Logic

What grounds the truth of logical inferences such as modus ponens or hypothetical syllogism? Are these logical truths grounded in "intuition" similar to Foundationalism?

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I hate to sound like, well, like a philosopher, but I think we need to get some terms straight before we begin: Logical inferences such as modus ponens (more properly, rules of inference) are neither true nor false. Truth and falsity are properties of things like sentences, statements, or propositions (depending on your ontology).

The analogue of truth values for rules of inference are "validity" and "invalidity". Very roughly, a rule of inference is valid if and only if it is truth-preserving. That is, it is valid if it will only allow you to infer truths from truths--if you input true propositions and apply a valid rule of inference to them, you will output only true propositions. (If you input a false proposition, anything can happen; "garbage in/garbage out" as they say.)

So, a slightly more accurate way to phrase your question is this: "What grounds the validity of a rule of inference?" And now, I think, the answer is clear: Just as something like "correspondence to reality" might be said to ground the truth of a proposition, so "being truth-preserving" grounds the validity of a rule of inference. That, in turn, might be said to be ultimately grounded in a correspondence to reality: Given some propositions that "correspond to reality", valid rules of inference will tell you other propositions that also "correspond to reality".

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