Abstract
This essays examines Hintikka’s trajectory through Semantic Representationalism from the classical, i.e. Wittgensteinian, Picture Theory of Meaning to Game-Theoretical Semantics. It starts by asking what makes a sentence a representation of a fact and what conditions enable a sentence to represent something. It is argued that at the end of his journey Hintikka conceives of the representational function of sentences as arising from the norms that regulate their place in verification practices. As a consequence of it, the analysis of semantic representation in terms of an isomorphic relation between sentences and facts is replaced by a theory based on the concept of winning strategy in a semantical game. This maneuver allows Hintikka to emphasize that semantical representation is shaped by normative constraints that rule the specific activities involved in those games.
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Notes
- 1.
In what follows the term ‘fact’ will be used to cover real-world facts as well as facts of any possible world. In commenting on the Tractatus’ ontology many scholars have traced out this distinction by means of the terms ‘fact’ and ‘states of affairs’. Since Hintikka has chosen the first alternative, I will opt for it too.
- 2.
To carry out this extension, Hintikka explicitly assumes that natural language can be translated into Principia Mathematica’s symbolism, or at least the part of that symbolism that is needed to state quantification theory. See [8, p. 31 and note 10].
- 3.
Admitedly, ‘successfully’ is rethorical, because Hintikka is assuming that every object in the universe of discourse has a name. Thus, Hintikka is abiding by the substitutional view of quantification, a commitment which he will finally release from twenty years later. See his [15] to spot the assumption that makes the difference.
- 4.
- 5.
In Hintikka’s journey this is the first moment in which the reader can detect what he has described as “my basic philosophical orientation”. This orientation is closely akin to Kant’s and emphasizes “the role of what we humans do in all parts of philosophy” [14, pp. 26f.] The significance of this Kantian perspective on semantic representation becomes more noticeable as Hintikka moves away from Tractarian PT and approaches GTS. He has even written that GTS is “the truly Kantian theory of the semantical basis of the most central parts of modern logic” [14, p. 30]. And in another place he speaks of “my Kantian (‘Copernican’) bent of mind” [17, p. 40]. However, in what follows I will not bring specific elements of Kant’s philosophy to bear on the analysis of Hintikka’s views on semantical representation.
- 6.
It could be said that what is really at stake in an indoor game is how to embed a sentence in a model set, while in an outdoor game what matters is whether a sentence is true in a model. However, I am not aiming at stressing such a difference, i.e., between questions of consistency and questions of truth (in a model). I am not, because I hold that Hintikka moved from a representationalist view of language and thought to a sort of pragmatic conception, and the position from which he departed already was a semantic, noy a syntactic, one. In other words, indoor games are vicariously semantic, so to say.
- 7.
An important exception to this requirement is provided by the semantical phenomenon that Hintikka calls strategic meaning. It so happens in the semantical analysis of conditionals, negation or anaphoric relations, to mention a few examples, that which choice one player makes in a semantical game depends on another choice the same player made in one subgame. In those cases a player’s strategy in a semantical game is a function of a strategy followed in a previously played subgame. These interesting matters are dealt with in [11, 22].
- 8.
- 9.
It can be seen that the substitutional view of quantification survived the transition from a Picture Theory of Meaning to Game-Theoretical Semantics. See note 24 for a flash of the reasons that finally led Hintikka to give up that view.
- 10.
Much later Hintikka has insisted that semantical games are not games played in using language, and that the players’ moves in a semantical game cannot be identified with any speaker’s linguistic acts. The place of semantical games in semantical analysis is an unusual one, because we do not play them. “We rely on them when we speak” [17, p. 69].
- 11.
Wittgenstein uses the term ‘proposition’ (‘Satz’) instead of ‘sentence’.
- 12.
“Propositions cannot represent logical form: it is mirrored in them./What finds its reflection in language, language cannot represent./What expresses itself in language, we cannot express by means of language./Propositions show the logical form of reality./They display it” (4.121).
- 13.
‘Absolutism’ is the term coined by Stegmüller to describe Wittgenstein’s philosophical stance. Instead of characterizing the Tractarian view of logical form by claiming that logic is absolute, that is, that there is no alternative to the kind of logic our language embodies, Hintikka follows the route of conceiving logic as language and then adds that language is the universal medium of thought and, in general, representation. See [16, 20, 27].
- 14.
Tractatus, 4.11: “The totality of true propositions is the whole of natural science (or the whole corpus of the natural science)”.
- 15.
See Tractatus §§ 2.033, 2.15, 2.151, 2.173 - 2.18, 3.14 - 3.1432, 3.31 - 3.313, 3.327, 4.0311 - 4.0312, 4.12 - 4.128, 5.13 - 5.132, 5.2 - 5.232, 5.24 - 5.242, 5.4 - 5.41, 5.4731, 5.54 - 5.5423, 5.55 - 5.5571, 6.12, 6.124, 6.13.
- 16.
It is the first chapter of [25, Part II], entitled “Atomic Propositional Thought”.
- 17.
Landini has argued that among Russell’s logical forms some are abstract general facts whereas others are objects. See [24, pp. 58ff.]. Landini comes close to the position here argued for save that he does not explain why logical forms constitute transcendental conditions for semantical representation. He is aware of the fact that if logical forms occur in sentences’ senses as other entities, i.e. individuals and universals, do, then nothing has been said about the pattern into which all these components have to fit. He even comes closer and acknowledges that Russell needs resorting to a battery of concepts (‘predicate’, ‘dual relation’, ‘complex’, ‘individual’, universal’, logical form’ and son on) whose use is forbidden to him. They are precisely Wittgenstein’s formal concepts—what explains why Wittgenstein considered Russell’s maneuvers in [25] as profoundly mistaken. However, Landini leaves one point without explanation, namely why Wittgenstein took these concepts to be pseudo-concepts or, what amounts to the same, why those concepts refer to a transcendental domain. Landini’s final view is that Wittgenstein’s criticisms apply to every theory that attempts to do semantics. Provided that Landini thinks this criticisms cannot be right, he condemns Wittgenstein without assessing all his arguments.
- 18.
“A proposition is not a blend of words.—Just as a theme in music is not a blend of notes.)/A proposition is articulate” (Tractatus, 3.141).
- 19.
That is, in Russell’s terminology the proposition expressed by a sentence is what Wittgenstein refers to as the sentence’s sense. See [25, p. 130].
- 20.
Hintikka uses ‘artificial’ as synonymous with ‘conventional’. See [8, p. 48].
- 21.
The fact that Hintikka places the term ‘natural’ between quotes suggests that he is not supporting a naturalistic interpretation of the role played by the isomorphism’s key.
- 22.
Normativity comes in two varieties: the evaluative variety and the deontic variety. The variety involved in GTS is evaluative. In saying of a player’s strategy that is a winning one, the strategy is evaluated, that is, classified as an adequate one provided that his or he choice aims at winning the game. As for the distinction between evaluative and deontic normativity, see [3].
- 23.
This is an extremely important philosophical point, for it is usually assumed that truth and other semantic relations are value-free. On this matter Hintikka is somewhat close to pragmatists like Sellars and Brandom, who reject that the relations between language and reality exist independently of human activities, a view that Hintikka emphatically denies. See Hintikka [15, p. 44].
- 24.
Such a profile may change depending on the specific demands the theoretical situation pose. For example, it can be assumed that the result of my seeking and finding a witness individual in a semantical game is independent of some of Nature’s previous choices. This amounts to moulding the interpretation of classical quantifiers on a non-classical net of dependence/independence relations. Since the 1990s Hintikka and Gabriel Sandu have developed a logical theory that articulates such an insight, i.e. the so-called IF logic. Another example is provided by the law of excluded middle. In classical GTS my having a winning strategy in a semantical game implies that Nature loses; and the other way around. However, one could deem it wise to cancel this constraint and grant that in certain conditions neither Nature nor I have a winning strategy. If so, the law of excluded middle is not underwritten. To go deeper into these interesting lines of research, see [15, 23].
- 25.
- 26.
(G. if) is a simplified version of a much more complex and interesting rule for dealing with conditional sentences, (G. cond), which is introduced and applied in Hintikka and Carlson (1979) as well as in [22], is sensitive to whatever dependency relations there could be between the antecedent and the consequent of a conditional. No such relations exist in [B], which explains why (G. if) is in charge en this case.
- 27.
Hintikka speaks of a “transcendental refutation” of certain views in philosophical logic and semantics in [12, pp. 33ff.]. In this case, his argument is that we can deduce the incorrectness of certain views on meaning, as well as the correction of GTS, by reflecting on the relation of meaning to “the activities through we come to know the relevant propositions. [...] In game-theoretical semantics, these verification processes are conceptualized as games against a recalcitrant Nature, who tries to frustrate my attempts” [12, p. 34].
- 28.
Further rules of this kind are introduced by Hintikka in [11, pp. 176f.].
- 29.
The relativity of logical form has been argued for by Hintikka in [13].
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Acknowledgements
The research leading to this essay was funded by the Spanish Ministerio de Educación y Ciencia (FFI2010-15704), and by the Andalusian Council for Innovación, Ciencia y Empresa (HUM-4099). I acknowledge my debt to Gabriel Sandu and Neftalí Villanueva for their thoughtful reading of previous versions of the text. Their remarks made it possible to zoom in on matters that I had overlooked and to correct a few mistakes.
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Acero, J.J. (2018). From Pictures to Semantical Games: Hintikka’s Journey Through Semantic Representationalism. In: van Ditmarsch, H., Sandu, G. (eds) Jaakko Hintikka on Knowledge and Game-Theoretical Semantics. Outstanding Contributions to Logic, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-62864-6_2
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