We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two kinds of import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotle's system appears then as a fragment of a broader system which can be developed by using FOL. 1 The case of Frege is more complex; in his Begriffsschrift, he presents a square he assumes to be valid; but he formalizes the propositions in exactly the same way as Russell, and these formalizations do invalidate the square. 2 See for instance Quine 1950, Chapter 15, French translation (p. 96) and Russell 1959, French translation, Chapter VI (p. 83)where both authors assume that the universals do not have an import, when translated by conditionals in the modern symbolism.
One of the most prominent myths in analytic philosophy is the socalled "Fregean Axiom", according to which the reference of a sentence is a truth value. In contrast to this referential semantics, a use-based formal semantics will be constructed in which the logical value of a sentence is not its putative referent but the information it conveys. Let us call by "Question Answer Semantics" (thereafter: QAS) the corresponding formal semantics: a non-Fregean many-valued logic, where the meaning of any sentence is an ordered n-tupled of yes-no answers to corresponding questions. A sample of philosophical problems will be approached in order to justify the relevance of QAS. These include:(1) illocutionary forces, and the logical analysis of speech-acts;(2) the variety of logical negations, and their characterization in terms of restricted ranges of logical values;(3) change in meaning, and the use of dynamic oppositions for belief sets.
The aim of this paper is to make sense of the Keynes-Johnson octagon of oppositions. We will discuss Keynes' logical theory, and examine how his view is reflected on this octagon. Then we will show how this structure is to be handled by means of a semantics of partition, thus computing logical relations between matching formulas with a semantic method that combines model theory and Boolean algebra.
A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.
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