[...] difficulties arise in the attempt to justify MPP which are analogous to notorious difficulties arising in the attempt to justify RI.
(3) I consider first the suggestion that deduction needs no justification, that the call for a proof that MPP is truth-preserving is somehow misguided.
An argument for this position might go as follows:
It is analytic that a deductively valid argument is truth-preserving, for by 'valid' we mean 'argument whose premisses could not be true without its conclusion being true too'. So there can be no serious question whether a deductively valid argument is truth-preserving.
It seems clear enough that anyone who argued like this would be the victim of a confusion. Agreed, if we adopt a semantic definition of 'deductively valid' it follows immediately that deductively valid arguments are truth-preserving. But the problem was, to show that a particular form of argument, a form deductively valid in the syntactic sense, is truth-preserving; and this is a genuine problem, which has simply been evaded. [...]
[...] Consider the following attempt to justify MPP:
A1 Suppose that 'A' is true, and that 'A => B' is true. By the truthtable for '=>', if 'A' is true and 'A => B' is true, then 'B' is true too. So 'B' must be true too.
This argument has a serious drawback: it is of the very form which it is supposed to justify. For it goes:
A1' Suppose C (that 'A' is true and that 'A => B' is true). If C then D (if 'A' is true and 'A => B' is true, 'B' is true). So, D ('B' is true too).
[...] one can support the intuition that there is something wrong with A1', in spite of its not being straightforwardly question-begging, by showing that if A1' supports MPP, an exactly analogous argument would support a deductively invalid rule, say:
MM (modus morons);
From: A => B and B
to infer: A.
A4 Supposing that 'A => B' is true and 'B' is true, 'A => B' is true => 'B' is true. Now, by the truth-table for '=>', if 'A' is true, then, if 'A => B' is true, 'B' is true. Therefore, 'A' is true.
This argument, like A1, has the very form which it is supposed to justify. For it goes:
A4' Suppose D (if 'A => B' is true, 'B' is true). If C, then D (if 'A' is true, then, if 'A => B' is true, 'B' is true). So, C ('A' is true).
It is no good to protest that A4' does not justify modus morons because it uses an invalid rule of inference, whereas A4' does justify modus ponens, because it uses a valid rule of inference — for to justify our conviction that MPP is valid and MM is not is precisely what is at issue.
Haack, S. (1976). The justification of deduction. Mind, 85 (337), 112-119.