By Jaakko Hintikka
Since the 1st bankruptcy of this publication provides an intro duction to the current nation of game-theoretical semantics (GTS), there is not any aspect in giving a briefer survey right here. in its place, it can be valuable to point what this quantity makes an attempt to do. the 1st bankruptcy supplies a brief intro duction to GTS and a survey of what's has comprehensive. bankruptcy 2 places the company of GTS into new philo sophical viewpoint through bearing on its easy rules to Kant's phi losophy of arithmetic, house, and time. Chapters 3-6 are samples of GTS's accomplishments in figuring out other forms of semantical phenomena, in most cases in typical languages. past featuring effects, a few of these chapters even have different goals. bankruptcy three relates GTS to a fascinating line of logical and foundational stories - the so-called practical interpretations - whereas bankruptcy four ends up in definite very important methodological theses. bankruptcy 7 marks an program of GTS in a extra philo sophical course by means of criticizing the Frege-Russell thesis that phrases like "is" are multiply ambiguous. This leads in flip to a feedback of modern logical languages (logical notation), which when you consider that Frege were in response to the ambi guity thesis, and likewise to definite methodological sug gestions. In bankruptcy eight, GTS is proven to have vital implications for our realizing of Aristotle's doctrine of different types, whereas bankruptcy nine maintains my past feedback of Chomsky's generative method of linguistic theorizing.
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Extra info for The Game of Language: Studies in Game-Theoretical Semantics and Its Applications
7 Cf. here chapter 8 below . 8 Aristotle uses different question words (and phrases) in ancient Greek as names for his categories; he introduces categories as semantically determined classes of simple predicates; he treats categories as the widest genera of entities we can meaningfully consider together; and he frequently says that the several categories go together with different senses or uses of t'O e:1'V(ll, the Greek verb for being . 9 See Jaakko Hintikka, The Semantics of Questions and the Questions of Semantics (Acta Philosophica Fennica, vol.
23 As was first pointed out by Dana Scott [IIA GameTheoretic Interpretation of Logical Formulae ll , McCarthy Seminar, Stanford University, July 1968 (unpublished)], we can, for instance, in this way obtain an eminently natural motivation for GOdel's interpretation of elementary arithmetic (see the preceding note). For other uses of functional interpretations, cf. Jaakko Hintikka and Lauri Carlson, .. Conditionals, Generic Quantifiers, and Other Applications of Subgames ll , in Saarinen, Game- Theoretical Semantics, pp.
Why does this make a difference? The answer must lie in the requirement that each subgame is played out completely in its own right. Now what does it mean, in game-theoretical terms, to play a game? The idea of a normal form gives us an answer. 6 To play a game is for each player to choose a strategy. Such strategy choices by all players conjointly uniquely determine the course and the outcome of the game. Hence, the upshot of the idea of completely playing out a subgame is that each player chooses a strategy and at least one of them reveals his or her strategy to his or her opponent.