A brief, non-technical introduction to technical and philosophical aspects of Frege's philosophy of arithmetic. The exposition focuses on Frege's Theorem, which states that the axioms of arithmetic are provable, in second-order logic, from a single non-logical axiom, "Hume's Principle", which itself is: The number of Fs is the same as the number of Gs if, and only if, the Fs and Gs are in one-one correspondence.

Gottlob Frege's Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, was intended to be his magnum opus, the book in which he would finally establish his logicist philosophy of arithmetic. But because of the disaster of Russell's Paradox, which undermined Frege's proofs, the more mathematical parts of the book have rarely been read. Richard G.

In The Varieties of Reference, Gareth Evans argues that the content of perceptual experience is nonconceptual, in a sense I shall explain momentarily. More recently, in his book Mind and World, John McDowell has argued that the reasons Evans gives for this claim are not compelling and, moreover, that Evans’s view is a version of “the Myth of the Given”: More precisely, Evans’s view is alleged to suffer from the same sorts of problems that plague sense-datum theories of perception. In (...) particular, McDowell argues that perceptual experience must be within “the space of reasons,” that perception must be able to give us reasons for, that is, to justify, our beliefs about the world: And, according to him, no state that does not have conceptual content can be a reason for a belief. Now, there are many ways in which Evans’s basic idea, that perceptual content is nonconceptual, might be developed; some of these, I shall argue, would be vulnerable to the objections McDowell brings against him. But I shall also argue that there is a way of developing it that is not vulnerable to these objections. (shrink)

In Mind and World, John McDowell argues against the view that perceptual representation is non-conceptual. The central worry is that this view cannot offer any reasonable account of how perception bears rationally upon belief. I argue that this worry, though sensible, can be met, if we are clear that perceptual representation is, though non-conceptual, still in some sense 'assertoric': Perception, like belief, represents things as being thus and so.

The paper formulates and proves a strengthening of ‘Frege’s Theorem’, which states that axioms for second-order arithmetic are derivable in second-order logic from Hume’s Principle, which itself says that the number of Fs is the same as the number ofGs just in case the Fs and Gs are equinumerous. The improvement consists in restricting this claim to finite concepts, so that nothing is claimed about the circumstances under which infinite concepts have the same number. ‘Finite Hume’s Principle’ also suffices for (...) the derivation of axioms for arithmetic and, indeed, is equivalent to a version of them, in the presence of Frege’s definitions of the primitive expressions of the language of arithmetic. The philosophical significance of this result is also discussed. (shrink)

Maybe the most important argument in David Chalmers’s monumental book Constructing the World is the one he calls the ‘Frontloading Argument’, which is used in Chapter 4 to argue for the book’s central thesis, A Priori Scrutability. And, at first blush, the Frontloading Argument looks very strong. I argue here, however, that it is incapable of securing the conclusion it is meant to establish.

In this exciting new collection, a distinguished international group of philosophers contribute new essays on central issues in philosophy of language and logic, in honor of Michael Dummett, one of the most influential philosophers of the late twentieth century. The essays are focused on areas particularly associated with Professor Dummett. Five are contributions to the philosophy of language, addressing in particular the nature of truth and meaning and the relation between language and thought. Two contributors discuss time, in particular the (...) reality of the past. The last four essays focus on Frege and the philosophy of mathematics. The volume represents some of the best work in contemporary analytical philosophy. (shrink)

Frege, famously, held that there is a close connection between our concept of cardinal number and the notion of one-one correspondence, a connection enshrined in Hume's Principle. Husserl, and later Parsons, objected that there is no such close connection, that our most primitive conception of cardinality arises from our grasp of the practice of counting. Some empirical work on children's development of a concept of number has sometimes been thought to point in the same direction. I argue, however, that Frege (...) was close to right, that our concept of cardinal number is closely connected with a notion like that of one-one correspondence, a more primitive notion we might call just as many. (shrink)

Contrairement à une croyance trop répandue, le darwinisme et son prolongement au XXe siècle — le néo-darwinisme — ne portent pas sur une idée de l'évolution fondée sur la simple notion de « la survie du plus apte ». Si la théorie de la sélection naturelle est partie intégrante du néo-darwinisme, plusieurs de ses fondateurs seront en quête d'une conception beaucoup plus généreuse, pleine et compréhensive de l'évolution. En réalité, la révolution dite darwinienne s'insère au coeur d'une révolution intellectuelle beaucoup (...) plus importante : la révolution transformiste. Avant d'être des darwiniens, de dignes représentants de cette mouvance s'afficheront comme étant des transformistes. Cela signifie que, en plus des mécanismes de l'évolution biologique, d'autres éléments tout aussi cruciaux seront pris en considération`, dans l'élaboration d'une véritable synthèse évolutionniste : les rapports entre l'évolution biologique et l'évolution cosmique ; les interrogations portant sur la question d'une possible direction évolutive ; l'enseignement à tirer pour l'homme de sa place et de son rôle dans la nature. A la croisée de l'histoire, de la philosophie et de la science, cet ouvrage cherche à démontrer, à travers l'analyse des travaux de plusieurs néo-darwiniens de premier plan, que la révolution darwinienne demeurera incomplète aussi longtemps que la révolution transformiste le restera. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 10.3 (2003) 255-259 [Access article in PDF] Illnesses and Likenesses Richard G. T. Gipps IN THIS RESPONSE to Neil Pickering's paper I shall focus only on what he describes as the "strong objection" to the typical use of the likeness argument. The likeness argument, to recap, has it that we can decide whether conditions such as schizophrenia, depression, or alcoholism do or do not (...) deserve the designation of illness depending on whether they possess features which, if they occurred in physical conditions, would enable one to decide for or against the designation. To take an implausible example, if it were decided that it would be enough to describe a physical condition as an illness if it involves pain not caused through injury, then a psychological condition would be appropriately described as an illness just to the extent that it too involved such pain.In arguing against typical deployments of the likeness argument, Pickering finds that it is only on questionable initial descriptions of psychological conditions that such conditions appear to share the features that, in physical conditions, would be taken to be indicative of illness. That is to say, theorists who deploy the likeness argument to urge either the reality or unreality of mental illnesses typically presuppose what both we and they had all along hoped would be demonstrated in their argument. In terms of the above example, we might say that a certain psychological condition can count as an illness if it involves psychic pain. The concept of psychic pain is however (so the argument would have it) contestable; there exist other descriptions that make no reference to pain and in so doing fail to provide what a user of the likeness argument would need to substantiate the claim that a conception of the condition as an illness is more than a façon de parler.By way of arriving at this conclusion the following precondition for the applicability of the likeness argument (Pickering's "assumption" (2)) is insisted on: "That, with respect to the presence or absence of [those features of conditions which features decide whether or not the conditions are illnesses], a condition such as schizophrenia [must be] describable independently of the category it is assigned to." This can seem a quite reasonable restriction, for—it could be said—one can only win an argument if it is first allowed that there is actually something to argue about. That is, it is only if both partisans and detractors of the illness conception first accept a certain description of schizophrenia as spelling out what schizophrenia essentially involves that they can then progress to determining whether or not such a condition so described is or is not an illness.Yet, whereas this seems like a perfectly reasonable requirement, it is I believe uncertain whether it will always capture the form of the intuitions of adherents and detractors of the illness conception—or of the form of philosophical arguments more generally. To be sure, some philosophical discussions can perhaps be reconstructed as debates about the validity of certain inferences [End Page 255] from mutually understood premises (i.e., given X, does Y follow or not?). Yet if this were the case, then genuinely interesting philosophical arguments would probably be few and far between. If we are agreed as to the precise significance of our premises, and are not furthermore just making straightforward mistakes in reasoning, it is hard to see how or why we could all fail to arrive at the same conclusions.In the Philosophical Investigations paragraph 128 Wittgenstein wrote that "If one tried to advance theses in philosophy, it would never be possible to question them, because everyone would agree to them" (Wittgenstein 1953). Now that proposition might seem on rather weak grounds, because all one has to do to actually disprove it is merely disagree with it. But presumably Wittgenstein is rather articulating his intuition that although philosophical arguments often take the form of clashes concerning what conclusions can be drawn from what premises, most of their substance comes from a prior failure to unpack the intrinsic significance... (shrink)

The 1920-1960 period saw the creation of the conditions for a unification of disciplines in the area of evolutionary biology under a limited number of theoretical prescriptions: the evolutionary synthesis. Whereas the sociological dimension of this synthesis was fairly successful, it was surprisingly loose when it came to the interpretation of the evolutionary mechanisms per se, and completely lacking at the level of the foundational epistemological and metaphysical commitments. Key figures such as Huxley, Simpson, Dobzhansky, and Rensch only paid lip (...) service to the conceptual dimension of the evolutionary synthesis, as they eventually realized that a number of evolutionary phenomena could not be explained by its narrow theoretical corpus. Apparently, the evolutionary synthesis constituted a premature event in the development of evolutionary biology. Not only are the real achievements of the evolutionary synthesis in need of reevaluation, but this reassessment also has important implications for the historiography of Darwinism and the current debates about the darwinian movement. (shrink)

Jim Joyce has presented an argument for Probabilism based on considerations of epistemic utility [Joyce, 1998]. In a recent paper, I adapted this argument to give an argument for Probablism and the Principal Principle based on similar considerations [Pettigrew, 2012]. Joyce’s argument assumes that a credence in a true proposition is better the closer it is to maximal credence, whilst a credence in a false proposition is better the closer it is to minimal credence. By contrast, my argument in that (...) paper assumed (roughly) that a credence in a proposition is better the closer it is to the objective chance of that proposition. In this paper, I present an epistemic utility argument for Probabilism and the Principal Principle that retains Joyce’s assumption rather than the alternative I endorsed in the earlier paper. I argue that this results in a superior argument for these norms. (shrink)

The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues.

As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell’s Paradox being derivable in it.This system is, except for minor differ...

THE PAPER EXAMINES WHAT IS MEANT BY ’EVIDENCE’ WHEN IT IS SAID THAT A THEORY IS PROBABLE ON CERTAIN EVIDENCE. IT CONSIDERS WHAT IS THE RELATION BETWEEN A THEORY BEING PROBABLE ON CERTAIN EVIDENCE, A THEORY BEING BELIEVED, AND A THEORY BEING CREDIBLE. IT DISTINGUISHES VARIOUS SENSES OF ’ACCEPT’ IN WHICH SCIENTISTS ARE SAID TO ACCEPT THEORIES, ONLY ONE OF WHICH IS THE SENSE OF ’ACCEPT’ IN WHICH IT IS EQUATED WITH ’BELIEVE’. IT ANALYSES THE LOGICAL RELATIONS BETWEEN A THEORY (...) BEING PROBABLE ON THE EVIDENCE, AND A THEORY BEING ACCEPTED, AND A THEORY BEING ACCEPTABLE, IN THE DIFFERENT SENSES OF ’ACCEPT’. (shrink)

Depression and the subjective experience of suffering are distinct forms of distress, but they are sometimes commingled with one another. Using a cross-sectional sample of flight attendants, we tested for further empirical evidence distinguishing depression and suffering. Correlations with 15 indices covering several dimensions of well-being indicated that associations with worse well-being were mostly stronger for depression than suffering. There was a large positive correlation between depression and suffering, but we also found evidence of notable non-concurrent depression and suffering in (...) the sample. After dividing participants into four groups that varied based on severity of depression and suffering, regression analyses showed higher levels of well-being among those with both none-mild depression and none-mild suffering compared to those with moderate-severe depression, moderate-severe suffering, or both. All indices of well-being were lowest among the group of participants with moderate-severe depression and moderate-severe suffering. In addition to providing further evidence supporting a distinction between depression and suffering, our findings suggest that concurrent depression and suffering may be more disruptive to well-being than when either is present alone. (shrink)

This chapter contains sections titled: The Climbing Grade Question Relationalism About Climbing Grades Climbing Grades as Emerging Real Dispositions Standard Climbers in Standard Climbing Conditions Relationalism: The Better Theory Notes.

In his paper on 'The Science of Psychoanalysis,' Lacewing helpfully distinguishes a central psychodynamic model of the mind, elaborated in the clinical theory of psychoanalysis, from certain of its metapsychological and etiological theories. Critics who view psychoanalysis as unscientific have tended to focus on the lack of evidential support for certain of its developmental claims or the lack of reliability and validity in its theoretical posits. Lacewing claims, however, that the model contained in the clinical theory is much more scientifically (...) respectable than its critics have made out. The data may not always be in, but Lacewing's argument is that there is nothing pseudoscientific about the central model that... (shrink)

My purpose is to account for some oddities in what Kant did and did not say about "moral worth," and for another in what commentators tell us about his intent. The stone with which I hope to dispatch these several birds is-as one would expect a philosopher's stone to be-a distinction. I distinguish between two things Kant might have had in mind under the heading of moral worth. They come readily to mind when one both takes account of what he (...) actually said about it and notices a fact which he did not seem to notice: namely, that dutiful action- action which, whatever its motive, fulfills a duty-can be over- determined, and determined in particular by both respect for duty and some consortium of inclinations and prudenc. (shrink)

Hartry Field has suggested that we should adopt at least a methodological deflationism: [W]e should assume full-fledged deflationism as a working hypothesis. That way, if full-fledged deflationism should turn out to be inadequate, we will at least have a clearer sense than we now have of just where it is that inflationist assumptions ... are needed. I argue here that we do not need to be methodological deflationists. More pre-cisely, I argue that we have no need for a disquotational truth-predicate; (...) that the word true, in ordinary language, is not a disquotational truth-predicate; and that it is not at all clear that it is even possible to introduce a disquotational truth-predicate into ordinary language. If so, then we have no clear sense how it is even possible to be a methodological deflationist. My goal here is not to convince a committed deflationist to abandon his or her position. My goal, rather, is to argue, contrary to what many seem to think, that reflection on the apparently trivial character of T-sentences should not incline us to deflationism. (shrink)

Using the case of an industrial accident involving a killer robot, the author successfully combines technical and ethical concepts to present to students and professionals real-life issues that they may one day have to confront.

The 'substitution argument' purports to demonstrate the falsity of Russellian accounts of belief-ascription by observing that, e.g., these two sentences: (LC) Lois believes that Clark can fly. (LS) Lois believes that Superman can fly. could have different truth-values. But what is the basis for that claim? It seems widely to be supposed, especially by Russellians, that it is simply an 'intuition', one that could then be 'explained away'. And this supposition plays an especially important role in Jennifer Saul's defense of (...) Russellianism, based upon the existence of an allegedly similar contrast between these two sentences: (PC) Superman is more popular than Clark. (PS) Superman is more popular than Superman. The latter contrast looks pragmatic. But then, Saul asks, why shouldn't we then say the same about the former? The answer to this question is that the two cases simply are not similar. In the case of (PC) and (PS), we have only the facts that these strike us differently, and that people will sometimes say things like (PC), whereas they will never say things like (PS). By contrast, there is an argument to be given that (LS) can be true even if (LC) is false, and this argument does not appeal to anyone's 'intuitions'. The main goal of the paper is to present such a version of the substitution argument, building upon the treatment of the Fregan argument against Russellian accounts of belief itself in "Solving Frege's Puzzle". A subsidiary goal is to contribute to the growing literature arguing that 'intuitions' simply do not play the sort of role in philosophical inquiry that so-called 'experimental philosophers' have supposed they do. (shrink)

Hartry Field has suggested that we should adopt at least a methodological deflationism: "[W]e should assume full-fledged deflationism as a working hypothesis. That way, if full-fledged deflationism should turn out to be inadequate, we will at least have a clearer sense than we now have of just where it is that inflationist assumptions... are needed". I argue here that we do not need to be methodological deflationists. More precisely, I argue that we have no need for a disquotational truth-predicate; that (...) the word 'true', in ordinary language, is not a disquotational truth-predicate; and that it is not at all clear that it is even possible to introduce a disquotational truth-predicate into ordinary language. If so, then we have no clear sense how it is even possible to be a methodological deflationist. My goal here is not to convince a committed deflationist to abandon his or her position. My goal, rather, is to argue, contrary to what many seem to think, that reflection on the apparently trivial character of T-sentences should not incline us to deflationism. (shrink)

Originally published between 1968 and 2009, this collection of 25 pieces includes six interviews translated into English for the first time and a new transcription of a Q&A session with Baudrillard following a lecture he gave in London in 1994. The guiding theme of the collection is Baudrillard's engagement with culture. The implications of the implosion of Western culture are dissected and documented in the rich range of material included here.

The paper argues, as against Thau and Caplan, that the traditional interpretation that Frege abandoned his earlier views about identity and identity--statements is correct.

This book by Richard G. Stevens is a comprehensive introduction to the nature of political philosophy. It offers definitions of philosophy and politics, showing the tension between the two and the origin of political philosophy as a means of resolution of that tension. Plato and Aristotle are examined in order to see the search for the best political order. Inquiry is then made into political philosophy's new tension brought about by the growth of revealed religion in the Middle Ages. (...) It then examines the changes introduced by modernity and gives an overview of postmodern political thought. The book covers the most influential philosophers and directs readers to the classics of political philosophy, guiding them in studying them. It is an approachable introduction to a complex subject, not just a history of it. It is a point of entry into the subject for students and for others as well. (shrink)

The purpose of this note is to present a strong form of the liar paradox. It is strong because the logical resources needed to generate the paradox are weak, in each of two senses. First, few expressive resources required: conjunction, negation, and identity. In particular, this form of the liar does not need to make any use of the conditional. Second, few inferential resources are required. These are: (i) conjunction introduction; (ii) substitution of identicals; and (iii) the inference: From ¬(p (...) ∧ p), infer ¬ p. It is, interestingly enough, also essential to the argument that the ‘strong’ form of the diagonal lemma be used: the one that delivers a term λ such that we can prove: λ = ¬ T(⌈λ⌉); rather than just a sentence Λ for which we can prove: Λ ≡ ¬T(⌈Λ⌉). The truth-theoretic principles used to generate the paradox are these: ¬(S ∧ T(⌈¬S⌉); and ¬(¬S ∧ ¬T(⌈¬S⌉). These are classically equivalent to the two directions of the T-scheme, but they are intuitively weaker. The lesson I would like to draw is: There can be no consistent solution to the Liar paradox that does not involve abandoning truth-theoretic principles that should be every bit as dear to our hearts as the T-scheme. So we shall have to learn to live with the Liar, one way or another. (shrink)

Frege's intention in section 31 of Grundgesetze is to show that every well-formed expression in his formal system denotes. But it has been obscure why he wants to do this and how he intends to do it. It is argued here that, in large part, Frege's purpose is to show that the smooth breathing, from which names of value-ranges are formed, denotes; that his proof that his other primitive expressions denote is sound and anticipates Tarski's theory of truth; and that (...) the proof that the smooth breathing denotes, while flawed, rests upon an idea now familiar from the completeness proof for first-order logic. The main work of the paper consists in defending a new understanding of the semantics Frege offers for the quantifiers: one which is objectual, but which does not make use of the notion of an assignment to a free variable. (shrink)

Ethical decisions have to be made by everyone. Yet Christians often find it difficult to know exactly how they should make them. Is there a better way than an emotional response or looking for a quick answer from the Bible? In the first of the book a sixth-former, Matthew, takes moral issues as the topic of his RS project. He has interviews with various people, such as a businessman, a scientist, a police officer, and a doctor as well as with (...) members of his own family and his minister. These open his eyes to problems that he had not thought about before. In the second part the issues that have been raised are examined more systematically. (shrink)