6 ideas
| 7791 | The simplest of the logics based on possible worlds is Lewis's S5 [Lewis,CI, by Girle] |
| Full Idea: C.I.Lewis constructed five axiomatic systems of modal logic, and named them S1 to S5. It turns out that the simplest of the logics based on possible worlds is the same as Lewis's S5. | |
| From: report of C.I. Lewis (works [1935]) by Rod Girle - Modal Logics and Philosophy 2.1 | |
| A reaction: Nathan Salmon ('Reference and Essence' 2nd ed) claims (on p.xvii) that "the correct modal logic is weaker than S5 and weaker even than S4". Which is the greater virtue, simplicity or weakness? |
| 17423 | The essence of natural numbers must reflect all the functions they perform [Sicha] |
| Full Idea: What is really essential to being a natural number is what is common to the natural numbers in all the functions they perform. | |
| From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2) | |
| A reaction: I could try using natural numbers as insults. 'You despicable seven!' 'How dare you!' I actually agree. The question about functions is always 'what is it about this thing that enables it to perform this function'. |
| 17425 | To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha] |
| Full Idea: A knowledge of 'how many' cannot be inferred from the equinumerosity of two collections; a numerical quantifier statement is needed. | |
| From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 3) |
| 17424 | Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha] |
| Full Idea: Counting is the activity of putting an initial segment of a serially ordered string in 1-1 correspondence with some other collection of entities. | |
| From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2) |
| 15049 | Metaphysical realists are committed to all unambiguous statements being true or not true [Dummett] |
| Full Idea: The anti-realist view undercuts the ground for accepting bivalence. ...Acceptance of bivalence should not be taken as a sufficient condition for realism. ..They accept the weaker principle that unambiguous statements are determinately true or not true. | |
| From: Michael Dummett (Realism and Anti-Realism [1992], p.467) | |
| A reaction: [cited by Kit Fine, when discussing anti-realism] I take it be quite an important component of realism that there might be facts which will never be expressed, or are even beyond our capacity to grasp or express them |
| 11002 | Equating necessity with informal provability is the S4 conception of necessity [Lewis,CI, by Read] |
| Full Idea: C.I.Lewis's S4 system develops a sense of necessity as 'provability' in some fairly informal sense. | |
| From: report of C.I. Lewis (works [1935]) by Stephen Read - Thinking About Logic Ch. 4 |