more on this theme     |     more from this text

Single Idea 8475

[filed under theme 5. Theory of Logic / G. Quantification / 4. Substitutional Quantification ]

Full Idea

The substitution view of quantification explains 'there-is-an-x-such-that x is a man' as true when it has a true substitution instance, as in the case of 'Socrates is a man', so the quantifier can be read as 'it is sometimes true that'.

Gist of Idea

The substitution view of quantification says a sentence is true when there is a substitution instance

Source

Alex Orenstein (W.V. Quine [2002], Ch.5)

Book Ref

Orenstein,Alex: 'W.V. Quine' [Princeton 2002], p.103

A Reaction

The word 'true' crops up twice here. The alternative (existential-referential) view cites objects, so the substitution view is a more linguistic approach.

The 14 ideas from Alex Orenstein

8452 Traditionally, universal sentences had existential import, but were later treated as conditional claims [Orenstein]
8454 The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein]
8457 The Principle of Conservatism says we should violate the minimum number of background beliefs [Orenstein]
8458 Just individuals in Nominalism; add sets for Extensionalism; add properties, concepts etc for Intensionalism [Orenstein]
8471 Three ways for 'Socrates is human' to be true are nominalist, platonist, or Montague's way [Orenstein]
8465 Mereology has been exploited by some nominalists to achieve the effects of set theory [Orenstein]
8474 Unlike elementary logic, set theory is not complete [Orenstein]
8472 Sentential logic is consistent (no contradictions) and complete (entirely provable) [Orenstein]
8476 Axiomatization simply picks from among the true sentences a few to play a special role [Orenstein]
8473 The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein]
8475 The substitution view of quantification says a sentence is true when there is a substitution instance [Orenstein]
8477 People presume meanings exist because they confuse meaning and reference [Orenstein]
8484 If two people believe the same proposition, this implies the existence of propositions [Orenstein]
8480 S4: 'poss that poss that p' implies 'poss that p'; S5: 'poss that nec that p' implies 'nec that p' [Orenstein]