Necessity and Probability: A Reply to Professors Ambrose and Lazerowitz

Abstract

Professor Lazcrowitz's main objection to the view that 'made probable by cvidence' and 'rendered improbable' have a correct application to noncontingent propositions is based on his rejection of my claim that 'it is probable that p' implies 'it is possible that -p' only if 'possible' means 'epistemically possible'. believes that '-p is epistemically possible' implies '-p is logically possible'; thus since, as we both agree, 'it is probable that p' implies 'it is epistemically possible that -p', he claims that 'it is probable that p' also implies 'it is logically possible that -p'. Hence, in his view 'it is probable that p', where p is a logically necessary proposition, implies a contradiction. Here I should add that I do not believe that 'it is probable that p' logically implies 'it is epistemically possible that -p'. The man who says 'it is probable that p' knowing that p is true (or who says '-p is improbable' knowing that p is true) is saying something misleading but not something self-contradictory. Compare such a case with the case of the man who, believing correctly that he knows p, says 'I believe that p'. In both cases a hearer would often be misled but not because 'X believes p' entails 'X does not know p' or because 'it is probable that p' entails 'p is not known'. I shall not pursue this point here since, firstly, to do so would be to shift my groumd so far as my disagreement with Lazerowitz is concerned and, secondly, I believe that, whether or not the implication is a logical one, there is no valid inferential route from that implication to Lazerowitz's claim that 'p is probable' implies 'it is logically possible that -p'. In making his objection Lazerowitz takes up the example I offer of a statement of possibility in which the notion of possibility involved is epistemic possibility; namely, the statement 'It is still possible that he will come today'. Lazerowitz says 'It seems plain with regard to the statement used to illustrate epistemic possibility that we know what it would be for him to come, and also what it would be for him not to come' and 'The proposition He will come has one of either of two truth-values, each of which is theoretically possible'. Now both of these claims are true so far as this example is concerned. However, Lazerowitz also says that 'this implies that we know that it is logically possible for him not to come' (my italics) and that 'In this case, clearly, to say that it is still possible that he will come today is to imply the logical possibility of his not coming today' (my italics). That there is this implication is what I deny and what Professor Lazerowitz needs to establish. In fact, he goes on to argue that that there is such an implication is implied by my saying that 'it is still possible