Deductive philosophical arguments are often presented semi-formally as a list of premises and the conclusion (and sometimes combinations of such sub-arguments). What is virtually never stated are the rules inference, probably because they're assumed to be uncontroversial.
E. g. in this argument:
first premise: if there is a chance of snow this weekend, I will not go out.
second premise: there is a chance of snow this weekend.
conclusion: I will not go out
the inference is just made by modus ponens, which can be easily omitted.
But e. g. in this rendering of Descartes' argument for the existence of the soul (Richard Swinburne: "Are We Bodies Or Souls?", p. 72f) :
first premise: I am a substance which is thinking.
second premise: it is conceivable that ‘I am thinking and I have no body’.
third premise: it is not conceivable that ‘I am thinking and I do not exist’.
lemma: I am a substance which, it is conceivable, can exist without a body.
conclusion: I am a soul, a substance, the essence of which is to think.
the rules of inference are not so simple. Certainly what's applied here (modal logic, identity of indiscernibles?) is more powerful and controversial than modus ponens.
But in a highly formal context the rules of inference are always explicitly stated. And there's a trade-off between
- large number of axioms and weak / simple rules of inference (Hilbert-style)
- few axioms and powerful rules of inference (natural deduction)
Is it possible to construct an example roughly analogous to these two approaches but for semi-formal philosophical reasoning?
I'm simply looking for a philosophical argument stated in two styles, first with more emphasis on the premises and then with more emphasis on the rules of inference.
