TIPS FOR GIVING METATHEORITIC PROOFS
Remember that truth and falsity are relative to truth value assignments whereas logical
properties and relations are absolute. So never say that something is true or false without
saying on what truth value assignment it is true or false, and never say that something is truth-
functionally true, false, indeterminate, inconsistent, valid, etc. on a truth value assignment.
Keep your categories straight. Only sentences can be true, false, t-f true, or t-f false, not sets
or arguments. Only sets can be t-f consistent or inconsistent, not sentences or arguments.
Only arguments can be t-f valid or invalid, not sets or sentences. Keep the relations between
these things straight. A set is (absolutely) t-f consistent if and only if each of the sentences in
that set is true on a truth value assignment. If there is no tva on which all the sentences in a set
are true the set is (absolutely) t-f inconsistent. An argument is (absolutely) t-f invalid if and only
if the set consisting of its premises plus the negation of its conclusion is (absolutely) t-f
inconsistent, that is, if and only if there is no tva on which all the sentences in this set are true.
{P} is the unit set of the sentence, P. And so on.
Keep the summary sheet for the semantics of SL at your elbow. It lays all these things out.
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