By Godehard Link
The philosophical strategy of this quantity is principally structuralist, utilizing logical instruments to enquire the formal constitution of varied forms of gadgets in our international, as characterized through language and as systematised by way of philosophy. This quantity quite often analyses the structural homes of collections or pluralities (with purposes to the philosophy of set theory), homogeneous items like water, and the semantics and philosophy of occasions. This ebook thereby enhances algebraic paintings that has been performed on different philosophical entities, i.e. propositions, homes, kin, or occasions. situated within the triangle of language, good judgment and philosophy, this quantity is exclusive in combining the assets of alternative ?elds in an interdisciplinary firm. 1/2 the fourteen chapters of this quantity are unique papers, complementing the gathering of the author's formerly released essays at the topic.
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Additional resources for Algebraic Semantics in Language and Philosophy
Tigers are striped. a. In revolutionary France high positions were occupied by members of political clubs. In revolutionary Prance there were high positions that were occupied by members of political clubs. b. (8) a. b. Whales will be extinct before long, Tranquilizers are widespread. Sentence (6a) has a strict universal meaning: every horse is a mammal. (6b) can only be said to be "quasi-universal": most tigers (or all typical tigers) are striped. (7a) has again the quasi-universal reading: A high position during the French revolution was, as a rule, occupied by a member of some political club.
P(a®b®c®d) ^ *P(b®d) a. b. (All) water is wet. \/x (Px —> Qx) (44) a. b. The water of the Rhine is dirty. Q (p,xPx) Px: x is (a quantity of) Rhine water (45) a. b. This ice cube is water. P LX(X > a) (46) a. b. The gold in Smith's ring is old, but Smith's ring is not old. 2 The Logic of Plurals and Mass Terms (LPM) (43) (contraction) Px: x is (a quantity of) water a: this ice cube; Px: as in (43) LPM is a first order predicate calculus with the usual logical constants '-i', 'V, 'A', '->•', 'o', 'V, '3', the description operator denoted by V, and the abstraction operator 'A'15 The syntactic variables are, for formulas of LPM, '$'> '^'5 'x'; for individual terms, 'a', '&', 'c'; for variables, 'a;', 'j/', V; for (1-place) predicates, 1P\ 1Q\ These symbols can also appear with primes and indices.
B. The animals died. So every animal died, *Q(a*xPx) => Vx (Px -> Qx) For non-distributive predicates we have, of course, no such result, witness carry: a® b might be in the extension of carry while a or b alone is not. Notice that these predicates enter formalizations unstarred. To illustrate, (31) a. b. The children gather around their teacher. , distributive predicates working on plural terms have to be starred, all the other predicates must not be. For distributivity seems to be a lexical feature.