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Single Idea 8476

[filed under theme 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL ]

Full Idea

In axiomatizing, we are merely sorting out among the truths of a science those which will play a special role, namely, serve as axioms from which we derive the others. The sentences are already true in a non-conventional or ordinary sense.

Gist of Idea

Axiomatization simply picks from among the true sentences a few to play a special role

Source

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

Book Ref

Orenstein,Alex: 'W.V. Quine' [Princeton 2002], p.109

A Reaction

If you were starting from scratch, as Euclidean geometers may have felt they were doing, you might want to decide which are the simplest truths. Axiomatizing an established system is a more advanced activity.

The 14 ideas from 'W.V. Quine'

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]