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Single Idea 8480

[filed under theme 4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic ]

Full Idea

The five systems of propositional modal logic contain successively stronger conceptions of necessity. In S4 'it is poss that it is poss that p' implies 'it is poss that p'. In S5, 'it is poss that it is nec that p' implies 'it is nec that p'.

Gist of Idea

S4: 'poss that poss that p' implies 'poss that p'; S5: 'poss that nec that p' implies 'nec that p'

Source

Alex Orenstein (W.V. Quine [2002], Ch.7)

Book Ref

Orenstein,Alex: 'W.V. Quine' [Princeton 2002], p.151

A Reaction

C.I. Lewis originated this stuff. Any serious student of modality is probably going to have to pick a system. E.g. Nathan Salmon says that the correct modal logic is even weaker than S4.

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]