Truthmaker theory and the entailment principle

I don't see an issue.

An oddity [of material implication] pointed out early by MacColl (1908) is the observation that of any two sentences of the form “not A or B” and “not B or A”, at least one must be true. Assuming the equivalence with the material conditional, this implies that either “if John is a physician, then he is red-haired” or “if John is red-haired, then he is a physician” must be true. Intuitively, however, one may be inclined to reject both conditionals. Similar complications, known as the paradoxes of material implication, concern the fact that for any sentences A and B, “if A then B” follows from “not A”, but also from “B”, thereby allowing true and false sentences to create true conditionals irrespective of their content (C. I. Lewis 1912). Another peculiarity looms large: the negation of “if A then B” is predicted to be “A and not B”, but intuitively one may deny that “if God exists, all criminals will go to heaven” without committing oneself to the existence of God (cited in Lycan 2001).

A fourth complication is that conditional sentences in natural language are not limited to indicative conditionals (“if I strike this match, it will light”), but also include subjunctive conditionals used to express counterfactual hypotheses (“if I had struck this match, it would have lit”). All counterfactual conditionals would be vacuously true if analyzed as material conditionals with a false antecedent, as pointed out by Quine (1950), an obviously inadequate result, suggesting that the interplay of grammatical tense and grammatical mood should also be of concern to understand the logic of conditionals.

To a large extent, the development of conditional logics over the past century has thus been driven by the quest for a more sophisticated account of the connection between antecedent and consequent in conditionals.

It's never the case that two and two is not four. So we are only considering implications in which the consequent is true. In all such cases, the implication is also true.

To a large extent, the development of conditional logics over the past century has thus been driven by the quest for a more sophisticated account of the connection between antecedent and consequent in conditionals.

So we are only considering implications in which the consequent is true. In all such cases

What is at stake here is the nature of implication, not the meaning of material implication. We are questioning whether material implication is an adequate account of implication. No one is confused about how material implication works.

For example, one might think that some sort of relevance notion of entailment is at stake (for example, Restall 1996); the hope is to develop a conception of entailment that maintains that while ‘Socrates is a philosopher’ en-tails ‘Someone is a philosopher’, it does not entail ‘2 + 2 =4’.