LOOKING FOR THE MISSING ANTECEDENT Draft of August 6, 2020 Matheus Silva Logic textbooks usually state that the conclusion of a valid deductive argument is contained in its premises. This is perplexing because it suggests that deductive arguments are merely tautological and non-informative. One way to explain why valid deductive arguments can be informative despite their tautological character is by maintaining that a deductive argument is an attempt to find the missing premises that together with one or more accepted premises will ensure the truth of the conclusion . The reasoner aims to find the missing link between known 1 premises and the conclusion she aims to prove. We tend to ignore this aspect because when we think about the nature of deductive arguments we usually have in mind the idealised argumentative forms we see in logic textbooks. These examples are interesting for pedagogical reasons but don't do justice to the complex character of deductive theorisation. For example, when Andrew Wiles prove Fermat's last conjecture by showing that the Taniyama-Shimura conjecture is true, he was actually finding the premises that connected the conclusion with known mathematical premises. Now, if p entails q, p → q is necessarily true, so necessarily true conditionals have a deductive-like character. Consequently, necessarily true conditionals should be merely tautological and non-informative because their consequents are contained in the antecedents. But that's obviously false because philosophy contains hundreds of informative conditionals that are defended as necessary truths. Some examples involve the nature of knowledge (if p weren't true, S wouldn't believe that p), the metaphysics of causality (if C had not occurred, E would not have occurred), or the necessity of identity (a = b → ⧠(a = b)). How is that possible? We could look for a missing premise that would help clarify the connection between the antecedent and the consequent, but we are dealing with conditionals, not arguments. So perhaps we could look for a missing proposition in the antecedent. The belief in q is justified by a belief in p. This inferential justification is conditional in nature, for the belief in q is only justified if p is justified. Now, the belief in p → q itself is also justified by one or more beliefs assumed in the background that motivated the conditional in the first place. Let's name these assumptions m, n and o. Thus, the proper logical form of the conditional would be (m&n&o&) → (p → q). In its expanded version, the conditional seems to be embedded as the consequent of another conditional. But we can tweak things a little bit more with importation and we will have m&n&o&p → q. This is the antecedent we were looking for. It still works as a premise in the sense it is the reason that motivated the connection between the antecedent and the consequent in the first place. Abraham, L. 1936. A Note on the Fruitfulness of Deduction. Philosophy of Science, 3(2), 152–155.