Objects, Discreteness, and Pure Power Theories:

Sydney Shoemaker??s causal theory of properties is an important starting place for some contemporary metaphysical perspectives concerning the nature of properties. In this paper, I discuss the causal and intrinsic criteria that Shoemaker stipulates for the identity of genuine properties and relations, and address George Molnar??s criticism that holding both criteria presents an unbridgeable hypothesis in the causal theory of properties. The causal criterion requires that properties and relations contribute to the causal powers of objects if they are to be deemed genuine rather than ??mere-Cambridge??. The intrinsic criterion requires that all genuine properties and relations be intrinsic. Molnar??s S-property argument says that these criteria conflict if one considers extrinsic spatiotemporal properties and relations to contribute causally. In this paper, I argue that a solution to the contradiction that Molnar identifies involves a denial of discreteness between objects, leading to a power holist perspective and a resulting deflationary account of intrinsicality.     

Van Gulick’s solution of the exclusion problem revisited

The anti-reductionist who wants to preserve the causal efficacy of mental phenomena faces several problems in regard to mental causation, i.e. mental events which cause other events, arising from her desire to accept the ontological primacy of the physical and at the same time save the special character of the mental. Psychology tries to persuade us of the former, appealing thereby to the results of experiments carried out in neurology; the latter is, however, deeply rooted in our everyday actions and beliefs and despite the constant opposition of science still very much alive. Difficulties, however, arise from a combination of two claims that are widely accepted in philosophy of mind, namely, physical monism and mental realism, the acceptance of which leads us to the greatest problem of mental causation: the problem of causal exclusion. Since physical causes alone are always sufficient for physical effects mental properties are excluded from causal explanations of our behaviour, which makes them “epiphenomenal”. The article introduces Van Gulick’s solution to the exclusion problem which tries to prove that physical properties, in contrast to mental properties, do not have as much of a privileged status with respect to event causation as usually ascribed. Therefore, it makes no sense to say that physical properties are causally relevant whereas mental properties are not. This is followed by my objection to his argument for levelling mental and physical properties with respect to causation of events. I try to show that Van Gulick’s argument rests on a premise that no serious physicalist can accept. Also called The Problem of Causal Exclusion.     

Direct realism: Proximate causation and the missing object

Direct Realists believe that perception involves direct awareness of an object not dependent for its existence on the perceiver. Howard Robinson rejects this doctrine in favour of a Sense-Datum theory of perception. His argument against Direct Realism invokes the principle ‘same proximate cause, same immediate effect’. Since there are cases in which direct awareness has the same proximate cerebral cause as awareness of a sense datum, the Direct Realist is, he thinks, obliged to deny this causal principle. I suggest that although Direct Realism is in more than one respect implausible, it does not succumb to Robinson’s argument. The causal principle is true only if ‘proximate cause’ means ‘proximate sufficient cause’, and the Direct Realist need not concede that there is a sufficient cerebral cause for direct awareness of independent objects.     

Program explanations and causal relevance

Frank Jackson and Philip Pettit have defended a non-reductive account of causal relevance known as the ‘program explanation account’. Allegedly, irreducible mental properties can be causally relevant in virtue of figuring in non-redundant program explanations which convey information not conveyed by explanations in terms of the physical properties that actually do the ‘causal work’. I argue that none of the possible ways to spell out the intuitively plausible idea of a program explanation serves its purpose, viz., defends non-reductive physicalism against Jaegwon Kim’s Causal Exclusion Argument according to which non-reductive physicalism is committed to epiphenomenalism because irreducible mental properties are ‘screened off’ from causal relevance by their physical realizers. Jackson and Pettit’s most promising explication of a program explanation appeals to the idea of invariance of effect under variation of realization, but I show that invariance of effect under variation of realization is neither necessary nor sufficient for causal relevance.     

The deliberative relevance of refraining from deciding: A response to McKenna and Pereboom

Readers familiar with Harry Frankfurt’s argument that we do not need leeway-liberty (or the power to bring about alternative possible actions or intentions) to be morally responsible will probably also know that the most famous and popular response on behalf of leeway-libertarianism remains a dilemma posed in similar forms by David Widerker, Robert Kane, and Carl Ginet: either the agent retains significant residual leeway in Frankfurt-style cases, or these cases beg the question by presupposing causal determinism. In the last few years, there have been several different attempts to defend Frankfurtian critiques of PAP in response this dilemma. In a novel approach, Derk Pereboom and Michael McKenna present cases in which all deliberatively relevant or “robust” alternatives are blocked, but the agent’s act or decision is not determined. Pereboom and McKenna argue that any plausible leeway-condition on responsibility must characterize the required alternatives as robust in two ways: being voluntary performances and having a practical relevance accessible to the agent’s mind. I agree with the requirement of robustness, and argue that we can build this notion into a complex concept of agent-possibility, or “agentive-can.” However, I argue that both McKenna’s and Pereboom’s conceptions of robustness are too demanding: they exclude alternatives that are intuitively relevant. Moreover, I argue that the alternative of refraining from deciding, or voluntarily failing to decide, is robust in the right sense. In agreement with a tradition running from Ockham back through Scotus to Aquinas, I argue that this robust alternative is necessary for responsibility. If the Frankfurt-controller eliminates it, then the agent’s responsibility is undermined. In particular, I argue that Pereboom’s tax evasion cases do not refute this leeway-condition on moral responsibility.     

Reflective equilibrium and underdetermination in epistemology

The basic aim of Alvin Goldman’s approach to epistemology, and the tradition it represents, is naturalistic; that is, epistemological theories in this tradition aim to identify the naturalistic, nonnormative criteria on which justified belief supervenes (Goldman, 1986; Markie, 1997). The basic method of Goldman’s epistemology, and the tradition it represents, is the reflective equilibrium test; that is, epistemological theories in this tradition are tested against our intuitions about cases of justified and unjustified belief (Goldman, 1986; Markie, 1997). I will argue that the prospect of having to reject their standard methodology is one epistemologists have to take very seriously; and I will do this by arguing that some current rival theories of epistemic justification are in fact in reflective equilibrium with our intuitions about cases of justified and unjustified belief. That is, I will argue that intuition underdetermines theory choice in epistemology, in much the way that observation underdetermines theory choices in empirical sciences. If reflective equilibrium leads to the underdetermination problem I say it leads to, then it cannot satisfy the aims of contemporary epistemology, and so cannot serve as its standard methodology.     

Is There A Quasi-Mereological Account of Property Incompatibility?

Armstrong’s combinatorial theory of possibility faces the obvious difficulty that not all universals are compatible. In this paper I develop three objections against Armstrong’s attempt to account for property incompatibilities. First, Armstrong’s account cannot handle incompatibilities holding among properties that are either simple, or that are complex but stand to one another in the relation of overlap rather than in the part/ whole relation. Secondly, at the heart of Armstrong’s account lies a notion of structural universals which, building on an objection by David Lewis, is shown to be incoherent. I consider and reject two alternative ways of construing the composition of structural universals in an attempt to meet Lewis’ objection. An important consequence of this is that all putative structural properties are in fact simple. Finally, I argue that the quasi-mereological account presupposes modality in a way that undermines the reductionist aim of the combinatorialist theory of which it is a central part. I conclude that Armstrong’ quasi-mereological account of property incompatibility fails. Without that account, however, Armstrong’s combinatorial theory either fails to get off the ground, or else must give up its goal of reducing the notion of possibility to something non-modal.     

Multiplicity and vanishing lemmas for differential and <Emphasis Type="Italic">q</Emphasis>-difference equations in the Siegel–Shidlovsky theory

We present a general multiplicity estimate for linear forms in solutions of various types of functional equations, which extends the zero estimates used in some recent works on the Siegel–Shidlovsky theorem and its q-analogues. We also present a dual version of this estimate, as well as a new interpretation of Siegel’s theorem itself in terms of periods of Deligne’s irregular Hodge theory.     

Some remarks on Reid on primary and secondary qualities

John Locke’s distinction between primary and secondary qualities of objects has meet resistance. In this paper I bypass the traditional critiques of the distinction and instead concentrate on two specific counterexamples to the distinction: Killer yellow and the puzzle of multiple dispositions. One can accommodate these puzzles, I argue, by adopting Thomas Reid’s version of the primary/secondary quality distinction, where the distinction is founded upon conceptual grounds. The primary/secondary quality distinction is epistemic rather than metaphysical. A consequence of Reid’s primary/ secondary quality distinction is that one must deny the original version of Molyneux’s question, while one must affirm an amended version of it. I show that these two answers to Molyneux’s question are not at odds with current empirical research.     

Artistic Expression Goes Green

The paper is a critical discussion of the rich and insightful final chapter of Mitchell Green’s Self-Expression. There, Green seeks to elucidate the compelling, but inchoate intuition that when we’re fully and most expertly expressing ourselves, we can ‘push out’ from within not just our inner representations, but also the ways that we feel. I question, first, whether this type of ‘qualitative expression’ is really distinct from the other expressive forms that Green explores, and also whether it’s genuinely ‘expressive’. I then scrutinize the nature of the ‘qualitative congruences’ that lie at the heart of Green’s theory; and I wonder whether they can play the role Green claims they can in providing a novel account of artistic expression.     

Retracing our steps: Fodor’s new old way with concept acquisition

The acquisition of concepts has proven especially difficult for philosophers and psychologists to explain. In this paper, I examine Jerry Fodor’s most recent attempt to explain the acquisition of concepts relative to experiences of their referents. In reevaluating his earlier position, Fodor attempts to co-opt informational semantics into an account of concept acquisition that avoids the radical nativism of his earlier views. I argue that Fodor’s attempts ultimately fail to be persuasive. He must either accept his earlier nativism or adopt a rational causal model of concept acquisition. His animus towards the latter dictates, in my view, a return to the nativism with which he began.     

Vagueness, ignorance, and margins for error

We argue that the epistemic theory of vagueness cannot adequately justify its key tenet-that vague predicates have precisely bounded extensions, of which we are necessarily ignorant. Nor can the theory adequately account for our ignorance of the truth values of borderline cases. Furthermore, we argue that Williamson’s promising attempt to explicate our understanding of vague language on the model of a certain sort of “inexact knowledge” is at best incomplete, since certain forms of vagueness do not fit Williamson’s model, and in fact fit an alternative model. Finally, we point out that a certain kind of irremediable inexactitude postulated by physics need not be-and is not commonly-interpreted as epistemic. Thus, there are aspects of contemporary science that do not accord well with the epistemicist outlook.     

Illusory possibilities and imagining counterparts

Given Kripke’s semantic views, a statement, such as ‘Water is H₂O’, expresses a necessary a posteriori truth. Yet it seems that we can conceive that this statement could have been false; hence, it appears that we can conceive impossible states of affairs as holding. Kripke used a de dicto strategy and a de re strategy to address three illusions that arise with respect to necessary a posteriori truths: (1) the illusion that a statement such as ‘Water is H₂O’ possibly expresses a falsehood, (2) the illusion that conceivability can fail to latch on to a genuine metaphysical possibility, and (3) the illusion that one can access a real metaphysical possibility by conceiving that water is not H₂O. In this paper I argue that while Kripke’s de dicto strategy dispels (1), his strategies do not enable him to dispel (2) and (3).     

Bar-On on Self-Knowledge and Expression

I critically discuss the account of self-knowledge presented in Dorit Bar-On’s Speaking My Mind (OUP 2004), focusing on Bar-On’s understanding of what makes our capacity for self-knowledge puzzling and on her ‘neo-expressivist’ solution to the puzzle. I argue that there is an important aspect of the problem of self-knowledge that Bar-On’s account does not sufficiently address. A satisfying account of self-knowledge must explain not merely how we are able to make accurate avowals about our own present mental states, but how we can reasonably regard ourselves as entitled to claim self-knowledge. Addressing this aspect of the problem of self-knowledge requires confronting questions about the metaphysical nature of mental states, questions that Bar-On’s approach seeks to avoid.     

A Critique of Armstrong’s Truthmaking Account of Possibility

In this paper I argue against Armstrong’s recent truthmaking account of possibility. I show that the truthmaking account presupposes modality in a number of different ways, and consequently that it is incapable of underwriting a genuine reduction of modality. I also argue that Armstrong’s account faces serious difficulties irrespective of the question of reduction; in particular, I argue that his Entailment and Possibility Principles are both false.

A variant of Chebyshev’s method with sixth-order convergence

In this paper, we present a new variant of Chebyshev’s method for solving non-linear equations. Analysis of convergence shows that the new method has sixth-order convergence. Per iteration the new method requires two evaluations of the function, one of its first derivative and one of its second derivative. Thus the efficiency, in term of function evaluations, of the new method is better than that of Chebyshev’s method. Numerical examples verifying the theory are given.      

Concept nativism and the rule following considerations

In this paper I argue that the most prominent and familiar features of Wittgenstein’s rule following considerations generate a powerful argument for the thesis that most of our concepts are innate, an argument that echoes a Chomskyan poverty of the stimulus argument. This argument has a significance over and above what it tells us about Wittgenstein’s implicit commitments. For, it puts considerable pressure on widely held contemporary views of concept learning, such as the view that we learn concepts by constructing prototypes. This should lead us to abandon our general default hostility to concept nativism and be much more sceptical of claims made on behalf of learning theories.     

Universal theory of dynamical chaos in nonlinear dissipative systems of differential equations

The article presents a new universal theory of dynamical chaos in nonlinear dissipative systems of differential equations, including autonomous and nonautonomous ordinary differential equations (ODE), partial differential equations, and delay differential equations. The theory relies on four remarkable results: Feigenbaum’s period doubling theory for cycles of one-dimensional unimodal maps, Sharkovskii’s theory of birth of cycles of arbitrary period up to cycle of period three in one-dimensional unimodal maps, Magnitskii’s theory of rotor singular point in two-dimensional nonautonomous ODE systems, acting as a bridge between one-dimensional maps and differential equations, and Magnitskii’s theory of homoclinic bifurcation cascade that follows the Sharkovskii cascade. All the theoretical propositions are rigorously proved and illustrated with numerous analytical examples and numerical computations, which are presented for all classical chaotic nonlinear dissipative systems of differential equations.     

Reply to Nathan: How to reconstruct the causal argument

Nicholas Nathan tries to resist the current version of the causal argument for sense-data in two ways. First he suggests that, on what he considers to be the correct re-construction of the argument, it equivocates on the sense of proximate cause. Second he defends a form of disjunctivism, by claiming that there might be an extra mechanism involved in producing veridical hallucination, that is not present in perception. I argue that Nathan’s reconstruction of the argument is not the appropriate one, and that, properly interpreted, the argument does not equivocate on proximate cause. Furthermore, I claim that his postulation of a modified mechanism for hallucinations is implausibly ad hoc.