The Opacity of Definition

This paper is concerned with logical attributes of (real) definition. In particular, I argue that substitution principles give rise to reflexive definitions: cases in which something is directly and exclusively defined in terms of itself. Many maintain that definition is both substitutable and irreflexive, so these standard commitments are at odds. As a corollary, I demonstrate that the claims in ‘Real Definition’ Rosen (2015) are logically inconsistent. I close with a brief discussion of the implications this has for the opacity of definition and for philosophical methodology more generally

Counterfactual Logic and the Necessity of Mathematics

This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne (2018), who seek to establish that mathematics is committed to its own necessity. I claim that their argument fails to establish this result for two reasons. First, their assumptions force our hand on a controversial debate within counterfactual logic. In particular, they license counterfactual strengthening— the inference from ‘If A were true then C would be true’ to ‘If A and B were true then C would be true’—which many reject. Second, the system they develop is provably equivalent to appending Deduction Theorem to a T modal logic. It is unsurprising that the combination of Deduction Theorem with T results in necessitation; indeed, it is precisely for this reason that many logicians reject Deduction Theorem in modal contexts. If Deduction Theorem is unacceptable for modal logic, it cannot be assumed to derive the necessity of mathematic

There Are no Metaphysical Primitives

Many metaphysicians posit primitives. These vary with respect to the theoretical work that they perform, but are all undefinable in more basic terms. I argue against the existence of metaphysical primitives on the grounds that, if they existed, they would be essentially primitive. However, if primitives were essentially primitive, then they would have an essence. Because they are primitive, they lack an essence, which undermines the original supposition that they are primitive. I close by mentioning some implications this has both for metaphysicians and for metaphysics more generally

Knowledge is Closed Under Analytic Content

I am concerned with epistemic closure—the phenomenon in which some knowledge requires other knowledge. In particular, I defend a version of the closure principle in terms of analyticity; if an agent S knows that p is true, then S knows that all analytic parts of p are true as well. After targeting the relevant notion of analyticity, I argue that this principle accommodates intuitive cases and possesses the theoretical resources to avoid the preface paradox. I close by arguing that contextualists who maintain that knowledge attributions are closed within—but not between—linguistic contexts are tacitly committed to this principle’s trut

The Semantic Foundations of Philosophical Analysis

I provide an analysis of sentences of the form ‘To be F is to be G’ in terms of exact truth-maker semantics—an approach that identifies the meanings of sentences with the states of the world directly responsible for their truth-values. Roughly, I argue that these sentences hold just in case that which makes something F is that which makes it G. This approach is hyperintensional, and possesses desirable logical and modal features. These sentences are reflexive, transitive and symmetric, and, if they are true, then they are necessarily true, and it is necessary that all and only Fs are Gs. I close by defining an asymmetric and irreflexive notion of analysis in terms of the reflexive and symmetric one

The Levels of the Empirical Sciences

It is the aim of this paper to develop and defend an interpretation of level of scientific discipline within the truth-maker framework. In particular, I exploit the mereological relation of proper parthood, which is integral to truth-maker semantics, in order to provide an account of scientific level

Mechanisms for the production of harmonics in free electron lasers

Harmonics in the radiation of a free electron laser are useful for extending the range of tuning, may originate in spontaneous or parametric processes, and can take part in stimulated emission or amplification. These mechanisms exhibit interesting analogies with those of nonlinear optics. Apart from the well known nonparametric gain analogous to stimulated Brillouin scattering, they include third-harmonic generation and other four-wave mixing parametric processes, with spatial harmonics of the electron density taking the place of the higher-order terms in the nonlinear dielectric susceptibility. We investigate these mechanisms using a one-dimensional model