Modal Tense and the Absolutely Unrestricted Quantifier

In this paper, I examine Takashi Yagisawa’s response to van Inwagen’s ontic objection against David Lewis. Van Inwagen criticizes Lewis’s commitment to the absolutely unrestricted sense of ‘there is,’ and Yagisawa claims that by adopting modal tenses he avoids commitment to absolutely unrestricted quantification. I argue that Yagisawa faces a problem parallel to the one Lewis faces. Although Yagisawa officially rejects the absolutely unrestricted sense of a quantifying expression, he is still committed to the absolutely unrestricted sense of ‘is _a real.’     

A Priori knowledge contextualised and Benacerraf’s dilemma

In this article, I discuss Hawthorne’s contextualist solution to Benacerraf’s dilemma. He wants to find a satisfactory epistemology to go with realist ontology, namely with causally inaccessible mathematical and modal entities. I claim that he is unsuccessful. The contextualist theories of knowledge attributions were primarily developed as a response to the skeptical argument based on the deductive closure principle. Hawthorne uses the same strategy in his attempt to solve the epistemologist puzzle facing the proponents of mathematical and modal realism, but this problem is of a different nature than the skeptical one. The contextualist theory of knowledge attributions cannot help us with the question about the nature of mathematical and modal reality and how they can be known. I further argue that Hawthorne’s account does not say anything about a priori status of mathematical and modal knowledge. Later, Hawthorne adds to his account an implausible claim that in some contexts a gettierized belief counts as knowledge.     

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.     

The Incoherence Objection in Moral Theory

J.J.C. Smart famously complained that rule utilitarianism is incoherent, and that rule utilitarians are guilty of “rule worship”. Much has been said about whether Smart’s complaint is justified, but I will assume for the sake of argument that Smart was on to something. Instead, I have three other goals. First, I want to show that Smart’s complaint is a specific instance of a more general objection to a moral theory—what I will call the Incoherence Objection. Second, I want to illustrate how the Incoherence Objection can apply both to consequentialist and, surprisingly, some nonconsequentialist theories. Finally, I want to demonstrate at least one way nonconsequentialist theories that make use of rules, principles, and the like can dodge the Incoherence Objection.     

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.     

Modal Truthmakers,Truth Conditions,and Analyses: or,How to Avoid the Humphrey Objection

Truthmakers, truth conditions, and analyses are closely related, but distinct in rather important ways. A failure to properly appreciate their differences has led to some confusion regarding the role that possible worlds ought to play with respect to modality. Those philosophers who initially proposed the existence of possible worlds were understood as providing an analysis of modality. More recently, many have interpreted them as providing modal truthmakers. But, possible worlds are (at best) only suited to serve as truth conditions for modal truths (or so I will argue). My goals are as follows: First, to dispel this confusion by detailing the differences between these three concepts. Second, to apply the lesson learned to the famous Humphrey objection against possible worlds. While this objection, if successful, does undermine Lewisian modal realism, it only partially undermines ersatzism, and leaves available a route by which ersatzers may avoid the objection altogether.     

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.     

The modality principle and work-relativity of modality

Davies argues that the ontology of artworks as performances offers a principled way of explaining work-relativity of modality. Object oriented contextualist ontologies of art (Levinson) cannot adequately address the problem of work-relativity of modal properties because they understand looseness in what counts as the same context as a view that slight differences in the work-constitutive features of provenance are work-relative. I argue that it is more in the spirit of contextualism to understand looseness as context-dependent. This points to the general problem—the context of appreciation is not robust enough to ground modal intuitions about objective entities. In general, when epistemology dictates ontology there is always a threat of anti-realism, scepticism and relativism. Davies also appeals to the modality principle—an entity’s essential properties are all and only its constitutive properties. Davies understands essentiality in a traditional way: a property P is an essential property of an object o iff o could not exist and lack P. Kit Fine has recently made a convincing case for the view that the notion of essence is not to be understood in modal terms. I explore some of the implications of this view for Davies’ modal argument for the performance theory.     

Kvanvig on Pointless Truths and the Cognitive Ideal

Jonathan Kvanvig has recently attempted to reconcile the problem of (apparently) pointless truths with the claim that the value of truth is unrestricted—that truth is always and everywhere valuable. In this paper, I critically evaluate Kvanvig’s argument and show it to be defective at a crucial juncture. I propose my own alternative strategy for generating Kvanvig’s result—an alternative that parts ways with Kvanvig’s own conception of the cognitively ideal.     

Deformed virasoro algebras andw-algebras from elliptic algebras

Deformedw _n -algebras in the classical case (i.e., Poisson structures) and in the quantum case (exchange algebras) are constructed from the elliptic algebras . In memory of M. Saveliev When I think about Misha, and this has been happening rather frequently these recent months, it is his enthusiasm and his communicative energy that first come to mind. Something very important to Misha was friendship. We scientists have the priviledge to possess friends, real friends, among our colleagues, and Misha was a friend. Something else was fundamental for Misha, his family, i.e., his parents, his wife, and his daughter. As Professor Manin said, summarizing Misha’s behavior very simply and elegantly, Misha was “a good son, a good husband, a good father.” Misha’s parents died about three years ago, and I remember how he was sad when I met him in Georgia in September 1996 and he informed me about his father’s and mother’s deaths a few months before. After that, he concentrated all his forces to protect his wife and daughter, the two Svetlanas, as he used to say! He was so proud of his gifted daughter, a good musician, a good painter, and a brilliant student. I wish to present them my most respectful thoughts. Misha was a great expert in integrable systems. He was deeply interested in developing models, which he did so nicely in the framework of Toda theories. I learned much from him about Toda theories and also continuous Lie algebras. Misha was highly convinced of the importance of symmetries and was especially interested in the use of infinite symmetries, the W-algebras among them. The landscape of continuous symmetries, and particularly of infinite-dimensional symmetries, is becoming richer and richer these years. I dare to think that Misha would have been interested in the modest seminar I now present. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 2, pp. 311–322, May, 2000.     

Multiplicative K-theory and K-theory of Functors

In this article we give a construction of Max Karoubi’s multiplicative K-theory as the K-theory of an appropriate functor between two categories. We use this construction to explain why the two definitions of relative multiplicative K-theory for a compact pair of manifolds we give in the article agree. Part of this work has been done while I was holding an EEC postdoctoral position funded by the network ‘Algebraic K-theory, linear algebraic groups and related structures’ at University College Dublin. I would like to thank Professor David Lewis for inviting me to Dublin. During the later stages of the work, I was supported by EPSERC grant GR/S08046/01.     

Confusion about Bohm

Conclusion  It is important to distinguish between physics, which is an experimental science, andphysicists, who are people. The latter are most certainlynot objective. Thus, Lipschütz-Yevick’s assertion that Ruskai says that the publication of Bohm’s controversial articles in thePhysical Review is evidence of the objectivity of the establishment towards [Bohm] is not supported by my statement It should be noted that even though studying the foundations of quantum mechanics has long been far from the mainstream, it has never been suppressed. The papers of Bohm, Bell,et al. were published in reputable journals, … Reasonable people may disagree on the significance of a particular theory or individual’s contribution. It is here, rather than in the physicsper se, that questions of social influence are likely to arise. I have commented elsewhere, e.g., [17], on the role that gender sometimes plays. In a subsequent article, I will also discuss the distinction between the effect of the social and political climate on the development of the careers of individuals and the development of physics. The articles by Cronin and Lipschütz-Yevick have stimulated me to think anew about a number of issues related to Bohmian mechanics, for which a full discussion requires clarification of some technical issues regarding the EPR experiment and non-locality. These will be discussed in a forthcoming article.     

Spectral structure of Anderson type Hamiltonians

We study self adjoint operators of the form?H _ω = H ₀ + ∑λ_ω(n) <δ _n ,·>δ _n ,?where the δ _n ’s are a family of orthonormal vectors and the λ_ω(n)’s are independently distributed random variables with absolutely continuous probability distributions. We prove a general structural theorem saying that for each pair (n,m), if the cyclic subspaces corresponding to the vectors δ _n and δ _m are not completely orthogonal, then the restrictions of H _ω to these subspaces are unitarily equivalent (with probability one). This has some consequences for the spectral theory of such operators. In particular, we show that “well behaved” absolutely continuous spectrum of Anderson type Hamiltonians must be pure, and use this to prove the purity of absolutely continuous spectrum in some concrete cases. Oblatum 27-V-1999 & 6-I-2000?Published online: 8 May 2000     

Modal Fictionalism, Possible Worlds, and Artificiality

Accounts of modality in terms of fictional possible worlds face an objection based on the idea that when modal claims are analysed in terms of fictions, the connection between analysans and analysandum seems artificial. Strong modal fictionalism, the theory according to which modal claims are analysed in terms of a fiction, has been defended by, among others, Seahwa Kim, who has recently claimed that the philosophical objection that the connection between modality and fictions is artificial can be met. I propose a new way of spelling out the intuition of artificiality and show that strong modal fictionalism should be rejected.     

Decidability results in non-classical logic. III

A Kripke type semantics is given to a large class of tense logics with statability operators (including PriorsQK _t) in such a manner as to obtain their decidability using Rabin’s theorem. Dedicated to the Memory of A. N. Prior     

LR(k) grammars and deterministic languages

A clear proof of the statement that every deterministic language has an LR(l) grammar is given. It uses a definition ofLR(k) grammars found in Lewis and Stearns and the Ginsburg’s simulation of apda by a contex-free grammar. This work is part of a Master’s thesis conducted under the supervision of Professor Eliahu Shamir.     

Lewis’ Modal Realism and Absence Causation

A major criticism of David Lewis’ counterfactual theory of causation is that it allows too many things to count as causes, especially since Lewis allows, in addition to events, absences to be causes as well. Peter Menzies has advanced this concern under the title “the problem of profligate causation.” In this paper, I argue that the problem of profligate causation provides resources for exposing a tension between Lewis’ acceptance of absence causation and his modal realism. The result is a different problem of profligate causation—one that attacks the internal consistency of Lewisian metaphysics rather than employing common sense judgments or intuitions that conflict with Lewis’ extensive list of causes.