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So why all the ‘α’ and ‘β’ malarky?

Here we see why we use Greek letters rather than upper case roman letters to talk about sentence and sentential clauses in our formal language.
A close up of a letter alpha followed by a question mark
© University of York

When we defined the meaning of ampersand with a truth-table, we said that, strictly speaking, we shouldn’t use sentence/statement letters (like ‘P’ and ‘Q’) but should instead use something else (we use Greek letters). We gave a rough explanation of why. Now we can see more clearly and accurately.

The reason is that, when we give the truth-conditions for ampersand, we are giving the truth-conditions for any ampersand phrase, including those where what’s plugged into ‘&’ are complex sentences—not just those we get by plugging in sentences that don’t have connectives in them. We want the rule about truth-conditions to apply to sentences like ‘(C & ~A)’ and ‘((A & B) & C)’, not just sentences like ‘~A’ and ‘(A & B)’. (And we also want the rule to apply to wffs which are sentential clauses in larger sentences.)

© University of York
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Logic: The Language of Truth

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