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Ideas for 'Philosophical Explanations', 'The Principles of Mathematics' and 'Epistemic Operators'

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4 ideas

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
14105 There seem to be eight or nine logical constants [Russell]
     Full Idea: The number of logical constants is not great: it appears, in fact, to be eight or nine.
     From: Bertrand Russell (The Principles of Mathematics [1903], §012)
     A reaction: There is, of course, lots of scope for interdefinability. No one is going to disagree greatly with his claim, so it is an interesting fact, which invites some sort of (non-platonic) explanation.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
18722 Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell]
     Full Idea: Russell explained ¬p by saying that ¬p is true if p is false and false if p is true. But this is not an explanation of negation, for it might apply to propositions other than the negative.
     From: comment on Bertrand Russell (The Principles of Mathematics [1903]) by Ludwig Wittgenstein - Lectures 1930-32 (student notes) B XI.3
     A reaction: Presumably he is thinking of 'the light is on' and 'the light is off'. A very astute criticism, which seems to be correct. What would Russell say? Perhaps we add that negation is an 'operation' which achieves flipping of the truth-value?
5. Theory of Logic / E. Structures of Logic / 3. Constants in Logic
14104 Constants are absolutely definite and unambiguous [Russell]
     Full Idea: A constant is something absolutely definite, concerning which there is no ambiguity whatever.
     From: Bertrand Russell (The Principles of Mathematics [1903], §006)
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
14114 Variables don't stand alone, but exist as parts of propositional functions [Russell]
     Full Idea: A variable is not any term simply, but any term as entering into a propositional function.
     From: Bertrand Russell (The Principles of Mathematics [1903], §093)
     A reaction: So we should think of variables entirely by their role, rather than as having a semantics of their own (pace Kit Fine? - though see Russell §106, p.107).