One recent `neologicist' claim is that what has come to be known as "Frege's Theorem"–the result that Hume's Principle, plus second-order logic, suffices for a proof of the Dedekind-Peano postulate–reinstates Frege's contention that arithmetic is analytic. This claim naturally depends upon the analyticity of Hume's Principle itself. The present paper reviews five misgivings that developed in various of George Boolos's writings. It observes that each of them really concerns not `analyticity' but either the truth of (...) class='Hi'>Hume's Principle or our entitlement to accept it and reviews possible neologicist replies. A two-part Appendix explores recent developments of the fifth of Boolos's objections–the problem of Bad Company–and outlines a proof of the principle $N^q$, an important part of the defense of the claim that what follows from Hume's Principle is not merely a theory which allows of interpretation as arithmetic but arithmetic itself. (shrink)

According to Hume’s principle, a sentence of the form ⌜The number of Fs = the number of Gs⌝ is true if and only if the Fs are bijectively correlatable to the Gs. Neo-Fregeans maintain that this principle provides an implicit definition of the notion of cardinal number that vindicates a platonist construal of such numerical equations. Based on a clarification of the explanatory status of Hume’s principle, I will provide an argument in favour of a nominalist construal (...) of numerical equations. The neo-Fregean objections to such a construal will be examined and rejected. And the implications of the nominalist construal for the use of numerals and for the understanding of ontological questions for the existence of numbers will be spelled out. (shrink)

This paper is a reply to George Boolos's three papers (Boolos (1987a, 1987b, 1990a)) concerned with the status of Hume's Principle. Five independent worries of Boolos concerning the status of Hume's Principle as an analytic truth are identified and discussed. Firstly, the ontogical concern about the commitments of Hume's Principle. Secondly, whether Hume's Principle is in fact consistent and whether the commitment to the universal number by adopting Hume's Principle might (...) be problematic. Also the so-called `surplus content' worry is discussed, which points out that the conceptual resources to grasp Hume's Principle vastly outstrip the conceptual resources employed in arithmetical reasoning. And lastly whether Hume's Principle is in bad company with other unsuccessful implicit definitions. In the last section, an account towards our entitlement to Hume&'s Principle is sketched. (shrink)

Debunking arguments against both moral and mathematical realism have been pressed, based on the claim that our moral and mathematical beliefs are insensitive to the moral/mathematical facts. In the mathematical case, I argue that the role of Hume’s Principle as a conceptual truth speaks against the debunkers’ claim that it is intelligible to imagine the facts about numbers being otherwise while our evolved responses remain the same. Analogously, I argue, the conceptual supervenience of the moral on the natural speaks (...) presents a difficulty for the debunker’s claim that, had the moral facts been otherwise, our evolved moral beliefs would have remained the same. (shrink)

In this note we derive Robinson???s Arithmetic from Hume???s Principle in the context of very weak theories of classes and relations.

In this paper, I shall discuss several topics related to Frege's paradigms of second-order abstraction principles and his logicism. The discussion includes a critical examination of some controversial views put forward mainly by Robin Jeshion, Tyler Burge, Crispin Wright, Richard Heck and John MacFarlane. In the introductory section, I try to shed light on the connection between logical abstraction and logical objects. The second section contains a critical appraisal of Frege's notion of evidence and its interpretation by Jeshion, the introduction (...) of the course-of-values operator and Frege's attitude towards Axiom V, in the expression of which this operator occurs as the key primitive term. Axiom V says that the course-of-values of the function f is identical with the course-of-values of the function g if and only if f and g are coextensional. In the third section, I intend to show that in Die Grundlagen der Arithmetik Frege hardly could have construed Hume's Principle as a primitive truth of logic and used it as an axiom governing the cardinality operator as a primitive sign. HP expresses that the number of Fs is identical with the number of Gs if and only if F and G are equinumerous. In the fourth section, I argue that Wright falls short of making a convincing case for the alleged analyticity of HP. In the final section, I canvass Heck's arguments for his contention that Frege knew he could deduce the simplest laws of arithmetic from HP without invoking Axiom V. I argue that they do not carry conviction. I conclude this section by rejecting an interpretation concerning HP suggested by MacFarlane. (shrink)

In this paper, I shall discuss several topics related to Frege’s paradigms of second-order abstraction principles and his logicism. The discussion includes a critical examination of some controversial views put forward mainly by Robin Jeshion, Tyler Burge, Crispin Wright, Richard Heck and John MacFarlane. In the introductory section, I try to shed light on the connection between logical abstraction and logical objects. The second section contains a critical appraisal of Frege’s notion of evidence and its interpretation by Jeshion, the introduction (...) of the course-of-values operator and Frege’s attitude towards Axiom V, in the expression of which this operator occurs as the key primitive term. Axiom V says that the course-of-values of the function f is identical with the course-of-values of the function g if and only if f and g are coextensional. In the third section, I intend to show that in Die Grundlagen der Arithmetik (1884) Frege hardly could have construed Hume’s Principle (HP) as a primitive truth of logic and used it as an axiom governing the cardinality operator as a primitive sign. HP expresses that the number of Fs is identical with the number of Gs if and only if F and G are equinumerous. In the fourth section, I argue that Wright falls short of making a convincing case for the alleged analyticity of HP. In the final section, I canvass Heck’s arguments for his contention that Frege knew he could deduce the simplest laws of arithmetic from HP without invoking Axiom V. I argue that they do not carry conviction. I conclude this section by rejecting an interpretation concerning HP suggested by MacFarlane. (shrink)

George Dickie argues that Hume's principles of taste have value-laden properties as their subjects, including those properties we now refer to as ‘aesthetic’. I counter that Hume's principles have value-neutral properties as their subjects, and so exclude those properties we now refer to as ‘aesthetic’. Dickie also argues that Hume's essay on taste provides ‘the conceptual means for recognizing the problem of the interaction of aesthetic properties with other properties of artworks’. I counter that the very passages (...) Dickie takes to provide these conceptual means in fact suggest that Hume recognizes no such problem. (shrink)

The question of the analyticity of Hume’s Principle (HP) is central to the neo-logicist project. We take on this question with respect to Frege’s definition of analyticity, which entails that a sentence cannot be analytic if it can be consistently denied within the sphere of a special science. We show that HP can be denied within non-standard analysis and argue that if HP is taken to depend on Frege’s definition of number, it isn’t analytic, and if HP is taken (...) to be primitive there is only a very narrow range of circumstances where it might be taken to be analytic. The latter discussion also sheds some light on the connections between the Bad Company and Caesar objections. (shrink)

One prominent criticism of the abstractionist program is the so-called Bad Company objection. The complaint is that abstraction principles cannot in general be a legitimate way to introduce mathematical theories, since some of them are inconsistent. The most notorious example, of course, is Frege’s Basic Law V. A common response to the objection suggests that an abstraction principle can be used to legitimately introduce a mathematical theory precisely when it is stable: when it can be made true on all (...) sufficiently large domains. In this paper, we raise a worry for this response to the Bad Company objection. We argue, perhaps surprisingly, that it requires very strong assumptions about the range of the second-order quantifiers; assumptions that the abstractionist should reject. (shrink)

In a recent article, I have explored the historical, mathematical, and philosophical issues related to the new theory of numerosities. The theory of numerosities provides a context in which to assign numerosities to infinite sets of natural numbers in such a way as to preserve the part-whole principle, namely if a set A is properly included in B then the numerosity of A is strictly less than the numerosity of B. Numerosities assignments differ from the standard assignment of size (...) provided by Cantor’s cardinality assignments. In this talk, I generalize some specific worries emerging from the theory of numerosities to a line of thought resulting in what I call a ‘good company’ objection to Hume’s Principle (HP). The talk has four main parts. The first takes a historical look at 19th-century attributions of equality of numbers in terms of one-one correlations and argues that there was no agreement as to how to extend such determinations to infinite sets of objects. This leads to the second part where I show that there are countably infinite many abstraction principles that are ‘good’, in the sense that they share the same virtues of HP and from which we can derive the axioms of second order arithmetic. The third part connects this material to a debate on Finite Hume Principle between Heck and MacBride and states the ‘good company’ objection. Finally, the last part gives a tentative taxonomy of possible neo-logicist responses to the ‘good company’ objection and makes a foray into the relevance of this material for the issue of cross-sortal identifications for abstractions. (shrink)

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)

Richard Kimberly Heck and Paolo Mancosu have claimed that the possibility of non-Cantorian assignments of cardinalities to infinite concepts shows that Hume's Principle (HP) is not implicit in the concept of cardinal number. Neologicism would therefore be threatened by the ‘good company' HP is kept by such alternative assignments. In his review of Mancosu's book, Bob Hale argues, however, that ‘getting different numerosities for different countable infinite collections depends on taking the groups in a certain order – but (...) it is of the essence of cardinal numbers that the cardinal size of a collection does not depend upon how its members are ordered'. This paper's goal is to implement Hale's response to the Good Company problem by producing a Cantorian argument for HP. In Section 2, we present the Heck-Mancosu argument against neologicism. In Section 3, we discuss Hale's defence of Hume's Principle. In Section 4, we discuss Cantor's abstractionist definitions of number. In Section 5, we argue that good abstraction must comply with what we call ‘Gödel’s Minimal Account of Abstraction’ (GMAA). We finally show (Sections 5 and 6) that non-Cantorian theories of cardinality fail to satisfy GMAA. (shrink)

This paper presents new constructions of models of Hume's Principle and Basic Law V with restricted amounts of comprehension. The techniques used in these constructions are drawn from hyperarithmetic theory and the model theory of fields, and formalizing these techniques within various subsystems of second-order Peano arithmetic allows one to put upper and lower bounds on the interpretability strength of these theories and hence to compare these theories to the canonical subsystems of second-order arithmetic. The main results of (...) this paper are: (i) there is a consistent extension of the hyperarithmetic fragment of Basic Law V which interprets the hyperarithmetic fragment of second-order Peano arithmetic, and (ii) the hyperarithmetic fragment of Hume's Principle does not interpret the hyperarithmetic fragment of second-order Peano arithmetic, so that in this specific sense there is no predicative version of Frege's Theorem. (shrink)

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 of Gs 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)

Hume's Principle, dear to neo-Logicists, maintains that equinumerosity is both necessary and sufficient for sameness of cardinal number. All the same, Whitehead demonstrated in Principia Mathematica's logic of relations that Cantor's power-class theorem entails that Hume's Principle admits of exceptions. Of course, Hume's Principle concerns cardinals and in Principia's ‘no-classes’ theory cardinals are not objects in Frege's sense. But this paper shows that the result applies as well to the theory of cardinal numbers as (...) objects set out in Frege's Grundgesetze. Though Frege did not realize it, Cantor's power-theorem entails that Frege's cardinals as objects do not always obey Hume's Principle. (shrink)

That no qualities ought to be ascribed to a cause beyond what are requisite for bringing about its effect(s) is a methodological principle Hume employs to evacuate arguments from design of much theological significance. In this article I defend Hume’s use of the principle against several objections brought against it by Richard Swinburne.

Sections “Introduction: Hume’s Principle, Basic Law V and Cardinal Arithmetic” and “The Julius Caesar Problem in Grundlagen—A Brief Characterization” are peparatory. In Section “Analyticity”, I consider the options that Frege might have had to establish the analyticity of Hume’s Principle, bearing in mind that with its analytic or non-analytic status the intended logical foundation of cardinal arithmetic stands or falls. Section “Thought Identity and Hume’s Principle” is concerned with the two criteria of thought identity that Frege states (...) in 1906 and their application to Hume’s Principle. In Section “The Nature ofion: A Critical Assessment of Grundlagen, §64”, I scrutinize Frege’s characterization of abstraction in Grundlagen, §64 and criticize in this context the currently widespread use of the terms “recarving” and “reconceptualization”. Section “Frege’s Proof of Hume’s Principle” is devoted to the formal details of Frege’s proof of Hume’s Principle. I begin by considering his proof sketch in Grundlagen and subsequently reconstruct in modern notation essential parts of the formal proof in Grundgesetze. In Section “Equinumerosity and Coextensiveness: Hume’s Principle and Basic Law V Again”, I discuss the criteria of identity embodied in Hume’s Principle and in Basic Law V, equinumerosity and coextensiveness. In Section “Julius Caesar and Cardinal Numbers—A Brief Comparison Between Grundlagen and Grundgesetze ”, I comment on the Julius Caesar problem arising from Hume’s Principle in Grundlagen and analyze the reasons for its absence in this form in Grundgesetze. I conclude with reflections on the introduction of the cardinals and the reals by abstraction in the context of Frege’s logicism. (shrink)

Hsueh M. Qu has recently argued that Hume’s famed ‘Separability Principle’ from the Treatise entangles him in a contradiction. Qu offers a modified principle as a solution but also argues that the mature Hume would not have needed to avail himself of it, given that Hume’s arguments in the first Enquiry do not depend on this principle in any form. To the contrary, I show that arguments in the first Enquiry depend on this principle, but I (...) agree with Qu that Qu’s solution to Hume’s quandary frees him of the contradiction. Next, I compare Qu’s solution to Hume’s original position. By analysing the divergent forms of 'Hume’s Dictum’ that follow from them, I show that Qu’s solution and Hume’s original position have significantly different consequences in a range of domains, including Hume’s modality. Generally, Qu’s solution fits better with Hume’s other commitments—even though Hume often fails to recognize it—thereby increasing its plausibility. (shrink)

Rachel Cohon's Hume is a moral sensing theorist, who holds both that moral qualities are mind-dependent and that there is such a thing as moral knowledge. He is an anti-rationalist about motivation, arguing that reason alone does not motivate, but allows that both beliefs and passions are motivating. And he is both a descriptive and a normative moral theorist who, despite having resources for putting checks on our sentimentally-based moral evaluations, does end up with a kind of a relativistic account (...) of the virtues and vices. Professor Cohon's arguments in Hume's Morality1 are tight and vigorous. Anyone working on these . (shrink)

In lieu of an abstract, here is a brief excerpt of the content:HUME'S BUNDLES, SELF-CONSCIOUSNESS AND KANT Even if we are inclined to view Hume's attempt to explain ascriptions of personal identity as an abysmal failure, we might still be sympathetic toward his proposal to replace the going substance theory of the nature of mind with his bundle account. Thus we might fault Hume for erecting an unachievably high standard for personal identity, or round on him for excluding (...) bodily criteria 2... from his solution, but nonetheless applaud his spiriting away of the Cartesian soul substance leaving his "true idea of the human mind" (261) as a collection of perceptions in its stead. However, Hume's concern to give an account of the idea of the unity of a human mind in terms of related perceptions has run into notoriously rough sledding, not the least of which is the fact that Hume himself in his Appendix to "Of Personal Identity" seems to abandon his bundle theory in despair. In this paper I shall first be concerned to examine the criticism of his bundle theory which Hume brings forth in the Appendix and explain why I think the core difficulty remains insoluble for Hume. I shall then go on to suggest that the unworkability of Húmete bundle theory is directly tied to his failure to appreciate certain features of the peculiarly first person nature of his question about the make-up of minds. In thus emphasizing the place of the first person voice in my interpretation I am stealing a leaf, if not a chapter, from Kant. But this is as it should be since one of the aims of this essay is to provide an interpretation of Hume's difficulties with his account of the nature of mind which explains part of the reason why 'self-consciousness' (or 'apperception') looms so very large in the Critique of Pure Reason attack upon Hume's type of bundle theory. 60. 1. Hume's Second Thoughts In a burst of self criticism at the Appendix to the section on personal identity, Hume brings forth this objection to his own efforts:...Having thus loosen' d all our particular perceptions, when I proceed to explain the principle of connexion, which binds them together, and makes us attribute to them a real simplicity and identity; I am sensible, that my account is very defective, and that nothing but the seeming evidence of the precedent reasonings cou'd have indue' d me to receive it (635). After additional reflections Hume encapsulates his objection thus:...All my hopes vanish, when I come to explain the principles, that unite our successive perceptions in our thought or consciousness (6SS-6). What is the defect Hume calls to our attention? Notice first that the footnote on page 635 explicitly refers us back to that part of his account Hume considers defective; and when we look back to the text of the Treatise in question, page 260, we find it is precisely there that Hume uses the analogy of a republic to sketch his bundle theory of the unity of mind in terms of the two associative principles, resemblance and causation. So it must somehow be that this account in terms of the associative principles is mistaken. But what then is the mistake? According to Hume it is that he cannot 'explain' the principles which unite the discrete percepts. Now it seems to me there are only two possible things Hume could mean in saying this. He could mean either (1) that the principles which connect the percepts of one mind are instances of the associative principles, but he cannot explain them; or (2) there must be other, non-associative, principles which connect the percepts of a single mind and these he cannot explain. 61. I think we can safely conclude (1) cannot represent Hume's misgivings when he says he is unable to explain the uniting principles of the mental bundles. There is first the fact that he does not call into question his general programme of accounting for the nature of the unity of complex things by the principles of causation, resemblance and contiguity — for example, ships, plants, animals, houses and rivers (e.g. 257f) — but only his... (shrink)

This article argues that a successful answer to Hume's problem of induction can be developed from a sub-genre of philosophy of science known as formal learning theory. One of the central concepts of formal learning theory is logical reliability: roughly, a method is logically reliable when it is assured of eventually settling on the truth for every sequence of data that is possible given what we know. I show that the principle of induction (PI) is necessary and sufficient (...) for logical reliability in what I call simple enumerative induction. This answer to Hume's problem rests on interpreting PI as a normative claim justified by a non-empirical epistemic means-ends argument. In such an argument, a rule of inference is shown by mathematical or logical proof to promote a specified epistemic end. Since the proof concerning PI and logical reliability is not based on inductive reasoning, this argument avoids the circularity that Hume argued was inherent in any attempt to justify PI. (shrink)

In this paper, I consider some ways in which the Copy Principle and Hume’s nominalism impinge on one another, concluding that the marriage is not a happy one. I argue for the following claims. First, Hume’s argument against indeterminate ideas isn’t cogent even if the Copy Principle is accepted. But this does not vindicate Locke: the imagistic conception of ideas, presupposed by the Copy Principle, will force Locke to accept something like Hume’s view of the way general (...) terms function, the availability of abstract ideas notwithstanding. Second, Hume’s discussion of nominalism provides support for the “old Hume” interpretation, which takes the Copy Principle to be a criterion of meaningfulness, as against the “new Hume” reading, according to which it constrains what we can know. Finally, nominalism forces Hume to adopt a more complicated theory of ideas. (shrink)

Hume considered his Enquiry Concerning the Principles of Morals to be one of his best works. In it he offers his most elegant and approachable account of the origins and scope of morality. With the hope of reaching a broad audience, he argues that morality is neither rigid nor austere, but is rather a product of sentiments that all human beings share, and which they are naturally inclined to recognize and act upon. In this Critical Guide, a team of distinguished (...) scholars discuss each section of the Enquiry, its place in Hume's philosophy as a whole, and its historical context; their topics include the nature of morals, talents and moral virtues, benevolence, sympathy, and the sources of moral disagreement. The volume will be valuable for scholars and advanced students working on Hume. (shrink)

Adherents of Ockham’s fundamental razor contend that considerations of ontological parsimony pertain primarily to fundamental objects. Derivative objects, on the other hand, are thought to be quite unobjectionable. One way to understand the fundamental vs. derivative distinction is in terms of the Aristotelian distinction between ontologically independent and dependent objects. In this paper I will defend the thesis that every natural number greater than 0 is an ontologically dependent object thereby exempting the natural numbers from Ockham’s fundamental razor.

I examine, in this paper, the contents of one of the most famous religious texts of the early modern period, The Whole Duty of Man, and I show that Hume's Enquiry Concerning the Principles of Man is an attempt to reappropriate and replace the Anglican devotional with his own moral philosophy. Hume would reject the devotional's general methodology, its claims about the foundation of morality, and its list of duties. However, a careful reading of The Whole Duty of Man (...) reveals that Hume shares its author's evaluation of pride and humility, and its insistence on utility and pleasure. Hume, I argue, would not think of this book as mortifying or monkish. Given the popularity of The Whole Duty of Man and Hume's desire to push religion back into the closet together with his passion for literary fame, we have good reasons to conclude that Hume was more envious than critical, and that the EPM was his own remastered version of what could be called ‘The Whole Merit of Man’. (shrink)

In this article, I explore why Hume regarded his Enquiry concerning the Principles of Morals “incomparably the best” of everything he wrote, while this judgement of his is not confirmed at all by the rankings in popularity of his works. Hume’s main reason for this judgment was the conviction that regarding the principles of morals he had reached the most satisfying, systematical and evidently true results of all his work. I argue that the general rejection of Hume’s own judgement is (...) based on prejudices that fail to take into account the way Hume himself thought that his works should be read. Hume’s wish to explain his “new and distinct notion of moral philosophy” led him to introduce many changes to this Enquiry even until few days before his death. Hume’s intention were to guide the reader thus to an understanding of his system of ethics, for he had become aware of the fact that, instead of using exact definitions, he should rely on natural descriptions and good examples to make his main point come out more clearly. Hume’s appeal to the obvious as a key to understanding seems to suggest that the Scottish philosopher was indeed “very far away from most of contemporary analytic philosophy.”. (shrink)

David Hume’s “Title Principle,” as it has come to be called, is a specification of the normative scope of reason: “Where reason is lively, and mixes itself with some propensity, it ought to be assented to. Where it does not, it never can have any title to operate on us.” This chapter seeks to answer four central questions about the principle. First, what does Hume mean by “reason” in it? Second, what particular kinds of beliefs does it mandate (...) or disallow? Third, what kind of normativity is expressed by its use of “ought”? Fourth, can it permit Hume properly to overcome—if only to some extent—the “doubts,” “contradictions and imperfections,” and “objections” concerning the use of reason that he describes prior to stating the principle? The chapter concludes with brief reflections on the significance for contemporary epistemology of Hume’s use of the Title Principle. (shrink)

Vivacity, the “liveliness” of perceptions, is central to Hume’s epistemology. Hume equated belief with vivid ideas. Vivacity is a conscious quality so believable ideas are felt to be lively. Hume’s empiricism revolves around a phenomenological, inner epistemology. Through copying, Hume bases vivacity in impressions. Sensory vivacity also concerns liveliness or patterns of change. Through learnt skillful use, it tracks change specific to intentional sense-perceptual experience, Hume’s “coherent and constant” complex impressions. Copying, in turn, communicates the conscious skill of vivacity to (...) ideas where it becomes an indicator of believable ideas. Hume’s copying concerns then the causation of conscious skills required for the identification of empirically warranted structures. Copying allows Hume to combine a radically externalist empiricism with a portable phenomenological inner epistemology. (shrink)

• Historical: Adam Smith, Thomas Reid; Kant; Bentham and Mill • Contemporary: Normative ethics: indirect influence through Utilitarian theory; Meta-ethics: “Humean” theories of moral motivation (Smith, Blackburn), (also influences accounts of rational action in general). Non-cognitivism (Mackie, Blackburn, Gibbard).

Many contemporary philosophers accept Hume's Dictum, according to which there are no metaphysically necessary connections between distinct, intrinsically typed entities. Tacit in Lewis 's work is a potential motivation for HD, according to which one should accept HD as presupposed by the best account of the range of metaphysical possibilities---namely, a combinatorial account, applied to spatiotemporal fundamentalia. Here I elucidate and assess this Ludovician motivation for HD. After refining HD and surveying its key, recurrent role in Lewis ’s work, (...) I present Lewis ’s appeal to HD as providing a broadly axiomatic generating basis for the space of metaphysical modality, and canvas the prima facie advantages of the resulting combinatorial principle---HD ---as being principled, extensionally adequate and modally reductive. Most criticisms of Lewis 's combinatorialism have targeted seeming ways in which the theory overgenerates the desired space; I rather argue that HD seriously undergenerates the desired space in three different ways. For each way I argue that available means of overcoming the undergeneration either fail to close the gap, undermine the claim that HD is a principled generator of metaphysical modal space, undermine the reductive status of Lewis 's combinatorialism, or call into question the truth of HD. (shrink)

Hume's Enlightenment Tract is the first full book-length study for forty years of David Hume's Enquiry concerning Human Understanding. The Enquiry has, contrary to its author's expressed wishes, long lived in the shadow of its predecessor, A Treatise of Human Nature. Stephen Buckle presents the Enquiry in a fresh light, and aims to raise it to its rightful position in Hume's work and in the history of philosophy. He argues that the Enquiry is not, as so often (...) assumed, a mere collection of watered-down extracts from the earlier work. It is, rather, a coherent work with a unified argument; and, when this argument is grasped as a whole, the Enquiry shows itself to be the best introduction to the lineaments of its author's general philosophy. Buckle offers a careful guide through the argument and structure of the work. He shows how the central sections of the Enquiry offer a critique of the dogmatic empiricisms of the ancient world, and set in place an alternative conception of human powers based on the sceptical principles of habit and probability. These principles are then put to work, to rule out philosophy's metaphysical ambitions and their consequences: religious systems and their attendant conception of human beings as semi-divine rational animals. Hume's scepticism, experimentalism, and naturalism are thus shown to be different aspects of the one unified philosophy - a sceptical version of the Enlightenment vision. (shrink)

Hume's Enlightenment Tract is the first full book-length study for forty years of David Hume's Enquiry concerning Human Understanding. The Enquiry has, contrary to its author's expressed wishes, long lived in the shadow of its predecessor, A Treatise of Human Nature. Stephen Buckle presents the Enquiry in a fresh light, and aims to raise it to its rightful position in Hume's work and in the history of philosophy. He argues that the Enquiry is not, as so often (...) assumed, a mere collection of watered-down extracts from the earlier work. It is, rather, a coherent work with a unified argument; and, when this argument is grasped as a whole, the Enquiry shows itself to be the best introduction to the lineaments of its author's general philosophy. Buckle offers a careful guide through the argument and structure of the work. He shows how the central sections of the Enquiry offer a critique of the dogmatic empiricisms of the ancient world, and set in place an alternative conception of human powers based on the sceptical principles of habit and probability. These principles are then put to work, to rule out philosophy's metaphysical ambitions and their consequences: religious systems and their attendant conception of human beings as semi-divine rational animals. Hume's scepticism, experimentalism, and naturalism are thus shown to be different aspects of the one unified philosophy - a sceptical version of the Enlightenment vision. (shrink)

Hume's arguments in the Treatise require him to employ not only the copy principle, which explains the intrinsic properties of perceptions, but also a thesis that explains the representational content of a perception. I propose that Hume holds the semantic copy principle, which states that a perception represents that of which it is a copy. Hume employs this thesis in a number of his most important arguments, and his doing so enables him to answer an important objection (...) concerning the status of the copy principle. I further argue that the semantic copy principle is necessary, a priori, and discovered through an analysis of our general idea of representational content. (shrink)

Given the sharp distinction that follows from Hume’s Fork, the proper epistemic status of propositions of mixed mathematics seems to be a mystery. On the one hand, mathematical propositions concern the relation of ideas. They are intuitive and demonstratively certain. On the other hand, propositions of mixed mathematics, such as in Hume’s own example, the law of conservation of momentum, are also matter of fact propositions. They concern causal relations between species of objects, and, in this sense, they are not (...) intuitive or demonstratively certain, but probable or provable. In this article, I argue that the epistemic status of propositions of mixed mathematics is that of matters of fact. I wish to show that their epistemic status is not a mystery. The reason for this is that the propositions of mixed mathematics are dependent on the Uniformity Principle, unlike the propositions of pure mathematics. (shrink)

Why believe Hume's Dictum, according to which there are, roughly speaking, no necessary connections between wholly distinct entities? Schaffer suggests that HD, at least as applied to causal or nomological connections, is motivated as required by the best account of of counterfactuals---namely, a similarity-based possible worlds account, where the operative notion of similarity requires 'miracles'---more specifically, worlds where entities of the same type that actually exist enter into different laws. The main cited motivations for such an account of similarity (...) are first, that some salient contexts presuppose CF asymmetry, and second, that accounts of CFs failing to presuppose CF asymmetry are epistemologically problematic, such that under conditions of determinism, the variations in initial micro-conditions needed to implement a given counterfactual antecedent would result in so many changes to macro-states that evaluation of CFs would be rendered practically impossible. Against the first reason, I argue that no non-artificial contexts presuppose CF asymmetry; against the second, I observe that such micro-variation is compatible, in principle, with significant similarity as regards macroscopic states of affairs---enough, in particular, to allow CFs to be appropriately evaluated. (shrink)