The logical form of an argument is made up of only symbol letters for simple sentences and operators that connect them together. One of the operators is the conjunction representing the english word ‘and’ which combines two simple sentences together. It can also itself be used repeatedly to combine a primary conjunction of two simple sentences together with a third one, or any number of further simple sentences. The premises of an argument can be conjoined together to make them one such compound sentence formed by conjunctions.
We can then also characterize the logical form of the argument by a conditional operator connecting the compound conjunction of premises as one sentence, with the consequence of the argument as the other. Every logical form has a corresponding conditional it can be transformed into by following this procedure. If any combination of truth values applied to the premises can be found to produce a false conclusion, then the argument is an invalid form. We can produce counterexamples which result in contradiction of the conditional by seeing whether we can take the truth values of all of the premises to be true and the consequence to be false. This is the only case in which the truth function of a conditional necessarily comes out not to be true in general. In the case that not both the antecendent and consequence are true, then the statement is contingent on what truth values are applied to each premise. However, if all of the premises are true and the consequence is true then the conditional is a tautology. A tautology will always be the case and so there will be no cases in which the corresponding argument is in contradiction, or in other words we have proved its validity.
This only preseves the logical form of the argument and not the content of the sentences. It need not be a problem for a given collection of premises and conclusion depending on how they are all related. But if the content of the premises are irrelevant to that of the conclusion then this does not seem to get fairly expressed by a conditional statement in which the conclusion is supposed to follow directly and necessarily from the antecedents. It is not an accidental or an indirect dependency. This loss of a normal intuition about conditional relations is a sacrifice that must be made whenever we are interested in getting at the logical form of an argument.