We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity of the underlying theory, and that a drop in pseudofinite dimension is equivalent to forking. Under a suitable assumption, a measure-theoretic condition is shown to be equivalent to local stability. Many examples are explored, including vector spaces over finite fields viewed as 2-sorted finite structures, and homocyclic groups. Connections are (...) made to products of sets in finite groups, in particular to word maps, and a generalization of Tao's Algebraic Regularity Lemma is noted. (shrink)

Given a theoryTextending that of dense linear orders without endpoints, in a language ℒ ⊇ {<}, we are interested in extensionsT′ ofTin languages extending ℒ by unary relation symbols that are each interpreted in models ofT′ as sets that are both dense and codense in the underlying sets of the models.There is a canonically “wild” example, namelyT= Th andT′ = Th. Recall thatTis o-minimal, and so every open set definable in any model ofThas only finitely many definably connected components. But (...) it is well known that 〈ℝ, <, +, · ℚ 〉 defines every real Borel set, in particular, every open subset of any finite cartesian power of ℝ and every subset of any finite cartesian power of ℚ. To put this another way, the definable open sets in models ofTare essentially as simple as possible, whileT′ has a model where the definable open sets are as complicated as possible, as is the structure induced on the new predicate.In contrast to the preceding example, if ℝalgis the set of real algebraic numbers andT′ Th, then no model ofT′ defines any open set that is not definable in the underlying model ofT. (shrink)

O-minimal structures have long been thought to occupy the base of a hierarchy of ordered structures, in analogy with the role that strongly minimal structures play with respect to stable theories. This is the first in an anticipated series of papers whose aim is the development of model theory for ordered structures of rank greater than one. A class of ordered structures to which a notion of finite rank can be assigned, the decomposable structures, is introduced here. These include all (...) ordered structures definable in o-minimal structures. The principal result in this paper, Theorem 5.1, asserts roughly that a decomposable structure [Formula: see text] can be partitioned into finitely many definable subsets such that on each set the restriction of < is a "twisted lexicographic" order. As a consequence, for all n and linear orders ≺ definable on a subset X ⊆ Mn in an o-minimal structure [Formula: see text], there is a definable partition of X such that the restriction of ≺ to each set in the partition is "lexicographic". (shrink)

We show, for various classes of totally ordered structures, including o‐minimal and weakly o‐minimal structures, that every definable partial order on a subset of extends definably in to a total order. This extends the result proved in for and o‐minimal.

We study o-minimal expansions of Archimedean totally ordered groups. We first prove that any such expansion must be elementarily embeddable via a unique (provided some nonzero element is 0-definable) elementary embedding into a unique o-minimal expansion of the additive ordered group of real numbers R. We then show that a definable function in an o-minimal expansion of R enjoys good differentiability properties and use this to prove that an Archimedean real closed field is definable in any nonsemilinear expansion of R. (...) Combining these results, we obtain several restrictions on possible o-minimal expansions of arbitrary Archimedean ordered groups and in particular of the rational ordered group. (shrink)

It is shown that if is an o-minimal structure such that is a dense total order and ≾ is a parameter-definable partial order on M, then ≾ has an extension to a definable total order.

For a countable complete o-minimal theory T, we introduce the notion of a sequentially complete model of T. We show that a model M of T is sequentially complete if and only if $\mathscr{M} \prec \mathscr{N}$ for some Dedekind complete model N. We also prove that if T has a Dedekind complete model of power greater than 2 ℵ 0 , then T has Dedekind complete models of arbitrarily large powers. Lastly, we show that a dyadic theory--namely, a theory relative (...) to which every formula is equivalent to a Boolean combination of formulas in two variables--that has some Dedekind complete model has Dedekind complete models in arbitrarily large powers. (shrink)

Review by: Michael Benedikt The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 112-115, March 2013.

This is a major and comprehensive study of the philosophy of Hegel, his place in the history of ideas, and his continuing relevance and importance. Professor Taylor relates Hegel to the earlier history of philosophy and, more particularly, to the central intellectual and spiritual issues of his own time. He engages with Hegel sympathetically, on Hegel's own terms and, as the subject demands, in detail. This important book is now reissued with a fresh new cover.

This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach through an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.

This previously-unpublished essay by the late Charles W. Mills (1951–2021) seeks to demonstrate the racially-structured character of the universe created by J. R. R. Tolkien in The Hobbit and The Lord of the Rings. Written long before the popular film series, the essay critically examines Tolkien's novels and comments on the nature of fictional creation. Mills argues that Tolkien designs a racial hierarchy in the novels that recapitulates the central racist myth of European thought.

The collapse of historicism was not merely the demise of an academic tradition but signified a shift in the understanding of hermeneutics and metaphysics. Whereas earlier books have explored the rise and dominance of historicism within academic history, this is the first to trace its collapse and to show how it was shaped by larger philosophical and scientific concerns. Charles R. Bambach's lucid account of the demise of historicism within the context of German metaphysics provides a rich new perspective (...) on the development of the young Heidegger's concept of "historicity" and on the origins of postmodern thought. Bambach reconstructs the methodological debates arising from a pervasive sense of crisis among German philosophers in the late nineteenth century. He details the divergent attempts by the Neo-Kantians, Nietzsche, and Dilthey to overcome the limitations of historical relativism. Heidegger's view of "historicity," Bambach shows, radically transforms the problematic of historicism into a discourse concerning the crisis of philosophical modernity. (shrink)

Reviews the scope, nature, and applications of the philosophical discipline, focusing on methods for distinguishing between valid and fallacious arguments and inferences.

"A beautiful piece of work on the theory of altered states of consciousness ." "Stanislav Grof, M.D. author of Realms of the Human Unconsciousness".

In reflecting on the relation between early empiricist conceptions of the mind and more experimentally motivated materialist philosophies of mind in the mid-eighteenth century, I suggest that we take seriously the existence of what I shall call ‘phantom philosophical projects’. A canonical empiricist like Locke goes out of his way to state that their project to investigate and articulate the ‘logic of ideas’ is not a scientific project: “I shall not at present meddle with the Physical consideration of the Mind” (...) (Essay, I.i.2). An equally prominent thinker, Immanuel Kant, seems to make an elementary mistake, given such a clear statement, when he claims that Locke’s project was a “physiology of the understanding,” in the Preface to the A edition of the first Critique). A first question, then, would be: what is this physiology of the understanding, if it was not Locke’s project? Did anyone undertake such a project? If not, what would it have resembled? My second and related case comes out of a remark the Hieronymus Gaub makes in a letter to Charles Bonnet of 1761: criticizing materialist accounts of mind and mind-body relations such as La Mettrie’s, Gaub suggests that what is needed is a thorough study of the “mechanics of the soul,” and that Bonnet could write such a study. What is the mechanics of the soul, especially given that it is presented as a non-materialist project? To what extent does it resemble the purported “physiology of the understanding”? And more generally, what do both of these phantom projects have to do with a process we might describe as a ‘naturalization of the soul’? (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)

The myth of the homeland -- The Nietzschean self-assertion of the German University -- The geo-politics of Heidegger's Mitteleuropa -- Heidegger's Greeks and the myth of autochthony -- Heidegger's "Nietzsche".

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)

Our aim in this paper is to bring to light the importance of the notion of économie animale in Montpellier vitalism, as a hybrid concept which brings together the structural and functional dimensions of the living body – dimensions which hitherto had primarily been studied according to a mechanistic model, or were discussed within the framework of Stahlian animism. The celebrated image of the bee-swarm expresses this structural-functional understanding of living bodies quite well: “One sees them press against each other, (...) mutually supporting each other, forming a kind of whole, in which each living part, in its own way, by means of the correspondence and directions of its motions, enables this kind of life to be sustained in the body” (Encyclopédie, article “Observation,” by Ménuret de Chambaud). What is important here is that every component part is always a living part, i.e., every structural unit is always functional. Interestingly, while the twin notions of ‘animal economy’ and organisation are presented as improvements over a mechanistic perspective, they are nonetheless compatible with an expanded sense of mechanism and by extension, with materialism as reflected notably in the writings of Ménuret and Bordeu. We thus propose both a revision and reconstruction of the historical status of the ‘animal economy’, and a reflection on its conceptual status. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

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)

In this essay I seek to critically evaluate some forms of holism and organicism in biological thought, as a more deflationary echo to Gilbert and Sarkar's reflection on the need for an 'umbrella' concept to convey the new vitality of holistic concepts in biology (Gilbert and Sarkar 2000). Given that some recent discussions in theoretical biology call for an organism concept (from Moreno and Mossio’s work on organization to Kirschner et al.’s research paper in Cell, 2000, building on chemistry to (...) articulate what they called “molecular vitalism,” studying the “vitalistic” properties of molecular, cellular, and organismal function, and Pepper and Herron’s suggestion in their 2008 paper that organisms define a category that evolutionary biology cannot do without), the question, what concept of organicism are they calling for? To what extent are such claims philosophically committed to a non-naturalistic concept of organism as organizing centre, as a foundational rather than heuristic concept – or possibly a “biochauvinism,” to use Di Paolo’s term (Di Paolo 2009)? My aim in this paper is to conceptually clarify the forms of holism and organicism that are involved in these cases (and I acknowledge that the study of early 20th-century holisms [Peterson 2010] indicates that not all of them were in fact ‘organicist’ or ‘biologistic’). I suggest that contemporary holists are still potentially beholden to a certain kind of vitalism or “biochauvinism”; but that when they reduce their claims to mere heuristics, conversely, they risk losing sight of a certain kind of organizational “thickness”, a “vital materiality” (Wheeler 2010) which is characteristic of biological systems (Bechtel 2007). And I ask if it is possible to articulate a concept of biological holism or organicism which is neither an empirical ‘biochauvinism’ nor a metaphysical ‘vitalism’? (shrink)

Few themes resonate as powerfully in Heidegger as those connected to homecoming, homeland, and Heimat. This emphasis plays out most powerfully in Heidegger's reading of Hölderlin and his turn towards language, art, and poetizing as a way of thinking through the poet's relevance in the epoch of homelessness and the abandonment of the gods. As the first book-length study in English of the Heidegger-Hölderlin relation, Of an Alien Homecoming addresses the tension within Heidegger's work between his disastrous political commitments during (...) the era of National Socialism and his attempts to open a path to a German future nurtured on Hölderlin's ideal of poetic dwelling. Charles Bambach reads this work on Hölderlin from 1934–1948 in conversation with the Black Notebooks and Heidegger's metapolitics, even as he uncovers an ethical dimension within Heidegger that pervades his reading of poetry. Throughout all of these various stages on Heidegger's thought path, Hölderlin remains the poet who poetizes the possibility of finding our lost home amidst the homelessness brought about in the epoch of technological thinking. (shrink)

The Enlightenment was the age in which the world became modern, challenging tradition in favor of reason, freedom, and critical inquiry. While many aspects of the Enlightenment have been rigorously scrutinized—its origins and motivations, its principal characters and defining features, its legacy and modern relevance—the geographical dimensions of the era have until now largely been ignored. Placing the Enlightenment contends that the Age of Reason was not only a period of pioneering geographical investigation but also an age with spatial dimensions (...) to its content and concerns. Investigating the role space and location played in the creation and reception of Enlightenment ideas, Charles W. J. Withers draws from the fields of art, science, history, geography, politics, and religion to explore the legacies of Enlightenment national identity, navigation, discovery, and knowledge. Ultimately, geography is revealed to be the source of much of the raw material from which philosophers fashioned theories of the human condition. Lavishly illustrated and engagingly written, Placing the Enlightenment will interest Enlightenment specialists from across the disciplines as well as any scholar curious about the role geography has played in the making of the modern world. (shrink)

The organism is neither a discovery like the circulation of the blood or the glycogenic function of the liver, nor a particular biological theory like epigenesis or preformationism. It is rather a concept which plays a series of roles – sometimes overt, sometimes masked – throughout the history of biology, and frequently in very normative ways, also shifting between the biological and the social. Indeed, it has often been presented as a key-concept in life science and the ‘theorization’ of Life, (...) but conversely has also been the target of influential rejections: as just an instrument of transmission for the selfish gene, but also, historiographically, as part of an outdated ‘vitalism’. Indeed, the organism, perhaps because it is experientially closer to the ‘body’ than to the ‘molecule’, is often the object of quasi-affective theoretical investments presenting it as essential, sometimes even as the pivot of a science or a particular approach to nature, while other approaches reject or attack it with equal force, assimilating it to a mysterious ‘vitalist’ ontology of extra-causal forces, or other pseudo-scientific doctrines. This paper does not seek to adjudicate between these debates, either in terms of scientific validity or historical coherence; nor does it return to the well-studied issue of the organism-mechanism tension in biology. Recent scholarship has begun to focus on the emergence and transformation of the concept of organism, but has not emphasized so much the way in which organism is a shifting, ‘go-between’ concept – invoked as ‘natural’ by some thinkers to justify their metaphysics, but then presented as value-laden by others, over and against the natural world. The organism as go-between concept is also a hybrid, a boundary concept or an epistemic limit case, all of which partly overlap with the idea of ‘nomadic concepts’. Thereby the concept of organism continues to function in different contexts – as a heuristic, an explanatory challenge, a model of order, of regulation, etc. – despite having frequently been pronounced irrelevant and reduced to molecules or genes. Yet this perpetuation is far removed from any ‘metaphysics of organism’, or organismic biology. (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)