Page 272 - Encyclopedia of Philosophy of Language

Language and Logic
3. FurtherConnections
Although Fine does not develop in any depth the implications of his theory for the semantics of natural language, there are interesting connections with the disciplines working in the tradition of R. Montague (1973). In the Theory of Generalized Quantifiers, the phrase 'every farmer' is interpreted as the set of all properties satisfied by all and only all farmers. Now, a uniform semantic interpretation of noun phrases is achieved by identifying an individual with the set of allitsproperties, thus assimilatingproper namesto the semantic category of quantifier phrases. The theory of arbitrary objects suggests the opposite identification. Here the quantifier phrase 'every farmer' is assimilated
to the semantic category of proper names, i.e., the category of entities, albeit arbitrary ones.
Bibliography
Barth E M 1974 The Logic of Articles in Traditional Phil- osophy. Reidel, Dordrecht
Fine K 198Sa Natural deduction and arbitrary objects. Jour- nal of Philosophical Logic 14:57-107
Fine K 1985b Reasoning with Arbitrary Objects. Blackwell, Oxford
Lewis D 1972 General semantics. In: Davidson D, Harman G (eds.) Semantics of Natural Language. Reidel, Dordrecht Montague R 1973 The proper treatment of quantification in ordinary English. In: Hintikka K J J, Moravcsik J M E, Suppes P (eds.) Approaches to Natural Language. Reidel,
Dordrecht
This article gives an account of Aristotle's con- tribution to logic. Although Aristotle did not use the word 'logic' in the modern sense, the scope of the study of logic was determined by the Organon—the collection of his logical treatises. This collection com- prises: The Categories, De Interpretation*, the Prior Analytics, the Topics, the De Sophisticis Elenchis, and the Posterior Analytics. This article examines the first three treatises.
1. The Categories
Since antiquity it has been suggested that in this work Aristotle classifies types of things by using language as a clue to the differences between them. Aristotle argues that expressions are simple or compound. Every simple expression corresponds to a category. Compound expressions are the bearers of truth values. Aristotle gives a list of 10 categories: 'substance' (man, horse); 'quantity' (two cubits long); 'quality' (white); 'relation' (greater); 'place' (in the Lyceum); 'tim e' (last year); 'situation' (lies); 'state' (is armed); 'action' (cuts); 'passion' (is cut).
Among substances Aristotle distinguishes primary and secondary substances. Primary substances cor- respond to individual objects like Socrates. Primary substances are not predicative in that they are not asserted of a subject. They are the ultimate subject of predication. Secondary substances are the genera and the species which include primary substances. They are predicative in that they might be asserted of the
subject. For Aristotle primary substances are the most real things. He makes clear that sentences involving secondary substances are dependent on sentences involving primary substances. For instance, he explains universal predication in terms of singular propositions. He says that a term A is predicate of all of another term B when no instance of B can be found of which A cannot be predicated. Similarly, he says that the sentence No A is Bis equivalent to No Bis A, because if A were predicated of an object c to which B is applied, it would no longer be true that B is not applied to any object to which A is applied, because c would be one of the A's.
In spite of this predicative dependence, Aristotle's logic concerns primarily secondary substances. The reason behind this approach seems to be that Aristotle considered that there cannot be a science of primary substances.
2. De Interpretation*
Aristotle begins his analysis of categorical (assertive) sentences with definitions of the expressions 'noun,' 'verb.' Nouns and verbs in themselves are significative, but they lack a truth value. Aristotle holds that a noun is a sound with conventional meaning, without time reference and whose parts lack independent meaning. A verb is like a noun except that it has time reference and that it indicates predication. Among sentences Aristotle distinguishes the categorical sentences as the only bearers of truth value and as such they are dis-
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Aristotle and Logic V. SanchezValencia