The rather unrestrained use of second-order logic in the neo-logicist program is critically examined. It is argued in some detail that it brings with it genuine set-theoretical existence assumptions and that the mathematical power that Hume’s Principle seems to provide, in the derivation of Frege’s Theorem, comes largely from the ‘logic’ assumed rather than from Hume’s Principle. It is shown that Hume’s Principle is in reality not stronger than the very weak Robinson Arithmetic Q. Consequently, only a few rudimentary facts (...) of arithmetic are logically derivable from Hume’s Principle. And that hardly counts as a vindication of logicism. (shrink)

There is a long-standing gap in the literature as to whether Gödelian incompleteness constitutes a challenge for Neo-Logicism, and if so how serious it is. In this paper, I articulate and address the challenge in detail. The Neo-Logicist project is to demonstrate the analyticity of arithmetic by deriving all its truths from logical principles and suitable definitions. The specific concern raised by Gödel’s first incompleteness theorem is that no single sound system of logic syntactically implies all arithmetical truths. I (...) set out some responses that initially seem appealing and explain why they are not compelling. The upshot is that Neo-Logicism either offers an epistemic route only to some truths of arithmetic; or that it has to move from a syntactic to a semantic notion of logical consequence, which risks undermining its epistemic goals. I conclude by considering Crispin Wright’s recent attempt to address Gödelian incompleteness, which I argue is not satisfactory. (shrink)

Abstract:Certain advocates of the so-called “neo-logicist” movement in the philosophy of mathematics identify themselves as “neo-Fregeans” (e.g., Hale and Wright), presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature and, when it is, often dismissed as not really logicism at all (in light of its assumption of axioms of infinity, reducibility and so on). In this paper I have three aims: firstly, to identify more clearly (...) the primary meta-ontological and methodological differences between Russell’s logicism and the more recent forms; secondly, to argue that Russell’s form of logicism offers more elegant and satisfactory solutions to a variety of problems that continue to plague the neo-logicist movement (the bad company objection, the embarrassment of richness objection, worries about a bloated ontology, etc.); thirdly, to argue that neo-Russellian forms of logicism remain viable positions for current philosophers of mathematics. (shrink)

In two recent papers, Bob Hale has attempted to free second-order logic of the 'staggering existential assumptions' with which Quine famously attempted to saddle it. I argue, first, that the ontological issue is at best secondary: the crucial issue about second-order logic, at least for a neo-logicist, is epistemological. I then argue that neither Crispin Wright's attempt to characterize a `neutralist' conception of quantification that is wholly independent of existential commitment, nor Hale's attempt to characterize the second-order domain in terms (...) of definability, can serve a neo-logicist's purposes. The problem, in both cases, is similar: neither Wright nor Hale is sufficiently sensitive to the demands that impredicativity imposes. Finally, I defend my own earlier attempt to finesse this issue, in "A Logic for Frege's Theorem", from Hale's criticisms. (shrink)

A speculative investigation of how Frege's logical views change between Begriffsschrift and Grundgesetze and how this might have affected the formal development of logicism.

Neo-logicism uses definitions and Hume's Principle to derive arithmetic in second-order logic. This paper investigates how much arithmetic can be derived using definitions alone, without any additional principle such as Hume's.

Neo-Fregean logicists claim that Hume's Principle (HP) may be taken as an implicit definition of cardinal number, true simply by fiat. A longstanding problem for neo-Fregean logicism is that HP is not deductively conservative over pure axiomatic second-order logic. This seems to preclude HP from being true by fiat. In this paper, we study Richard Kimberly Heck's Two-sorted Frege Arithmetic (2FA), a variation on HP which has been thought to be deductively conservative over second-order logic. We show that it (...) isn't. In fact, 2FA is not conservative over $n$-th order logic, for all $n \geq 2$. It follows that in the usual one-sorted setting, HP is not deductively Field-conservative over second- or higher-order logic. (shrink)

An overview of what Frege accomplishes in Part II of Grundgesetze, which contains proofs of axioms for arithmetic and several additional results concerning the finite, the infinite, and the relationship between these notions. One might think of this paper as an extremely compressed form of Part II of my book Reading Frege's Grundgesetze.

The question of the applicability of mathematics is an epistemological issue that was explicitly raised by Kant, and which has played different roles in the works of neo-Kantian philosophers, before becoming an essential issue in early analytic philosophy. This paper will first distinguish three main issues that are related to the application of mathematics: indispensability arguments that are aimed at justifying mathematics itself; philosophical justifications of the successful application of mathematics to scientific theories; and discussions on the application of real (...) numbers to the measurement of physical magnitudes. A refinement of this tripartition is suggested and supported by a historical investigation of the differences between Kant’s position on the problem, several neo-Kantian perspectives, early analytic philosophy, and late 19th century mathematicians. Finally, the debate on the cogency of an application constraint in the definition of real numbers is discussed in relation to a contemporary debate in neo-logicism, in order to suggest a comparison not only with Frege’s original positions, but also with the ideas of several neo-Kantian scholars, including Hölder, Cassirer, and Helmholtz. (shrink)

It has been known for a few years that no more than Pi-1-1 comprehension is needed for the proof of "Frege's Theorem". One can at least imagine a view that would regard Pi-1-1 comprehension axioms as logical truths but deny that status to any that are more complex—a view that would, in particular, deny that full second-order logic deserves the name. Such a view would serve the purposes of neo-logicists. It is, in fact, no part of my view that, say, (...) Delta-3-1 comprehension axioms are not logical truths. What I am going to suggest, however, is that there is a special case to be made on behalf of Pi-1-1 comprehension. Making the case involves investigating extensions of first-order logic that do not rely upon the presence of second-order quantifiers. A formal system for so-called "ancestral logic" is developed, and it is then extended to yield what I call "Arché logic". (shrink)

We note that a plural version of logicism about arithmetic is suggested by the standard reading of Hume's Principle in terms of `the number of Fs/Gs'. We lay out the resources needed to prove a version of Frege's principle in plural, rather than second-order, logic. We sketch a proof of the theorem and comment philosophically on the result, which sits well with a metaphysics of natural numbers as plural properties.

Although the economic thought of Marshall and Pigou was united by ethical positions broadly considered utilitarian, differences in their intellectual milieu led to degrees of difference between their respective philosophical visions. This change in milieu includes the influence of the little understood period of transition from the early idealist period in Great Britain, which provided the context to Marshall’s intellectual formation, and the late British Idealist period, which provided the context to Pigou’s intellectual formation. During this latter period, the pervading (...) Hegelianism and influences of naturalism arising from the ideas of Charles Darwin and Herbert Spencer were challenged by Hermann Lotze, a key transitional thinker influencing the Neo-Kantian movement, who recognised significant limits of naturalism, on the one hand, and the metaphysical tenor of absolute idealism, on the other, and attempted to provide a balance between the two. The goal of this paper is to make the provisional case for the argument that Pigou’s views on ethics were not only directly influenced by utilitarian thinkers like Mill and Sidgwick, but they were also indirectly influenced by Hermann Lotze, via the influence of the Neo- Kantian movement on late British idealism. To that end, Pigou’s essays in The Trouble with Theism (1908), including his sympathetic consideration of the ethics of Friedrich Nietzsche, reflect the influence of Lotze indirectly through the impact at Cambridge of: James Ward’s critique of associationist psychology, and consideration of the limits of naturalism including the critique of evolutionary ethics; Bertrand Russell’s rejection of neo-Hegelianism and, together with Alfred North Whitehead, the development of Logicism; and G.E. Moore’s critique of utilitarian ethics on the basis of the naturalistic fallacy and the development of his own intuitionist system of ethics. (shrink)

A crucial part of the contemporary interest in logicism in the philosophy of mathematics resides in its idea that arithmetical knowledge may be based on logical knowledge. Here an implementation of this idea is considered that holds that knowledge of arithmetical principles may be based on two things: (i) knowledge of logical principles and (ii) knowledge that the arithmetical principles are representable in the logical principles. The notions of representation considered here are related to theory-based and structure-based notions of (...) representation from contemporary mathematical logic. It is argued that the theory-based versions of such logicism are either too liberal (the plethora problem) or are committed to intuitively incorrect closure conditions (the consistency problem). Structure-based versions must on the other hand respond to a charge of begging the question (the circularity problem) or explain how one may have a knowledge of structure in advance of a knowledge of axioms (the signature problem). This discussion is significant because it gives us a better idea of what a notion of representation must look like if it is to aid in realizing some of the traditional epistemic aims of logicism in the philosophy of mathematics. (shrink)

Abstract:According to Quine, Charles Parsons, Mark Steiner, and others, Russell’s logicist project is important because, if successful, it would show that mathematical theorems possess desirable epistemic properties often attributed to logical theorems, such as aprioricity, necessity, and certainty. Unfortunately, Russell never attributed such importance to logicism, and such a thesis contradicts Russell’s explicitly stated views on the relationship between logic and mathematics. This raises the question: what did Russell understand to be the philosophical importance of logicism? Building on (...) recent work by Andrew Irvine and Martin Godwyn, I argue that Russell thought a systematic reduction of mathematics increases the certainty of known mathematical theorems (even basic arithmetical facts) by showing mathematical knowledge to be coherently organized. The paper outlines Russell’s theory of coherence, and discusses its relevance to logicism and the certainty attributed to mathematics. (shrink)

In this work I study the main tenets of the logicist philosophy of mathematics. I deal, basically, with two problems: (1) To what extent can one dispense with intuition in mathematics? (2) What is the appropriate logic for the purposes of logicism? By means of my considerations I try to determine the pros and cons of logicism. My standpoint favors the logicist line of thought. -/- .

This paper describes both an exegetical puzzle that lies at the heart of Frege’s writings—how to reconcile his logicism with his definitions and claims about his definitions—and two interpretations that try to resolve that puzzle, what I call the “explicative interpretation” and the “analysis interpretation.” This paper defends the explicative interpretation primarily by criticizing the most careful and sophisticated defenses of the analysis interpretation, those given my Michael Dummett and Patricia Blanchette. Specifically, I argue that Frege’s text either are (...) inconsistent with the analysis interpretation or do not support it. I also defend the explicative interpretation from the recent charge that it cannot make sense of Frege’s logicism. While I do not provide the explicative interpretation’s full solution to the puzzle, I show that its main competitor is seriously problematic. (shrink)

This paper objectively defines the three main contemporary philosophies of mathematics: formalism, logicism, and intuitionism. Being the three leading scientists of each: Hilbert (formalist), Frege (logicist), and Poincaré (intuitionist).

In this extended critical discussion of 'Kant's Modal Metaphysics' by Nicholas Stang (OUP 2016), I focus on one central issue from the first chapter of the book: Stang’s account of Kant’s doctrine that existence is not a real predicate. In §2 I outline some background. In §§3-4 I present and then elaborate on Stang’s interpretation of Kant’s view that existence is not a real predicate. For Stang, the question of whether existence is a real predicate amounts to the question: ‘could (...) there be non-actual possibilia?’ (p.35). Kant’s view, according to Stang, is that there could not, and that the very notion of non-actual or ‘mere’ possibilia is incoherent. In §5 I take a close look at Stang’s master argument that Kant’s Leibnizian predecessors are committed to the claim that existence is a real predicate, and thus to mere possibilia. I argue that it involves substantial logical commitments that the Leibnizian could reject. I also suggest that it is danger of proving too much. In §6 I explore two closely related logical commitments that Stang’s reading implicitly imposes on Kant, namely a negative universal free logic and a quantified modal logic that invalidates the Converse Barcan Formula. I suggest that each can seem to involve Kant himself in commitment to mere possibilia. (shrink)

Bertrand Russell was one of the best-known proponents of logicism: the theory that mathematics reduces to, or is an extension of, logic. Russell argued for this thesis in his 1903 The Principles of Mathematics and attempted to demonstrate it formally in Principia Mathematica (PM 1910–1913; with A. N. Whitehead). Russell later described his work as a further “regressive” step in understanding the foundations of mathematics made possible by the late 19th century “arithmetization” of mathematics and Frege’s logical definitions of (...) arithmetical concepts. The logical system of PM sought to improve on earlier attempts by solving the contradictions found in, e.g., Frege’s system, by employing a theory of types. In this article, I also consider and critically evaluate the most common objections to Russell’s logicism, including the claim that it is undermined by Gödel’s incompleteness results, and Putnam's charge of “if-thenism”. I suggest that if we are willing to accept a slightly revisionist account of what counts as a mathematical truth, these criticisms do not obviously refute Russell’s claim to have established that mathematical truths generally are a species of logical truth. (shrink)

Fogelin’s neo-Pyrrhonism is skepticism about epistemology and philosophy more generally. Philosophical reflection on ordinary epistemic practices leads us to deny the possibility of knowledge and justified belief. However, instead of accepting the dogma that knowledge and justified beliefs are impossible, a neo-Pyrrhonist rejects the philosophical premises that lead to this conclusion. Fogelin argues in particular that contemporary theories of justification cannot avoid dogmatic skepticism, because they are committed to the premises of the skeptical argument deriving from the modes of Agrippa. (...) It is argued against Fogelin that those theories can and typically do deny one or another of the premises and thus can avoid the skeptical conclusion. Neo-Pyrrhonism should rather be defended by arguing that the premises of the Agrippan argument are intuitively plausible and that neo-Pyrrhonism provides the best resolution of the resulting paradox. Only neo-Pyrrhonism both explains the intuitive plausibility of the premises and avoids dogmatic skepticism. (shrink)

Neo-Aristotelian naturalism purports to explain morality in terms of human nature, while maintaining that the relevant aspects of human nature cannot be known scientifically. This has led some to conclude that neo-Aristotelian naturalism is not a form of ethical naturalism in the standard, metaphysical sense. In this paper, I argue that neo-Aristotelian naturalism is in fact a standard form of ethical naturalism that is committed to metaphysical naturalism about moral truths and presents a distinctive and underappreciated argument for it. I (...) reconstruct the neo-Aristotelian argument for ethical naturalism in terms of a continuity between the ethical domain and the natural domain of life. I argue that clarifying the meta-ethical import of neo-Aristotelian naturalism not only helps to situate it among other positions in meta-ethics, but also facilitates better critical engagement with the view. (shrink)

It is commonly assumed that Aristotle's ethical theory shares deep structural similarities with neo-Aristotelian virtue ethics. I argue that this assumption is a mistake, and that Aristotle's ethical theory is both importantly distinct from the theories his work has inspired, and independently compelling. I take neo-Aristotelian virtue ethics to be characterized by two central commitments: (i) virtues of character are defined as traits that reliably promote an agent's own flourishing, and (ii) virtuous actions are defined as the sorts of actions (...) a virtuous agent reliably performs under the relevant circumstances. I argue that neither of these commitments are features of Aristotle's own view, and I sketch an alternative explanation for the relationship between virtue and happiness in the Nicomachean Ethics. Although, on the interpretation I defend, we do not find in Aristotle a distinctive normative theory alongside deontology and consequentialism, what we do find is a way of thinking about how prudential and moral reasons can come to be aligned through a certain conception of practical agency. (shrink)

This paper approaches the current epistemological debate on peer disagreement from a neo-Pyrrhonian perspective, thus adopting a form of skepticism which is more radical than those discussed in the literature. It makes use of argumentative strategies found in ancient Pyrrhonism both to show that such a debate rests on problematic assumptions and to block some maneuvers intended to offer an efficacious way of settling a considerable number of peer disputes. The essay takes issue with three views held in the peer (...) disagreement debate: there is an objective fact of the matter about at least most controversial questions; we possess theory-neutral evidence bearing on those questions which grants us access to the truth of the matter; and many peer controversies are resolved by attending to which disputant has correctly evaluated the objective evidence. With respect to the first two views, it is argued that the belief in both objective facts and theory-neutral evidence is subject to fierce dispute, and should not therefore be taken for granted in the discussion of peer disagreement. As for the third view, it is argued that from either a first- or a third-person perspective, there seems to be epistemic symmetry between the disputants which makes it necessary to suspend judgment. (shrink)

Plenitude, roughly, the thesis that for any non-empty region of spacetime there is a material object that is exactly located at that region, is often thought to be part and parcel of the standard Lewisian package in the metaphysics of persistence. While the wedding of plentitude and Lewisian four-dimensionalism is a natural one indeed, there are a hand-full of dissenters who argue against the notion that Lewisian four-dimensionalism has exclusive rights to plentitude. These ‘promiscuous’ three-dimensionalists argue that a temporalized version (...) of plenitude is entirely compatible with a three-dimensional ontology of enduring entities. While few would deny the coherence of such a position, and much work has been done by its proponents to appease critics, there has been surprisingly little by way of exploring the various forms such an ontology might take as well as the potential advantages of one plenitudinous three-dimensional ontology over another. Here I develop a novel form of plenitudinous three-dimensionalism, what John Hawthorne (Metaphysical essays, 2006a, b) has called “Neo-Aristotelian Plenitude,” and argue that if one is inclined to endorse an abundant three-dimensional ontology, one is wise to opt for a plenitude of accidental unities. (shrink)

Johannes Daubert he was an acknowledged leader, and in some respects the founder, of the early phenomenological movement, and was considered – as much by its members as by Husserl himself – the most brilliant member of the group. In Daubert’s unpublished writings we find a series of reflections on Lask, and on Neo-Kantianism, which form the subject-matter of this paper. They range over topics such as the ontology of the ‘Sachverhalt’ or state of affairs, truthvalues (Wahrheitswerte) and the value (...) of truth, negative judgments and the copula, and the relation between perception and judgment. (shrink)

Review of Logic as Universal Science: Russell’s Early Logicism and Its Philosophical Context, by Anssi Korhonen (Palgrave Macmillan 2013).

In the Foundations of Mathematics, Ramsey attempted to amend Principia Mathematica’s logicism to meet serious objections raised against it. While Ramsey’s paper is well known, some questions concerning Ramsey’s motivations to write it and its reception still remain. This paper considers these questions afresh. First, an account is provided for why Ramsey decided to work on his paper instead of simply accepting Wittgenstein’s account of mathematics as presented in the Tractatus. Secondly, evidence is given supporting that Wittgenstein was not (...) moved by Ramsey’s objection against the Tractarian account of arithmetic, and a suggestion is made to explain why Wittgenstein reconsidered Ramsey’s account in the early thirties on several occasions. Finally, a reading is formulated to understand the basis on which Wittgenstein argues against Ramsey’s definition of identity in his 1927 letter to Ramsey. (shrink)

This article discusses an interpretation of Kant's conception of transcendental subjectivity, which manages to avoid many of the concerns that have been raised by analytic interpreters over this doctrine. It is an interpretation put forward by selected C19 and early C20 neo-Kantian writers. The article starts out by offering a neo-Kantian interpretation of the object as something that is constituted by the categories and that serves as a standard of truth within a theory of judgment. The second part explicates transcendental (...) subjectivity as the system of categories, which is self-referential and constitutes objects, in order to then evaluate this conception by means of a comparison with Hegel's absolute subject. Rather than delineating the differences between neo-Kantian writers, the article systematically expounds a shared project, which consists in providing the ultimate foundation for judgments by means of an anti-psychologist and non-metaphysical interpretation of transcendental subjectivity. (shrink)

Many physicists have thought that absolute time became otiose with the introduction of Special Relativity. William Lane Craig disagrees. Craig argues that although relativity is empirically adequate within a domain of application, relativity is literally false and should be supplanted by a Neo-Lorentzian alternative that allows for absolute time. Meanwhile, Craig and co-author James Sinclair have argued that physical cosmology supports the conclusion that physical reality began to exist at a finite time in the past. However, on their view, the (...) beginning of physical reality requires the objective passage of absolute time, so that the beginning of physical reality stands or falls with Craig's Neo-Lorentzian metaphysics. Here, I raise doubts about whether, given Craig's NeoLorentzian metaphysics, physical cosmology could adequately support a beginning of physical reality within the finite past. Craig and Sinclair's conception of the beginning of the universe requires a past boundary to the universe. A past boundary to the universe cannot be directly observed and so must be inferred from the observed matter-energy distribution in conjunction with auxilary hypotheses drawn from a substantive physical theory. Craig's brand of Neo Lorentzianism has not been sufficiently well specified so as to infer either that there is a past boundary or that the boundary is located in the finite past. Consequently, Neo Lorentzianism implicitly introduces a form of skepticism that removes the ability that we might have otherwise had to infer a beginning of the universe. Furthermore, in analyzing traditional big bang models, I develop criteria that Neo-Lorentzians should deploy in thinking about the direction and duration of time in cosmological models generally. For my last task, I apply the same criteria to bounce cosmologies and show that Craig and Sinclair have been wrong to interpret bounce cosmologies as including a beginning of physical reality. (shrink)

Neo-Aristotelian metaethical naturalism is a modern attempt at naturalizing ethics using ideas from Aristotle’s teleological metaphysics. Proponents of this view argue that moral virtue in human beings is an instance of natural goodness, a kind of goodness supposedly also found in the realm of non-human living things. Many critics question whether neo-Aristotelian naturalism is tenable in light of modern evolutionary biology. Two influential lines of objection have appealed to an evolutionary understanding of human nature and natural teleology to argue against (...) this view. In this paper, I offer a reconstruction of these two seemingly different lines of objection as raising instances of the same dilemma, giving neo-Aristotelians a choice between contradicting our considered moral judgment and abandoning metaethical naturalism. I argue that resolving the dilemma requires showing a particular kind of continuity between the norms of moral virtue and norms that are necessary for understanding non-human living things. I also argue that in order to show such a continuity, neo-Aristotelians need to revise the relationship they adopt with empirical science and acknowledge that the latter is relevant to assessing their central commitments regarding living things. Finally, I argue that to move this debate forward, both neo-Aristotelians and their critics should pay attention to recent work on the concept of organism in evolutionary and developmental biology. (shrink)

An objection that has been raised to the conciliatory stance on the epistemic significance of peer disagreement known as the Equal Weight View is that it is self-defeating, self-undermining, or self-refuting. The proponent of that view claims that equal weight should be given to all the parties to a peer dispute. Hence, if one of his epistemic peers defends the opposite view, he is required to give equal weight to the two rival views, thereby undermining his confidence in the correctness (...) of the Equal Weight View. It seems that the same objection could be leveled against those who claim to suspend judgment in the face of pervasive unresolvable disagreements, as do the Pyrrhonian skeptics. In this paper, I explore the kind of response to the objection that could be offered from a neo-Pyrrhonian perspective, with the aim of better understanding the intriguing character of Pyrrhonian skepticism. (shrink)

I discuss the peculiar optimism present in an influential strand of analytic philosophy, and compare it with the more morose philosophical anthropology one might naturally pick up from other fields.

L’analyse logiciste des constructions savantes a pour but de mettre à nu leurs composantes symboliques : une base de données (observations et présuppositions) et un ensemble d’opérations de réécriture exprimant le raisonnement qui relie cette base aux thèses de la construction. Les travaux inspirés de ce programme depuis une vingtaine d’années soulèvent des questions intéressantes dans les perspectives d’une épistémologie pratique maintes fois exposées. L’étude des conflits d’interprétation y tient une large place ; elle s’apparente à l’analyse des controverses scientifiques (...) mais vise moins à expliquer celles-ci, du point de vue socio-historique, qu’à mieux définir les voies choisies pour les résoudre, les éluder ou les dépasser, selon les cas. Le questionnement logiciste porte sur les conséquences intellectuelles et institutionnelles de ces choix. L’affirmation de sa pérennité procède à la fois d’un constat et d’un pari, l’un et l’autre argumentés dans cet article. (shrink)

Proponents of the problem of animal suffering claim that the millions of years of apparent nonhuman animal pain and suffering provides evidence against the existence of God. Neo-Cartesianism attempts to avoid this problem mainly by denying the existence of phenomenal consciousness in nonhuman animals. However, neo-Cartesian options regarding animal minds have failed to compel many. In this essay, I explore an answer to the problem of animal suffering inspired by the medieval theologian Thomas Aquinas. Instead of focusing on phenomenal consciousness, (...) the neo-Thomistic view of animal minds focuses on self-awareness. After proposing and providing evidence for this view, I conclude that nonhuman animal suffering is not morally significant. (shrink)

The revival of Aristotelian virtue ethics can be seen as a response to the modern problem of disenchantment, that is, the perceived loss of meaning in modernity. However, in Virtue and Meaning, David McPherson contends that the dominant approach still embraces an overly disenchanted view. In a wide-ranging discussion, McPherson argues for a more fully re-enchanted perspective that gives better recognition to the meanings by which we live and after which we seek, and to the fact that human beings are (...) the meaning-seeking animal. In doing so, he defends distinctive accounts of the relationship between virtue and happiness, other-regarding demands, and the significance of linking neo-Aristotelian virtue ethics with a view of the meaning of life and a spiritual life where contemplation has a central role. This book will be valuable for philosophers and other readers who are interested in virtue ethics and the perennial question of the meaning of life. (shrink)

This paper has two separate aims, with obvious links between them. First, to present Charles S. Peirce and the pragmatist movement in a historical framework which stresses the close connections of pragmatism with the mainstream of philosophy; second, to deal with a particular controversial issue, that of the supposed logicistic orientation of Peirce's work.

Edward Feser defends the ‘Neo-Platonic proof ’ for the existence of the God of classical theism. After articulating the argument and a number of preliminaries, I first argue that premise three of Feser’s argument—the causal principle that every composite object requires a sustaining efficient cause to combine its parts—is both unjustified and dialectically ill-situated. I then argue that the Neo-Platonic proof fails to deliver the mindedness of the absolutely simple being and instead militates against its mindedness. Finally, I uncover two (...) tensions between Trinitarianism and the Neo-Platonic proof. (shrink)

ABSTRACTThe proper role of intuitions in philosophy has been debated throughout its history, and especially since the turn of the twenty-first century. The context of this recent debate within analytic philosophy has been the heightened interest in intuitions as data points that need to be accommodated or explained away by philosophical theories. This, in turn, has given rise to a sceptical movement called experimental philosophy, whose advocates seek to understand the nature and reliability of such intuitions. Yet such scepticism of (...) intuition or introspective methods can be found in earlier periods and across philosophical traditions. Indeed, the Neo-Confucian philosophers of the Song and Ming dynasties seem to exemplify this very tension, as they can be divided into an intuitionistic school on the one hand and an investigative school on the other. In this paper, I argue that, notwithstanding some obvious d... (shrink)

Some materialists believe that physics is rich enough to bridge Levine's Explanatory Gap1, while others believe that it is not. Here I promote an intermediate position holding that physics is rich enough to explain why this gap seems more intractable than similar inter-theoretic explanatory gaps, without providing a full-blown “physical” explanation of consciousness. At a minimum, such an approach needs to explore the prospects of empirical discoveries that can diminish the power of anti-physicalist arguments like Chalmers's “conceivability argument”2 and Jackson's (...) “knowledge argument.” While this is not an easy task, recent advances in the physics of spacetime and information convince us that these prospects are not poor. The empirical bent of this approach suggests framing it as a naturalist theory of mind seeking to situate or make room for consciousness within our great naturalist system, but the reliance of this approach on recent (re)conceptions of time and information pulls the carpet out from under essential concepts like concreteness and causation, thus demanding a radically reconfigured naturalism, or neo-naturalism. The question that will frame this discussion is, “What could possibly count as an empirical fact that can help naturalize consciousness?”. (shrink)

he paper analyses migration flows from the Philippines in two gendered occupations: domestic helpers and computer programmers. The international division of labour theory claims that foreign investment determines migration from developing countries, especially of women, towards low-skilled gendered occupations in developed countries. This paper shows that the division of labour is neither gendered nor international in the predicted sense. For instance, data from Philippines Overseas Employment Agency shows that the theory is Eurocentric as Northern America and Europe are destinations for (...) only 3 per cent of domestic workers’ flows. The paper argues that neo-Marxism creates bias in gender and migration research and hinders understanding of important gendered effects concerning migrants. Two examples of such gendered effects are highlighted here: the higher vulnerability to legislative change of migrant men employed as domestic workers in Italy and the higher penetration of women into computer programming in the migrant flows to the U.S. (shrink)

According to the received view in metaethics, a Neo-Humean theory of rationality entails that there cannot be any objective moral reasons, i.e. moral reasons that are independent of actual desires. In this paper, I argue that there is a version of this theory that is compatible with the existence of objective moral reasons. The key is to distinguish between (i) the process of rational deliberation that starts off in an agent's actual desires, and (ii) the rational principle that an agent (...) employs in such a process. I maintain that it is the latter which explains why it is rational for an agent to have a certain desire, not the former. As a result, there might be two types of principles. The second type of principle leaves room for objective moral reasons. (shrink)

In a previous issue of Philosophia Christi, Kirk MacGregor responded to an essay of mine in which I argued for a neo-Molinist account of open theism. The argument demonstrated how, given standard counterfactual semantics, one could derive an “open future square of opposition,” that is, a depiction of the logical relations that hold between future-tense statements from an open theistic standpoint. Conceding the validity of the argument, MacGregor nevertheless sought to deny its soundness by criticizing both its conclusion and the (...) Stalnaker-Lewis semantics on which the argument was based. In this paper, I argue that MacGregor’s reasons for rejecting the open future square, as well as his Molinist alternative to the Stalnaker-Lewis semantics, are uncompelling. (shrink)

The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...) granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter. According to that, both papers (1930; 1931) can be seen as advocating Russell’s logicism or the intensional propositional logic versus both extensional arithmetic and set theory. Reconstructing history of philosophy, Aristotle’s logic and doctrine can be opposed to those of Plato or the pre-Socratic schools as establishing ontology or intensionality versus extensionality. Husserl’s phenomenology can be analogically realized including and particularly as philosophy of mathematics. One can identify propositional logic and set theory by virtue of Gödel’s completeness theorem (1930: “Satz VII”) and even both and arithmetic in the sense of the “compactness theorem” (1930: “Satz X”) therefore opposing the latter to the “incompleteness paper” (1931). An approach identifying homomorphically propositional logic and set theory as the same structure of Boolean algebra, and arithmetic as the “half” of it in a rigorous construction involving information and its unit of a bit. Propositional logic and set theory are correspondingly identified as the shared zero-order logic of the class of all first-order logics and the class at issue correspondingly. Then, quantum mechanics does not need any quantum logics, but only the relation of propositional logic, set theory, arithmetic, and information: rather a change of the attitude into more mathematical, philosophical, and speculative than physical, empirical and experimental. Hilbert’s epsilon calculus can be situated in the same framework of the relation of propositional logic and the class of all mathematical theories. The horizon of Part III investigating Hilbert mathematics (i.e. according to the Pythagorean viewpoint about the world as mathematical) versus Gödel mathematics (i.e. the usual understanding of mathematics as all mathematical models of the world external to it) is outlined. (shrink)

Logicism is the view that mathematical truths are logical truths. But a logical truth is commonly thought to be one with a universally valid form. The form of “7 > 5” would appear to be the same as “4 > 6”. Yet one is a mathematical truth, and the other not a truth at all. To preserve logicism, we must maintain that the two either are different subforms of the same generic form, or that their forms are not (...) at all what they appear. The historical record shows that Russell pursued both these options, but that the struggle with the logical paradoxes pushed him away from the first kind of response and toward the second. An object cannot itself have a kind of inner logical complexity that makes a proposition have a different logical form merely in virtue of being about it, nor can their representatives in logical forms be single things different for different forms, at least not without postulating too many such objects and thereby creating Cantorian diagonal paradoxes. There are only apparent objects which are actually fragments of logical forms, different in different cases. (shrink)

This paper critically evaluates what it identifies as ‘the institutional theory of freedom’ developed within recent neo-Hegelian philosophy. While acknowledging the gains made against the Kantian theory of autonomy as detachment it is argued that the institutional theory ultimately undermines the very meaning of practical agency. By tying agency to institutionally sustained recognition it effectively excludes the exercise of practical reason geared toward emancipation from a settled normative order. Adorno's notion of autonomy as resistance is enlisted to develop an account (...) of practical reason that is neither institutionally constrained nor without appropriate consideration of the historical location of the practical agent. (shrink)

Neo‐Aristotelian Plenitude is the thesis that, necessarily, any property that could be had essentially by something or other is had essentially by something or other if and only if and because it is instantiated; any essentializable property is essentialized iff and because it is instantiated. In this paper, I develop a partial nonmodal characterization of ‘essentializable' and show it cannot be transformed into a full characterization. There are several seemingly insurmountable obstacles that any full characterization of essentializability must overcome. Moreover, (...) these obstacles threaten other views in the conceptual neighborhood such as Counterpart Theoretic Plenitude and Conceptualist Plenitude. (shrink)