This paper argues that the conventional contribution of the If P, Q form to communicated contents is radically dependent on pragmatic factors that vary with context of utterance and contents of if-clause and main clause. That pragmatics play a considerable role in the understanding of conditionals is familiar, and although some accounts of conditionals exclude non-conditional conditionals, such as (1) There are biscuits on the table if you want some. and conditional bets or requests, others want to include those (Stephen Barker 1995, DeRose and Grandy 1999, David Barnett 2006, Smith and Smith 1988, Noh 1996), and all standard accounts are meant to cover all paradigmatic “conditional” conditionals, such as (2) If Sarah has the measles, she will be having a fever. (3) If you are really hungry, Bill still won’t share his food. Standard accounts can be represented by materialism, expressivism and credalism. According to materialism, indicative conditionals express material implications: asserting a conditional like (2) “if Sarah has the measles, she will be having a fever” is asserting that it isn’t both the case that Sarah has the measles and that she doesn’t have a fever. According to expressivism, conditionals lack truth-conditions, but asserting (2) is expressing a high subjective probability for Sarah’s having a fever conditional on her having the measles. (Adams 1975; Bennett 2003; Edgington 1995) And according credalism, asserting (2) is asserting that Sarah has a fever in all relevant possible worlds in which she has the measles and which matches the present world with respect to what we believe or know. (Nolan 2003; Stalnaker 1981; Weatherson 2001) Two things are notable about these accounts: (A) They all take the conventional contribution of conditionals to determine a truth- or assertability condition in a context according to some conventional rule. (Although assumptions about the relation between the semantics of conditionals and the process of interpretation are seldom detailed, I will assume that these theories take normal utterance interpretation to proceed by taking this content as input, to be modified by pragmatic processes.) (B) They take this content to be mute on whether the consequent would follow from or holds independently of the antecedent. When we sense that (2), unlike (3), communicates that the consequent would follow from the antecedent, we have added to the literal content of the conditional. If the argument of this paper is correct, neither (A) nor (B) is sustainable. What the arguments suggest, instead, is that the conventional contribution of the If P, Q form is restricted to the following: Non-assertoric Introduction: If-clauses introduce a proposition without presenting it as true it so that the main clause can be understood in relation to it. According to this hypothesis – relational contextualism – the content of conditionals could be represented as follows at the most abstract level: (4) If P, Q / Q if P =df R(P, Q) R would be supplied by context, and could take such values as (a) THE POSSIBILITY … MAKES THE ASSERTION OF … RELEVANT (b) UNDER CIRCUMSTANCES LIKE THE PRESENT, THE POSSIBILITY … HAS … AS A CONSEQUENCE where (a) would provide the relevant relation for normal interpretations of (1) and (b) the relation for (2), to provide two examples. (Notice that only parts of the content would be understood as asserted content: it is not asserted that the antecedent represents a possibility rather than the truth, and utterances of conditionals of form (a) typically assert their consequents.) In the paper, I pose three kinds of problem for standard accounts, and offer relational contextualism as the solution to these problems. The first problem is that neither of these accounts make good sense of how we learn to use sentences of the If P, Q form. A child who is learning to use and interpret conditionals will have to grasp non-assertoric introduction before understanding that conditionals convey the relation of material implication or any other relation postulated as the literal content by standard theories of conditionals. Furthermore, there are reasons to think that the relations that standard accounts take to provide the literal meaning of conditionals are too abstract to be grasped to be associated with the conditional form. Grasping these contents could only be the result of fairly sophisticated abstraction. For learners who have not reached that level of sophistication, interpretation would have to proceed along the very lines suggested by relational contextualism. The second problem is that even if such abstraction could take place, a child who has grasped non-assertoric introduction has nothing to gain but something to loose in interpretive effectiveness by assuming that the conditional form itself conveys any of these other relations. The third problem for standard accounts is that they fail to provide adequate explanations of why some conditionals that would be literally true or acceptable are normally perceived to be false or meaningless. For example, in the case of both of the following conditionals, I am right now fairly confident that the consequent is true, independently of the antecedent: (5) If I go to the movies tonight, it will rain tomorrow. (6) If Berne is the capital of Switzerland, John Lennon was killed in 1980. Their literal contents are obviously acceptable on both materialism, expressivism and credalism. Nevertheless, (5) seems false to me – tomorrow’s weather is independent of my cinematic activities – and (6) seems nonsensical. Studies of students of different backgrounds at different universities show that such verdicts are very common (even among people with some familiarity with logic). Proponents of standard accounts hope to explain such reactions with reference to conversational pragmatics, but it is unclear what principles would support these explanations. As I make clear, standard explanations in terms of Gricean maxims or relevance theoretic constraints seem to yield the wrong results. By contrast, relational contextualism can explain typical reaction to both (5) and (6) and standard epistemic constraints on indicative conditionals.