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.

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)

Why do people in more unequal societies have worse health and shorter lives than those in less unequal ones? Why do more unequal societies tend to have more violence and weaker community life? This paper discusses the research evidence on the psychosocial pathways which suggest how and why we are affected by inequality.How big income differences are in any society seems to serve as an indicator of the scale of social differentiation and social distances within it. The evidence shows that (...) more hierarchical societies incur a wide range of social costs reflecting the corrosive effects of inequality. But why are we so sensitive to inequality? Epidemiological research on health inequalities and the social determinants of health has demonstrated that the quality of the social environment has powerful effects on health. Particularly important are social status, friendship and early childhood experience. The indications are that poor health may share causal pathways with many other social problems associated with relative deprivation - including violence.Summarizing my recent book, The Impact of Inequality , this paper provides an account of how inequality gets under the skin to affect both health and wellbeing. Rather than making comparisons with some impractical state of complete equality, all the evidence presented shows the importance of the differences in inequality between different states of the USA or between different developed market democracies: it shows that even small increases in equality matter. (shrink)

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.

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)

Some years ago, Machery, Mallon, Nichols, and Stich reported the results of experiments that reveal, they claim, cross-cultural differences in speaker’s ‘intuitions’ about Kripke’s famous Gödel–Schmidt case. Several authors have suggested, however, that the question they asked their subjects is ambiguous between speaker’s reference and semantic reference. Machery and colleagues have since made a number of replies. It is argued here that these are ineffective. The larger lesson, however, concerns the role that first-order philosophy should, and more importantly should not, (...) play in the design of such experiments and in the evaluation of their results. (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.

In his paper “Flaws of Formal Relationism”, Mahrad Almotahari argues against the sort of response to Frege's Puzzle I have defended elsewhere, which he dubs ‘Formal Relationism’. Almotahari argues that, because of its specifically formal character, this view is vulnerable to objections that cannot be raised against the otherwise similar Semantic Relationism due to Kit Fine. I argue in response that Formal Relationism has neither of the flaws Almotahari claims to identify.

A chance-credence norm states how an agent's credences in propositions concerning objective chances ought to relate to her credences in other propositions. The most famous such norm is the Principal Principle (PP), due to David Lewis. However, Lewis noticed that PP is too strong when combined with many accounts of chance that attempt to reduce chance facts to non-modal facts. Those who defend such accounts of chance have offered two alternative chance-credence norms: the first is Hall's and Thau's New Principle (...) (NP); the second is Ismael's General Recipe (IP). Thus, the question arises: Should we adopt NP or IP or both? In this paper, I argue that IP has unacceptable consequences when coupled with reductionism, so we must accept NP alone. (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.

The main focus of my comments is the role played in Dickie's view by the idea that "the mind has a need to represent things outside itself". But there are also some remarks about her (very interesting) suggestion that descriptive names can sometimes fail to refer to the object that satisfies the associated description.

This paper dates from about 1994: I rediscovered it on my hard drive in the spring of 2002. It represents an early attempt to explore the connections between the Julius Caesar problem and Frege's attitude towards Basic Law V. Most of the issues discussed here are ones treated rather differently in my more recent papers "The Julius Caesar Objection" and "Grundgesetze der Arithmetik I 10". But the treatment here is more accessible, in many ways, providing more context and a better (...) sense of how this issue relates to broader issues in Frege's philosophy. (shrink)

John MacFarlane has made relativism popular again. Focusing just on his original discussion, I argue that the data he uses to motivate the position do not, in fact, motivatie it at all. Many of the points made here have since been made, independently, by Hermann Cappelen and John Hawthorne, in their book Relativism and Monadic Truth.

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)

Written as a comment on Crispin Wright's "Vagueness: A Fifth Column Approach", this paper defends a form of supervaluationism against Wright's criticisms. Along the way, however, it takes up the question what is really wrong with Epistemicism, how the appeal of the Sorities ought properly to be understood, and why Contextualist accounts of vagueness won't do.

Scaffolds are fundamental to many cellular signaling pathways. In this essay, a novel class of scaffolds are proposed, whose action bears striking resemblance to kinetic proofreading. Commonly, scaffold proteins are thought to work as tethers, bringing different components of a pathway together to improve the likelihood of their interaction. However, recent studies show that the cytoskeletal scaffold, anillin, supports contractile signaling by a novel, non‐tethering mechanism that controls the membrane dissociation kinetics of RhoA. More generally, such proof‐reading‐like scaffolds are distinguished (...) from tethers by a rare type of cooperativity, manifest as a super‐linear relationship between scaffold concentration and signaling efficiency. The evidence for this hypothesis is reviewed, its conceptual ramifications are considered, and research questions for the future are discussed. (shrink)

Why should one think Frege's definition of the ancestral correct? It can be proven to be extensionally correct, but the argument uses arithmetical induction, and that seems to undermine Frege's claim to have justified induction in purely logical terms. I discuss such circularity objections and then offer a new definition of the ancestral intended to be intensionally correct; its extensional correctness then follows without proof. This new definition can be proven equivalent to Frege's without any use of arithmetical induction. This (...) proves, without any use of arithmetical induction, that Frege's definition is extensionally correct and so answers the circularity objections. (shrink)

Book reviewed in this article: Eros as the Educational Principle of Democracy Kerry T.Burch. Feeling Power—emotions and education Megan Boler. The Students are Watching: schools and the moral contract Theodore R.Sizer & Nancy Faust Sizer.

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.

After the Jewish War Josephus was taken to Rome by Titus and then enjoyed the favour of Vespasian . The first task set him was to write a history of it in Aramaic for the ‘upper barbarians’, by which he means Parthians, Babylonians, Jews beyond Euphrates and Adiabenians . For his work he doubtless had access to the ‘commentarii’ of the emperor. This task may not have taken him long, but the translation into Greek which we possess took longer, and (...) was finished before the emperor's death, but after the dedication of the Forum Pacis . In its leisurely composition he tells us later that he had ‘certain assistants’ in the Greek language. As the work is quite uniform and smooth in style, we can only assume that J. turned his Aramaic into Greek himself to start with, and then placed the MS in the hands of assistants who systematically revised it, rewriting where necessary. No other hypothesis is possible; for no assistant could have been found sufficiently familiar with both Aramaic and literary Greek—at least it is highly improbable—and we have no reason to disbelieve J. when he says he translated his original treatise. (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)

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)

Discusses Frege's formal definitions and characterizations of infinite and finite sets. Speculates that Frege might have discovered the "oddity" in Dedekind's famous proof that all infinite sets are Dedekind infinite and, in doing so, stumbled across an axiom of countable choice.

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.

A revelatory alternative to the standard economic models of human behavior that proposes an exciting new way to understand decision-making "Willful is a breakthrough in economics. Richard Robb's tremendously insightful book shows how much of our behavior is not explained by existing theories of human action and explains in sparkling prose why understanding decisions made seemingly without reason presents a fuller picture of our world."--Edmund S. Phelps, Nobel Laureate in Economics Why do we do the things we do? The (...) classical view of economics is that we are rational individuals, making decisions with the intention of maximizing our preferences. Behaviorists, on the other hand, see us as relying on mental shortcuts and conforming to preexisting biases. Richard Robb argues that neither explanation accounts for those things that we do for their own sake, and without understanding these sorts of actions, our picture of decision-making is at best incomplete. Robb explains how these choices made seemingly without reason belong to a realm of behavior he identifies as "for-itself." A provocative combination of philosophy and economics that offers a key to many of our quixotic choices, this groundbreaking volume provides a new way to understand everything from investing to how hard we work to how we manage daily interactions. (shrink)

Psychoanalysis is often equated with Sigmund Freud, but this comparison ignores the wide range of clinical practices, observational methods, general theories, and cross-pollinations with other disciplines that characterise contemporary psychoanalytic work. Central psychoanalytic concepts to do with unconscious motivation, primitive forms of thought, defence mechanisms, and transference form a mainstay of today's richly textured contemporary clinical psychological practice. -/- In this landmark collection on philosophy and psychoanalysis, leading researchers provide an evaluative overview of current thinking. Written at the interface between (...) these two disciplines, the Oxford Handbook of Philosophy and Psychoanalysis contains original contributions that will shape the future of debate. With 34 chapters divided into eight sections covering history, clinical theory, phenomenology, science, aesthetics, religion, ethics, and political and social theory, this Oxford Handbook displays the enduring depth, breadth, and promise of integrating philosophical and psychoanalytic thought. -/- Anyone interested in the philosophical implications of psychoanalysis, as well as philosophical challenges to and re-statements of psychoanalysis, will want to consult this book. It will be a vital resource for academic researchers, psychoanalysts and other mental health professionals, graduates, and trainees. (shrink)

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...

In lieu of an abstract, here is a brief excerpt of the content:Madness, Reason, and PrideRichard G.T. Gipps, PhD (bio)MadnessQuestions such as “what’s madness?” or “what’s reason?” carry no singular sense about with them wherever they go—which isn’t to say that, asked out of a particular interest in a particular context, they can’t be perfectly intelligible. Garson (2023) is wise to this when he follows “what is madness?” with “as opposed to what?”, even if this latter question itself hardly enjoys (...) a clear sense in the initial context of his asking. What counts as a satisfactory answer to “what’s x?” varies, so that sometimes we’ll be satisfied with a name, at other times by information about something’s genus, origin, function, or composition. Things get notoriously tricky when in the philosophical context the question is asked with a presumption of intelligibility despite ‘x’ being, say, an abstract noun formed from an adjective (‘consciousness’ out of ‘conscious’; ‘happiness’ out of ‘happy’; ‘madness’ out of ‘mad,’ etc.). For “what is?” questions are typically most perspicuously mooted when what’s being pursued are enquiries into (what we might call) the ‘essential nature’ of (what philosophers used to call) ‘substances’ or (of what are more ordinarily called) types of ‘thing’ or ‘entity.’ Invoke, by taking one’s lead from the fact that an ‘x’ is grammatically speaking a substantive, the specter of substance, and you can endlessly baffle yourself by now pondering the mysteries of the putative thing. (Vide discussions of “the nature of consciousness.”) Hence the boon of instead pursuing questions of an ‘opposed to what?’ sort; hence Wittgenstein considering using the Earl of Kent’s “I’ll teach you differences” (King Lear) as a motto for his Investigations. Rather more reflective wisdom regarding ‘x’ may thus be gained when we learn to contrast it with ‘y’ and ‘z’ than when peering into x’s non-existent constitution or groping for its never-instituted genus.Later, I make the case that Garson’s conception of reason itself might suffer from a form of substantialization and that, if I’m right in this, troubling implications follow for his approach to madness. But let’s begin by considering his enquiry into the relation of madness, idiocy and reason. So perhaps we’re reflecting on matters legal, and considering—since we’d hitherto been inclined to take ‘reason’ as univocal—what justifies our different treatments of the insane, the intellectually subnormal, and the normal. Or perhaps—proceeding from the same inclination—we’re puzzled by how someone may boast an exceptional IQ or demonstrate marvelous formal rationality (i.e., make deductions of a sort which would please the logician if no-one else) and yet still be quite mad. And then we realize that at which Garson’s Late Moderns seem to have been gesturing: The lack of reason qua intelligence in idiocy is a different [End Page 307] species from the lack of reason qua sanity in madness. An amethyst is lifeless in a different manner than an expired possum (it was never living, never moribund); the arational lack reason in a different sense than do the irrational (and a baobab cannot jump to conclusions.) There is, say his Late Modern theorists, something ‘perverse’ rather than simply deficient about the irrationality of madness.Now an important part of Garson’s thesis has it that “idiocy is a better candidate for the opposite of reason than madness.” One of the reasons for his making this claim is that he follows his Late Moderns in claiming that madness has reason somehow alive within it, albeit in an unconventional or surprising form. I return to his own explication of this below. Consider first, though, the different thought-referencing descriptions under which the speech acts of the thought-disordered, the speech-disordered, the delusional, and the learning disabled subject may be brought. The sufferer of speech disorder has difficulty with fluency or sound production, but once we get used to this we can find our way to the bona fide rational thought immanent within their discourse. The speech acts of the intellectually impaired subject aren’t chaotic, but instead want for invention and richness; they fail to express... (shrink)