Andreas Ditter

The concept of essence is a paradigm case of a putatively hyperintensional concept in metaphysics, a concept that can draw distinctions between necessarily equivalent propositions. Yet as several authors have recently emphasized, fine-grained distinctions in metaphysics come with a substantial risk of inconsistency, due to the Russell-Myhill paradox and its variants. This concern is especially pressing for hyperintensionalists about essence because the hyperintensionality of essence has been motivated primarily by examples. This paper presents a novel, more systematic case for the hyperintensionality of essence that shows that the relevant distinctions can be systematically modeled in a natural theoretical framework. I start by offering a general heuristic to motivate a range of examples of fine-grained essentialist distinctions. I then present a higher-order logical framework for regimenting essentialist statements and provide a general argument for hyperintensionality on the basis of minimal assumptions about the logic of essence. Finally, I address the question of consistency by developing a semantic framework that demonstrates that the relevant fine-grained distinctions can indeed be consistently drawn.

This paper develops a logic of essence (HLE) in the framework of higher-order logic. The theory aims to provide a general framework for theorizing about the essences of objects, properties, propositions, and logical operations like conjunction, negation, quantification, etc. The first part of the paper presents the formal language and axiom system of HLE. After that, some theorems of the system are proved and it is shown how the logic of metaphysical necessity can be developed within the framework of HLE. The second part of the paper develops a possible worlds semantics for HLE, gives a proof of soundness, and provides examples of models that demonstrate the consistency of some simple essentialist theories.

In his paper ‘The possibility of vagueness’ (Fine in Synthese 194(10):3699–3725, 2017), Kit Fine proposes a new logic of vagueness, CL, that promises to provide both a solution to the sorites paradox and a way to avoid the impossibility result from Fine (Philos Perspect 22(1):111–136, 2008). The present paper presents a challenge to his new theory of vagueness. I argue that the possibility theorem stated in Fine (Synthese 194(10):3699–3725, 2017), as well as his solution to the sorites paradox, fail in certain reasonable extensions of the language of CL. More specifically, I show that if we extend the language with any negation operator that obeys reductio ad absurdum, we can prove a new impossibility result that makes the kind of indeterminacy that Fine takes to be a hallmark of vagueness impossible. I show that such negation operators can be conservatively added to CL and examine some of the philosophical consequences of this result. Moreover, I demonstrate that we can define a particular negation operator that behaves exactly like intuitionistic negation in a natural and unobjectionable propositionally quantified extension of CL. Since intuitionistic negation obeys reductio, the new impossibility result holds in this propositionally quantified extension of CL. In addition, the sorites paradox resurfaces for the new negation.

Let an iterated essentialist statement be a statement of the form 'It lies in the nature of x1,x2,... that it lies in the nature of y1,y2,... that φ'. Let Iteration be the thesis that there are true iterated essentialist statements. Iteration has recently been disputed by Dasgupta (2014) and Glazier (2017). Both authors take the falsity of Iteration to be central to the explanatory role of essentialist truths. An important consequence that is not explicitly noted by them is that the falsity of Iteration would entail that metaphysical necessity is not reducible to essence in the manner suggested by Fine (1994). This paper defends Iteration against these challenges, drawing attention to some features of the collective essences of properties, propositions, and logical operations that have been largely neglected in discussions about essence.

What is the relation between metaphysical necessity and essence? This paper defends the view that the relation is one of identity: metaphysical necessity is a special case of essence. My argument consists in showing that the best joint theory of essence and metaphysical necessity is one in which metaphysical necessity is just a special case of essence. The argument is made against the backdrop of a novel, higher-order logic of essence, whose core features are introduced in the first part of the paper. The second part investigates the relation between metaphysical necessity and essence in the context of HLE. Reductive hypotheses are among the most natural hypotheses to be explored in the context of HLE. But they also have to be weighed against their non-reductive rivals. I investigate three different reductive hypotheses and argue that two of them fare better than their non-reductive rivals: they are simpler, more natural, and more systematic. Specifically, I argue that one candidate reduction, according to which metaphysical necessity is truth in virtue of the nature of all propositions, is superior to the others, including one proposed by Kit Fine, according to which metaphysical necessity is truth in virtue of the nature of all objects. The paper concludes by offering some reasons to think that the best joint theory of essence and metaphysical necessity is one in which the logic of metaphysical necessity includes S4, but not S5.

In "Essence and Modality", Kit Fine proposes that for a proposition to be metaphysically necessary is for it to be true in virtue of the nature of all objects whatsoever. Call this view Fine's Thesis. This paper is a study of Fine's Thesis in the context of Fine's logic of essence (LE). Fine himself has offered his most elaborate defense of the thesis in the context of LE. His defense rests on the widely shared assumption that metaphysical necessity obeys the laws of the modal logic S5. In order to get S5 for metaphysical necessity, he assumes a controversial principle about the nature of all objects. I will show that the addition of this principle to his original system E5 leads to inconsistency with an independently plausible principle about essence. In response, I develop a theory that avoids this inconsistency while allowing us to maintain S5 for metaphysical necessity. However, I conclude that our investigation of Fine's Thesis in the context of LE motivates the revisionary conclusion that metaphysical necessity obeys the principles of the modal logic S4, but not those of S5. I argue that this constitutes a distinctively essentialist challenge to the received view that the logic of metaphysical necessity is S5.

Intellectualism about knowledge-how is the view that knowing how to do something amounts to knowing a fact. The version of intellectualism defended by Jason Stanley and Timothy Williamson holds that knowledge-how is a species of knowledge-wh, i.e., knowledge-where, -when, -who, etc. It draws its major motivation from the uniformity between ascriptions of knowledge-how and ascriptions of knowledge-wh in English, being all infinitival embedded question constructions. My aim in this paper is to challenge intellectualism of this sort. I argue that the linguistic motivation for the view is not preserved across languages and that it cannot be sustained from the perspective of other languages. I will show this by examining ascriptions of practical knowledge and knowledge-wh in Russian, Turkish and German. The cross-linguistic data further suggest that ‘know how’ is ambiguous in English. In the end, the cross-linguistic data will be used to question an argument for the propositionality of practical knowledge.