This is a pretty basic question, but I haven't been able to find a clear answer in the various sources I've looked at, including the Kneales' chapter on conditionals in 'The Development of Logic'.
In propositional logic, when modus ponens stands in for a syllogistic/categorical argument, with the antecedent being the conjunction of the original syllogism's premises, and the consequent the conclusion, is it the standard interpretation to regard the affirmation of the antecedent as thereby entailing the conclusion only on the assumption that the original argument was valid, i.e the validity is external to the conditional itself, as opposed to that validity somehow being transferred to the conditional so long as the antecedent-as-premises is affirmed?
And more broadly, is propositional logic just a logic of "this is what follows, assuming not only that the statements p, q, etc, are true but also that the rules of inference do actually represent valid arguments" (insofar as validity is the aim, rather than, say, causal arguments)?
In answer to Graham, I'm adding this to the original question because of the text limit for comments.
In propositional logic, syllogistic, i.e. categorical, arguments are regularly expressed using modus ponens, with the conjunction of the two premises (e.g. "all men are mortal & Socrates is a man") serving as the antecedent of the conditional, if p then q, and the consequent ("Socrates is mortal") as the conclusion. Stating this in the form of a conditional statement is recognized to not be sufficient for the conclusion to be entailed by the premises per se, but when the conjunction of the premises, 'p', is then affirmed to be true, which turns the conditional into a modus ponens argument, then the logic textbooks describe the conclusion, 'q', as then being 'inferred'. But surely this can't be the case, and my question was "is it generally recognised that this is not the case".
As an example of why this can't be so, take the enthymeme "Socrates is a man, therefore Socrates is mortal", which is an invalid argument as it stands, but if you add the missing premise "all men are mortal" then it becomes a valid syllogism, yet modus ponens doesn't differentiate between the two - so long as the premises are affirmed to be true, then the conclusion that "Socrates is mortal" can in both cases be 'inferred'. Surely this means that whatever validity there was in the original argument has not been carried over to the modus ponens formulation.
Yes, a valid syllogism doesn't ever become invalid when expressed using modus ponens, but only because the validity provided by the original logical form has disappeared (if this were not the case, then we should not be able to 'infer' a consequent that stands for a syllogism's conclusion, from the affirmation of an antecedent that stands for an enthymeme's premise, yet we can). It seems to me that the conclusion is only 'inferred' if the syllogism has already been proved outside the system and then assumed within it. And even then, what kind of inference is "this is a valid argument and its premises are true, so it's a sound argument too, which means its conclusion is also true"? This merely declares that a valid argument, made elsewhere, is sound. You don't infer something from an affirmation that something is the case, but rather, if an inference is valid to the effect that something must follow from something else, then an affirmation of that first thing entitles you to affirm, not infer, the second thing.
In other words, in a syllogism, a conclusion is true on the condition that the premises are true, only because such an argument is already valid, whereas with modus ponens, when used to express such an argument, the conclusion is only true on the condition that the premises are true AND that it's a valid argument to begin with. And affirming the antecedent merely affirms the former. If that is right, then propositional logic, which is heavily reliant on material implication, is not 'truth-preserving' in the sense that actually valid arguments are truth-preserving, i.e. where you can only go from true premises to true conclusions because there's a valid form that is prior to any claim of soundness, but instead, if we grant from the outset that certain statements are true and that certain material implications are also true, i.e. truly stand for valid arguments, then from this we can say (not 'infer' or 'conclude', except indirectly and implicitly) that other things have to be true. Again, for all I know all of this all might be commonplace, but the purpose of my original question was just to check if that was so.
