Ideas from 'Substitutional Classes and Relations' by Bertrand Russell [1906], by Theme Structure

[found in 'Essays in Analysis' by Russell,Bertrand (ed/tr Lackey,Douglas) [George Braziller 1973,0-8076-0699-5]].

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2. Reason / D. Definition / 7. Contextual Definition

21560

Any linguistic expression may lack meaning when taken out of context

			Full Idea: Any sentence, a single word, or a single component phrase, may often be quite devoid of meaning when separated from its context.
			From: Bertrand Russell (Substitutional Classes and Relations [1906], p.165)
			A reaction: Contextualism is now extremely fashionable, in philosophy of language and in epistemology. Here Russell is looking for a contextual way to define classes [so says Lackey, the editor].

2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes

21561

'The number one is bald' or 'the number one is fond of cream cheese' are meaningless

			Full Idea: 'The number one is bald' or 'the number one is fond of cream cheese' are, I maintain, not merely silly remarks, but totally devoid of meaning.
			From: Bertrand Russell (Substitutional Classes and Relations [1906], p.166)
			A reaction: He connects this to paradoxes in set theory, such as the assertion that 'the class of human beings is a human being' (which is the fallacy of composition).

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility

18130

Axiom of Reducibility: there is always a function of the lowest possible order in a given level

			Full Idea: Russell's Axiom of Reducibility states that to any propositional function of any order in a given level, there corresponds another which is of the lowest possible order in the level. There corresponds what he calls a 'predicative' function of that level.
			From: report of Bertrand Russell (Substitutional Classes and Relations [1906]) by David Bostock - Philosophy of Mathematics 8.2

8. Modes of Existence / A. Relations / 1. Nature of Relations

21562

There is no complexity without relations, so no propositions, and no truth

			Full Idea: Relations in intension are of the utmost importance to philosophy and philosophical logic, since they are essential to complexity, and thence to propositions, and thence to the possibility of truth and falsehood.
			From: Bertrand Russell (Substitutional Classes and Relations [1906], p.174)
			A reaction: Should we able to specify the whole of reality, if we have available to us objects, properties and relations? There remains indeterminate 'stuff', when it does not compose objects. There are relations between pure ideas.