Donald T. Campbell outlines an epistemological theory that attempts to be faithful to evolution through natural selection. He takes his position to be consistent with that of Karl R. Popper, whom he credits as the primary advocate of his day for natural selection epistemology. Campbell writes that neither he nor Popper want to give up the goal of objectivity or objective truth, in spite of their evolutionary epistemology. In discussing the conflict between an epistemology based on natural selection and objective (...) truth, Campbell cites an article by the German sociologist and philosopher Georg Simmel entitled 'On a Connection of Selection Theory to Epistemology', as presenting the issue in a notably forthright manner.The present essay summarizes Simmel's article, with the purpose of clarifying, in terms that Campbell apparently finds satisfactory, the conflict that Campbell acknowledges between an evolutionary epistemology and ultimate truth; the essay then examines the responses of Campbell and Popper to Simmel's position. While Campbell and Popper acknowledge the work of Simmel, their responses suggest something less than a full consideration of Simmel's position. (shrink)

The views of John Dewey and Kurt Vonnegut are often criticized for opposite reasons: Dewey’s philosophy is said to be naively optimistic while Vonnegut’s work is read as cynical. The standard debates over the views of the two thinkers cause readers to overlook the similarities in the way each approaches tragic experience. This paper examines Dewey’s philosophic account of time and meaning and Vonnegut’s use of time travel in his autobiographical novel Slaughterhouse-Five to illustrate these similarities. This essay demonstrates how (...) both Dewey and Vonnegut embrace the ameliorative possibilities of art for preserving individuality and meaning in the face of tragic experience. (shrink)

Richard Rorty has argued that Donald Davidson can be classified as a neopragmatist. To this end, Rorty has tried to show that Davidson's views share important similarities with those of Peirce, James, and Dewey. Davidson, for his part, has tended to resist Rorty's attempts to classify his views in this way. Interestingly, the reasons for Rorty's classification and the reasons for Davidson's resistance share a common trait: an appeal to the elimination of the dualism of conceptual scheme and experiential content (...) on the basis of an assumed background of shared beliefs. According to Rorty, Davidson's background of shared beliefs is closely related to the notion of funded experience found in those thinkers often. (shrink)

There is a traditional interpretation of the work of Ralph Waldo Emerson that portrays him as a champion of nature, wilderness, or country life and an opponent of the city, technology, or urban life. Such a view, though, neglects the role of human activity in the universe as Emerson saw it. Furthermore, this view neglects the proper relation between soul and nature in the universe and risks entailing a philosophy of materialism--an unacceptable position for Emerson. An examination of Emerson's philosophy (...) will show that it is not fundamentally hostile to urban life or technology, and that, in fact, an anti-urban position is opposed to the most central themes of Emerson's philosophical vision. (shrink)

American poet Ezra Pound wrote a letter on February 6, 1940, inviting American philosopher George Santayana to join poet T. S. Eliot and himself in writing “a volume . . . on the Ideal University, or The Proper Curriculum, or how it would be possible to educate and/or (mostly or) civilize the university student.” Santayana declined the invitation and claimed to have no ideas on the subject of education. Participation would have been morally impossible, he wrote, because unlike Pound and (...) Eliot, whom he regarded as “reformers, full of prophetic zeal and faith in the Advent of the Lord.” Santayana was “cynically content to let people educate or neglect themselves as they may prefer.”. (shrink)

According to Larry Hickman, John Dewey’s general philosophical project of analyzing and critiquing human experience may be understood in terms of technological inquiry (Hickman 1990, 1). Following this, I contend that technology provides a model for Dewey’s analysis of language and meaning, and this analysis suggests a treatment of linguistic metaphor as a way of meeting new demands of experience with old tools of a known and understood language. An account of metaphor consistent with Dewey’s views on language and meaning (...) avoids a strict dualism of literal meaning and metaphorical meaning as well as the explanatory shortcomings of a nondualistic theory like that found in Donald Davidson’s well-known paper ”What Metaphors Mean” (1978).2 A Deweyan explanation of. (shrink)

Martin E. Rosenberg -/- The Gift of Silence: Towards an Anthropology of Jazz Improvisation as Neuro-Resistance. -/- ABSTRACT: -/- This essay addresses how the complex processes that occur during jazz improvisation enact behaviors that resemble the logic of gift exchange first described by Marcel Mauss. It is possible to bring to bear structural, sociological, political economical, deconstructive or even ethical approaches to what constitutes gift exchange during the performance of jazz. Yet, I would like to shift from focusing this (...) analysis of jazz improvisation with reference to the language of music as symbolic action (which all of these approaches require), to grounding improvisation in embodied and distributed cognition, the performance of which begins with a ritual gift of silence. By silence, I refer to the embodied, yet shared pure duration as felt synchrony within an individual performer, that extends to the members of an ensemble. Thus, I refer to both aesthetic and micro-political implications of embodied, yet also distributed musical cognition in real time. -/- For jazz musicians, embodied silence becomes the initial condition for processes of cognitive bifurcation. For it is bifurcation that attracts us to jazz in the first place. Here I expand my previous work establishing similarities in the behavior of bifurcating systems in physical and cognitive sciences to the unfolding of ambiguity in real time during improvisation with respect to polyphony, polytonality and polyrhythms in the history of jazz from Charlie Parker to Ornette Coleman. We can therefore re-conceptualize jazz improvisation as a subversive antidote for processes of determination identified in a sub-discipline of cultural studies called “cognitive capitalism.” By examining silence from this anthropological perspective, we can conceive of jazz performance as a ritualized resistance to top-down cognitive control immanent with social and digital networks. The ritual enactment that is jazz improvisation points towards an aesthetics of bifurcation that is simultaneously a micro-politics of neuro-resistance. In other words, I argue that freedom of thought requires freedom from thought as an initial condition. -/- Yet, I emphasize the empirical rather than mystical grounds to this gift of silence. The valorization of silence by jazz musicians is not simply etiquette, an ethics of reciprocity for performers exchanging “riffs,” but an initial condition that jazz performers (and, I would argue, listeners) experience in their bodies, thus linking embodied cognition to a collective field of cultural production that emerges from each embodied individual, and yet also pervades the ensemble in ways reminiscent of feedback loops in complex systems. The recent and remarkable research on music and the brain has demonstrated that it is now possible to describe jazz improvisation as possessing both embodied and distributed cognitive properties. The emergent neuronal ensemble behavior within the individual that is visible in jazz improvisors, discovered by the neuroscientists at Johns Hopkins led by Charles Limb, bears striking resemblance to the interactive behaviors of the jazz ensemble itself. Thus, it is by recourse to recent research by myself and others into the cognitive neuroscience of music generally, and jazz improvisation specifically, that the empirical grounds for an anthropology of neuro-resistance become visible. (shrink)

A ‘lottery belief’ is a belief that a particular ticket has lost a large, fair lottery, based on nothing more than the odds against it winning. The lottery paradox brings out a tension between the idea that lottery beliefs are justified and the idea that that one can always justifiably believe the deductive consequences of things that one justifiably believes – what is sometimes called the principle of closure. Many philosophers have treated the lottery paradox as an argument against the (...) second idea – but I make a case here that it is the first idea that should be given up. As I shall show, there are a number of independent arguments for denying that lottery beliefs are justified. (shrink)

This paper proposes a view of time that takes passage to be the most basic temporal notion, instead of the usual A-theoretic and B-theoretic notions, and explores how we should think of a world that exhibits such a genuine temporal passage. It will be argued that an objective passage of time can only be made sense of from an atemporal point of view and only when it is able to constitute a genuine change of objects across time. This requires that (...) passage can flip one fact into a contrary fact, even though neither side of the temporal passage is privileged over the other. We can make sense of this if the world is inherently perspectival. Such an inherently perspectival world is characterized by fragmentalism, a view that has been introduced by Fine in his ‘Tense and Reality’ (2005). Unlike Fine's tense-theoretic fragmentalism though, the proposed view will be a fragmentalist view based in a primitive notion of passage. (shrink)

My concern in this paper is with the claim that knowledge is a mental state – a claim that Williamson places front and centre in Knowledge and Its Limits. While I am not by any means convinced that the claim is false, I do think it carries certain costs that have not been widely appreciated. One source of resistance to this claim derives from internalism about the mental – the view, roughly speaking, that one’s mental states are determined by one’s (...) internal physical state. In order to know that something is the case it is not, in general, enough for one’s internal physical state to be a certain way – the wider world must also be a certain way. If we accept that knowledge is a mental state, we must give up internalism. One might think that this is no cost, since much recent work in the philosophy of mind has, in any case, converged on the view that internalism is false. This thought, though, is too quick. As I will argue here, the claim that knowledge is a mental state would take us to a view much further from internalism than anything philosophers of mind have converged upon. (shrink)

In this paper, I offer reasons for thinking that two prominent sceptical arguments in the literature – the underdetermination-based sceptical argument and the closure-based sceptical argument – are less philosophically interesting than is commonly supposed. The underdetermination-based argument begs the question against a non-sceptic and can be dismissed with little fanfare. The closure-based argument, though perhaps not question-begging per se, does rest upon contentious assumptions that a non-sceptic is under no pressure to accept.

Argument mapping is a way of diagramming the logical structure of an argument to explicitly and concisely represent reasoning. The use of argument mapping in critical thinking instruction has increased dramatically in recent decades. This paper overviews the innovation and provides a procedural approach for new teaches wanting to use argument mapping in the classroom. A brief history of argument mapping is provided at the end of this paper.

Material from this paper appears in Chap. 7 of my book Reason and Being, but there is also stuff here that isn't in the book. In particular, it discusses the claims that, for Spinoza, conceiving implies explaining and that existence is identical to or reducible to conceivability. So, if you're interested in those issues, this paper might be worth a read.

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the Universe or its initial state this becomes a particularly pressing issue. How to assess the probability of the Universe as a whole is empirically ambiguous, since we can examine only part of a single realisation of the system under investigation: at some point, data will (...) run out. We review the basics of applying Bayesian statistical explanation to the Universe as a whole. We argue that a conventional Bayesian approach to model inference generally fails in such circumstances, and cannot resolve, e.g., the so-called 'measure problem' in inflationary cosmology. Implicit and non-empirical valuations inevitably enter model assessment in these cases. This undermines the possibility to perform Bayesian model comparison. One must therefore either stay silent, or pursue a more general form of systematic and rational model assessment. We outline a generalised axiological Bayesian model inference framework, based on mathematical lattices. This extends inference based on empirical data (evidence) to additionally consider the properties of model structure (elegance) and model possibility space (beneficence). We propose this as a natural and theoretically well-motivated framework for introducing an explicit, rational approach to theoretical model prejudice and inference beyond data. (shrink)

What is critical thinking, especially in the context of higher education? How have research and scholarship on the matter developed over recent past decades? What is the current state of the art here? How might the potential of critical thinking be enhanced? What kinds of teaching are necessary in order to realize that potential? And just why is this topic important now? These are the key questions motivating this volume. We hesitate to use terms such as “comprehensive” or “complete” or (...) “definitive,” but we believe that, taken in the round, the chapters in this volume together offer a fair insight into the contemporary understandings of higher education worldwide. We also believe that this volume is much needed, and we shall try to justify that claim in this introduction. (shrink)

La posverdad es un fenómeno mediático referido a la tergiversación de la verdad en los medios de comunicación, especialmente por la proliferación de noticias falsas. En este artículo definiré los principales elementos de este fenómeno, los hechos que han generado su aparición, y un marco filosófico para su análisis ético profundo. Explico además por qué la simple asociación de la posverdad con la mentira es insuficiente, y planteo que la ampliación del marco conceptual para su análisis, con la introducción de (...) la idea de charlatanería desarrollada por el filósofo Harry Frankfurt, junto con la noción de emotivismo de Alasdair MacIntyre, nos pueden ayudar a entender mejor sus efectos perjudiciales. Afirmo que sin estos conceptos no es posible entender la intrínseca complejidad de la posverdad, y sus repercusiones más nocivas en la sociedad. Finalmente, muestro los principales peligros de la posverdad en la era poscovid debidos, especialmente, a la desconfianza generada por la evidente manipulación de la verdad, y la fragilidad ética y antropológica en la que se encuentra el ser humano en la actualidad. (shrink)

This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...) abnormal in the sense of calling for special, independent explanation. This conception of justification bears upon a range of topics in epistemology and beyond. Ultimately, this way of looking at justification guides us to a new, unfamiliar picture of how we should respond to our evidence and manage our own fallibility. This picture is developed here. (shrink)

In this paper, I respond to criticisms of my book Being and Reason recently made by Yitzhak Melamed.

There is something puzzling about statistical evidence. One place this manifests is in the law, where courts are reluctant to base affirmative verdicts on evidence that is purely statistical, in spite of the fact that it is perfectly capable of meeting the standards of proof enshrined in legal doctrine. After surveying some proposed explanations for this, I shall outline a new approach – one that makes use of a notion of normalcy that is distinct from the idea of statistical frequency. (...) The puzzle is not, however, merely a legal one. Our unwillingness to base beliefs on statistical evidence is by no means limited to the courtroom, and is at odds with almost every general principle that epistemologists have proposed as to how we ought to manage our beliefs. (shrink)

According to a captivating picture, epistemic justification is essentially a matter of epistemic or evidential likelihood. While certain problems for this view are well known, it is motivated by a very natural thought—if justification can fall short of epistemic certainty, then what else could it possibly be? In this paper I shall develop an alternative way of thinking about epistemic justification. On this conception, the difference between justification and likelihood turns out to be akin to the more widely recognised difference (...) between ceteris paribus laws and brute statistical generalisations. I go on to discuss, in light of this suggestion, issues such as classical and lottery-driven scepticism as well as the lottery and preface paradoxes. (shrink)

Similarity and difference, patterns of variation, consistency and coherence: these are the reference points of the philosopher. Understanding experience, exploring ideas through particular instantiations, novel and innovative thinking: these are the reference points of the artist. However, at certain points in the proceedings of our Symposium titled, Next to Nothing: Art as Performance, this characterisation of philosopher and artist respectively might have been construed the other way around. The commentator/philosophers referenced their philosophical interests through the particular examples/instantiations created by the (...) artist and in virtue of which they were then able to engage with novel and innovative thinking. From the artists’ presentations, on the other hand, emerged a series of contrasts within which philosophical and artistic ideas resonated. This interface of philosopher-artist bore witness to the fact that just as art approaches philosophy in providing its own analysis, philosophy approaches art in being a co-creator of art’s meaning. In what follows, we discuss the conception of philosophy-art that emerged from the Symposium, and the methodological minimalism which we employed in order to achieve it. We conclude by drawing out an implication of the Symposium’s achievement which is that a counterpoint to Institutional theories of art may well be the point from which future directions will take hold, if philosophy-art gains traction. (shrink)

According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, 2019). This paradox synthesises elements (...) of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes :2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (shrink)

This volume draws connections between Wittgenstein's philosophy and the work of Saul Kripke, especially his Naming and Necessity. Saul Kripke is regarded as one of the foremost representatives of contemporary analytic philosophy. His most important contributions include the strict distinction between metaphysical and epistemological questions, the introduction of the notions of contingent a priori truth and necessary a posteriori truth and original accounts of names, descriptions, identity, necessity and realism. The chapters in this book elucidate the relevant connections between Kripke's (...) work and Wittgenstein, specifically concerning the standard meter, contingent apriori and rule-following. The contributions shed light on how Kripke's philosophical outlook was influenced by Wittgenstein, and how mainstream analytic philosophy and Wittgensteinian philosophy can fruitfully engage with one another. Kripke and Wittgenstein will be of interest to philosophers working on Wittgenstein, Kripke, and the history of analytic philosophy. (shrink)

Theories of epistemic justification are commonly assessed by exploring their predictions about particular hypothetical cases – predictions as to whether justification is present or absent in this or that case. With a few exceptions, it is much less common for theories of epistemic justification to be assessed by exploring their predictions about logical principles. The exceptions are a handful of ‘closure’ principles, which have received a lot of attention, and which certain theories of justification are well known to invalidate. But (...) these closure principles are only a small sample of the logical principles that we might consider. In this paper, I will outline four further logical principles that plausibly hold for justification and two which plausibly do not. While my primary aim is just to put these principles forward, I will use them to evaluate some different approaches to justification and (tentatively) conclude that a ‘normic’ theory of justification best captures its logic. (shrink)

In 1990 Edward Craig published a book called Knowledge and the State of Nature in which he introduced and defended a genealogical approach to epistemology. In recent years Craig’s book has attracted a lot of attention, and his distinctive approach has been put to a wide range of uses including anti-realist metaepistemology, contextualism, relativism, anti-luck virtue epistemology, epistemic injustice, value of knowledge, pragmatism and virtue epistemology. While the number of objections to Craig’s approach has accumulated, there has been no sustained (...) attempt to develop answers to these objections. In this paper we provide answers to seven important objections in the literature. (shrink)

Is it right to convict a person of a crime on the basis of purely statistical evidence? Many who have considered this question agree that it is not, posing a direct challenge to legal probabilism – the claim that the criminal standard of proof should be understood in terms of a high probability threshold. Some defenders of legal probabilism have, however, held their ground: Schoeman (1987) argues that there are no clear epistemic or moral problems with convictions based on purely (...) statistical evidence, and speculates that our aversion to such convictions may be nothing more than an irrational bias. More recently, Hedden and Colyvan (2019, section VI) describe our reluctance to convict on the basis of purely statistical evidence as an ‘intuition’, but suggest that there may be no ‘in principle’ problem with such convictions (see also Papineau, forthcoming, section 6). In this paper, I argue that there is, in some cases, an in principle problem with a conviction based upon statistical evidence alone – namely, it commits us to a precedent which, if consistently followed through, could lead to the deliberate conviction of an innocent person. I conclude with some reflections on the idea that the criminal justice system should strive to maximise the accuracy of its verdicts – and the related idea that we should each strive to maximise the accuracy of our beliefs. (shrink)

A de minimis risk is defined as a risk that is so small that it may be legitimately ignored when making a decision. While ignoring small risks is common in our day-to-day decision making, attempts to introduce the notion of a de minimis risk into the framework of decision theory have run up against a series of well-known difficulties. In this paper, I will develop an enriched decision theoretic framework that is capable of overcoming two major obstacles to the modelling (...) of de minimis risk. The key move is to introduce, into decision theory, a non-probabilistic conception of risk known as normic risk. (shrink)

Recent years have seen an explosion of interest in metaphysical explanation, and philosophers have fixed on the notion of ground as the conceptual tool with which such explanation should be investigated. I will argue that this focus on ground is myopic and that some metaphysical explanations that involve the essences of things cannot be understood in terms of ground. Such ‘essentialist’ explanation is of interest, not only for its ubiquity in philosophy, but for its being in a sense an ultimate (...) form of explanation. I give an account of the sense in which such explanation is ultimate and support it by defending what I call the inessentiality of essence. I close by suggesting that this principle is the key to understanding why essentialist explanations can seem so satisfying. (shrink)

Metaphysical rationalism, the doctrine which affirms the Principle of Sufficient Reason (the PSR), is out of favor today. The best argument against it is that it appears to lead to necessitarianism, the claim that all truths are necessarily true. Whatever the intuitive appeal of the PSR, the intuitive appeal of the claim that things could have been otherwise is greater. This problem did not go unnoticed by the great metaphysical rationalists Spinoza and Leibniz. Spinoza’s response was to embrace necessitarianism. Leibniz’s (...) response was to argue that, despite appearances, rationalism does not lead to necessitarianism. This paper examines the debate between these two rationalists and concludes that Leibniz has persuasive grounds for his opinion. This has significant implications both for the plausibility of the PSR and for our understanding of modality. (shrink)

Los autores son miembros del grupo Ciencia, Razón y Fe (CRYF) de la Universidad de Navarra, y llevan trabajando en este grupo de forma interdisciplinar durante casi una década en temas de antropología y ética. Como dice Javier Bernácer en el prólogo de este libro, los profesores Montoya Camacho y Giménez Amaya han realizado una obra profunda, académica, y al mismo tiempo de fácil lectura. Los autores apoyándose en el filósofo anglosajón Alasdair MacIntyre señalan que «la fragilidad del ser humano (...) es un elemento vertebral de su actuar ético». Una vez que se descubre de modo natural el sentido de la vulnerabilidad, tanto propia como ajena, el ser humano desarrolla una serie de virtudes, que, por definición, llevan a la culminación de una vida realizada: la felicidad como eudemonía. No es el camino más fácil, pero sí el más directo a una existencia llena de sentido. [Portada e índice]. (shrink)

One of the most intriguing claims in Sven Rosenkranz’s Justification as Ignorance is that Timothy Williamson’s celebrated anti-luminosity argument can be resisted when it comes to the condition ~K~KP—the condition that one is in no position to know that one is in no position to know P. In this paper, I critically assess this claim.

In this paper I draw attention to a peculiar epistemic feature exhibited by certain deductively valid inferences. Certain deductively valid inferences are unable to enhance the reliability of one's belief that the conclusion is true—in a sense that will be fully explained. As I shall show, this feature is demonstrably present in certain philosophically significant inferences—such as GE Moore's notorious 'proof' of the existence of the external world. I suggest that this peculiar epistemic feature might be correlated with the much (...) discussed phenomenon that Crispin Wright and Martin Davies have called 'transmission failure'—the apparent failure, on the part of some deductively valid inferences to transmit one's justification for believing the premises. (shrink)

This article explores aspects of Rosenzweig’s Star of Redemption from the perspective of systems theory. Mosès, Pollock, and others have noted the systematic character of the Star. While “systematic” does not mean “systems theoretic,” the philosophical theology of the Star encompasses ideas that are salient in systems theory. The Magen David star to which the title refers, and which deeply structures Rosenzweig’s thought, fits the classic definition of “system” – a set of elements (God, World, Human) and relations between the (...) elements (Creation, Revelation, Redemption). The Yes and No of the elements and their reversals illustrate the bridging of element and relation with the third category of “attribute,” a notion also central to the definition of “system.” In the diachronics of “the All,” the relations actualize what is only potential in the elements in their primordial state and thus remedy the incompleteness of these elements, fusing them into an integrated whole. Incompleteness is a major theme of systems theory, which also explicitly examines the relations between wholes and parts and offers a formal framework for expressing such fusions. In this article, the systems character of Parts I & II of the Star is explored through extensive use of diagrams; a systems exploration of Part III is left for future work. Remarkably, given its highly architectonic character, diagrams are absent in Rosenzweig’s book, except for the triangle of elements, the triangle of relations, and the hexadic star, which are presented on the opening page of each part of the book. While structures can be explicated entirely in words, diagrams are a visual medium of communication that supplements words and supports a nonverbal understanding that structures both thought and experience. (shrink)

In this paper I respond to Marcello Di Bello’s criticisms of the ‘normic account’ of the criminal standard of proof. In so doing, I further elaborate on what the normic account predicts about certain significant legal categories of evidence, including DNA and fingerprint evidence and eyewitness identifications.

In Groenendijk & Stokhof [1989] a system of dynamic predicate logic (DPL) was developed, as a compositional alternative for classical discourse representation theory (DRT ). DPL shares with DRT the restriction of being a first-order system. In the present paper, we are mainly concerned with overcoming this limitation. We shall define a dynamic semantics for a typed language with λ-abstraction which is compatible with the semantics DPL specifies for the language of first-order predicate logic. We shall propose to use this (...) new logical system as the semantic component of a Montague-style grammar (referred to as dynamic Montague grammar, DMG), which will enable us to extend the compositionality of DPL to the subsentential level. Furthermore, we shall extend this analysis also in this sense that we shall add new, dynamic interpretations for logical constants which in DPL were treated in a static fashion. This will substantially increase the descriptive coverage of DMG. (shrink)

The Catastrophe Theory of Rene Thom and E. C. Zeeman suggests a mathematical interpretation of certain aspects of Hegelian and Marxist dialectics. Specifically, the three 'classical' dialectical principles, (1) the transformation of quantity into quality, (2) the unity and struggle of opposites, and (3) the negation of negation, can be modeled with the seven 'elementary catastrophes' given by Thorn, especially the catastrophes known as the 'cusp' and the 'butterfly'. Far from being empty metaphysics or scholasticism, as critics have argued, the (...) dialectical principles embody genuine insights into a class of phenomena, insights which can now be expressed within a precise mathematical formalism. This fact does not, however, support the claim that these principles, possibly modified or supplemented, constitute the laws of motion for human thought and for natural and social processes or even just the last of these. (shrink)

Our understanding of subjunctive conditionals has been greatly enhanced through the use of possible world semantics and, more precisely, by the idea that they involve variably strict quantification over possible worlds. I propose to extend this treatment to ceteris paribus conditionals – that is, conditionals that incorporate a ceteris paribus or ‘other things being equal’ clause. Although such conditionals are commonly invoked in scientific theorising, they traditionally arouse suspicion and apprehensiveness amongst philosophers. By treating ceteris paribus conditionals as a species (...) of variably strict conditional I hope to shed new light upon their content and their logic. (shrink)