[...] 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.

Thus:

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.

+1 for "Note that due to Agrippa's Trilemma, ... infinite regress. Or, of course, a combination of the three." The Albert's original presentation doesn't include the "combination of the three" part, so this casts a nice shadow of doubt on the correct interpretation of the trilemma... – Thomas Klimpel – 2013-05-30T07:47:18.113