LOGIC AND LANGUAGE We can ask not just what individual words signify, but also what whole sentences signify Abelard deWnes a proposition as ‘an utterance signifying truth or falsehood’ Once again, ‘signify’ has a double sense A true sentence expresses a true thought, and it states what is in fact the case (proponit id quod in re est) It is the second sense of ‘signiWcation’ that is important when we are doing logic, for we are interested in what states of aVairs follow from other states of aVairs, rather than in the sequence of thoughts in anybody’s mind (D 154) The enunciation of the state of aVairs (rerum modus habendi se) that a proposition states to be the case is called by Abelard the dictum of the proposition (LI 275) A dictum is not a fact in the world, because it is something that is true or false: it is true if the relevant state of aVairs obtains in the world; otherwise it is false What is a fact is the obtaining (or not, as the case may be) of the state of aVairs in question Abelard, unlike some other logicians, medieval and modern, made a clear distinction between predication and assertion A subject and predicate may be put together without any assertion or statement being made ‘God loves you’ is a statement; but the same subject and predicate are put together in ‘If God loves you, you will go to heaven’ and again in ‘May God love you!’ without that statement being made (D 160) Abelard deWnes logic as the art of judging and discriminating between valid and invalid arguments or inferences (LNPS 506) He does not restrict inferences to syllogisms: he is interested in a more general notion of logical consequence He does not use the Latin word ‘consequentia’ for this: in common with other authors he uses that word to mean ‘conditional proposition’—a sentence of the form ‘If p then q’ The word he uses is ‘consecutio’, which we can translate as ‘entailment’ The two notions are related but not identical When ‘If p then q’ is a logical truth, then p entails q, and q follows from p; but ‘If p then q’ is very often true without p entailing q For p to entail q it is essential that ‘If p then q’ be a necessary truth; but for Abelard this is not suYcient ‘If Socrates is a stone, then he is a donkey’ is a necessary truth: it is impossible for Socrates to be a stone, and so impossible that he should be a stone without being a donkey (D 293) Abelard demands not just that ‘If p then q’ be a necessary truth, but that its necessity should derive from the content of the antecedent and the consequent ‘Inference consists in a necessity of entailment: namely, that what is meant by the consequence is determined by the sense of the antecedent’ (D 253) 126