5 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? |
8920 | Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz] |
Full Idea: A relation R on a non-empty set S is an equivalence relation if it is reflexive (for each member a, aRa), symmetric (if aRb, then bRa), and transitive (aRb and bRc, so aRc). It tries to classify objects that are in some way 'alike'. | |
From: Seymour Lipschutz (Set Theory and related topics (2nd ed) [1998], 3.9) | |
A reaction: So this is an attempt to formalise the common sense notion of seeing that two things have something in common. Presumably a 'way' of being alike is going to be a property or a part |
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 |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
Full Idea: Archelaus was the first person to say that the universe is boundless. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |