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Moschovakis's notion of meaning as applied to linguistics

from ARTICLES

Published online by Cambridge University Press:  31 March 2017

By
Michiel van Lambalgen  and
Fritz Hamm
Edited by
Matthias Baaz ,
Sy-David Friedman  and
Jan Krajíček
Matthias Baaz
Affiliation:
Technische Universität Wien, Austria
Sy-David Friedman
Affiliation:
Universität Wien, Austria
Jan Krajíček
Affiliation:
Academy of Sciences of the Czech Republic, Prague
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Summary

Wenn man nicht weiß was man selber will,muß man zuerst wissen was die anderen wollen.

General Stumm von Bordwehr

§1. Introduction: Moschovakis's approach to intensionality. G. Frege introduced two concepts which are central tomodern formal approaches to natural language semantics; i.e., the notion of reference (denotation, extension, Bedeutung) and sense (intension, Sinn) of proper names2. The sense of a proper name is wherin the mode of presentation (of the denotation) is contained. For Frege proper names include not only expressions such as Peter, Shakespeare but also definite descriptions like the point of intersection of line l1 and l2 and furthermore sentences which are names for truth values. Sentences denote the True or the False. The sense of a sentence is the proposition (Gedanke) the sentence expresses. In the tradition of possible world semantics the proposition a sentence expresses ismodelled via the set ofworlds in which the sentence is true. This strategy leads to well known problems with propositional attitudes and other intensional constructions in natural languages since it predicts for example that the sentences in (1) are equivalent.

  1. (1) a. Jacob knows that the square root of four equals two.

  2. b. Jacob knows that any group G is isomorphic to a transformation group.

Even an example as simple as (1) shows that the standard concept of proposition in possible world semantics is not a faithful reconstruction of Frege's notion sense.

Frege developed his notion of sense for two related but conceptually different reasons. We already introduced the first one by considering propositional attitudes. The problem here is how to develop a general concept which can handle the semantics of Frege's ungerade Rede. The second problem is how to distinguish a statement like a = a which is rather uninformative from the informative statement a = b or phrased differently how to account for the semantic difference between (2-a) and (2-b).

  1. (2) a. Scott is Scott.

  2. b. Scott is the author ofWaverly.

Frege's intuitive concept of sense therefore was meant both to model information and provide denotations for intensional constructions.

[12] develops a formal analysis of sense and denotation which is certainly closer to Frege's intentions than is possible world semantics. Moschovakis's motivations are (at least) twofold. The first motivation is to give a rigorous definition of the concept algorithm [13] and thereby provide the basics for a mathematical theory of algorithms.

Type
Chapter
Information
Logic Colloquium '01 , pp. 255 - 280
Publisher: Cambridge University Press
Print publication year: 2005

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References

[1] K., Doets, From logic to logic programming, The MIT Press, Cambridge,MA, 1994.
[2] D., Dowty, Word meaning and Montague grammar, Reidel, Dordrecht, 1979.
[3] G., Frege, On sense and denotation, Translations from the PhilosophicalWritings of Gottlob Frege (P., Geach and M., Black, editors), Blackwell, Oxford, 1952.
[4] G., Frege, Sinn und Bedeutung, G. Frege: Funktion, Begriff, Bedeutung. Fünf logische Studien (G., Patzig, editor), Vandenhoeck, Göttingen, 1962.
[5] F., Hamm and M., van Lambalgen, Event calculus, nominalisation and the progressive, Linguistics and Philosophy, vol. 26 (2003), pp. 381–458.Google Scholar
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[9] R., Montague, The proper treatment of quantification in ordinary english, Formal philosophy (R., Thomason, editor), Yale University Press, Yale, 1974.
[10] Y., Moschovakis, The formal language of recursion, The Journal of Symbolic Logic, vol. 54 (1989), pp. 1216–1252.Google Scholar
[11] Y., Moschovakis, A mathematical modeling of pure recursive algorithms, Logic at Botik –89 (A., Meyer and M., Taitslin, editors), Lecture Notes in Computer Science, vol. 363, Springer Verlag, Berlin, 1989.
[12] Y., Moschovakis, Sense and denotation as algorithm and value, Logic colloquium –90 (J., Oikkonen and J., Väanänen, editors), Lecture Notes in Logic, vol. 2, Springer, Berlin, 1994, pp. 210–249.
[13] Y., Moschovakis, What is an algorithm, Mathematics unlimited – 2001 and beyond (B., Engquist and W., Schmid, editors), Springer, Berlin, 2001.
[14] M. P., Shanahan, Solving the frame problem, The MIT Press, Cambridge,MA, 1997.
[15] R. F., Stärk, From logic programs to inductive definitions, Logic: from foundations to applications (European Logic Colloquium –93) (W., Hodges, M., Hyland,C., Steinhorn, and J., Truss, editors), Oxford University Press, Oxford, 1996, pp. 453–481.
[16] P. J., Stuckey, Negation and constraint logic programming, Information and Computation, vol. 118 (1995), pp. 12–33.Google Scholar

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