Spurious Arguments from Context

Suppose that \[A \land B \longrightarrow Q;\]

then \[A \land B \land C \longrightarrow Q\]

as well -- no matter what the wff \(C\) represents -- and so we can rewrite that (exportation) as

then \[A \land B \longrightarrow (C \longrightarrow Q)\] "Given that \(A\) and \(B\), then \(C \longrightarrow Q\). But this "argument" -- that \[C \longrightarrow Q\] is spurious -- there's really no information there. It's not an argument, because in the context of \(A \land B\), \(Q\) follows -- is always true; so anything else is incidental, and irrelevant.

Any implication with \(Q\) as the consequent is always and trivially true, because \(Q\) is true in this context.


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