By Paul Gochet
1. value OF the topic In 1900, in A severe Exposition of the Philosophy of Leihniz, Russell made the next statement: "That all sound philosophy may still start with an research of propositions is a fact too glaring, maybe, to call for a proof". 1 40 years later, the curiosity aroused by means of this proposal had now not diminished. C. J. Ducasse wrote within the magazine of Philosophy: "There is likely to be no doubt extra uncomplicated for the speculation of information than that of the character of two propositions and their family to judgments, sentences, proof and inferences". this day, the nice variety of guides at the topic is evidence that it truly is nonetheless of curiosity. one of many difficulties raised by means of propositions, the matter of deter mining no matter if propositions, statements or sentences are the first bearers of fact and falsity, is even within the eyes of Bar-Hillel, "one of the key goods that the long run philosophy oflanguage must discuss". three gave an accurate precis of the location while he wrote in his Ph. Devaux Russell (1967): in view that Peano and Schroder who, in truth, adhered extra faithfully to Boole's good judgment of periods, the logical and epistemological prestige of the proposition including its research haven't ceased to be the item of effective philosophical controversies. and particularly so because the institution of latest symbolic good judgment, the rules four of that have been laid out through Russell and Whitehead. * 2.
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Extra info for Outline of a Nominalist Theory of Propositions: An Essay in the Theory of Meaning and in the Philosophy of Logic
Obviously, in proving the existence of an optimum in the analysis, we have not yet proven the non-existence of a maximum; that is to say, the inexistence of propositional atoms refractory to all further analysis. We have, however, at least deprived the realist of the support he had hoped to find in logical syntax and there by displaced the burden of proof. In a formalized system, the distinction between complete and incomplete proofs is clear. The same is true for the distinction between complete and incomplete axiom systems.
The resemblance between schematic letters and variables poses no problem. We shall therefore concentrate on the differences. (a) A variable is an 'indeterminate name'. It is linked to the constants in its value-range by the semantic relation of denotation. A schematic letter is linked to what it schematizes by a syntactic relation: it abstracts the structure common to several sentences. In other words, while the variable is related to the objects in its range by the semantic relation of name to object named, the schematic letter is related to what it schematizes by the syntactic relation linking a variable to its substituends.
V. O. Quine, 'Replies', Synthese 19 (1963) 287; repro in D. Davidson and J. ), Words and Objections, Reidel, Dordrecht, 1969, p. 315. 5 K. H. Potter, 'Negation, Names and Nothing', Philosophical Studies, (1964) 52. 6 Ch. Cheng and M. Resnik, 'Ontic Commitment and the Empty Universe', Journal of Philosophy LXII, (1965) 361. 7 G. J. Warnock, 'Metaphysics in Logic', Proceedings of the Aristotelian Society, 19501951, repro in A. 87. , p. 81. , p. 87. , p. 87. , p. 88. , p. 87. 13 R. Carnap, 'Empiricism, Semantics and Ontology', Revue Internationale de Philosophie (1950); repr.