 217–18].

  73. 73.

    [27, p. 216].

  74. 74.

    [27, p. 216].

  75. 75.

    The following passages support this reconstruction: ‘it is quite obscure in what the knowledge of the conditions under which a sentence is true can consist, when that condition is not one which is always capable of being recognized as obtaining’ [27, p. 224]; ‘any behaviour which displays a capacity for acknowledging the sentence as being true in all cases in which the condition for its truth can be recognized as obtaining will fall short of being a full manifestation of the knowledge of the conditions for its truth: it shows only that the condition can be recognized in certain cases, not that we have a grasp of what, in general, it is for that condition to obtain even in those cases when we are incapable of recognizing that it does’ [27, p. 225].

  76. 76.

    [29, pp. 3, 35].

  77. 77.

    [29, p. 37]. For this tripartite conception of the ‘theory of meaning’, see [86, §3].

  78. 78.

    [29, p. 36]. To advert a misunderstanding, the notion of ‘implicit knowledge’ discussed here is not that of [8]. For a discussion of game semantics in terms of the latter, see [70].

  79. 79.

    [79, pp. 36–37].

  80. 80.

    Compare [27, p. 451]. See also footnote 1 above.

  81. 81.

    See also [27, p. 217].

  82. 82.

    [29, pp. 45–46].

  83. 83.

    [29, p. 46].

  84. 84.

    This might explain why Ranta chose simply to by-pass the Manifestation Argument in [69, p. 386].

  85. 85.

    The standard ‘behaviourist’ readings of the Manifestation Argument consists in transcribing it in terms of Quine’s ‘dispositions to verbal behaviour’, e.g., dispositions to assent or dissent from a sentence when its truth condition obtains or fails to obtain. See [82, pp. 38f.]. There are passages where Dummett criticizes Quine’s impoverished conception of language use, e.g., [28, p. 614], that should alert one to the fact that this transcription could not be faithful to Dummett’s views. Furthermore, dispositions to assent or dissent are meant to provide a valuation of atomic propositions, they could not be what Dummett, who was consciously shedding valuations, was looking for.

  86. 86.

    [82, p. 61].

  87. 87.

    [82, p. 50]. One may wish to speak here more generally about ‘expressions’, instead of ‘statements’.

  88. 88.

    The example of ‘dialectical games’ is particularly apt, since they were played before Aristotle ushered logic by introducing his syllogistic in Prior Analytics. The point is historical but serves to illustrate that the introduction of logical rules can be seen as making explicit rules already in use in a practice. What made Athens in the fourth century BCE peculiar was the regimentation of those ‘dialectical games’, which forced one to provide training for them in the form of recipes, that were eventually to become Aristotle’s syllogistic.

  89. 89.

    I got this notion from reading [77].

  90. 90.

    It should be understood, of course, that what is at stake here is not a revival of the ‘verificationism’ of the logical positivists.

  91. 91.

    [29, p. 74].

  92. 92.

    See [44, pp. 250–73] for a paper with this very title.

  93. 93.

    [44, p. 255]. The point expressed here in Hintikka’s last sentence is quite correct, inasmuch that the contrary claim would embroil its supporters in ridiculous claims about the fact that chess players would not know how to play chess unless they would know a winning strategy for all possible configurations of the board. Winning strategies are known for some simple configurations close to check mate, but it would be ridiculous to claim that one who does not know them does not know how to play chess.

  94. 94.

    [44, p. 257].

  95. 95.

    For example, when in a Hintikka game P has to choose which of \(A \vee B\) she should defend, she gets her answer from the model. This corresponds to the intuitionist notion of disjunction.

  96. 96.

    See [68, p. 203] and [48, pp. 158–59].

References

  1. Abramsky, S. 1997. “Semantics of Interaction: An Introduction to Game Semantics.” In Semantics and Logics of Computation, edited by A. M. Pitts and P. Dybjer, 1–31. Cambridge, MA: Cambridge University Press.

    Chapter  Google Scholar 

  2. Abramsky, S. 2006. “Socially Responsive, Environmentally Friendly Logic.” In Truth and Games. Essays in Honour of Gabriel Sandu, edited by T. Aho and A.-V. Pietarinen, 17–45. Helsinki: Societas Philosophicas Fennica.

    Google Scholar 

  3. Abramsky, S., and R. Jagadeesan. 1994. “Games and Full Completeness for Multiplicative Linear Logic.” Journal of Symbolic Logic 59:543–74.

    Article  Google Scholar 

  4. Aho, T., and A.-V. Pietarinen, eds. 2006. Truth and Games. Essays in Honour of Gabriel Sandu. Special issue of Acta Philosophica Fennica 78.

    Google Scholar 

  5. Annas, J. 1981. An Introduction to Plato’s Republic. Oxford: Clarendon Press.

    Google Scholar 

  6. Beall, J. C., and G. Restall. 2006. Logical Pluralism. Oxford: Clarendon Press.

    Google Scholar 

  7. Belnap, N. 1962. “Tonk, Plonk and Plink.” Analysis 22:130–34.

    Article  Google Scholar 

  8. van Benthem, J. 1991. “Reflections on Epistemic Logic.” Logique et Analyse 133–134:5–14.

    Google Scholar 

  9. van Benthem, J., G. Heinzmann, M. Rebuschi, and H. Visser, eds. 2006. The Age of Alternative Logics. Assessing Philosophy of Logic and Mathematics Today. Dordrecht: Springer.

    Google Scholar 

  10. Blass, A. 1992. “A Game Semantics for Linear Logic.” Annals of Pure and Applied Logic 56:183–220.

    Article  Google Scholar 

  11. Brandom, R. 1983. “Asserting.” Noûs 17:637–40.

    Article  Google Scholar 

  12. Brandom, R. 1994. Making It Explicit. Reasoning, Representing & Discursive Commitment. Cambridge, MA: Harvard University Press.

    Google Scholar 

  13. Brandom, R. 2000. Articulating Reasons. An Introduction to Inferentialism. Cambridge, MA: Harvard University Press.

    Google Scholar 

  14. Brandom, R. 2008. Between Saying and Doing. Towards an Analytic Pragmatism. Oxford: Oxford University Press.

    Book  Google Scholar 

  15. Carroll, L. 1895. “What the Tortoise Said to Achilles.” Mind n.s., 4: 278–80.

    Article  Google Scholar 

  16. Castelnérac, B., and M. Marion. 2009. “Arguing for Inconsistency: Dialectical Games in the Academy.” In Acts of Knowledge: History, Philosophy and Logic. Essays Dedicated to Göran Sundholm, edited by G. Primiero and S. Rahman, 37–76. London: College Publication.

    Google Scholar 

  17. Church, A. 1956. Introduction to Mathematical Logic. Princeton, NJ: Princeton University Press.

    Google Scholar 

  18. Collingwood, R. G. 1938. The Principles of Art. Oxford: Clarendon Press.

    Google Scholar 

  19. Collingwood, R. G. 1939. An Autobiography. Oxford: Clarendon Press.

    Google Scholar 

  20. Corcoran, J. 1974. “Aristotle’s Natural Deductive System.” In Ancient Logic and Its Modern Interpretations, edited by J. Corcoran, 85–131. Dordrecht: D. Reidel.

    Google Scholar 

  21. di Cosmo, R., and D. Miller. 2010. “Linear Logic.” In The Stanford Encyclopedia of Philosophy, edited by E. N. Zalta. http://plato.stanford.edu/entries/logic-linear/#ComSciImp/.

  22. Davidson, D. 1984. Inquiries into Truth and Interpretation. Oxford: Clarendon Press.

    Google Scholar 

  23. Davidson, D. 2001. Subjective, Intersubjective, Objective. Oxford: Clarendon Press.

    Book  Google Scholar 

  24. Dosen, K. 1989 “Logical Constants as Punctuation Marks.” Notre Dame Journal of Formal Logic 30:362–81.

    Article  Google Scholar 

  25. Dubucs, J. 2002. “Feasibility in Logic.” Synthese 132:213–37.

    Article  Google Scholar 

  26. Dubucs, J., and M. Marion. 2003. “Radical Anti-realism and Substructural Logics.” In Philosophical Dimensions of Science. Selected Contributed Papers from the 11th International Congress of Logic. Methodology, and the Philosophy of Science, Krakow, 1999, edited by A. Rojszczak† , J. Cachro, and G. Kurczewski, 235–49. Dodrecht: Kluwer.

    Google Scholar 

  27. Dummett, M. A. E. 1978. Truth and Other Enigmas. London: Duckworth.

    Google Scholar 

  28. Dummett, M. A. E. 1981. Frege. Philosophy of Language. London: Duckworth.

    Google Scholar 

  29. Dummett, M. A. E. 1993. The Seas of Language. Oxford: Clarendon Press.

    Google Scholar 

  30. Dutilh Novaes, C. 2007. Formalizing Medieval Logical Theories. Suppositio, Consequentiae and Obligationes. Dordrecht: Springer.

    Google Scholar 

  31. Felscher, W. 1985. “Dialogues, Strategies, and Intuitionistic Provability.” Annals of Pure and Applied Logic 28:217–54.

    Article  Google Scholar 

  32. Felscher, W. 1986. “Dialogues as a Foundation for Intuitionistic Logic.” In Handbook of Philosophical Logic, edited by D. Gabbay and F. Guenthner, vol. III, 341–72. Dordrecht: D. Reidel.

    Google Scholar 

  33. Fontaine, M., and J. Redmond. 2008. Logique Dialogique: une introduction, Volume 1: Méthode de Dialogique: Régles et Exercices. London: College Publications.

    Google Scholar 

  34. Gabbay, D., and F. Guenthner, eds. 1986. Handbook of Philosophical Logic, vol. III. Dordrecht: D. Reidel.

    Google Scholar 

  35. Gentzen, G. 1969. The Collected Papers of Gerhard Gentzen, edited by M. E. Szabo. Amsterdam: North Holland.

    Google Scholar 

  36. Girard, J.-L. 2001. “Locus Solum.” Mathematical Structures in Computer Science 11:301–506.

    Article  Google Scholar 

  37. Habermas, J. 1981. The Theory of Communicative Action, vol. 1. Boston, MA: Beacon Press.

    Google Scholar 

  38. Habermas, J. 1998. On the Pragmatics of Communication. Cambridge, MA: MIT Press.

    Google Scholar 

  39. Habermas, J. 2005. Truth and Justification. Cambridge, MA: MIT Press.

    Google Scholar 

  40. Heath, J. 1998. “What Is a Validity Claim?” Philosophy and Social Cricitism 24/4:23–41.

    Article  Google Scholar 

  41. Hintikka, J. 1973. Logic, Language Games, and Information. Oxford: Oxford University Press.

    Google Scholar 

  42. Hintikka, J. 1987. “Replies and Comments.” In Jaakko Hintikka, edited by R. Bogdan, 277–344. Dordrecht: D. Reidel.

    Google Scholar 

  43. Hintikka, J. 1996. Selected Papers Volume 1, Ludwig Wittgenstein: Half Truths and One-and-a- Half Truth. Dordrecht: Kluwer.

    Google Scholar 

  44. Hintikka, J. 1998. Selected Papers Volume 4. Paradigms for Language Theory and other Essays. Dordrecht: Kluwer.

    Google Scholar 

  45. Hintikka, J., and J. Kulas. 1985. The Game of Language. Studies in Game-Theoretical Semantics and its Applications. Dordrecht: D. Reidel.

    Google Scholar 

  46. Hintikka, J., and G. Sandu. 1997. “Game-Theoretical Semantics.” In Handbook of Logic and Language, edited by J. van Benthem and A. ter Meulen, 361–410. Amsterdam: Elsevier.

    Chapter  Google Scholar 

  47. Japaridze, G. 1997. “A Constructive Game Semantics for the Language of Linear Logic.” Annals of Pure and Applied Logic 85:87–156.

    Article  Google Scholar 

  48. Keiff, L., and S. Rahman. 2010. “La dialectique, entre logique et rhétorique.” Revue de métaphysique et de morale (2):149–78.

    Google Scholar 

  49. Lewis, D. 1983. “Scorekeeping in a Language Game.” In Philosophical Papers, vol. I, 233–49. Oxford: Oxford University Press.

    Google Scholar 

  50. Lorenz, K. 1981. “Dialogical Logic.” In Dictionary of Logic as Applied in the Study of Language, edited by W. Marciszewski, 117–25. The Hague: Martinus Nijhoff.

    Google Scholar 

  51. Lorenzen, P., and K. Lorenz. 1978. Dialogische Logik. Darmstadt: Wissenschaftliche Buchgesellschaft.

    Google Scholar 

  52. Majer, O., A.-V. Pietarinen, and T. Tulenheimo, eds. 2009. Games: Unifying Logic, Language, and Philosophy. Dordrecht: Springer.

    Google Scholar 

  53. Marion, M. 2006. “Hintikka on Wittgenstein: From Language-Games to Game Semantics.” In Truth and Games. Essays in Honour of Gabriel Sandu, edited by T. Aho and A.-V. Pietarinen, 255–74. Helsinki: Societas Philosophicas Fennica.

    Google Scholar 

  54. Marion, M. 2009. “Why Play Logical Games?” In Games: Unifying Logic, Language, and Philosophy, edited by O. Majer, A.-V. Pietarinen, and T. Tulenheimo, 3–26. Dordrecht: Springer.

    Chapter  Google Scholar 

  55. Marion, M. 2009. “Radical Anti-realism, Wittgenstein, and the Length of Proofs.” Synthese 171:419–32.

    Article  Google Scholar 

  56. Marion, M. 2010. “Between Saying and Doing: From Lorenzen to Brandom and Back.” In Construction. Festschrift for Gerhard Heinzmann, edited by P. E. Bour, M. Rebuschi, and L. Rollet, 489–97. London: College Publications.

    Google Scholar 

  57. Marion, M., and M. Sadrzadeh. 2004. “Reasoning About Knowledge in Linear Logic: Modality & Complexity.” In Logic, Epistemology and the Unity of Science, Cognitive Science Series, edited by D. Gabbay, S. Rahman, J. M. Torres, and J.-P. Van Bendegem, 327–50. Dordrecht: Hermes.

    Chapter  Google Scholar 

  58. McDowell, J. 1981. “Anti-realism and the Epistemology of Understanding.” In Meaning and Understanding, edited by H. Parret and J. Bouveresse, 225–48. Berlin: de Gruyter.

    Google Scholar 

  59. McGinn, C. 1980. “Truth and Use.” In Reference, Truth and Reality, edited by M. Platts, 19–40. London: Routledge & Kegan Paul.

    Google Scholar 

  60. Pagin, P. 2004. “Is Assertion Social?” Journal of Pragmatics 36:833–59.

    Article  Google Scholar 

  61. Pagin, P. 2009. “Assertion.” In The Stanford Encyclopedia of Philosophy, edited by E. N. Zalta. http://plato.stanford.edu/entries/assertion/.

  62. Panaccio, C. 1999. Le discours intérieur de Platon à Guillaume d’Ockham. Paris: Éditions du Seuil.

    Google Scholar 

  63. Prawitz, D. 1977. “Meaning and Proofs: On the Conict Between Classical and Intuitionistic Logic.” Theoria 43:1–40.

    Google Scholar 

  64. Priest, G. 1979. “Two Dogmas of Quineanism.” Philosophical Quarterly 29:289–301.

    Article  Google Scholar 

  65. Prior, A. N. 1960. “The Runabout Inference-Ticket.” Analysis 21:38–39.

    Article  Google Scholar 

  66. Quine, W. V. O 1986. Philosophy of Logic (2nd Edition). Cambridge MA: Harvard University Press.

    Google Scholar 

  67. Rahman, S., and L. Keiff. 2005. “How to Be a Dialogician.” In Logic, Thought and Action, edited by D. Vanderveken, 359–408. Dordrecht: Springer.

    Chapter  Google Scholar 

  68. Rahman, S., and T. Tulenheimo. 2009. “From Games to Dialogues and Back.” In Games: Unifying Logic, Language, and Philosophy, edited by O. Majer, A.-V. Pietarinen, and T. Tulenheimo, 153–208. Dordrecht: Springer.

    Chapter  Google Scholar 

  69. Ranta, A. 1988. “Propositions as Games as Types.” Synthese 76:377–95.

    Article  Google Scholar 

  70. Rebuschi, M. 2009. “Implicit Versus Explicit Knowledge in Dialogical Logic.” In Games: Unifying Logic, Language, and Philosophy, edited by O. Majer, A.-V. Pietarinen, and T. Tulenheimo, 229–46. Dordrecht: Springer.

    Chapter  Google Scholar 

  71. Restall, G. 2000. An Introduction to Substructural Logics. Oxford: Clarendon Press.

    Google Scholar 

  72. Robinson, R. 1953. Plato’s Earlier Dialectic. Oxford: Clarendon Press.

    Google Scholar 

  73. Rödl, S. 2007. Self-Consciousness. Cambridge, MA: Harvard University Press.

    Google Scholar 

  74. Rückert, H. 2001. “Why Dialogical Logic?” In Essays on Non-Classical Logic, edited by H. Wansing, 165–85. Hackensack, NJ/London: World Scientific.

    Chapter  Google Scholar 

  75. Rückert, H. 2007. “Dialogues as Dynamic Framework for Logic.” Doctoral diss., University of Leiden. http://www.phil.uni-mannheim.de/fakul/phil2/rueckert/pdf/Rueckert_PhD_Dialogues.pdf.

  76. Ryle, G. 1949. The Concept of Mind. London: Hutchinson.

    Google Scholar 

  77. Scharp, K. 2003. “Communication and Content: Circumstances and Consequences of the Habermas-Brandom Debate.” International Journal of Philosophical Studies 11/1:43–61.

    Article  Google Scholar 

  78. Schmidt, D. A. 1997. “On the Need for a Popular Formal Semantics.” ACM SIGPLAN Notices 32(1):115–16.

    Article  Google Scholar 

  79. Schroeder-Heister, P., and K. Dosen, eds. 1993. Substructural Logics. Oxford: Clarendon Press.

    Google Scholar 

  80. Sellars, W. 1997. Empiricism and the Philosophy of Mind. Cambridge, MA: Harvard University Press.

    Google Scholar 

  81. Shapiro, S. 2000. “The Status of Logic.” In New Essays on the a priori, edited by P. Boghossian and C. Peacocke, 333–66. Oxford: Clarendon Press.

    Google Scholar 

  82. Shieh, S. 1998. “On the Conceptual Foundations of Anti-realism.” Synthese 115:33–70.

    Article  Google Scholar 

  83. Shieh, S. 1998. “Undecidability in Anti-realism.” Philosophia Mathematica 6:324–33.

    Google Scholar 

  84. Smiley, T. 1973. “What Is a Syllogism?” Journal of Philosophical Logic 2:136–54.

    Article  Google Scholar 

  85. Stenius, E. 1967. “Mood and Language-Game.” Synthese 17:254–74.

    Article  Google Scholar 

  86. Sundholm. G. 1986. “Proof Theory and Meaning.” In Handbook of Philosophical Logic, edited by D. Gabbay and F. Guenthner, vol. III, 471–506. Dordrecht: D. Reidel.

    Google Scholar 

  87. Tennant, N. 1979. “Language Games and Intuitionism.” Synthese 42:297–314.

    Article  Google Scholar 

  88. Tennant, N. 1987. Anti-Realism and Logic. Truth as Eternal. Oxford: Clarendon Press.

    Google Scholar 

  89. Watson, G. 2004. “Asserting and Promising.” Philosophical Studies 117:57–77.

    Article  Google Scholar 

  90. Wittgenstein, L. 1961. Tractatus Logico-Philosophicus. Translated by D. Pears and B. F. McGuinness. London: Routledge & Kegan Paul.

    Google Scholar 

  91. Wittgenstein, L. 2009. Philosophical Investigations (4th Edition). Translated by G. E. M. Anscombe, P. M. S. Hacker, and J. Schulte. Oxford: Blackwell.

    Google Scholar 

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Acknowledgments

Many thanks to Aude Bandini, Benoît Castelnérac and, especially, Helge Rückert for helpful conversations on points raised in the paper, and Shahid Rahman for comments on an earlier version.

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  1. Canada Research Chair in the Philosophy of Logic and Mathematics, Université du Québec à Montréal, Montréal, QC, Canada

    Mathieu Marion

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    Shahid Rahman

  2. Centre for Logic & Philosophy of Sc, Philosophy & Moral Science Dept., Ghent University, Blandijnberg 2, Gent, 9000, Belgium

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  3. , Département de philosophie, Université du Québec à Montréal, Succursale Centre-Ville 8888 C.P., Montreal, H3C 3P8, Canada

    Mathieu Marion

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Marion, M. (2012). Game Semantics and the Manifestation Thesis. In: Rahman, S., Primiero, G., Marion, M. (eds) The Realism-Antirealism Debate in the Age of Alternative Logics. Logic, Epistemology, and the Unity of Science, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1923-1_8

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