Logic

It seems that many philosophers use the "socrates" argument to explain a simple deductive argument. This argument is P1: All men are mortal P2: Socrates is a man C: Therefore, Socrates is mortal. However, is this not begging the question because P1 assumes that Socrates is mortal?

Comments

An argument like the one that you presented, which has the form: (1) P; (2) P-->Q (i.e., If P, then Q); Therefore, (3) Q, if introduced in order to explain a simple deductive argument, is meant only to illustrate the concept of soundness. An argument is sound if the conclusion follows logically from the premises. But a sound argument need not be valid, or yield a true conclusion. An argument is only valid if it is sound, its premises are true, and the conclusion follows non-circularly from the premises. Although the argument that you present is--at least to the best of my knowledge--not only sound, but valid, the two can of course come apart. So, for example, the following argument: (1) The sun always shines in Southern California; (2) Los Angeles is in Southern California; (3) Therefore the sun is always shining in Los Angles is valid, it's not--_mirabile dictu_ sound.

In response to the original question. We might have general grounds for thinking that all men are mortal -- e.g. general beliefs about the structure of human beings and about the relevant biological laws -- which we accept on inductive grounds (in a broad sense of inductive) and where our supporting evidence, as it happens, doesn't depend on inspecting Socrates in particular. So there need be nothing "question-begging" in any sense in then going on to deduce a claim about Socrates.

In response to Sean Greenberg, (a) it should be noted that the Socrates argument is not a simple modus ponens of the form (1), (2), (3) (the main logical operator in the "all" premiss is a quantifier, not a conditional). Also (b) he uses "sound" and "valid" the wrong way round in the first part of his answer, though that slip seems to be corrected in the last sentence. For the record, in by far the dominant modern usage, an argument is "valid" if the conclusion follows logically from the premisses, and "sound" if it is valid and has true premisses. (c) It is non-standard to add "follows non-circularly from the premisses" to the definition of "sound" -- if only because it is pretty unclear what "non-circularly" means.

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