Can identity itself be vague? Can there be vague objects? Does a positive answer to either question entail a positive answer to the other? In this paper we answer these questions as follows: No, No, and Yes. First, we discuss Evans’s famous 1978 argument and argue that the main lesson that it imparts is that identity itself cannot be vague. We defend the argument from objections and endorse this conclusion. We acknowledge, however, that the argument does not by itself establish (...) either that there cannot be vague objects or that there cannot be identity statements that are indeterminate for ontic reasons. And we further acknowledge that it does not by itself establish that there cannot be identity statements that are indeterminate in virtue of the existence of vague objects. We then go on to argue that, despite this, one who believes in vague objects cannot endorse Evans’s argument. To establish this we offer supplementary arguments that show that if vague objects exist then identity is vague, and that if identity is vague then vague objects exist. Finally we draw attention to an argument parallel to that of Evans’s, but safer, which can be employed against the putative ontic indeterminacy in identity of vague objects which can be differentiated by identity-free properties. (shrink)

The naive theory of vagueness holds that the vagueness of an expression consists in its failure to draw a sharp boundary between positive and negative cases. The naive theory is contrasted with the nowadays dominant approach to vagueness, holding that the vagueness of an expression consists in its presenting borderline cases of application. The two approaches are briefly compared in their respective explanations of a paramount phenomenon of vagueness: our ignorance of any sharp boundary between positive and negative cases. These (...) explanations clearly do not provide any ground for choosing the dominant approach against the naive theory. The decisive advantage of the former over the latter is rather supposed to consist in its immunity to any form of sorites paradox. But another paramount phenomenon of vagueness is higher-order vagueness: the expressions introduced in order to express in the object language the vagueness of the object language are themselves vague. Two highly plausible claims about higher-order vagueness are articulated and defended: the existence of “definitely ω ” positive and negative cases and the “radical” character of higher-order vagueness itself. Using very weak logical principles concerning vague expressions and the ‘definitely’-operator, it is then shown that, in the presence of higher-order vagueness as just described, the dominant approach is subject to higher-order sorites paradoxes analogous to the original ones besetting the naive theory, and therefore that, against the communis opinio, it does not fare substantially better with respect to immunity to any form of sorites paradox. (shrink)

The paper critically discusses two prominent arguments against closure principles for knowledge. The first one is the “argument from aggregation”, claiming that closure under conjunction has the consequence that, if one individually knows i premises, one also knows their i-fold conjunction—yet, every one of the premises might exhibit interesting positive epistemic properties while the i-fold conjunction might fail to do so. The second one is the “argument from concatenation”, claiming that closure under entailment has the consequence that, if one knows (...) a premise, one also knows each of its remote consequences one arrives at—yet, again, the premise might exhibit interesting positive epistemic properties while some of its remote consequences might fail to do so. The paper firstly observes that the ways in which these two arguments try to establish that the relevant closure principle has the relevant problematic consequence are strikingly similar. They both crucially involve showing that, given the features of the case, the relevant closure principle acts in effect as a soritical principle, which is in turn assumed to lead validly to the relevant problematic consequence. There are however nontransitive logics of vagueness where soritical principles do not have any problematic consequence. Assuming that one of these logics is the correct logic of vagueness, the paper secondly observes that both arguments describe situations where knowledge is arguably vague in the relevant respects, so that a tolerant logic should be used in reasoning about it, with the effect that the relevant soritical principle no longer validly leads to the relevant problematic consequence. This shows an interesting respect in which the gap between validity and good inference that arguably arises in a transitive framework can be bridged in a tolerant one, thereby approximating better certain features of our epistemic lives as finite subjects. Moreover, even for those who do not subscribe to tolerant logics, the paper’s two observations jointly indicate that, for all the arguments from aggregation and concatenation show, the status of the relevant closure principles should be no worse than that assigned by one’s favoured theory of vagueness to soritical principles, which only rarely is plain falsity and can indeed get arbitrarily close to full truth. (shrink)