Lesson 5

# Lesson 5 - Chp 5 In large measure our discussion in Russell...

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Chp. 5 In large measure, our discussion in Russell has so far focused on how various propositions relate to facts, particulars and other items that are self-subsistent. Since propositions have their existence dependently, they must relate to things that have their existence independently (such as facts and particulars). So, for example, atomic propositions relate to atomic facts. Molecular propositions involving logical operators (other than ‘not’) relate to two or more atomic facts. Negative propositions relate to negative facts. Propositional attitude reports (which are themselves propositions) relate to molecular facts (facts involving two relations.) (And it’s something of a misnomer to call these propositional attitude reports, since the object one is related to in believing isn’t really a proposition, but a bunch of parts of propositions.) So that’s a great many propositions related to a great many things that have independent existence. But we haven’t yet discussed all the propositions that Russell enumerated to begin with. In particular, we haven’t discussed general propositions, and that is what Russell sets out to discuss in chapter 5. General Propositions: Remember from earlier on that Russell distinguished general propositions from particular  propositions He said we couldn’t do away with general propositions and facts.  (If we set out to  explain everything in the world, would have to say all this and nothing more before the  explanation was complete.) There are two kinds of general propositions: 1. Those about all 2. Those about some For each proposition of one of these forms its negation is a proposition of the other form. So, if you say, “All men are mortal,” the negation of this proposition is, “Some men are  not mortal.” General propositions don’t involve the existence of the things they talk about in general  terms.  So if I say, “All Greeks are mortal,” it doesn’t imply the existence of Greeks.

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That’s really a commitment of logic…but why might try to motivate it by thinking of  sentences such as, “All unicorns have horns,” “Some dwarves live in gold mines,” “Some  Greek gods are unfaithful,” etc. So, with those preliminaries out of the way, we now come to the crucial question: how do  general propositions relate to facts, particulars, or other things that have their existence  independently? Russell claims that, unlike non-general atomic or molecular propositions, general  propositions do not assert facts.
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