Validity and Necessity

In this paper I argue against the commonly received view that Kripke’s formal Possible World Semantics (PWS) reflects the adoption of a metaphysical interpretation of the modal operators. I consider in detail Kripke’s three main innovations vis-à-vis Carnap’s PWS: a new view of the worlds, variable domains of quantification, and the adoption of a notion of universal validity. I argue that all these changes are driven by the natural technical development of the model theory and its related notion of validity: they are dictated by merely formal considerations, not interpretive concerns. I conclude that Kripke’s model theoretic semantics does not induce a metaphysical reading of necessity, and is formally adequate independently of the specific interpretation of the modal operators.     

Genuine Violations of Laws

Could laws of nature be violated, in the sense that some proposition is both a law and false? I argue that opponents of regularity theories of laws should accept the metaphysical possibility of such genuine violations. I begin with a clarification of this claim. The main argument is then developed in three steps. I first argue that opponents of regularity theory should endorse the modal-essence view: certain modal principles are essential to the laws of nature. Second, I argue that the modal-essence view entails sophisticated modal primitivism. Third, I argue from sophisticated primitivism to the metaphysical possibility of genuine violations of laws.     

Tarski ‐ a dilemma

Tarski's correspondence theory of truth (which he spells out in his semantic conception of truth) is open to two interpretations. This ambiguity in the theory has led philosophers to find support in it for metaphysical reali sm. In fact, Tarski's theory turns out to support a form of ontological relativism. In different passages Tarski himself gives support to each of these interpretations. The first interpretation leads to ontological relativism, while the second sacrifices the connection between language and the world. I clarify the dilemma that I see in having to choose between these two interpretations, explain how these interpretations have their source in different problems which occupied Tarski, and consider a possible solution to the dilemma. Finally, finding good reasons to claim that Tarski's theory is indeed a correspondence theory of truth, I argue in favour of the first interpretation with its relativistic implications.     

The aim of Russell’s early logicism: a reinterpretation

I argue that three main interpretations of the aim of Russell’s early logicism in The Principles of Mathematics (1903) are mistaken, and propose a new interpretation. According to this new interpretation, the aim of Russell’s logicism is to show, in opposition to Kant, that mathematical propositions have a certain sort of complete generality which entails that their truth is independent of space and time. I argue that on this interpretation two often-heard objections to Russell’s logicism, deriving from Gödel’s incompleteness theorem and from the non-logical character of some of the axioms of Principia Mathematica respectively, can be seen to be inconclusive. I then proceed to identify two challenges that Russell’s logicism, as presently construed, faces, but argue that these challenges do not appear unanswerable.     

Freedom,Frailty, and Impurity

The central question in Heidegger's philosophy, early and late, is that concerning the meaning of being. Recently, some have suggested that Heidegger himself interprets being to mean presence (Anwesen, Anwesenheit, Praesenz), citing as evidence lectures dating from the 1920s to the 1960s. I argue, on the contrary, that Heidegger regards the equation between being and presence as the hallmark of metaphysical thinking, and that it only ever appears in his texts as a gloss on the philosophical tradition, not as an expression of his own ontological commitments. In his early work Heidegger seeks to confront and even correct the traditional interpretation of being by challenging its narrow preoccupation with presence and the present. By the 1930s, however, he abandons the idea that there is anything to‐be intrinsically right or wrong about with regard to the meaning of being and turns his attention instead to what he calls ‘appropriation’ (Ereignis) or the truth of being, that is, the essentially ahistorical condition for the possibility of all historically contingent interpretations of being, including the metaphysical interpretation of being as presence.     

Dewey and the Question of Realism

An interpretation is given of John Dewey's views about “realism” in metaphysics, and of how these views relate to contemporary debates. Dewey rejected standard formulations of realism as a general metaphysical position, and interpreters have often been taken him to be sympathetic to some form of verificationism or constructivism. I argue that these interpretations are mistaken, as Dewey's unease with standard formulations of realism comes from his philosophical emphasis on intelligent control of events, by means of ordinary action. Because of his views about relations, Dewey's views in this area do risk collapsing into an overly holistic position. I discuss how these problems might be avoided, and consider also how Dewey's views about naturalism and realism might usefully inform ongoing work.     

Why Is a Valid Inference a Good Inference?

True beliefs and truth‐preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth‐preserving, but truth‐preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: (i) the orthodox definition given in terms of interpretations or models, (ii) a metaphysical definition given in terms of possible worlds, and (iii) a substitutional definition defended by Quine. I argue that the orthodox notion is poorly suited to explain what's good about a Modus Ponens inference. I argue that there is something good that is explained by a certain kind of truth across possible worlds, but the explanation is not provided by metaphysical validity in particular; nothing of value is explained by truth across all possible worlds. Finally, I argue that the substitutional notion of validity allows us to correctly explain what is good about a valid inference.     

Mereology in Aristotle's Assertoric Syllogistic

How does Aristotle think about sentences like ‘Every x is y’ in the Prior Analytics? A recently popular answer conceives of these sentences as expressing a mereological relationship between x and y: the sentence is true just in case x is, in some sense, a part of y. I argue that the motivations for this interpretation have so far not been compelling. I provide a new justification for the mereological interpretation. First, I prove a very general algebraic soundness and completeness result that unifies the most important soundness and completeness results to date. Then I argue that this result vindicates the mereological interpretation. In contrast to previous interpretations, this argument shows how Aristotle's conception of predication in mereological terms can do important logical work.     

The Metamathematics of Putnam’s Model-Theoretic Arguments

Putnam famously attempted to use model theory to draw metaphysical conclusions. His Skolemisation argument sought to show metaphysical realists that their favourite theories have countable models. His permutation argument sought to show that they have permuted models. His constructivisation argument sought to show that any empirical evidence is compatible with the Axiom of Constructibility. Here, I examine the metamathematics of all three model-theoretic arguments, and I argue against Bays (2001, 2007) that Putnam is largely immune to metamathematical challenges.     

The reference class problem is your problem too

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all “no-theory” theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions. I distinguish a “metaphysical” and an “epistemological” reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains.     

Descartes' Metaphysical Doubts about Clear and Distinct Perception

Descartes' metaphysical doubts in the Third and Fifth Meditations present a scenario like this:it is possible that I (the Meditator) am so imperfect as to be deceived by my author (i.e.,an omnipotent God/Deceiver) in the matters which I think I perceive clearly and distinctly.The metaphysical doubts attempt to cast doubt on beliefs based on present or recollected clear and distinct perceptions.This paper clarifies the intension of the metaphysical doubts by answering the question of how an omnipotent God/Deceiver might exercise a deceptive influence on clear and distinct perception.My analysis shows:(1) the memory interpretation and the retrospective interpretation to be implausible;(2) the incoherence interpretation to be ill-founded,though its conclusion is partly right,such that we should accept a weaker version of it;(3) the misrepresentation interpretation,the defective-origin interpretation,the truth-value variation interpretation and the radical interpretation to be plausible;(4) all of these credible interpretations to be compatible with each other as well.     

What is Presentism?

Different versions of the A‐theory of time (according to which some instant of time is absolutely, objectively present) are traditionally defined in terms of whether everything is present, or whether there are also past and future things. In this paper I argue that the traditional way of defining A‐theories should be abandoned. I focus on the traditional definition of presentism, according to which always, everything is present (§2). First, I argue that there are good reasons to reject all the most plausible interpretations of the predicate ‘is present’ as it appears in the traditional definition of presentism (§3). It follows that there are also good reasons to reject the most plausible interpretations of the traditional definitions of the other A‐theories. I then argue that there is a better way of defining the A‐theories, in terms of the question of whether existence has a beginning and an end (§4). Finally, I argue that what goes for the traditional definition of presentism goes for the traditional definition of its modal analogue actualism, according to which necessarily, everything is actual (§5): there are good reasons to reject the traditional definition of actualism in favour of a definition in terms of contingent existence.     

On the Prospects for Ontology: Deflationism,Pluralism, and Carnap's Principle of Tolerance

In this paper, I critically discuss recent work on the role that the principle of tolerance plays in Rudolf Carnap's philosophy. Specifically, I consider how two prominent interpretations of Carnap's principle of tolerance can be used to argue for Carnap's anti‐metaphysical views. I then argue that there are serious problems with these arguments, and I diagnose those problems as resulting, in part, from a tension between competing goals of Carnap's philosophical project.     

THE POINT OF KANT'S AXIOMS OF INTUITION

Abstract: Kant's Critique of Pure Reason makes important claims about space, time and mathematics in both the Transcendental Aesthetic and the Axioms of Intuition, claims that appear to overlap in some ways and contradict in others. Various interpretations have been offered to resolve these tensions; I argue for an interpretation that accords the Axioms of Intuition a more important role in explaining mathematical cognition than it is usually given. Appreciation for this larger role reveals that magnitudes are central to Kant's philosophy of mathematics and to the part that intuition plays in it.     

Interpretations of Einstein’s Equation E = mc 2

Interpretations of Einstein’s equation differ primarily concerning whether E = mc² entails that mass and energy are the same property of physical systems, and hence whether there is any sense in which mass is ever ‘converted’ into energy (or vice versa). In this paper, I examine six interpretations of Einstein’s equation and argue that all but one fail to satisfy a minimal set of conditions that all interpretations of physical theories ought to satisfy. I argue that we should prefer the interpretation of Einstein’s equation that holds that mass and energy are distinct properties of physical systems. This interpretation also carries along the view that while most cases of ‘conversion’ are not genuine examples of mass being ‘converted’ into energy (or vice versa), it is possible that the there are such ‘conversions’ in the sense that a certain amount of energy ‘appears’ and an equivalent of mass ‘disappears’. Finally, I suggest that the interpretation I defend is the only one that does not blur the distinction between what Einstein called ‘principle’ and ‘constructive’ theories. This is philosophically significant because it emphasizes that explanations of Einstein’s equation and the ‘conversion’ of mass and energy must be top‐down explanations.     

Indefinite Divisibility

Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the intrinsic interest of this metaphysical picture, it has important consequences for the debate over absolute generality. It is often thought that ‘indefinite extensibility’ arguments at best make trouble for mathematical platonists; but the contact arguments show that nominalists face the same kind of difficulty, if they recognize even the metaphysical possibility of the picture I sketch.     

What Kind of Theory is the Humean Theory of Motivation?

I consider an underappreciated problem for proponents of the Humean theory of motivation (HTM). Namely, it is unclear whether is it to be understood as a largely psychological or largely metaphysical theory. I show that the psychological interpretation of HTM will need to be modified in order to be a tenable view and, as it will turn out, the modifications required render it virtually philosophically empty. I then argue that the largely metaphysical interpretation is the only a plausible interpretation of HTM's central claim that desires are necessary conditions for motivation. This interpretation also fits better with the important roles that HTM plays in both moral psychological and metaethical debates. 1     

EXAMINING THE BODHISATTVA'S BRAIN

Owen Flanagan's The Bodhisattva's Brain aims to introduce secular‐minded thinkers to Buddhist thought and motivate its acceptance by analytic philosophers. I argue that Flanagan provides a compelling caution against the hasty generalizations of recent “science of happiness” literature, which correlates happiness with Buddhism on the basis of certain neurological studies. I contend, however, that his positive account of Buddhist ethics is less persuasive. I question the level of engagement with Buddhist philosophical literature and challenge Flanagan's central claim, that a Buddhist version of eudaimonia is a common core conception shared by all Buddhists. I argue that this view is not only a rational reconstruction in need of argumentation but is in tension with competing Buddhist metaphysical theories of self, including the one Flanagan himself endorses.     

The cost of closure: logical realism,anti-exceptionalism,and theoretical equivalence

Philosophers of science often assume that logically equivalent theories are theoretically equivalent. I argue that two theses, anti-exceptionalism about logic (which says, roughly, that logic is not a priori, that it is revisable, and that it is not special or set apart from other human inquiry) and logical realism (which says, roughly, that differences in logic reflect genuine metaphysical differences in the world) make trouble for this commitment, as well as a closely related commitment to theories being closed under logical consequence. I provide three arguments. The first two show that anti-exceptionalism about logic provides an epistemic challenge to both the closure and the equivalence claims; the third shows that logical realism provides a metaphysical challenge to both the closure and the equivalence claims. Along the way, I show that there are important methodological upshots for metaphysicians and philosophers of logic, in particular, lessons about certain conceptions of naturalism as constraining the possibilities for metaphysics and the philosophy of logic.

     

The myth of the categorical counterfactual

I aim to show that standard theories of counterfactuals are mistaken, not in detail, but in principle, and I aim to say what form a tenable theory must take. Standard theories entail a categorical interpretation of counterfactuals, on which to state that, if it were that A, it would be that C is to state something, not relative to any supposition or hypothesis, but categorically. On the rival suppositional interpretation, to state that, if it were that A, it would be that C is to state that it would be that C relative to the supposition that it were that A. The two interpretations make incompatible predictions concerning the correct evaluation of counterfactuals. I argue that the suppositional interpretation makes the correct prediction.