The Phenomenal Sorites and Response Dependence 1

Natural-kind essentialism faces an important but neglected difficulty: the problem of complex essences (PCE). This is the question of how to account for the unity of an instantiated kind-essence when that essence consists of multiple distinct properties, some of which lack an inherent necessary connection between them. My central goal here is to propose an essentialism-friendly solution to this problem. Along the way I also employ some points from that solution to argue for the necessary truth of essentialism (necessary, that is, in all possible worlds in which there are material objects), and to support the essentialist ontology of laws over and against a major rival.     

Chain-Arguments and the Sorites Paradox

A finite chain of valid arguments can never lead from truth to falsehood. Call this the concatenation principle, or CP. Some propose to reject CP in response to the sorites paradox. I offer a justification of a restricted version of CP based on intuitively-appealing principles, all of which are already assumed in mathematics. The restricted version excludes soritical cases, but covers intuitively correct applications of CP in mathematics and elsewhere. The upshot is that the cost of rejecting the unrestricted CP is much lower than is often assumed.     

Strict Finitism and the Happy Sorites

Call an argument a ‘happy sorites’ if it is a sorites argument with true premises and a false conclusion. It is a striking fact that although most philosophers working on the sorites paradox find it at prima facie highly compelling that the premises of the sorites paradox are true and its conclusion false, few (if any) of the standard theories on the issue ultimately allow for happy sorites arguments. There is one philosophical view, however, that appears to allow for at least some happy sorites arguments: strict finitism in the philosophy of mathematics. My aim in this paper is to explore to what extent this appearance is accurate. As we shall see, this question is far from trivial. In particular, I will discuss two arguments that threaten to show that strict finitism cannot consistently accept happy sorites arguments, but I will argue that (given reasonable assumptions on strict finitistic logic) these arguments can ultimately be avoided, and the view can indeed allow for happy sorites arguments.     

Higher-Order Sorites Paradox

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 (such as ‘borderline’ and ‘definitely’) 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.     

The Self and the Phenomenal

As is widely appreciated and easily demonstrated, the notion that we are essentially experiential (or conscious) beings has a good deal of appeal; what is less obvious, and more controversial, is whether it is possible to devise a viable account of the self along such lines within the confines of a broadly naturalistic metaphysical framework. There are many avenues to explore, but here I confine myself to outlining the case for one particular approach. I suggest that we should think of ourselves (or our essential cores) as being composed of experience‐producing systems, and that such systems belong to the same self when they have the capacity to contribute to unified streams of consciousness. The viability of this proposal rests in turn on a particular conception of the structure of consciousness, both at and over time; this conception is defended in the first part of the paper     

A Wittgensteinian Solution to the Sorites

I develop a solution to the Sorites Paradox, according to which a concatenation of valid arguments need not itself be valid. I specify which chains of valid arguments are those that do not preserve validity: those that pass the vague boundary between cases where the relevant concept applies and cases where that concept does not apply. I also develop various criticisms of this solution and show why they fail; basically, they all involve a petitio at some stage. I criticise the conviction that if every short argument in a long concatenated argument is valid, so is the long argument: it is, I argue, the result of an unjustified generalisation from the case of arguments that do not employ vague concepts (as in mathematics) to arguments that do employ them. My approach is Wittgensteinian in its “leaving everything as it is,” in its claiming that the “beginning” has been searched too far back (see paper's epigraph) and in its claim that the paradox was generated by a misapplication of a partial picture of the behaviour of arguments. I conclude my paper by comparing and contrasting my approach to the few precedents found in the vagueness literature and by answering a few additional objections that were raised there.