Errol E. Harris, Formal, Transcendental, and Dialectical Thinking: Logic and Reality (SUNY Press, 1987), pp. 38-39:
Sometimes an excuse is offered for the paradoxical (one might say, illogical) character of material implication on the ground that the Philonian interpretation of the conditional is the weakest which will satisfy the requirement that the rule of detachment gives a valid inference. But it is obvious from the foregoing that it does not satisfy this requirement; for unless there is some essential connection between p and q we cannot validly argue "If p then q, and p; therefore q." We ought not even to assert, "If p then q" except on the condition that there is a connection between what the propositions express. The Philonian interpretation licenses the schema "If p, then q" whether or not there is any connection, so we might argue:
If pigs cannot fly, Socrates is mortal;
but pigs cannot fly,
therefore, Socrates is mortal.Although this argument is valid according to the current doctrine, the conclusion, as long as it includes the word "therefore," is false, because it alleges in effect that the reason for Socrates' mortality is the flightlessness of pigs. Accordingly, we have an implicitly false conclusion from true premisses, and that is precisely what the rule of detachment is supposed to preclude.
P1
P2
Therefore
C
This makes it clear that the relation between premises and conclusion lies between premises and conclusion and is not part of the premises or the conclusion. Once one grasps this simple point one sees that Harris's argument collapses: it is not the case that 'Socrates is mortal' is false, nor is 'therefore, Socrates is mortal' "implicitly false." What could that mean? Such talk rests on a confusion of truth/falsity with validity/invalidity.
Harris thinks that there must be an "essential connection," a connection at the level of meaning, between p and q if we are to be able to assert 'If p then q.' But this is just plain false.
Suppose I encounter a flat-earther who tries to convert me to his doctrine. I cut him off with 'If the earth is flat, then I'm the Pope!' There is obviously no relation of semantic entailment between the antecedent and the consequent in this example. They have 'nothing to do with each other.' But the sentence is obviously assertible — it has a use and makes a move in a language-game — and it has a clear sense which can be paraphrased as follows: 'It is no more the case that the earth is flat than that I am the Pope!' If the flat-earther is particularly dense, as one might expect such a lunatic (geotic?) to be, I might expand my enthymeme into an explicit argument of the form modus tollendo tollens:
If the earth is flat, then I am the Pope
I am not the Pope
Therefore
The earth is not flat.
The reasoning in this argument is perfectly clear and perfectly valid. The argument is sound in addition to being valid: its premises are true. Now no proposition can have a truth-value unless it is meaningful. It follows that the conditional is meaningful, pace Harris. I submit that this conditional is at once both a material conditional and a piece of ordinary language. Thus here we have an ordinary language example of a material conditional. So although the material conditional is a theoretical construct for logical purposes, it is exemplified in natural language.