William Bondi Knowles

ABSTRACT According to what Hume termed an ‘establish’d maxim’, nothing absolutely impossible is imaginable. It has recently been claimed against this that given the ubiquity of stipulative imagination, where one imagines a proposition simply by adding it as a stipulation about the imagined situation, it seems that we can imagine any impossibility whatsoever, even plain contradictions: all we need to do is add them as stipulations. The aim of this article is both to defend Hume’s maxim against this objection and – hopefully interestingly – to do so while granting the assumption that adding something as a stipulation is a valid way of imagining something. To this end, appeal is made to a particular development of a second Humeanism, according to which necessary truths are analytic in the sense that their truth follows from their meaning. Their analyticity, it is then argued, secures that they are true in all imagined situations. Therefore, even if it is right that a valid way of imagining something is to add it as a stipulation, attempting to stipulate that, say, some imaginary bachelor is also married is bound to fail: you can’t stipulate it to be the case because it really isn’t the case.

In the last half-century increased awareness of modal issues has been brought to bear on the free will debate. It has been argued that the context dependence of possibility claims can be exploited to mount a defence of compatibilism, the idea being that the kind of possibility to do otherwise ruled out by determinism is distinct from the kind of possibility to do otherwise needed for free will. The potency of this idea, however, is still under-appreciated. It is often confused with conditional analyses of alternative possibilities, and many assume that the forms of possibility the compatibilist points to are somehow less “categorical” than the incompatibilist’s preferred all-in possibility. Moreover, Christian List’s questionable agent-level compatibilism has recently become the main representative of the idea. In fact what is needed—so it is argued here—is to combine increased modal awareness with the traditional compatibilist picture of the relevant freedom being freedom from external compulsion.

A common assessment of Liar sentences is that they malfunction and fail to say what they appear to say. The purpose of this article is to highlight a couple of limitations of this “malfunctionalism”, to which end two recalcitrant paradoxes will be presented. The first shows that there are Liar paradoxes where malfunctionalism must concede that there is no way of stating what is apparently the case. The second is the Yablo-style infinite sequence Liar, which is out of malfunctionalism’s reach altogether and in need of a different solution.

Fitch's knowability paradox shows that for each unknown truth there is also an unknowable truth, a result which has been thought both odd in itself and at odds with views which impose epistemic constraints on truth and/or meaningfulness. Here a solution is considered which has received little attention in the debate but which carries prima facie plausibility. The decidability solution is to accept that Fitch sentences are unknowably true but deny the significance of this on the grounds that Fitch sentences are nevertheless decidable. The decidability solution is particularly attractive for those whose primary concern is an epistemic constraint on meaningfulness (‘verificationists’). For those whose main concern is truth (‘anti-realists’), the situation is more complex: Melia takes the solution to exonerate anti-realism completely; Williamson sees it as completely irrelevant. The truth lies between these two extremes: there is one broad anti-realist commitment to which the solution does not apply, but there is also one, the “fundamental tenet” of anti-realism according to Dummett, to which it does.

According to what Hume termed an ‘establish’d maxim’, nothing absolutely impossible is imaginable. It has recently been claimed against this that given the ubiquity of stipulative imagination, where one imagines a proposition simply by adding it as a stipulation about the imagined situation, it seems that we can imagine any impossibility whatsoever, even plain contradictions: all we need to do is add them as stipulations. The aim of this article is both to defend Hume’s maxim against this objection and – hopefully interestingly – to do so while granting the assumption that adding something as a stipulation is a valid way of imagining something. To this end, appeal is made to a particular development of a second Humeanism, according to which necessary truths are analytic in the sense that their truth follows from their meaning. Their analyticity, it is then argued, secures that they are true in all imagined situations. Therefore, even if it is right that a valid way of imagining something is to add it as a stipulation, attempting to stipulate that, say, some imaginary bachelor is also married is bound to fail: you can’t stipulate it to be the case because it really isn’t the case.

Blackburn’s dilemma (as commonly understood) is that in explaining truths of the form ‘Necessarily-P’ we have to appeal either to a necessary truth, in which case we don’t seem to make the right kind of progress, or to a contingent truth, in which case we seem to undermine the necessity we were meant to be explaining. This paper advances two claims. First, it is argued that the dilemma is wider in scope than usually supposed. The standard assumption (evident also in Black-burn’s original paper (1993)) is that the dilemma applies to explanations of truths of the form ‘Necessarily-P’. I argue that the real problem identified by Blackburn doesn’t just apply to explanations of truths of this form, but to explanations of necessary truths in general (e.g. truths of logic, mathematics, etc.). In the course of this argument it also transpires that the real problem on the necessity horn is rather different—and rather less susceptible to obvious objections—than it is usually taken to be. It concerns the antinaturalistic core of necessity. Second, it is argued that there is an escape from the antinaturalistic core on the contingency horn. In the footsteps of Wright (1985), the claim is that the contingency horn is tenable for those who believe that the necessary truth in question is analytic, i.e. follows from its meaning.

It is widely believed that some a priori necessary truths are not analytic in the sense of transformable by substitution of synonyms into logical truths. One much-cited example comes from the supposed incompatibility between colour predicates. The idea is that sentences like “Nothing is both blue all over (or uniformly or at a point) and also red” are not transformable into a logical truth in the same way as “Nothing is both a bachelor and married” because the requisite conceptual link between “bachelor” and “not married” is absent between “blue” and “not red”. This paper examines whether colour exclusion may be more like the bachelor case than it initially appears. It transpires that the most promising line of thought is not, however, as has been argued at length in the literature, that “blue” in some more or less convoluted way manages to mean “not red”. Instead it is suggested that the requisite conceptual link may reside in the oft-ignored qualifications (“all over”, “uniformly”, etc.), without which there is no incompatibility in the first place.