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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives

[minimal connectives needed for a logic system]

3 ideas
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.
In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp]
     Full Idea: In sentential logic there is a simple proof that all truth functions, of any number of arguments, are definable from (say) 'not' and 'and'.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §0)
     A reaction: The point of 'say' is that it can be got down to two connectives, and these are just the usual preferred pair.
Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]
     Full Idea: In propositional logic, any set containing ¬ and at least one of ∧, ∨ and → is expressively complete.
     From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.8)