In Formal Symbolic Logic, is there any other way to symbolize an "if, then" statement besides material?

Hi

You could remove the arrow of material implication from your set of logical connectives without any "logical loss", as you put it, in the sense that the material conditional can be captured as either a disjunction or a negated conjunction. For example, 'P > Q' is logically equivalent to both '~P v Q' and '~(P & ~Q)', so any proposition that contains '>' can be converted into a formula that contains only '~' and either 'v' or '&'.

I guess that you could replace material implication with strict implication. P strictly implies Q just in case P implies Q necessarily. P materially implies Q just so long as it is not in fact the case that P is true but Q false. P strictly implies Q just so long as it is not possible that P should be true but Q false.

Some people hold that the indicative conditional 'If P, then Q' should be formalized as 'P strictly implies Q', not 'P materially implies Q', as the former comes closer to capturing what we suppose indicatives to mean.

Remember, though, that strict implication cannot be captured in classical logic, as classical logic lacks modal operators. In general, then, whether or not it is possible in symbolic logic to treat indicatives as strict conditionals will depend on the expressive power of our language.

Dorothy Edgington, among others, argues that conditionals do not express propositions. Conditionals, she thinks, lack truth conditions: for any conditional C, there is no state of affairs whose obtaining is both necessary and sufficient for C's being true. Thus, conditionals lack truth values; they are neither true nor false. So conceived, conditionals cannot be captured in any orthodox logical system, as in any such system, validity is grounded in entailment. Thus, since it is held that one proposition entails another just in case it is logically impossible that the former should be true but the latter false, it would seem that conditionals will admit of capture in logic only so long as we suppose that they possess truth conditions; if we follow Edgington in denying that conditionals express propositions, then we must revise our conception of what it is for one statement to entail another if we are to keep the conditional within the scope of logic.

I hope that this helps a little :-) Good luck!