Chaïm Perelman, alone, and in collaboration with Lucie Olbrechts-Tyteca, developed the New Rhetoric Project, which is in use throughout the world. This book offers the first deep contextualization of the project’s origins and original translations of their work from French into English.

The importance of Georg Cantor’s religious convictions is often neglected in discussions of his mathematics and metaphysics. Herein I argue, pace Jan ́e (1995), that due to the importance of Christianity to Cantor, he would have never thought of absolutely infinite collections/inconsistent multiplicities,as being merely potential, or as being purely mathematical entities. I begin by considering and rejecting two arguments due to Ignacio Jan ́e based on letters to Hilbert and the generating principles for ordinals, respectively, showing that my reading (...) of Cantor is consistent with that evidence. I then argue that evidence from Cantor’s later writings shows that he was still very religious later in his career, and thus would not have given up on the reality of the absolute, as that would imply an imperfection on the part of God. (shrink)

This article examines the business case for diversity, according to which diversity should be promoted because diverse groups outperform nondiverse groups. Philosophers who defend BCD usually...

In Winter 2017, the first author piloted a course in formal logic in which we aimed to (a) improve student engagement and mastery of the content, and (b) reduce maths anxiety and its negative effects on student outcomes, by adopting student oriented teaching including peer instruction and classroom flipping techniques. The course implemented a partially flipped approach, and incorporated group-work and peer learning elements, while retaining some of the traditional lecture format. By doing this, a wide variety of student learning (...) preferences could be provided for. (shrink)

G. Genzten’s 1938 proof of the consistency of pure arithmetic was hailed as a success for finitism and constructivism, but his proof requires induction along ordinal notations in Cantor normal form up to the first epsilon number, ε0. This left the task of giving a finitisically acceptable proof of the well-ordering of those ordinal notations, without which Gentzen’s proof could hardly be seen as a success for finitism. In his seminal book Proof Theory G. Takeuti provides such a proof. After (...) a brief philosophical introduction, we provide a reconstruction of Takeuti’s proof including corrections, comments, re-organization and notational adjustments for the sake of clarity. The result is a much longer, but much more tractable proof of the well-ordering of ordinal notations in Cantor normal form less than ε0, that nevertheless follows Takeuti’s strategy closely. We end with some more general comments about that proof strategy and the notion of accessibility more generally. (shrink)

The aim of this paper is to explain why, while Charles Darwin was well recognized as a scientific leader of his time, Claude Bernard never really regarded Darwinism as a scientific theory. The lukewarm reception of Darwin at the Académie des Sciences of Paris and his nomination to a chair only after 8 years contrasts with his prominence, and Bernard’s attitude towards Darwin’s theory of species evolution belongs to this French context. Yet we argue that Bernard rejects the scientific value (...) of Darwinian principles mainly for epistemological reasons. Like Darwin, Bernard was interested in hereditary processes, and planned to conduct experiments on these processes that could lead to species transformation. But the potential creation of new forms of life would not vindicate Darwinism since biologists can only explain the origin of morphotypes and morphological laws by the means of untestable analogies. Because it can be the object neither of experiments nor of any empirical observation, phylogeny remains out of science’s scope. Around 1878 Bernard foresaw a new general physiology based on the study of protoplasm, which he saw as the agent of all basic living phenomena. We will analyze why Bernard regarded Darwinism as part of metaphysics, yet still referred to Darwinians in his latter works in 1878. Basically, the absence of a scientific reception of Darwinism in Bernard's work should not obscure its philosophical reception, which highlights the main principles of Bernard’s epistemology. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 36.3 (2003) 177-188 [Access article in PDF] Chaïm Perelman's "First Philosophies and Regressive Philosophy":Commentary and Translation David A. Frank Michelle K. Bolduc Chaïm Perelman's 1949 article, "First Philosophies and Regressive Philosophy," has remained unavailable to readers unable to read French. Our commentary and translation is intended to provide English readers access to the context, influences, and themes that make the article an extraordinarily important work (...) in the history of twentieth-century rhetoric. In this article, Perelman offers a powerful critique of first philosophies and anticipates the problems of radical postmodernity. "First Philosophies" remains a strikingly elegant attempt to foil what Foucault (1984, 41-42) has called the "Enlightenment blackmail of reason," the assumption held by logical positivists and radical skeptics that if reason does not yield absolute and eternal Enlightenment knowledge, there can be no knowledge.Perelman and Lucie Olbrechts-Tyteca's New Rhetoric project avoids Enlightenment blackmail by charting a third way between logical positivism and radical relativism, and "First Philosophies" sets forth the project's philosophical blueprint. Commencing in 1947 and culminating in 1958 with the publication of Traité de l'argumentation: La nouvelle rhétorique, Perelman and Olbrechts-Tyteca sought, discovered, and developed a philosophical system designed as a rapprochement between dialectic (reason and logic) and rhetoric (the art of adapting arguments to audiences). Historians of rhetoric judge the work a "grand revolution" (Meyer 1999, 259), believing it marks a rhetorical renaissance in Europe, and suggest nothing like it will appear for another 100 years after its publication (Johnstone 1971). The New Rhetoric project influenced Gadamer and a host of post-war European and American thinkers (Mootz 1998). Michael Leff calls the 1970 English translation of Traité a "bombshell" (1994, 510). Beyond its historical importance, Crosswhite suggests that the New Rhetoric project is "the single most important event in contemporary rhetorical theory" (1996, 35)and "First Philosophies" marks Perelman's turn from logical [End Page 177] positivism to rhetoric, offering prescient answers to the post-World War II crises of reason, and the ideas in the article provide the Traité'sphilosophical glue (see in particular the English translation, 62).Perelman joined many post-war theorists, including Horkheimer and Adorno (1972), in the resistance to the reign of a disembodied Enlightenment rationality. However, Perelman identified what Habermas (1987, 119) would later call the "performative contradiction" in the conclusion that radical skepticism was the only alternative to Enlightenment rationality. In "First Philosophies," Perelman responds directly to Sartre's 1943 Being and Nothingness (198; see translation below) by exposing the failure of radical skeptics to see that they had been held hostage by Enlightenment blackmail in accepting the Enlightenment criterion for truth, rejecting it, and then making skepticism an absolute. Indeed, "First Philosophies" navigates from this performative contradiction to chart a third way between Enlightenment rationality and radical skepticism with an approach that he labels regressive philosophy. Regressive philosophy, Perelman argues, provides the human community with a mode of philosophical reasoning located between the extremes of Enlightenment rationality and radical skepticism. In this space between extremes, Perelman identifies contingent truths and values dependent on a rhetorical mode of reasoning, one making moral judgments possible.To best understand "First Philosophies," we recognize the importance of historical context in the development of social theories of knowledge (see Delacampagne 1999; Kennedy 1999). The intellectual networks in which philosophers operate also influence the development of philosophical systems, as Randall Collins has aptly documented. In addition to historical context and intellectual networks, Frederick Beiser has recently noted: "[t] he best introduction to any philosophy is the biography of the person who created it" (1999, 5). He argues that textual analysis alone cannot illuminate the motivation or meaning of a philosophy. A sense of Perelman's biography and the cultural influences that gave rise to "First Philosophies" are necessary for a proper understanding of its themes. For Perelman, the primary intellectual exigencies of the post-war period were the interrelated crises of justice, philosophical reasoning, and responsibility to which "First Philosophies" is a... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 36.3 (2003) 177-188 [Access article in PDF] Chaïm Perelman's "First Philosophies and Regressive Philosophy":Commentary and Translation David A. Frank Michelle K. Bolduc Chaïm Perelman's 1949 article, "First Philosophies and Regressive Philosophy," has remained unavailable to readers unable to read French. Our commentary and translation is intended to provide English readers access to the context, influences, and themes that make the article an extraordinarily important work (...) in the history of twentieth-century rhetoric. In this article, Perelman offers a powerful critique of first philosophies and anticipates the problems of radical postmodernity. "First Philosophies" remains a strikingly elegant attempt to foil what Foucault (1984, 41-42) has called the "Enlightenment blackmail of reason," the assumption held by logical positivists and radical skeptics that if reason does not yield absolute and eternal Enlightenment knowledge, there can be no knowledge.Perelman and Lucie Olbrechts-Tyteca's New Rhetoric project avoids Enlightenment blackmail by charting a third way between logical positivism and radical relativism, and "First Philosophies" sets forth the project's philosophical blueprint. Commencing in 1947 and culminating in 1958 with the publication of Traité de l'argumentation: La nouvelle rhétorique, Perelman and Olbrechts-Tyteca sought, discovered, and developed a philosophical system designed as a rapprochement between dialectic (reason and logic) and rhetoric (the art of adapting arguments to audiences). Historians of rhetoric judge the work a "grand revolution" (Meyer 1999, 259), believing it marks a rhetorical renaissance in Europe, and suggest nothing like it will appear for another 100 years after its publication (Johnstone 1971). The New Rhetoric project influenced Gadamer and a host of post-war European and American thinkers (Mootz 1998). Michael Leff calls the 1970 English translation of Traité a "bombshell" (1994, 510). Beyond its historical importance, Crosswhite suggests that the New Rhetoric project is "the single most important event in contemporary rhetorical theory" (1996, 35)and "First Philosophies" marks Perelman's turn from logical [End Page 177] positivism to rhetoric, offering prescient answers to the post-World War II crises of reason, and the ideas in the article provide the Traité'sphilosophical glue (see in particular the English translation, 62).Perelman joined many post-war theorists, including Horkheimer and Adorno (1972), in the resistance to the reign of a disembodied Enlightenment rationality. However, Perelman identified what Habermas (1987, 119) would later call the "performative contradiction" in the conclusion that radical skepticism was the only alternative to Enlightenment rationality. In "First Philosophies," Perelman responds directly to Sartre's 1943 Being and Nothingness (198; see translation below) by exposing the failure of radical skeptics to see that they had been held hostage by Enlightenment blackmail in accepting the Enlightenment criterion for truth, rejecting it, and then making skepticism an absolute. Indeed, "First Philosophies" navigates from this performative contradiction to chart a third way between Enlightenment rationality and radical skepticism with an approach that he labels regressive philosophy. Regressive philosophy, Perelman argues, provides the human community with a mode of philosophical reasoning located between the extremes of Enlightenment rationality and radical skepticism. In this space between extremes, Perelman identifies contingent truths and values dependent on a rhetorical mode of reasoning, one making moral judgments possible.To best understand "First Philosophies," we recognize the importance of historical context in the development of social theories of knowledge (see Delacampagne 1999; Kennedy 1999). The intellectual networks in which philosophers operate also influence the development of philosophical systems, as Randall Collins has aptly documented. In addition to historical context and intellectual networks, Frederick Beiser has recently noted: "[t] he best introduction to any philosophy is the biography of the person who created it" (1999, 5). He argues that textual analysis alone cannot illuminate the motivation or meaning of a philosophy. A sense of Perelman's biography and the cultural influences that gave rise to "First Philosophies" are necessary for a proper understanding of its themes. For Perelman, the primary intellectual exigencies of the post-war period were the interrelated crises of justice, philosophical reasoning, and responsibility to which "First Philosophies" is a... (shrink)

In a recent paper, Potochnik (Biol Philos 24(2):183–197, 2009) analyses some uses of optimality modelling in light of the anti-adaptationism criticism. She distinguishes two broad classes of such uses (weak and strong) on the basis of assumptions held by biologists about the role and the importance of natural selection. This is an interesting proposal that could help in the epistemological characterisation of some biological practices. However, Potochnik’s distinction also rests on the assumption that all optimality modelling represent the selection dynamic (...) involved in the system of phenomena being considered. Since this assumption does not hold for models belonging to optimal foraging theory (OFT)—one of behavioural ecology’s important modelling traditions—Potochnik’s proposal has to be critically reappraised. In this paper, we briefly discuss what is optimality modelling and what it means for a model to represent a dynamic of selection or of evolution. Then, we demonstrate that OFT modelling is unable to represent either past or contemporary selection dynamics. In order to make this point, we carefully delineate the theory’s rationale. This allows us to identify and analyse the assumptions on which the theory is built, and to circumscribe precisely the role that natural selection plays in it. Next, we show that the distinction of weak and strong uses of optimality modelling is seriously weakened when OFT modelling is taken into account. More precisely, the distinction is either irrelevant (if the assumption that selection dynamics are represented in all optimality modelling is held) or of a modest utility (if the assumption is dropped). However, we suggest that Potochnik’s original proposal could be saved, and that it even constitutes a tool to appraise the marks left in the literature by the evolution of optimality modelling practices in the last four decades, provided that it is made into a tripartite distinction. (shrink)

Since Krebs and Davies’s (1978) landmark publication, it is acknowledged that behavioural ecology owes much to the ethological tradition in the study of animal behaviour. Although this assumption seems to be right—many of the first behavioural ecologists were trained in departments where ethology developed and matured—it still to be properly assessed. In this paper, I undertake to identify the approaches used by ethologists that contributed to behavioural ecology’s constitution as a field of inquiry. It is my contention that the current (...) practices in behavioural biology owe ethology something much subtler than the simple transposition of Tinbergen’s Four Problems for heuristic purposes. Demonstrating what ethology inherited from the long naturalist tradition shows the tensions that strained the field and that later led to the loss of both its unity and its specificity. It also allows for a precise delineating of what behavioural ecology picked up from the ethological practice, and it helps to cast some light on the introduction of economical thinking in behavioural sciences. (shrink)

"The last third of the twentieth century," Gerard Hauser writes, was marked by "a flurry of intellectual work aimed at theorizing rhetoric in new terms" (2001, 1). The year 1958 was key in this flurry, with five major works appearing on a rhetorically inflected philosophy and theory of argumentation: Hannah Arendt's The Human Condition (on the relationship between the vita contemplativa and vita activa); Michael Polanyi's Personal Knowledge (on the role of tacit knowledge, emotion, and commitment in science); Stephen Toulmin's (...) Uses of Argument (on the use of argument in nonformal contexts); Walter Ong's Ramus, Method, and the Decay of Dialogue: From the Art of Discourse to the Art of Reason (on the history of the .. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 36.3 (2003) 177-188 [Access article in PDF] Chaïm Perelman's "First Philosophies and Regressive Philosophy":Commentary and Translation David A. Frank Michelle K. Bolduc Chaïm Perelman's 1949 article, "First Philosophies and Regressive Philosophy," has remained unavailable to readers unable to read French. Our commentary and translation is intended to provide English readers access to the context, influences, and themes that make the article an extraordinarily important work (...) in the history of twentieth-century rhetoric. In this article, Perelman offers a powerful critique of first philosophies and anticipates the problems of radical postmodernity. "First Philosophies" remains a strikingly elegant attempt to foil what Foucault (1984, 41-42) has called the "Enlightenment blackmail of reason," the assumption held by logical positivists and radical skeptics that if reason does not yield absolute and eternal Enlightenment knowledge, there can be no knowledge.Perelman and Lucie Olbrechts-Tyteca's New Rhetoric project avoids Enlightenment blackmail by charting a third way between logical positivism and radical relativism, and "First Philosophies" sets forth the project's philosophical blueprint. Commencing in 1947 and culminating in 1958 with the publication of Traité de l'argumentation: La nouvelle rhétorique, Perelman and Olbrechts-Tyteca sought, discovered, and developed a philosophical system designed as a rapprochement between dialectic (reason and logic) and rhetoric (the art of adapting arguments to audiences). Historians of rhetoric judge the work a "grand revolution" (Meyer 1999, 259), believing it marks a rhetorical renaissance in Europe, and suggest nothing like it will appear for another 100 years after its publication (Johnstone 1971). The New Rhetoric project influenced Gadamer and a host of post-war European and American thinkers (Mootz 1998). Michael Leff calls the 1970 English translation of Traité a "bombshell" (1994, 510). Beyond its historical importance, Crosswhite suggests that the New Rhetoric project is "the single most important event in contemporary rhetorical theory" (1996, 35)and "First Philosophies" marks Perelman's turn from logical [End Page 177] positivism to rhetoric, offering prescient answers to the post-World War II crises of reason, and the ideas in the article provide the Traité'sphilosophical glue (see in particular the English translation, 62).Perelman joined many post-war theorists, including Horkheimer and Adorno (1972), in the resistance to the reign of a disembodied Enlightenment rationality. However, Perelman identified what Habermas (1987, 119) would later call the "performative contradiction" in the conclusion that radical skepticism was the only alternative to Enlightenment rationality. In "First Philosophies," Perelman responds directly to Sartre's 1943 Being and Nothingness (198; see translation below) by exposing the failure of radical skeptics to see that they had been held hostage by Enlightenment blackmail in accepting the Enlightenment criterion for truth, rejecting it, and then making skepticism an absolute. Indeed, "First Philosophies" navigates from this performative contradiction to chart a third way between Enlightenment rationality and radical skepticism with an approach that he labels regressive philosophy. Regressive philosophy, Perelman argues, provides the human community with a mode of philosophical reasoning located between the extremes of Enlightenment rationality and radical skepticism. In this space between extremes, Perelman identifies contingent truths and values dependent on a rhetorical mode of reasoning, one making moral judgments possible.To best understand "First Philosophies," we recognize the importance of historical context in the development of social theories of knowledge (see Delacampagne 1999; Kennedy 1999). The intellectual networks in which philosophers operate also influence the development of philosophical systems, as Randall Collins has aptly documented. In addition to historical context and intellectual networks, Frederick Beiser has recently noted: "[t] he best introduction to any philosophy is the biography of the person who created it" (1999, 5). He argues that textual analysis alone cannot illuminate the motivation or meaning of a philosophy. A sense of Perelman's biography and the cultural influences that gave rise to "First Philosophies" are necessary for a proper understanding of its themes. For Perelman, the primary intellectual exigencies of the post-war period were the interrelated crises of justice, philosophical reasoning, and responsibility to which "First Philosophies" is a... (shrink)

ABSTRACT This study explores the influence of the French Symbolist poet, novelist, and literary critic Remy de Gourmont on Chaïm Perelman and Lucie Olbrechts-Tyteca's conception of dissociation. It proposes translatio—the medieval trope describing a transfer of ideas—as a lens through which to read the significance of Gourmont's thought on the New Rhetoric Project. Thus forgoing more traditional comparative approaches such as intertextuality, this study argues that translatio serves here as a particularly valuable conceptual tool: it unveils the evolution of Perelman's (...) thought over time, and Olbrechts-Tyteca's significant contribution to it; it also provides a clearer understanding of the relationship between association and dissociation in the NRP than what is generally understood by scholars of the Traité. More importantly, translatio unveils the features that make their conception of dissociation one of the truly innovative aspects of the NRP. (shrink)

Face aux tentatives des logiciens de démontrer la validité ou l'invalidité du Maître-argument de Diodore Kronos en s'empressant de déclarer un gagnant à l'argumentaire opposant le philosophe de Mégare à Aristote, nous esquissons par ce présent article une analyse globale du dogme diodoréen qui considère l'ensemble des témoignages antiques répertoriés sur sa pensée, permettant de dresser un portait cohérent d'une pensée positive qui le plus souvent n'est considérée que de façon éristique. Cette approche permet de mettre en lumière les assises (...) dogmatiques du Maître-argument, notamment en relation avec les arguments sur les corps sans parties ; si le monde physique est composé d'ultimes corps indivisibles et sans parties, ces unités ne peuvent être dans le même lieu et dans un autre lieu au même instant, alors « rien ne se meut » . Si Diodore reprend la thèse éléatique de l'impossibilité d'appréhender logiquement le mouvement, il renouvèle toutefois la tradition mégarique en affirmant l'existence du mouvement achevé, car l'on constate bien qu'un corps est passé d'un lieu à l'autre, et donc qu'il s'est mû! Or nous démontrons que l'affirmation singulière d'un mouvement exclusivement conjugué au passé, et donc jamais soumis au devenir, a vraisemblablement des origines aristotéliciennes. En effet, Diodore semble soumettre certains développements de La Physique à une analyse strictement logique en fondant sa conception du temps dans son unité , là où Aristote privilégiait l'analyse empirique dans une conception continue du temps et du mouvement. C'est donc à partir de cette divergence fondamentale d'approche épistémologique qu'il faut comprendre le débat sur le possible. En définissant le mouvement comme « l'acte de l'étant en puissance » , Aristote pense le possible à partir des possibilités ontiques de la substance , tandis que Diodore, en identifiant le possible à l'acte, évite le danger de spéculer sur des possibles qui ne se réalisent pas et ainsi de confondre être et non-être; or en distinguant le possible et le nécessaire, il dément la tradition qui lui attribuait un simple nécessitarisme et renouvèle véritablement l'ontologie éléate. À partir de développements préliminaires de Robert Muller, ce présent article démontre ainsi la pertinence d'interpréter la pensée diodoréenne comme une ontologie du dévoilement rendue possible par une critique et une appropriation mégarique de la pensée aristotélicienne. (shrink)

Le problème de l'être-avec et de la socialité chez Heidegger a déjà une longue tradition de commentateurs. Ceux-ci se distinguent par la pluralité de leurs approches: se situant parfois à l'opposé de la méthode d'Être et temps, ils se portent alors à la défense d'autrui, insistent sur l'aspect dialogique et sur l'importance de la rationalité du discours dans le monde de la vie. D'autres encore, sans nécessairement remettre en question la méthodologie heideggérienne, défendent ou réinterprètent autrement sa phénoménologie de l'existence (...) d'autrui: parmi eux, certains s'en tiennent uniquement à l'analytique existentiale, tandis que d'autres élargissent l'horizon de leurs critiques en tenant compte du projet global de la pensée de Heidegger. Il y a enfin les commentateurs pour lesquels cette question n'est abordée que dans le contexte politique de sa pensée. (shrink)

Le but de cet ouvrage est de démontrer, à travers une reconstruction rationnelle des étapes historiques fondatrices de l'embryologie expérimentale, l'importance des concepts de préformation et d'épigenèse aux origines de cette discipline. L'analyse porte sur trois périodes charnières de l'histoire de l'embryologie : (1) la réforme mécaniste et darwinienne de l'embryologie descriptive par Ernst Haeckel (1866); (2) l'avènement d'une physiologie réductionniste du développement menée par Wilhelm His (1874); (3) la création d'une "mécanique du développement" par Wilhelm Roux (1885) et les (...) interprétations néo-darwinienne (A. Weismann), néo-vitaliste (H. Driesch) et organiciste (O. Hertwig) de ses résultats les plus significatifs (1888-1908). J'y défends qu'une logique de la découverte structurait ces développements, où les modèles mécaniques d'explication devaient constamment être renouvelés lorsque leur examen empirique engendrait la découverte de phénomènes épigénétiques inédits. L'étude réalisée traite d'un enjeu fondamental de la philosophie des sciences : le rapport entre la rationalité scientifique et la découverte. Elle offre aussi un éclairage sur une question très actuelle de la philosophie de la biologie, soit les transformations de la notion d'épigenèse en rapport avec les théories épigénétiques contemporaines. La méthodologie adoptée s'inscrit dans la tradition de l'épistémologie historique, consacrée à l'étude du développement des structures du savoir scientifique. Cette tâche exige l'analyse historique de diverses sources documentaires; mais un éclairage théorique constitué tant de modèles provenant de la philosophie des sciences que de connaissances scientifiques demeure indispensable. Ici le modèle d'Imre Lakatos, centré sur la notion de programme de recherche, est entre autres privilégié."--provided by publisher. (shrink)

This paper examines two conflicts that emerge in the engagement between monotheism, especially as it is expressed in its fundamentalist form in both Christianity and Islam, and the separation of church and state. The first conflict involves intellectual compartmentalizing. The second conflict concerns the possibility that the contract may require that all "absolute truths" be assigned metaphorical status.

(2005). The Bachelardian Tradition in the Philosophy of Science. Angelaki: Vol. 10, continental philosophy and the sciences the french tradition issue editor: andrew aitken, pp. 79-87.

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

If it could be shown that one of Gentzen's consistency proofs for pure number theory could be shown to be finitistically acceptable, an important part of Hilbert's program would be vindicated. This paper focuses on whether the transfinite induction on ordinal notations needed for Gentzen's second proof can be finitistically justified. In particular, the focus is on Takeuti's purportedly finitistically acceptable proof of the well-ordering of ordinal notations in Cantor normal form. The paper begins with a historically informed discussion of (...) finitism and its limits, before introducing Gentzen and Takeuti's respective proofs. The rest of the paper is dedicated to investigating the finitistic acceptability of Takeuti's proof, including a small but important fix to that proof. That discussion strongly suggests that there is a philosophically interesting finitist standpoint that Takeuti's proof, and therefore Gentzen's proof, conforms to. (shrink)

If one of Gentzen’s consistency proofs for pure number theory could be shown to be finitistically acceptable, an important part of Hilbert’s program would be vindicated. This paper focuses on whether the transfinite induction on ordinal notations needed for Gentzen’s second proof can be finitistically justified. In particular, the focus is on Takeuti’s purportedly finitistically acceptable proof of the well ordering of ordinal notations in Cantor normal form.The paper begins with a historically informed discussion of finitism and its limits, before (...) introducing Gentzen and Takeuti’s respective proofs. The rest of the paper is dedicated to investigating the finitistic acceptability of Takeuti’s proof, including a small but important fix to that proof. That discussion strongly suggests that there is a philosophically interesting finitist standpoint that Takeuti’s proof, and therefore Gentzen’s proof, conforms to. (shrink)

If one of Gentzen’s consistency proofs for pure number theory could be shown to be finitistically acceptable, an important part of Hilbert’s program would be vindicated. This paper focuses on whether the transfinite induction on ordinal notations needed for Gentzen’s second proof can be finitistically justified. In particular, the focus is on Takeuti’s purportedly finitistically acceptable proof of the well ordering of ordinal notations in Cantor normal form.The paper begins with a historically informed discussion of finitism and its limits, before (...) introducing Gentzen and Takeuti’s respective proofs. The rest of the paper is dedicated to investigating the finitistic acceptability of Takeuti’s proof, including a small but important fix to that proof. That discussion strongly suggests that there is a philosophically interesting finitist standpoint that Takeuti’s proof, and therefore Gentzen’s proof, conforms to. (shrink)

forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), symbolizing English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as modal logic, soundness, and functional completeness. Exercises with solutions are available. (...) It is provided in PDF (for screen reading, printing, and a special version for dyslexics), HTML, and in LaTeX source code. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 36.3 (2003) 189-206 [Access article in PDF] First Philosophies and Regressive Philosophy Chaïm Perelman "As a crystal reconstitutes itself from one of its particles, all philosophy creates itself from the idea of an open dialectic, and carries, in itself, the same dialectical character." —Ferdinand Gonseth A number of metaphysicians, including Bergson and Heidegger, consider metaphysics the only knowledge of consequence and use the word to refer (...) to their own philosophies. But a large number of eminent metaphysicians, among them Descartes, Spinoza, Kant, Fichte and Hegel had only disdain for metaphysics and used the word to discredit the philosophy of their adversaries. D'Alembert (602-604) once noted that those referred to as metaphysicians had little regard for one another. "I have no doubt," he added, "that this title will soon be an insult to our great minds, just as the name sophist which, although it meant wise, was debased in Greece by those who bore it and rejected by the true philosophers."The preceding remarks should, I think, convince the few who would still doubt it that declaring oneself an adversary of metaphysics does not mean that one does not do metaphysics. On the contrary, the very fact of opposing a certain conception of metaphysics presupposes that one advocates another conception of metaphysics; this needs to be made explicit, if it is only implicit. In a very interesting study, Mr. Everett W. Hall has recently analyzed the metaphysical assumptions of four types of positivism (Mach, Comte, Watson, Carnap). Even without this analysis the conclusion is predictable; he who is opposed to a certain manner of treating a problem remains himself within the same problematic. Indeed, such oppositions produce a continuous expansion and dialogue about the meaning of the word "metaphysics." This happens not through an automatic and necessary dialectic, but through the dialectic directed by the philosopher's concerns.The first metaphysicians set forth a particular philosophy of being [être]; those opposed advocated a different philosophy of being. By expanding its meaning, Aristotle gave metaphysics its first dialectical movement and identified it as the study of being as being and ontology. Kantian criticism treats dogmatic metaphysics with disdain, and shows that all theories [End Page 189] of being must be preceded by a theory of knowledge: the first principles of philosophy would be those of epistemology and not those of ontology. Since Kant, and for more than a century, metaphysical debates would be about the primacy of ontology or epistemology, and the opposition to their variants, realism and idealism. Then, at the end of the nineteenth century, the debate broadened. Under the influence of pragmatism, the philosophy of values, and Bergsonism, a strong current of philosophical thinking developed, which integrated the theory of knowledge into a general theory of action. It proclaimed the primacy of a philosophy of action, philosophy of life, and philosophy of values. It is within a metaphysics broadened by these various developments that different conceptions of metaphysics will struggle to establish the primacy of their principles. But, despite their differences, all of these metaphysics can be considered first philosophies.Aristotle wrote a treatise on first philosophy, the first to be called metaphysics. First philosophies refer to any metaphysics that purports to determine first principles such as the fundamentals of being (ontology), of knowledge (epistemology), or of action (axiology). First philosophies position first principles as absolute and that they underlie all philosophical questions. The word "first" informs the argumentation used to establish the primacy of first philosophies. A principle is first when it comes before all others in a temporal, logical, epistemological or ontological order; the insistence on this point serves to emphasize its primacy or axiologic pre-eminence. That which is first or basic, that which precedes or presupposes all the rest, is also first in order of importance.As systematic metaphysics, first philosophies establish an interdependence among ontology, epistemology, and axiology. The course taken by first philosophies is determined by a starting point constituted by a necessary reality, a self-evident concept, or an absolute value before which one can... (shrink)

This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. A series of chapters all set in the eighteenth century consider topics such as John Marsh’s techniques (...) for the computation of decimal fractions, Euler’s efforts to compute the surface area of scalene cones, a little-known work by John Playfair on the practical aspects of mathematics, and Monge’s use of descriptive geometry. After a brief stop in the nineteenth century to consider the culture of research mathematics in 1860s Prussia, the book moves into the twentieth century with an examination of the historical context within which the Axiom of Choice was developed and a paper discussing Anatoly Vlasov’s adaptation of the Boltzmann equation to ionized gases. The remaining chapters deal with the philosophy of twentieth-century mathematics through topics such as an historically informed discussion of finitism and its limits; a reexamination of Mary Leng’s defenses of mathematical fictionalism through an alternative, anti-realist approach to mathematics; and a look at the reasons that mathematicians select specific problems to pursue. Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics. (shrink)

forall x: Dortmund is an adaptation and German translation of forall x: Calgary. As such, it is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity, the syntax of truth-functional (propositional) logic and truth-table semantics, the syntax of first-order (predicate) logic with identity and first-order interpretations, formalizing German in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as the (...) syntax and (Kripke-)semantics of modal logic. The book is provided in PDF and in LaTeX source code. A booklet with solutions for the exercises in the book is available. (shrink)

Livro-texto de introdução à lógica, com (mais do que) pitadas de filosofia da lógica, produzido como uma versão revista e ampliada do livro Forallx: Calgary. Trata-se da versão de 13 de outubro de 2022. Comentários, críticas, correções e sugestões são muito bem-vindos.

This booklet is a Korean adaptation and translation of Part VIII of forall x: Calgary (Fall 2021 edition), which is intended to be introductory material for modal logic. The original text is based on Robert Trueman's A Modal Logic Primer, which is revised and expanded by Richard Zach and Aaron Thomas-Bolduc in forall x: Calgary. (forall x: Calgary is based on forall x: Cambridge by Tim Button, which is in turn based on forall x by P. D. Magnus, and (...) also includes material from forall x: Lorain County Remix by Cathal Woods and J. Robert Loftis.) This booklet is licensed under a Creative Commons Attribution 4.0 license. (shrink)