Mathematical formalism is the the view that numbers are "signs" and that arithmetic is like a game played with such signs. Frege's colleague Thomae defended formalism using an analogy with chess, and Frege's critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. I argue that (...) for Thomae, the formal standpoint is an _algebraic perspective_ on a domain of objects, and a "sign" is not a linguistic expression or mark, but a representation of an object within that perspective. Thomae exploits a shift into this perspective to give a purely algebraic construction of the real numbers from the rational numbers. I suggest that Thomae's chess analogy is intended to provide a model for such shifts in perspective. (shrink)

Frege says, at the end of a discussion of formalism in the Foundations of Arithmetic, that his own foundational program “could be called formal” but is “completely different” from the view he has just criticized. This essay examines Frege’s relationship to Hermann Hankel, his main formalist interlocutor in the Foundations, in order to make sense of these claims. The investigation reveals a surprising result: Frege’s foundational program actually has quite a lot in common with Hankel’s. This undercuts Frege’s claim that (...) his own view is completely different from Hankel’s formalism, and motivates a closer examination of where the differences lie. On the interpretation offered here, Frege shares important parts of the formalist perspective, but differs in recognizing a kind of content for arithmetical terms which can only be made available via proof from prior postulates. (shrink)

Frege famously held that numbers play the role of objects in our language and thought, and that this role is on display when we use sentences like "The number of Jupiter's moons is four". I argue that this role is an example of a general pattern that also encompasses persons, times, locations, reasons, causes, and ways of appearing or acting. These things are 'objects' simply in the sense that they are answers to questions: they are the sort of thing we (...) search for and specify during investigation or inquiry. I support this epistemological conception of objects by studying specificational sentences, a class of sentences which includes Frege's original example. I defend an analysis of such sentences as question-answer pairs, and show how to formally represent this analysis using game-theoretical semantics. (shrink)

What does it mean to ‘give’ the value of a variable in an algebraic context, and how does giving the value of a variable differ from merely describing it? I argue that to answer this question, we need to examine the role that giving the value of a variable plays in problem-solving practice. I argue that four different features are required for a statement to count as giving the value of a variable in the context of solving an elementary algebra (...) problem: the variable must be in the scope opened by the problem statement; the values given must be in the range of the variable, which is determined by the problem; the statement giving the values must represent a complete solution; and it must be in a canonical form. This account helps us better understand elementary algebra itself, as well as the use of algebraic tools to analyze phenomena in natural language. (shrink)

Hossack’s project in this book is to provide a new foundation for the philosophy of number inspired by the traditional idea that numbers are magnitudes.

In §57 of the Foundations of Arithmetic, Frege famously turns to natural language to support his claim that numbers are ‘self-subsistent objects’:I have already drawn attention above to the fact th...

Is it possible to recognize the limits of rationality, and thus to embrace moral pluralism, without embracing moral relativism? My answer is yes; nevertheless, certain anti-foundational positions, both recent and ancient, take a cynical stance toward the possibility of any critical moral judgment, and as such, must be regarded as relativistic.1 It is such cynicism, I argue, whether openly announced or unknowingly implied, that marks the distinction between relativism and pluralism.2 The danger of this cynicism is not so much that (...) it renders the categorical acceptance of a particular moral view unattainable, but that it renders categorical condemnation of any particular position (or action) impossible.3 Two .. (shrink)

In this paper we look at the manual analysis of arguments and how this compares to the current state of automatic argument analysis. These considerations are used to develop a new approach combining a machine learning algorithm to extract propositions from text, with a topic model to determine argument structure. The results of this method are compared to a manual analysis.

Examines the theories of Socrates, Kant, Dewey, Piaget, and others to explore the implications of Socrates' question "what is a virtuous man, and what is a virtuous school and society which educates virtuous men.".

Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to establish it. In this paper, I explore which formulations of the norm are supported by which arguments. In their standard formulations, each of the arguments I consider here depends on the same assumption, which I call Deterministic Updating. I will investigate whether it is possible to amend these arguments so that they no longer depend (...) on it. As I show, whether this is possible depends on the formulation of the norm under consideration. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given time; (...) an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

In this paper I defend what I call the argument from epistemic reasons against the moral error theory. I argue that the moral error theory entails that there are no epistemic reasons for belief and that this is bad news for the moral error theory since, if there are no epistemic reasons for belief, no one knows anything. If no one knows anything, then no one knows that there is thought when they are thinking, and no one knows that they (...) do not know everything. And it could not be the case that we do not know that there is thought when we believe that there is thought and that we do not know that we do not know everything. I address several objections to the claim that the moral error theory entails that there are no epistemic reasons for belief. It might seem that arguing against the error theory on the grounds that it entails that no one knows anything is just providing a Moorean argument against the moral error theory. I show that even if my argument against the error theory is indeed a Moorean one, it avoids Streumer's, McPherson's and Olson's objections to previous Moorean arguments against the error theory and is a more powerful argument against the error theory than Moore's argument against external world skepticism is against external world skepticism. (shrink)

The dispute about the role of class in understanding the life situations of people of color has tended to be overpolarized, between a class reductionism and an “it's only race” position. Class processes shape racial groups’ life situations. Race and class are also distinct axes of injustice; but class injustice informs racial injustice. Some aspects of racial injustice can be expressed only in concepts associated with class (e.g., material deprivation, inferior education). But other aspects of racial injustice or other harms, (...) such as racial discrimination or stigma, are not reducible to class concepts and cannot be fully addressed through class-focused policies. Overall, any attempt to fully secure racial justice for a racial group will require a combination of race-focused and class-focused policies. Anti-racist outlooks often neglect or downplay either the normative or the explanatory significance of class, or both—for example, by overlooking or downplaying the dignitary harms of class and the material harms of race; missing the historical dimension of class injustice; masking class by a narrowing of the complex normative structure of racial disparities; or not recognizing that a class-focused initiative (like raising the minimum wage) can address substantial racial justice concerns, even though not all of them. “Systemic racism” terminology recognizes class explanatorily but suppresses it normatively. Charles Mills's influential notion of “white supremacy,” while a powerful tool for conceptualizing and illuminating racial injustice, can also contribute to minimizing or masking the justice-related impact of class, as do some of Mills's specific discussions of class in various writings. (shrink)

Many philosophers nowadays believe Frege was right about belief, but wrong about language: The contents of beliefs need to be individuated more finely than in terms of Russellian propositions, but the contents of utterances do not. I argue that this 'hybrid view' cannot offer no reasonable account of how communication transfers knowledge from one speaker to another and that, to do so, we must insist that understanding depends upon more than just getting the references of terms right.

All humans have an equal basic moral status. They possess the same fundamental rights, and the comparable interests of each person should count the same in calculations that determine social policy. Neither supposed racial differences, nor skin color, sex, sexual orientation, ethnicity, intelligence, nor any other differences among humans negate their fundamental equal worth and dignity. These platitudes are virtually universally affirmed. A white supremacist racist or an admirer of Adolf Hitler who denies them is rightly regarded as beyond the (...) pale of civilized dialogue. However, a very simple line of argument developed by Peter Singer challenges our understanding of these platitudes and forces us to rethink the basis and nature of the moral equality of all humans. What I call the “Singer Problem” arises if one accepts that the morally significant cognitive capacities that are relevant to the determination of the fundamental moral status of a being vary from individual to individual by degree. The problem is to specify a moral principle determining fundamental moral status that assigns a superior status to humans compared to other animals on the basis of the superior cognitive capacities of humans but also assigns all human persons an equal fundamental moral status regardless of their differing cognitive capacities. More broadly posed, the problem is to specify moral principles that yield intuitively satisfactory implications for the treatment of human individuals and other individual animals given that cognitive capacities differ across species and individuals. A search for a resolution of the Singer problem leads to disappointing results. (shrink)

Since the publication of Andrews Reath's “Two Conceptions of the Highest Good in Kant” (Journal of the History of Philosophy 26:4 (1988)), most scholars have come to accept the view that Kant migrated away from an earlier “theological” version to one that is more “secular.” The purpose of this paper is to explore the roots of this interpretative trend, re-assess its merits, and then examine how the Highest Good is portrayed in Kant’s Religion within the Boundaries of Mere Reason. As (...) will be argued, it is in this text more so than any other where Kant develops his most philosophically sophisticated account of the Highest Good. Because of the central significance of Kant’s doctrine of the Highest Good for both his ethical theory and philosophy of religion, this paper therefore seeks to provide an important corrective to the current received views. (shrink)

The scientific consensus regarding anthropogenic climate change is firmly established yet climate change denialism, a species of what I call pseudoskepticism, is on the rise in industrial nations most responsible for climate change. Such denialism suggests the need for a robust ethics of inquiry and public discourse. In this paper I argue: (1) that ethical obligations of inquiry extend to every voting citizen insofar as citizens are bound together as a political body. (2) It is morally condemnable for public officials (...) to put forward assertions contrary to scientific consensus when such consensus is decisive for public policy and legislation. (3) It is imperative upon educators, journalists, politicians and all those with greater access to the public forum to condemn, factually and ethically, pseudoskeptical assertions made in the public realm without equivocation. (shrink)

In the Fifth Meditation, Descartes makes a remarkable claim about the ontological status of geometrical figures. He asserts that an object such as a triangle has a 'true and immutable nature' that does not depend on the mind, yet has being even if there are no triangles existing in the world. This statement has led many commentators to assume that Descartes is a Platonist regarding essences and in the philosophy of mathematics. One problem with this seemingly natural reading is that (...) it contradicts the conceptualist account of universals that one finds in the Principles of Philosophy and elsewhere. In this paper, I offer a novel interpretation of the notion of a true and immutable nature which reconciles the Fifth Meditation with the conceptualism of Descartes' other work. Specifically, I argue that Descartes takes natures to be innate ideas considered in terms of their so-called 'objective being'. (shrink)

This paper is concerned with neo-Fregean accounts of reference to abstract objects. It develops an objection to the most familiar such accounts, due to Bob Hale and Crispin Wright, based upon what I call the 'proliferation problem': Hale and Wright's account makes reference to abstract objects seem too easy, as is shown by the fact that any equivalence relation seems as good as any other. The paper then develops a response to this objection, and offers an account of what it (...) is for abstracta to exist that is Fregean in spirit but more robust than familiar views. (shrink)

Neoliberalism is an approach to social policy, now globally influential, that applies market approaches to all aspects of social life, including education. Charter schools, privately operated but publicly funded, are its most prominent manifestation in the U.S. The neoliberal principles of competition, consumerism, and choice cannot serve as foundations of a sound and equitable public education system. Neoliberalism embraces socio-economic inequality overall and in doing so constricts any justice mission its adherents espouse in virtue of serving a relatively disadvantaged student (...) population, as charter schools often (by no means always) do. It constricts educational justice by (1) embracing a “human capital” approach as the primary good of education, (2) creating educational inequality through (unofficially) selecting a relatively advantaged segment of the disadvantaged demographic it serves, (3) denying the effect of poverty on educational performance, and (4) devaluing its students’ familial ethnic cultures. (shrink)

An investigation of Frege’s various contributions to the study of language, focusing on three of his most famous doctrines: that concepts are unsaturated, that sentences refer to truth-values, and that sense must be distinguished from reference.

The Intergovernmental Panel on Climate Change has developed a novel framework for assessing and communicating uncertainty in the findings published in their periodic assessment reports. But how should these uncertainty assessments inform decisions? We take a formal decision-making perspective to investigate how scientific input formulated in the IPCC’s novel framework might inform decisions in a principled way through a normative decision model.

I argue that Descartes intended the so-called ontological "argument" as a self-validating intuition, rather than as a formal proof. The textual evidence for this view is highly compelling, but the strongest support comes from understanding Descartes's diagnosis for why God's existence is not 'immediately' self-evident to everyone and the method of analysis that he develops for making it self-evident. The larger aim of the paper is to use the ontological argument as a case study of Descartes's nonformalist theory of deduction (...) and his method of analysis, showing how he conceives the latter as a form of philosophical therapy. (shrink)

Observers have noted a decline (in the US) in attributions of genetically-based inferiority (e.g. in intelligence) to Blacks, and a rise in attributions of culturally-based inferiority. Is this "culturalism" merely warmed-over racism ("cultural racism") or a genuinely distinct way of thinking about racial groups? The question raises a larger one about the relative place of biology and culture in racist thought. I develop a typology of culturalisms as applied to race: (1) inherentist or essentialist culturalism (inferiorizing cultural characteristics wrongly but (...) intelligibly regarded as inhering in the nature of racial groups). This view has an historical pedigree in the work of J.G. von Herder, and the tradition of "national racism." (2) non-inherentist culturalism (groups regarded as possessing changeable, malleable inferiorizing cultural characteristics). (3) colonalist culturalism (colonial subjects regarded as uncivilized but capable of becoming civilized under European tutelage). (4) neo-racism (cultures of former colonial subjects in or potentially immigrating to European countries are regarded in an inherentist manner and incompatible with but not inferior to European cultures). Non-inherentist culturalism (#2) can be put to either a racist or an anti-racist use. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 43.1 (2005) 55-81 [Access article in PDF] Self-Knowledge in Descartes and Malebranche Lawrence Nolan John Whipple 1. Introduction Descartes's notorious claim that mind is better known than body has been the target of repeated criticisms, but none appears more challenging than that of his intellectual heir Nicolas Malebranche.1 Whereas other critics—especially twentieth-century philosophers eager to use Descartes as their whipping boy—have often (...) been uncharitable, Malebranche accepts many of the fundamental Cartesian doctrines, including mind-body dualism. But he argues that Descartes's position on knowledge of the mind is internally inconsistent. Malebranche agrees with Descartes that the existence of the mind is better known than that of body, but he vehemently denies that the nature of the mind is better known. This denial is based on his view that we lack a clear idea of the mind.2 [End Page 55]Malebranche's polemic has attracted much attention in recent scholarship.3 The growing consensus among commentators is that Malebranche develops a devastating internal critique of Descartes's theory of the mind. For example, Nicholas Jolley writes: "In his case for his negative thesis [concerning knowledge of the mind] Malebranche mounted a powerful, even annihilating, critique of Descartes. This critique embodies the remarkable insight that there is a serious muddle at the heart of Descartes's whole theory of knowledge."4 In a book-length defense of Malebranche's critique, Tad Schmaltz also emphasizes its internal character: "the interpretation here of Malebranche's theory presents it as fundamentally Cartesian, and thereby serves to reinforce his own view that he has provided an authoritative interpretation of the account of mind in the writings of Descartes and other Cartesians."5 Schmaltz also asserts: "Malebranche took his negative thesis concerning our knowledge of the soul to involve not so much a rejection of Cartesianism as an internal correction of it."6We think such remarks misstate the case. Indeed, we argue in this paper that Malebranche's polemic fails as an internal critique of Descartes's theory of the mind. Although we do not here aspire to defend Descartes's strong thesis—that mind is better known than body—we do think he can consistently maintain that we have a clear and distinct idea of the mind, and thus that our knowledge of the mind's nature is at least on a par with our knowledge of corporeal nature.7 While Malebranche's rhetoric would encourage us to think that the debate between him and his predecessor is being fought on common or neutral ground, the fact is that Malebranche often appeals to assumptions and aspects of his own theory of "Vision in God" that Descartes would reject. Once more, he interprets Descartes's theory of knowledge in ways that are misguided and sometimes even uncharitable. If Malebranche's critique succeeds at all, it succeeds only against a straw man—Malebranche's Descartes and not the historical figure.Ours is not the first effort to defend Descartes against this particular attack. When Malebranche first published his critique in Book Three of his first great work, The Search After Truth (1674),8 Descartes had been dead for over two decades, [End Page 56] but he was ably defended by the famous Cartesian Antoine Arnauld in On True and False Ideas (1683). In the ensuing debate Arnauld was clearly the superior dialectician, but while winning several tactical points, he appears not to fully appreciate the crux of Malebranche's argument, or at least that is the view of Jolley and Schmaltz.9 We have a somewhat higher opinion of Arnauld's side of the debate. Granted, some of his defenses are facile and can be easily dismissed; others however are quite compelling when properly developed. In at least one instance, we attempt to provide that development. At the same time we think it is a mistake to treat Arnauld as Descartes's surrogate or as if he had issued the final salvo from the camp of the orthodox Cartesians. Arnauld was a... (shrink)

Nichols’s view of empathy (in Sentimental Rules) in light of experimental moral psychology suffers from several deficiencies: (1) It operates with an impoverished view of the altruistic emotions (empathy, sympathy, concern, compassion, etc.) as mere short-term, affective states of mind, lacking any essential connection to intentionality, perception, cognition, and expressiveness. (2) It fails to keep in focus the moral distinction between two very different kinds of emotional response to the distress and suffering of others—other-directed, altruistic, emotions that have moral value, (...) and self-directed emotional responses, such as personal distress, that do not. (3) Nichols is correct to see morality as requiring affectivity, and the capability of emotional response to others; but his incorrect view of altruistic emotions (and of emotions in general) leads him to misstate the connection between morality and emotion. (4) Nichols’s specific attempt to ground moral judgment in emotion fails, but the argument he provides for it is part of the explanation of point (2), his failure to sustain the distinction between egoistic and altruistic emotions. (5) Without in any way denying that moral philosophy is strengthened by knowledge of empirical psychology, I suggest that the foregoing failures of Nichols’s argument are partly due to his misuse of particular empirical results and findings, and possibly in part to a weakened commitment to the distinctive contribution the humanistic methods of philosophy make to our understanding of the moral dimension of life. (shrink)

Nicolas Malebranche holds that we see all things in the physical world by means of ideas in God (the doctrine of "vision in God"). In some writings he seems to posit ideas of particular bodies in God, but when pressed by critics he insists that there is only one general idea of extension, which he calls “intelligible extension.” But how can this general and “pure” idea represent particular sensible objects? I develop systematic solutions to this and two other putative difficulties (...) with Malebranche’s theory of sensory cognition by appealing to the notion of “seeing as” and to his doctrine that ideas in God have causal powers to affect the mind. (shrink)

I argue that physicians can save women from life-threatening pregnancies by performing a craniotomy, placentectomy, or salpingotomy without intending death or harm. To support this conclusion, I defend the relevance thesis about intentions (a person intends X only if X explains the action). I then criticize the identity thesis (if a person intends X and knows X is Y then the person intends Y) and three mistakenly strict moral principles: (1) one may not intend something that is a serious harm (...) for an innocent person, (2) one may not intend to terminate pregnancy before viability, which would prohibit, and (3) one may not act on a person’s body in a harmful way in order to benefit another person. (1) would prohibit procuring organs from living donors, (2) would prohibit treating hepatic pregnancies and other ectopic pregnancies, and (3) would prohibit procuring organs from living donors and performing many prenatal surgeries. (shrink)

A framework is developed for understanding what is “taken for granted” both in philosophy and in life generally, which may serve to orient philosophical inquiry and make it more effective. The framework takes in language and its development, as well as mathematics, logic, and the empirical sphere with particular reference to the exigencies of life. It is evaluated through consideration of seven philosophical issues concerned with such topics as solipsism, sense data as the route to knowledge, the possible reduction of (...) geometry to logic, and the existence and status of human rights. Various dichotomies and the notion of continuity are evidently highly strategic. (shrink)

Politics never became a central intellectual interest of Murdoch’s, but she produced one important and visionary political essay in the ‘50’s, several popular writings on political matters, and a significant chapter in Metaphysics as a Guide to Morals that echoes throughout that book. In the 1958 “House of Theory,” she sees the welfare state as having almost entirely failed to address the deeper problems of capitalist society, including a failure to create the conditions for values she saw as central to (...) the socialist tradition—equality, absence of exploitation, meaningful work, and a sense of community. In Metaphysics as a Guide to Morals, Murdoch abandons the idea that moral ideals provide a guide to constructing a good society. She retains from her earlier work that the individual-moral domain is governed by perfectionism, but society cannot be. ‘Society must be thought of as a bad job to be made the best of’, for example, through the liberal idea of rights. Murdoch had a lifelong engagement with Marxism as a philosophy, introduced to her as a member of the Communist Party in the late ‘30’s and ‘40’s, and continuing through her subsequent long Labour period, and even when she moved to the Right in the Thatcher era. Marx and Marxism were always part of her mental universe, and she continued to work out what she agreed and disagreed with in it. (shrink)

Unusual among Western philosophers, Schopenhauer explicitly drew on Hindu and especially Buddhist traditions inhis moral philosophy. He saw plurality, especially the plurality of human persons, as a kind of illusion; in reality all is one, and compassionate acts express an implicit recognition of this oneness. Max Scheler retains the transcendence of self aspect of compassion but emphasizes that the subject must have a clear, lived sense of herself as a distinct individual in order for that transcendence to take place properly. (...) This feature is absent in the Buddhist tradition. Feminist philosophers of the early second wave built on this insight (only occasionally drawing it from Scheler) to recognize ways women are often not socialized to develop this distinctive sense of self, therefore harming their ability to engage in compassion and other forms of care for others. Iris Murdoch adds a Freudian-inspired (though Freud influenced Scheler also) pessimism about the ability of humans to keep their identities sufficiently distinct from the other to allow a clear view of the other, and thus real care and help to the other to take place. But in her later work, Murdoch explicitly recognizes and draws on the Buddhist tradition of oneness and transcendence of the self. Group solidarities can partake of aspects of Buddhist oneness and self-transcendence, for example the sense of fellowship in a social justice movement in which Blacks draw on a shared identity to experience connection, compassion, empathy, and solidarity with one another. But social justice movements also allow for a solidarity across racial lines, grounded in the shared commitment to justice, including justice for one of the groups in the solidarity community. (All these issues are powerfully portrayed in the 2014 film, Selma.) None of these solidarities, however, express the universalistic dimension of Buddhist oneness. (shrink)

Solidarity within a group facing adversity exemplifies certain human goods, some instrumental to the goal of mitigating the adversity, some non-instrumental, such as trust, loyalty, and mutual concern. Group identity, shared experience, and shared political commitments are three distinct but often-conflated bases of racial group solidarity. Solidarity groups built around political commitments include members of more than one identity group, even when the political focus is primarily on the justice-related interests of only one identity group (such as African Americans). A (...) solidarity group is more than a mere political coalition or alliance. Two other forms of political- commitment solidarity groups are ones devoted to racial justice more generally, and social justice even more generally. Racially plural political solidarity groups realize values beyond the afore-mentioned solidaristic ones, in meeting the challenges of different races working together. (shrink)

Religion emerged among early humans because both purposive and non-purposive explanations were being employed but understanding was lacking of their precise scope and limits. Given also a context of very limited human power, the resultant foregrounding of agency and purposive explanation expressed itself in religion’s marked tendency towards anthropomorphism and its key role in legitimizing behaviour. The inevitability of death also structures the religious outlook; with ancestors sometimes assigned a role in relation to the living. Subjective elements such as the (...) experience of dreams and the internalization of moral precepts also play their part. Two important sources of variation among religions concern the adoption of a dualist or non-dualist perspective, and whether or not the religion’s early political experience is such as to generate a systematic doctrine subordinating politics to religion. The near ubiquity and endurance of religion are further illuminated by analysis of its functions and ideological role. Religion tends to be socially conservative but has the potential to be revolutionary. (shrink)

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...) successes, and generated important advances in logical theory and metatheory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s. (shrink)

Carl Gillett has defended what he calls the “dimensioned” view of the realization relation, which he contrasts with the traditional “flat” view of realization (2003, 2007; see also Gillett 2002). Intuitively, the dimensioned approach characterizes realization in terms of composition whereas the flat approach views realization in terms of occupiers of functional roles. Elsewhere we have argued that the general view of realization and multiple realization that Gillett advances is not able to discharge the theoretical duties of those relations (Shapiro (...) 2004, unpublished manuscript; Polger 2004, 2007, forthcoming). Here we focus on an internal objection to Gillett’s account and then raise some broader reasons to reject it. (shrink)

Satisficing Consequentialism is often rejected as hopeless. Perhaps its greatest problem is that it risks condoning the gratuitous prevention of goodness above the baseline of what qualifies as "good enough". I propose a radical new willpower-based version of the view that avoids this problem, and that better fits with the motivation of avoiding an excessively demanding conception of morality. I further demonstrate how, by drawing on the resources of an independent theory of blameworthiness, we may obtain a principled specification of (...) what counts as "good enough". (shrink)

After a brief introduction and orientation (section I), this dialogue between Levinasian and Beckerian thought is approached along the lines of two major themes concerning consciousness which emerge in very different contexts and registers in their work (sections II and III), and one tantalizing question that is raised with great force by the dialogue (section IV). The two themes revolve around the subtle dialectical interplay that runs throughout the thought of both Levinas and Becker – the switching between internality and (...) externality, non-rational and rational; otherness and sameness; life and death – an interplay that is summed up in the dialectic between non-reflexive and reflexive consciousness. The Beckerian and Levinasian notions of the non-reflexive consciousness (section II) relate to their respective and in many ways convergent claims about a non-rational primal human state characterized by global vulnerability, awe and guilt, especially before the face of the other. Their analyses of reflexive consciousness (section III) relate to their interpretations of the problematic ideal of the free, self-constituting and self-mastering individual, and the impetus located therein towards the repression of what is Other to the self. Finally (section IV), the question is raised as to whether (and to what extent), following Levinas, sources of compelling ethical value might be legitimately understood as emerging out of Becker’s conception of primordial human vulnerability. (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

This paper argues that it is morally irresponsible for modern medical providers or health care institutions to support and advocate the integration of CAM practices (i.e. homeopathy, acupuncture, energy healing, etc.) with conventional modern medicine. The results of such practices are not reliable beyond that of placebo. As a corollary, it is argued that prescribing placebos perceived to stand outside the norm of modern medicine is morally inappropriate. Even when such treatments do no direct physical harm, they create unnecessary barriers (...) to patients' informed understanding of their health. (shrink)

Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein’s philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein’s distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation or theorem (...) and its proof. An attempt is made to meet directly some of Wittgenstein’s critical comments on the mathematical treatment of infinity and irrational numbers. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.