We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.

Wright's _Truth and Objectivity_ seeks to systematise a variety of anti-realist positions. I argue that many objections to the system are avoided by transposing its talk of truth into talk of warrant. However, a problem remains about debates involving 'direction-of-fit'. -/- Dummett introduced 'anti-realism' as a philosophical view informed by mathematical intuitionism. Subsequently, the term has been associated with many debates, ancient and modern. _Truth and Objectivity_ proposes that truth admits of different characteristics; these various debates then concern which characteristics (...) truth has, in a given area. This pluralism of truth is at odds with deflationism. I find fault with Wright's argument against deflationism. However, transmission of warrant across the Disquotational Schema suffices to ground Wright's proposal, which survives as a pluralism of classes of warrant. -/- The two main debates concern whether truths are always knowable (Epistemic Constraint) and whether disagreements in an area must be down to some fault of one of those involved (Cognitive Command). I introduce Assertoric Constraint, relating to Epistemic Constraint, where truths cannot outstrip the availability of warrant for their assertion. I solve a structural problem by a comparison with a constitutive analysis of Moore's Paradox. The relativism of blameless disagreement is problematic. Wright's response invokes a sort of ignorance which he calls `Quandary'. I criticise this before proposing an alternative. -/- I agree with Wright that Dummett's original anti-realism does not belong among the positions which Wright seeks to systematise. However, two candidates show that the proposal suffers a weakness. Wright thinks Expressivism misguided, and implicitly rules out his earlier non-cognitivism about necessity. I argue that Expressivism has promise, and I endorse Wright's Cautious Man argument for non-cognitivism about necessity; both involve play with `direction-of-fit'. I conclude that this sort of anti-realist debate needs to be accommodated by the proposal. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...) to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions. (shrink)

In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how `intuitively plausible' an axiom is, whereas extrinsic justification supports an axiom by identifying certain `desirable' consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor (...) sufficiently precise. Instead, we suggest that the process of justification in set theory should not be thought of as neatly divisible in this way, but should rather be understood as a conceptually indivisible notion linked to the goal of explanation. (shrink)

It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that (...) the continuum is a proper class. We examine several principles based on maximality considerations in this framework, and show how some (namely Ordinal Inner Model Hypotheses) enable us to incorporate standard set theories (including ZFC with large cardinals added). We conclude that the systems considered raise questions concerning the foundational purposes of set theory. (shrink)

Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...) work in numerical cognition and ontogenetic studies. (shrink)

A pervasive thought in contemporary philosophy of mathematics is that in order to justify reflection principles, one must hold universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting universism with a Zermelian form of multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the universist, then the Zermelian can use similar justifications. However, I note that for some forms of richness argument, (...) the status of reflection principles as axioms is left open for the Zermelian. (shrink)

Let's suppose you think that there are no uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes---you've prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that there are some considerations based on a formal notion of restrictiveness which suggest that it is restrictive to hold that there are uncountable sets.

This article articulates and assesses an imperatival approach to the foundations of mathematics. The core idea for the program is that mathematical domains of interest can fruitfully be viewed as the outputs of construction procedures. We apply this idea to provide a novel formalisation of arithmetic and set theory in terms of such procedures, and discuss the significance of this perspective for the philosophy of mathematics.

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...) and meta-theoretic properties when comparing first-order and second-order logic. (shrink)

We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width (...) reflection in contrast to the usual height reflection of the Lévy–Montague reflection theorem. They are each equiconsistent with ZFC and indeed \Pi_2-conservative over ZFC, being forceable by class forcing while preserving any desired rank-initial segment of the universe. Furthermore, the inner-model reflection principle is a consequence of the existence of sufficient large cardinals, and lightface formulations of the reflection principles follow from the maximality principle MP and from the inner-model hypothesis IMH. We also consider some questions concerning the expressibility of the principles. (shrink)

Let mathematical justification be the kind of justification obtained when a mathematician provides a proof of a theorem. Are Gettier cases possible for this kind of justification? At first sight we might think not: The standard for mathematical justification is proof and, since proof is bound at the hip with truth, there is no possibility of having an epistemically lucky justification of a true mathematical proposition. In this paper, I argue that Gettier cases are possible (and indeed actual) in mathematical (...) reasoning. By analysing these cases, I suggest that the Gettier phenomenon indicates some upshots for actual mathematical practice. (shrink)

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' perspective (...) to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

How does our language relate to reality? This is a question that is especially pertinent in set theory, where we seem to talk of large infinite entities. Based on an analogy with the use of models in the natural sciences, we argue for a threefold correspondence between our language, models, and reality. We argue that so conceived, the existence of models can be underwritten by a weak notion of existence, where weak existence is to be understood as existing in virtue (...) of language. (shrink)

In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views.

Much of the discussion of set-theoretic independence, and whether or not we could legitimately expand our foundational theory, concerns how we could possibly come to know the truth value of independent sentences. This paper pursues a slightly different tack, examining how we are ignorant of issues surrounding their truth. We argue that a study of how we are ignorant reveals a need for an understanding of set-theoretic explanation and motivates a pluralism concerning the adoption of foundational theory.

Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing considerations of (...) perturbations in modal space to bear on the debate, we will suggest that a promising option for representing current set-theoretic thought is given by formulating set theory using quasi-weak second-order logic. These observations indicate that the usual division of structures into \particular (e.g. the natural number structure) and general (e.g. the group structure) is perhaps too coarse grained; we should also make a distinction between intentionally and unintentionally general structures. (shrink)

The relevance of analytic metaphysics has come under criticism: Ladyman & Ross, for instance, have suggested do discontinue the field. French & McKenzie have argued in defense of analytic metaphysics that it develops tools that could turn out to be useful for philosophy of physics. In this article, we show first that this heuristic defense of metaphysics can be extended to the scientific field of applied ontology, which uses constructs from analytic metaphysics. Second, we elaborate on a parallel by French (...) & McKenzie between mathematics and metaphysics to show that the whole field of analytic metaphysics, being useful not only for philosophy but also for science, should continue to exist as a largely autonomous field. (shrink)

Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular ways) face (...) complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often model-theoretic constructions that add sets to models are cited as evidence in favour of the latter. This paper informs this debate by developing a way for a Universist to interpret talk that (...) seems to necessitate the addition of sets to V. We argue that, despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We present a method of interpreting extension-talk (V-logic), and show how it captures satisfaction in `ideal' outer models and relates to impredicative class theories. We provide some reasons to regard the technique as philosophically virtuous, and argue that it opens new doors to philosophical and mathematical discussions for the Universist. (shrink)

My aim here is to make sense of Plato's account of desire in the middle dialogues. To do that I need to unify or reconcile what are at first sight two quite different accounts: the doctrine of eros in the Symposium and the tripartite theory of motivation in the Republic. It may be that the two theories are after all irreconcilable, that Plato simply changed his mind on the nature of human desire after writing the Symposium and before composing the (...) Republic. But that conclusion can be justified only if attempts to reconcile the two theories end in failure. The attempt must be made first. (shrink)

Newton’s impact on Enlightenment natural philosophy has been studied at great length, in its experimental, methodological and ideological ramifications. One aspect that has received fairly little attention is the role Newtonian “analogies” played in the formulation of new conceptual schemes in physiology, medicine, and life science as a whole. So-called ‘medical Newtonians’ like Pitcairne and Keill have been studied; but they were engaged in a more literal project of directly transposing, or seeking to transpose, Newtonian laws into quantitative models of (...) the body. I am interested here in something different: neither the metaphysical reading of Newton, nor direct empirical transpositions, but rather, a more heuristic, empiricist construction of Newtonian analogies. Figures such as Haller, Barthez, and Blumenbach constructed analogies between the method of celestial mechanics and the method of physiology. In celestial mechanics, they held, an unknown entity such as gravity is posited and used to mathematically link sets of determinate physical phenomena (e.g., the phases of the moon and tides). This process allows one to remain agnostic about the ontological status of the unknown entity, as long as the two linked sets of phenomena are represented adequately. Haller et. al. held that the Newtonian physician and physiologist can similarly posit an unknown called ‘life’ and use it to link various other phenomena, from digestion to sensation and the functioning of the glands. These phenomena consequently appear as interconnected, goal-oriented processes which do not exist either in an inanimate mechanism or in a corpse. In keeping with the empiricist roots of the analogy, however, no ontological claims are made about the nature of this vital principle, and no attempts are made to directly causally connect such a principle and observable phenomena. The role of the “Newtonian analogy” thus brings together diverse schools of thought, and cuts across a surprising variety of programs, models and practices in natural philosophy. (shrink)

The category of ‘organism’ has an ambiguous status: is it scientific or is it philosophical? Or, if one looks at it from within the relatively recent field or sub-field of philosophy of biology, is it a central, or at least legitimate category therein, or should it be dispensed with? In any case, it has long served as a kind of scientific “bolstering” for a philosophical train of argument which seeks to refute the “mechanistic” or “reductionist” trend, which has been perceived (...) as dominant since the 17th century, whether in the case of Stahlian animism, Leibnizian monadology, the neo-vitalism of Hans Driesch, or, lastly, of the “phenomenology of organic life” in the 20th century, with authors such as Kurt Goldstein, Maurice Merleau-Ponty, and Georges Canguilhem. In this paper I try to reconstruct some of the main interpretive ‘stages’ or ‘layers’ of the concept of organism in order to critically evaluate it. How might ‘organism’ be a useful concept if one rules out the excesses of ‘organismic’ biology and metaphysics? Varieties of instrumentalism and what I call the ‘projective’ concept of organism are appealing, but perhaps ultimately unsatisfying. (shrink)

Black holes are extremely relativistic objects. Physical processes around them occur in a regime where the gravitational field is extremely intense. Under such conditions, our representations of space, time, gravity, and thermodynamics are pushed to their limits. In such a situation philosophical issues naturally arise. In this chapter I review some philosophical questions related to black holes. In particular, the relevance of black holes for the metaphysical dispute between presentists and eternalists, the origin of the second law of thermodynamics and (...) its relation to black holes, the problem of information, black holes and hypercomputing, the nature of determinisim, and the breakdown of predictability in black hole space-times. I maintain that black hole physics can be used to illuminate some important problems in the border between science and philosophy, either epistemology and ontology. (shrink)

There are a bewildering variety of claims connecting Darwin to nineteenth-century philosophy of science—including to Herschel, Whewell, Lyell, German Romanticism, Comte, and others. I argue here that Herschel’s influence on Darwin is undeniable. The form of this influence, however, is often misunderstood. Darwin was not merely taking the concept of “analogy” from Herschel, nor was he combining such an analogy with a consilience as argued for by Whewell. On the contrary, Darwin’s Origin is written in precisely the manner that one (...) would expect were Darwin attempting to model his work on the precepts found in Herschel’s Preliminary Discourse on Natural Science. While Hodge has worked out a careful interpretation of both Darwin and Herschel, drawing similar conclusions, his interpretation misreads Herschel’s use of the vera causa principle and the verification of hypotheses. The new reading that I present here resolves this trouble, combining Hodge’s careful treatment of the structure of the Origin with a more cautious understanding of Herschel’s philosophy of science. This interpretation lets us understand why Darwin laid out the Origin in the way that he did and also why Herschel so strongly disagreed, including in Herschel’s heretofore unanalyzed marginalia in his copy of Darwin’s book. (shrink)

LandryElaine, * ed. Categories for the Working Philosopher. Oxford University Press, 2017. ISBN 978-0-19-874899-1 ; 978-0-19-106582-8. Pp. xiv + 471.

Canguilhem is known to have regretted, with some pathos, that Life no longer serves as an orienting question in our scientific activity. He also frequently insisted on a kind of uniqueness of organisms and/or living bodies – their inherent normativity, their value-production and overall their inherent difference from mere machines. In addition, Canguilhem acknowledged a major debt to the German neurologist-theoretician Kurt Goldstein, author most famously of The Structure of the Organism in 1934; along with Merleau-Ponty, Canguilhem was the main (...) figure who introduced the work of Goldstein and his ‘phenomenology of embodiment’ into France. In this paper I inquire if we should view Canguilhem and Goldstein as ‘biochauvinists’, that is, as thinkers who consider that there is something inherently unique about biological entities as such, and if so, of what sort. (shrink)

La pertinence de la métaphysique analytique a fait l'objet de critiques : Ladyman et Ross, par exemple, ont suggéré d'abandonner ce domaine. French et McKenzie ont défendu la métaphysique analytique en affirmant qu'elle développe des outils qui pourraient s'avérer utiles pour la philosophie de la physique. Dans cet article, nous montrons dans un premier temps que cette défense heuristique de la métaphysique peut être étendue au domaine scientifique de l'ontologie appliquée, qui utilise des théories et outils issus de la métaphysique (...) analytique. Dans un deuxième temps, nous développons le parallèle que font French et McKenzie entre les mathématiques et la métaphysique pour montrer que l'ensemble du domaine de la métaphysique analytique, étant donné son utilité non seulement pour la philosophie mais également pour la science, devrait continuer à exister en tant que domaine largement autonome. (shrink)

Philosophers of science often make reference — whether tacitly or explicitly — to the notion of a scientific community. Sometimes, such references are useful to make our object of analysis tractable in the philosophy of science. For others, tracking or understanding particular features of the development of science proves to be tied to notions of a scientific community either as a target of theoretical or social intervention. We argue that the structure of contemporary scientific research poses two unappreciated, or at (...) least underappreciated, challenges to this concept of the “scientific community” in the philosophy of science. In particular, we will present two case studies from robotics research, broadly construed, which show that (1) the boundedness of the scientific community is threatened when private citizens can develop scientific and technological advances at minimal expense (democratization), and (2) the discreteness of scientific research programs is threatened by the complexly interrelated environment of contemporary scientific work (interconnectivity). Taken together, the extent of democratization and interconnectivity present a significant challenge for any practically oriented philosophy of science, one which we hope will be taken on directly by philosophers in the future. (shrink)

Table of contents for MONSTERS AND PHILOSOPHY, edited by Charles T. Wolfe (London 2005) -/- List of Contributors iii Acknowledgments vii List of Abbreviations ix -/- Introduction xi Charles T. Wolfe The Riddle of the Sphinx: Aristotle, Penelope, and 1 Empedocles Johannes Fritsche Science as a Cure for Fear: The Status of Monsters in 21 Lucretius Morgan Meis Nature and its Monsters During the Renaissance: 37 Montaigne and Vanini Tristan Dagron Conjoined Twins and the Limits of our Reason (...) 61 Annie Bitbol-Hespériès Degeneration and Hybridism in the Early Modern Species 109 Debate: Towards the Philosophical Roots of the Creation-Evolution Controversy Justin E. H. Smith Leibniz on the Unicorn and Various other Curiosities 131 Roger Ariew The Creativity of God and the Order of Nature: 153 Anatomizing Monsters in the Early Eighteenth Century Anita Guerrini The Status of Anomalies in the Philosophy of Diderot 169 Annie Ibrahim The Materialist Denial of Monsters 187 Charles T. Wolfe Cerebral Assymetry, Monstrosities and Hegel. 205 On the Situation of the Life Sciences in 1800 Michael Hagner The Lady Knight of the Perilous Place 217 Elfriede Jelinek Monster: More than a Word. . . From Portent to Anomaly, 231 the Extraordinary Career of Monsters Beate Ochsner Index 281 . (shrink)

Well prior to the invention of the term ‘biology’ in the early 1800s by Lamarck and Treviranus, and also prior to the appearance of terms such as ‘organism’ under the pen of Leibniz in the early 1700s, the question of ‘Life’, that is, the status of living organisms within the broader physico-mechanical universe, agitated different corners of the European intellectual scene. From modern Epicureanism to medical Newtonianism, from Stahlian animism to the discourse on the ‘animal economy’ in vitalist medicine, models (...) of living being were constructed in opposition to ‘merely anatomical’, structural, mechanical models. It is therefore curious to turn to the ‘passion play’ of the Scientific Revolution – whether in its early, canonical definitions or its more recent, hybridized, reconstructed and expanded versions: from Koyré to Biagioli, from Merton to Shapin – and find there a conspicuous absence of worry over what status to grant living beings in a newly physicalized universe. Neither Harvey, nor Boyle, nor Locke (to name some likely candidates, the latter having studied with Willis and collaborated with Sydenham) ever ask what makes organisms unique, or conversely, what does not. In this paper I seek to establish how ‘Life’ became a source of contention in early modern thought, and how the Scientific Revolution missed the controversy. (shrink)

Sensibility, in any of its myriad realms – moral, physical, aesthetic, medical and so on – seems to be a paramount case of a higher-level, intentional property, not a basic property. Diderot famously made the bold and attributive move of postulating that matter itself senses, or that sensibility (perhaps better translated ‘sensitivity’ here) is a general or universal property of matter, even if he at times took a step back from this claim and called it a “supposition.” Crucially, sensibility is (...) here playing the role of a ‘booster’: it enables materialism to provide a full and rich account of the phenomena of conscious, sentient life, contrary to what its opponents hold: for if matter can sense, and sensibility is not a merely mechanical process, then the loftiest cognitive plateaus are accessible to materialist analysis, or at least belong to one and the same world as the rest of matter. This was noted by the astute anti-materialist critic, the Abbé Lelarge de Lignac, who, in his 1751 Lettres à un Amériquain, criticized Buffon for “granting to the body [la machine, a common term for the body at the time] a quality which is essential to minds, namely sensibility.” This view, here attributed to Buffon and definitely held by Diderot, was comparatively rare. If we look for the sources of this concept, the most notable ones are physiological and medical treatises by prominent figures such as Robert Whytt, Albrecht von Haller and the Montpellier vitalist Théophile de Bordeu. We then have, or so I shall try to sketch out, an intellectual landscape in which new – or newly articulated – properties such as irritability and sensibility are presented either as an experimental property of muscle fibers, that can be understood mechanistically (Hallerian irritability, as studied recently by Hubert Steinke and Dominique Boury) or a property of matter itself (whether specifically living matter as in Bordeu and his fellow montpelliérains Ménuret and Fouquet, or matter in general, as in Diderot). I am by no means convinced that it is one and the same ‘sensibility’ that is at issue in debates between these figures (as when Bordeu attacks Haller’s distinction between irritability and sensibility and claims that ‘his own’ property of sensibility is both more correct and more fundamental in organic beings), but I am interested in mapping out a topography of the problem of sensibility as property of matter or as vital force in mid-eighteenth-century debates – not an exhaustive cartography of all possible positions or theories, but an attempt to understand the ‘triangulation’ of three views: a vitalist view in which sensibility is fundamental, matching up with a conception of the organism as the sum of parts conceived as little lives (Bordeu et al.); a mechanist, or ‘enhanced mechanist’ view in which one can work upwards, step by step from the basic property of irritability to the higher-level property of sensibility (Haller); and, more eclectic, a materialist view which seeks to combine the mechanistic, componential rigour and explanatory power of the Hallerian approach, with the monistic and metaphysically explosive potential of the vitalist approach (Diderot). It is my hope that examining Diderot in the context of this triangulated topography of sensibility as property sheds light on his famous proclamation regarding sensibility as a universal property of matter. (shrink)

A chapter on the specifically 'medical' Epicureanism of La Mettrie, connecting his materialist approach to mind-body issues and his hedonistic ethics.

Despite his position as one of the first philosophers to write in the “post- Darwinian” world, the critique of Darwin by Friedrich Nietzsche is often ignored for a host of unsatisfactory reasons. I argue that Nietzsche’s critique of Darwin is important to the study of both Nietzsche’s and Darwin’s impact on philosophy. Further, I show that the central claims of Nietzsche’s critique have been broadly misunderstood. I then present a new reading of Nietzsche’s core criticism of Darwin. An important part (...) of Nietzsche’s response can best be understood as an aesthetic critique of Darwin, reacting to what he saw as Darwin having drained life of an essential component of objective aesthetic value. For Nietzsche, Darwin’s theory is false because it is too intellectual, because it searches for rules, regulations, and uniformity in a realm where none of these are to be found – and, moreover, where they should not be found. Such a reading goes furthest toward making Nietzsche’s criticism substantive and relevant. Finally, I attempt to relate this novel explanation of Nietzsche’s critique to topics in contemporary philosophy of biology, particularly work on the evolutionary explanation of culture. (shrink)

The materialist approach to the body is often, if not always understood in ‘mechanistic’ terms, as the view in which the properties unique to organic, living embodied agents are reduced to or described in terms of properties that characterize matter as a whole, which allow of mechanistic explanation. Indeed, from Hobbes and Descartes in the 17th century to the popularity of automata such as Vaucanson’s in the 18th century, this vision of things would seem to be correct. In this paper (...) I aim to correct this inaccurate vision of materialism. On the contrary, the materialist project on closer consideration reveals itself to be, significantly if not exclusively, (a) a body of theories specifically focused on the contribution that ‘biology’ or rather ‘natural history’ and physiology make to metaphysical debates, (b) much more intimately connected to what we now call ‘vitalism’ (a case in point is the presence of Théophile de Bordeu, a prominent Montpellier physician and theorist of vitalism, as a fictional character and spokesman of materialism, in Diderot’s novel D’Alembert’s Dream), and ultimately (c) an anti-mechanistic doctrine which focuses on the unique properties of organic beings. To establish this revised vision of materialism I examine philosophical texts such as La Mettrie’s Man a Machine and Diderot’s D’Alembert’s Dream; medical entries in the Encyclopédie by physicians such as Ménuret and Fouquet; and clandestine combinations of all such sources (Fontenelle, Gaultier and others). (shrink)

In this paper I raise concerns that I have with what I perceive to be as a complete lack of warrant for Hume’s assertion that there are only two types of reasoning – demonstrative and probable. (Hume’s fork) What I leave for others to decide is whether this lack of warrant therefore successfully undercuts Hume’s argument for the Problem of Induction.

This book presents and analyzes the most important arguments in the history of Western philosophy's skeptical tradition. It demonstrates that, although powerful, these arguments are quite limited and fail to prove their core assertion that knowledge is beyond our reach. Argues that skepticism is mistaken and that knowledge is possible Dissects the problems of realism and the philosophical doubts about the accuracy of the senses Explores the ancient argument against a criterion of knowledge, Descartes' skeptical arguments, and skeptical arguments applied (...) to inductive inference and self-knowledge Uses Moore's proof of an external world and the reliabilist conception of knowledge to illustrate that the traditional skeptical arguments fail to meet their mark. (shrink)

Can an explanation of a set of beliefs cast doubt on the things believed? In particular, can an evolutionary explanation of religious beliefs call the contents of those beliefs into question? Yes - under certain circumstances. I distinguish between natural histories of beliefs and genealogies. A natural history of a set of beliefs is an explanation that puts them down to naturalistic causes. (I try to give an account of natural explanations which favors a certain kind of ‘methodological atheism’ without (...) begging any crucial questions against theists.) A genealogy is an explanation which somehow subverts the claims believed, usually by putting down the beliefs to unreliable causal mechanisms. Some genealogies are natural histories, such as Aquinas’s explanation of the prevalence of Islam and Gibbon’s explanation of the prevalence of Christianity. But not all genealogies are natural histories and not all natural histories are genealogies: witness the Primitive Christians’ explanation of the prevalence of Paganism which relies crucially on supernatural agencies and Hume’s explanation of our moral beliefs which defines moral truth in terms of the idealized outputs of our natural belief-forming mechanisms. However both believers and non-believers postulate a natural propensity of to devotion on the part of human beings a ‘sensus divinitatis’ which often results in false positives and is therefore unreliable. Thus the evolutionary explanation of this propensity does not add much to the skeptical case against religion. I conclude by arguing, as against Plantinga that since on his own showing our sensus divinitatis often malfunctions under optimum conditions, its unreliability constitutes a defeater for the claim that Christian beliefs are properly basic. (shrink)

I provide an examination and comparison of modal theories for underwriting different non-modal theories of sets. I argue that there is a respect in which the `standard' modal theory for set construction---on which sets are formed via the successive individuation of powersets---raises a significant challenge for some recently proposed `countabilist' modal theories (i.e. ones that imply that every set is countable). I examine how the countabilist can respond to this issue via the use of regularity axioms and raise some questions (...) about this approach. I argue that by comparing them with the `standard' uncountabilist theory, a new approach that brings in arbitrariness rather than the strict controls of forcing is desirable. (shrink)

In his Philosophical Inquiry concerning Human Liberty (1717), the English deist Anthony Collins proposed a complete determinist account of the human mind and action, partly inspired by his mentor Locke, but also by elements from Bayle, Leibniz and other Continental sources. It is a determinism which does not neglect the question of the specific status of the mind but rather seeks to provide a causal account of mental activity and volition in particular; it is a ‘volitional determinism’. Some decades later, (...) Diderot articulates a very similar determinism, which seeks to recognize the existence of “causes proper to man” (as he says in the Réfutation d’Helvétius). The difference with Collins is that now biological factors are being taken into account. Obviously both the ‘volitional’ and the ‘biological’ forms of determinism are noteworthy inasmuch as they change our picture of the nature of determinism itself, but my interest here is to compare these two determinist arguments, both of which are broadly Spinozist in nature – and as such belong to what Jonathan Israel called in his recent book “the radical Enlightenment,” i.e. a kind of underground Enlightenment constituted by Spinozism – and to see how Collins’ specifically psychological vision and Diderot’s specifically biological vision correspond to their two separate national contexts: determinism in France in the mid-1750s was a much more medico-biological affair than English determinism, which appears to be on a ‘path’ leading to Mill and associationist psychology. (shrink)

This paper reaches the conclusion that, while there are ordinary cases in which the pretending possibility is reasonable, these cases always contain some element that makes it reasonable. This will be the element we ask for when we ask why pretending possibility is raised. Knowledge that someone else is in pain is a matter of eliminating the proposed element or neutralizing its pain-negating aspect.

A conception of pragmatics distinguishes pragmatics from semantics proper in terms of indexicality: semantics is conceived as the quest for a truth definition for languages without indexical expressions; pragmatics is conceived as a quest for a truth definition for languages with indexical expressions. I argue that indexicality is not a feature that can be used to capture anything like what Morris and Carnap had in mind.

The eminent French biologist and historian of biology, François Jacob, once notoriously declared “On n’interroge plus la vie dans les laboratoires”: laboratory research no longer inquires into the notion of ‘Life’. Nowadays, as David Hull puts it, “both scientists and philosophers take ontological reduction for granted… Organisms are ‘nothing but’ atoms, and that is that.” In the mid-twentieth century, from the immediate post-war period to the late 1960s, French philosophers of science such as Georges Canguilhem, Raymond Ruyer and Gilbert Simondon (...) returned to Jacob’s statement with an odd kind of pathos: they were determined to reverse course. Not by imposing a different kind of research program in laboratories, but by an unusual combination of historical and philosophical inquiry into the foundations of the life sciences (particularly medicine, physiology and the cluster of activities that were termed ‘biology’ in the early 1800s). Even in as straightforwardly scholarly a work as La formation du concept de réflexe aux XVIIe et XVIIIe siècles (1955), Canguilhem speaks oddly of “defending vitalist biology,” and declares that Life cannot be grasped by logic (or at least, “la vie déconcerte la logique”). Was all this historical and philosophical work merely a reassertion of ‘mysterian’, magical vitalism? In order to answer this question we need to achieve some perspective on Canguilhem’s ‘vitalism’, notably with respect to its philosophical influences such as Kurt Goldstein. (shrink)

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a ‘structural’ perspective (...) to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

Taking my cue from Michael Smith, I try to extract a decent argument for non-cognitivism from the text of the Treatise. I argue that the premises are false and that the whole thing rests on a petitio principi. I then re-jig the argument so as to support that conclusion that Hume actually believed (namely that an action is virtuous if it would excite the approbation of a suitably qualified spectator). This argument too rests on false premises and a begged question. (...) Thus the Motivation Argument fails BOTH as an argument for noncognitivism AND as an argument for what Hume actually believed, that moral distinctions are not derived from reason and that moral properties are akin to secondary qualities. So far as the Motivation Argument is concerned, both cognitivists and rationalists can rest easy. Themes: 1) Hume’s Slavery of Reason thesis is only defensible if passions are not only desires but sometimes dispositions to acquire desires (DTADs). 2) A desire for our good on the whole, which Humeans need to posit to fend off apparent counterexamples to the Slavery of Reason Thesis, does not sit well with the Humean theory of how novel desires arise (an objection due originally to Reid). 3) Hume is wrong to suppose that ‘abstract or demonstrative reasoning never influences any of our actions, but only as it directs our judgment concerning causes and effects’ as the examples of Russell and Hobbes convincingly demonstrate. This ironic as both Russell and Hobbes subscribed to the Slavery of Reason Thesis. 4) I critique Michael Smith’s critique of motivational externalism. (shrink)

Locke and Leibniz deny that there are any such beings as ‘monsters’ (anomalies, natural curiosities, wonders, and marvels), for two very different reasons. For Locke, monsters are not ‘natural kinds’: the word ‘monster’ does not individuate any specific class of beings ‘out there’ in the natural world. Monsters depend on our subjective viewpoint. For Leibniz, there are no monsters because we are all parts of the Great Chain of Being. Everything that happens, happens for a reason, including a monstrous birth. (...) But what about materialism? Well, beginning with the anatomical interest into ‘monstrous births’ in the French Académie des Sciences in the first three decades of the eighteenth century, there is a shift away from ‘imaginationist’ claims such as those of Malebranche, that if a woman gives birth to a monstrous child it is a consequence of something she imagined. Anatomists such as Lemery and Winslow try to formulate a strictly mechanical explanation for such events, rejecting moral and metaphysical explanations. Picking up on this work, materialist thinkers like Diderot are compelled to reject the very idea of monsters. We are all material beings produced according to the same mechanisms or laws, some of us are more ‘successful’ products than others, i.e. some live longer than others. In his late Eléments de physiologie he says “L’homme est un effet commun, le monstre un effet rare.” Ultimately he arrives at a materialist version of Leibniz’s position: there are no monsters, we are all monsters in each other’s eyes, at one time or another. This conclusion is a pregnant one in light of twentieth century interest in the problem of ‘the normal and the pathological’ (Canguilhem), and the broader question of how materialism relates to the biological world. (shrink)