I claim that, in the Topics, Aristotle advises dialectical questioners to intentionally argue fallaciously in order to escape from some dialectically awkward positions, and I work through the consequences of that claim. It will turn out that, although there are important exceptions, the techniques for finding arguments described in Topics I–VII are, by and large, locations that Aristotle thought of as appropriate for use in philosophical inquiry. The text that grounds this claim, however, raises a further problem: it highlights the (...) solitary nature of philosophical inquiry, which puts into question the philosophical relevance of Topics VIII. I find that the Topics provides inadequate grounds for thinking that Aristotle saw Topics VIII as describing standards or techniques of argument that were appropriate for philosophy, and so these texts cannot be used by contemporary commentators to shed light on Aristotle's philosophical practice. Finally, although Aristotle saw philosophy as a solitary activity, he th.. (shrink)

This paper examines the nature of ‘reasonable’ argumentation in Generation of Animals III.10. Its aim is to develop an alternative to the dialectical construal of reasonable argumentation in Aristotle recently favoured by Robert Bolton. On the basis of a close textual analysis I show that the reasonable arguments deployed in Generation of Animals III.10 do not appeal to endoxa or reputable beliefs per se. Instead, they rely upon general facts about animals established by empirical induction. This implies that, contra Bolton, (...) not all reasonable arguments in Aristotle are dialectical; some, in fact, are thoroughly empirical and scientific. I conclude by suggesting that such empirical reasonable arguments even have a place in the De Caelo, the treatise that Bolton primarily focused upon when developing his interpretation. (shrink)

This paper attempts to clarify the nature and the importance of a third kind of sophistic argument that is not always found in the classification of those arguments in the secondary literature. An argument of the third kind not only is a valid one, but is also constituted of true propositions. What makes it a sophistic argument is the fact that it produces a false semblance of scientific explanation: its explanation seems to be appropriate to the explanandum without being so. (...) Evidence from this kind of argument comes from Sophistic Refutations 11, and Brison’s attempt to square the circle should be counted as one of its instances. (shrink)

Examino Acerca del cielo (De caelo) I 2 con el fin de mostrar allí la presencia de la demostración científica. Este desarrollo pretende aportar nueva evidencia en favor de la no discrepancia entre teoría y praxis científica en Aristóteles (Barnes, 1969) y de relativizar la interpretación de que el método real y únicamente usado es la dialéctica (cuyo antecedente se remonta a Owen, 1980). Además, siguiendo la propuesta hermenéutica de Gotthelf (1987) y Detel (1993 y 1997), mostraré de qué modo (...) se utiliza la demostración científica en la prueba de la existencia del cuerpo simple o éter. Ofreceré también una reconstrucción de las pruebas mediante la elaboración de un esquema que abarque el conjunto de las deducciones. Estos últimos desarrollos constituyen el aporte más novedoso del presente artículo. I examine On the Heavens (DC) 12 in order to show there the presence of scientific demonstration. This development tries to contribute new evidence in favor of the not discrepancy between theory and scientific practice in Aristotle (Barnes, 1969) and to make the interpretation that method real and solely used is dialectic relative (whose precedent goes back to Owen, 1980). In addition, following the hermeneutic proposal of Gotthelf (1987) and Detel (1993 and 1997), I will show how scientific demonstration is used in the proof of simple body (ether) existence. I will offer also a reconstruction of the proof by means of the elaboration of a scheme that includes the set of deductions. The latter developments constitute the most new contribution of the present paper. (shrink)

We argue that common knowledge, of the kind used in reasoning in law and computing is best analyzed using a dialogue model of argumentation (Walton & Krabbe 1995). In this model, implicit premises resting on common knowledge are analyzed as endoxa or widely accepted opinions and generalizations (Tardini 2005). We argue that, in this sense, common knowledge is not really knowledge of the kind represent by belief and/or knowledge of the epistemic kind studied in current epistemology. This paper takes a (...) different approach, defining it in relation to a common commitment store of two participants in a rule-governed dialogue in which two parties engage in rational argumentation (Jackson & Jacobs 1980; van Eemeren & Grootendorst 2004). A theme of the paper is how arguments containing common knowledge premises can be studied with the help of argumentation schemes for arguments from generally accepted opinion and expert opinion. It is argued that common knowledge is a species of provi- sional acceptance of a premise that is not in dispute at a given point in a dia- logue, but may later be defeated as the discussion proceeds . (shrink)

Aristotle's conception and use of ta endoxa are key points to our understanding of Aristotelian dialectic. But, nowadays, they are not of historical or hermeneutic importance alone, as, in Aristotle's treatment of endoxa, we still see a relevant contribution to the modern study of argumentation. I propose here an interpretation of endoxa to that effect: namely, as plausible propositions. This version is not only defensible in the Aristotelian context, it may also shed new light on some of his assumptions and (...) methodological shortcomings – e.g. concerning the 'plausible/implausible' pair –; finally, it will even enable us to show certain basic hints and guidelines, advanced by Aristotle's study of endoxa, which still serve nowadays to orientate our studies of argumentation from the angle of a theory of plausible argument currently under construction. These hints and guidelines suggest a pragmatic, gradual and comparative discursive concept of plausibility, and point, in particular, towards the reasonable dealing with, and weighing up of, differences of opinion within this frame of reference. (shrink)

The purpose of this paper is an attempt to delimitate what the dialectical syllogism looks like in Aristotle’s Topics. Aristotle never gave an example of a dialectical syllogism, but we have some clues spread over books I and VIII of the Topics which make it possible to understand at least what within a dialectical debate is a dialectical syllogism. The interpretation advanced here distinguishes the logical order of the dialectical argumentation from the order of the debate. This distinction enables us (...) to have a better understand of what is and how the dialectical syllogism is identified in the debate. In addition, we can solve some interpretative difficulties other interpretations could not solve, and have a more solid grasp of how endoxa are used in a dialectical debate. (shrink)

According to the standard and largely traditional interpretation, Aristotle’s conception of nous, at least as it occurs in the Posterior Analytics, is geared against a certain set of skeptical worries about the possibility of scientific knowledge, and ultimately of the knowledge of Aristotelian first principles. On this view, Aristotle introduces nous as an intuitive faculty that grasps the first principles once and for all as true in such a way that it does not leave any room for the skeptic to (...) press his skeptical point any further. Thus the tradi- tional interpretation views Aristotelian nous as having an internalist justificatory role in Aristotelian epistemology. In contrast, a minority (empiricist) view that has emerged recently holds the same internalist justificatory view of nous but rejects its internally certifiable infallibility by stressing the connection between nous and Aristotelian induction. I argue that both approaches are flawed in that Aristotle’s project in the Posterior Analytics is not to answer the skeptic on internalist justificatory grounds, but rather lay out a largely externalist explication of scientific knowledge, i.e. what scientific knowledge consists in, without worrying as to whether we can ever show the skeptic to his satisfaction that we do ever possess knowledge so defined. (shrink)

A methodological statement that occurs at Nicomachean Ethics vii 1 and its implementation in the subsequent discussion has widely been called ‘the method of endoxa’. According to the received interpretation, this method follows some strict steps and epitomizes the dialectical method of inquiry. I question the received interpretation and argue for a deflationary and non-dialectical account which, I believe, conforms with Aristotle’s scientifically oriented general methodology.

Este livro marca o início da Série Investigação Filosófica. Uma série de livros de traduções de textos de plataformas internacionalmente reconhecidas, que possa servir tanto como material didático para os professores das diferentes subáreas e níveis da Filosofia quanto como material de estudo para o desenvolvimento pesquisas relevantes na área. Nós, professores, sabemos o quão difícil é encontrar bons materiais em português para indicarmos. E há uma certa deficiência na graduação brasileira de filosofia, principalmente em localizações menos favorecidas, com relação (...) ao conhecimento de outras línguas, como o inglês e o francês. Tentamos, então, suprir essa deficiência, ao introduzirmos traduções de textos importantes ao público de língua portuguesa, sem nenhuma finalidade comercial e meramente pela glória da filosofia. O presente volume é constituído de três traduções de verbetes importantes sobre lógica, da Enciclopédia de Filosofia da Stanford: (1) A Lógica de Aristóteles, (2) Lógica Clássica, (3) Lógica Modal. (shrink)

In the eighth chapter of De Sophisticis Elenchis, Aristotle introduces a mode of sophistical refutation that constitutes an addition to the taxonomy of the earlier chapters of the treatise. The new mode is pseudo-scientific refutation, or “the [syllogism or refutation] which though real, [merely] appears appropriate to the subject matter”. Against the grain of its most commonly accepted reading, I argue that Aristotle is not concerned in SE 8 to establish that both the apparent refutations of SE 4–7 and pseudo-scientific (...) refutations issue in false conclusions. His concern rather is to provide a causal analysis of both classes of apparent refutation alike which will explain why both kinds of apparent refutation are sophistical – and whose solutions are therefore the task of no special science but of a dialectical σλλογιστιϰή τέχνη. I conclude my analysis with the observation that Aristotle exploits the results of SE 8 to fend off inSE 9, 10, and 11 respectively a triad of threats to the very existence of a τέχνη of the resolution of sophistical refutation. The three threats are: the impossibility of omniscience; the relativity of semantic beliefs; and the incapacity of a questioner ignorant of a science to expose the ignorance of a pretender to scientific expertise. (shrink)

La exposición y crítica de las doctrinas antiguas tiene un lugar importante en los escritos de Aristóteles. Sin embargo, ciertas dudas se han vuelto corrientes acerca de la confiabilidad de sus descripciones. Más aún, se ha sostenido que Aristóteles deforma la comprensión histórica a través de la introducción de conceptos y términos propios. En este libro se aborda el problema a través de un análisis de las críticas que Aristóteles dirige a la teoría platónica de las Ideas, que permite explicar (...) la constitución y desarrollo de importantes conceptos aristotélicos a partir de la confrontación dialéctica con las doctrinas de su maestro. En efecto, las dificultades genuinas que Aristóteles descubre en el platonismo constituyen el motor para gestar nuevos conceptos, que no son ajenos, sino que surgen como implicaciones del examen crítico. Así, la imposición de términos propios no debe interpretarse como distorsión, sino como el modo que Aristóteles adopta para exhibir su particular solución a los problemas que los filósofos anteriores dejaron sin solución. (shrink)

In this paper, I analyse EE I 6, where Aristotle presented a famous methodological digression. Many interpreters have taken this chapter as advocating a dialectical procedure of enquiry. My claim is that Aristotle does not keep a dialectical attitude towards endoxa or phainomena in this chapter. In order to accomplish my goal, I shall show that EE I 6 does not provide enough evidence for the dialectical construal of it, and that this construal, in turn, hangs on some assumptions brought (...) out from other Aristotelian works (EN and Top.), which do not provide good evidence as well. By the analysis of these assumptions, I intend to show that Aristotle is not carrying out any sort of dialectic, especially dialectic conceived as conceptual analysis seeking the salvage of phainomena or endoxa. (shrink)

What role, if any, does dialectic play in Aristotle’s epistemology in the Topics? In this paper I argue that it does play a role, but a role that is independent of endoxa. In the first section, I sketch the case for thinking that dialectic plays a distinctively epistemological role—not just a methodological role, or a merely instrumental role in getting episteme. In the second section, I consider three ways it could play that role, on two of which endoxa play at (...) least a co-starring role. But in the third section, I argue that endoxa don’t play that co-starring role, by arguing for a deflationary account of what endoxa are. For that reason, the third view emerges as the most plausible; but the third view is, I’ll suggest, Platonic. (shrink)

In Sophistical Refutations 8 Aristotle claims that every sophistical refutation depends on a false belief which is implicitly held by the victim of the fallacy and can normally be elicited from him as an explicit additional premiss. In this case the fallacious argument will be turned into a valid one, albeit with a false premiss. The paper discusses the nature of the FVP and tries to discover how it works when it tacitly causes the false appearance of a fallacious argument.

The Middle Included is a systematic exploration of the meanings of logos throughout Aristotle’s work. It claims that the basic meaning is “gathering,” a relation that holds its terms together without isolating them or collapsing one to the other. This meaning also applies to logos in the sense of human language. Aristotle describes how some animals are capable of understanding non-firsthand experience without being able to relay it, while others relay it without understanding. Aygün argues that what distinguishes human language, (...) for Aristotle, is its ability to both understand and relay firsthand and non-firsthand experiences. This ability is key to understanding the human condition: science, history, news media, propaganda, gossip, utopian fiction, and sophistry, as well as philosophy. Ömer Aygün finds Aristotle’s name for this peculiar but crucial human ability of “gathering” both experiences is logos, and this leads to a claim about the specificity of human rationality and language. (shrink)

Books M and N of Aristotle's Metaphysics receive relatively little careful attention. Even scholars who give detailed analyses of the arguments in M-N dismiss many of them as hopelessly flawed and biased, and find Aristotle's critique to be riddled with mistakes and question-begging. This assessment of the quality of Aristotle's critique of his predecessors (and of the Platonists in particular), is widespread. The series of arguments in M 2 (1077a14-b11) that targets separate mathematical objects is the subject of particularly strong (...) criticism by Annas and Ross. Two related arguments in this series (1077a14-20 and 1077a24-31) will serve as cases in point. The principal charges made against these arguments (that Aristotle misunderstands or misrepresents his opponents' views, and that he engages in question-begging because he presupposes his own metaphysical views) are frequently made against Aristotle's critique of Platonist positions more generally. If, as I argue, these charges are false for our two test case arguments, then there is good reason to think that they might also be false when they are leveled against the other arguments in this M 2 series. And, although presenting an argument for this is beyond the scope of this paper, this suggests that these two charges are more often than not false when applied to Aristotle's critique of Platonist mathematical views in M-N and beyond. (shrink)

En el presente trabajo nos interesa analizar cómo Aristóteles formula los principios de la física a partir de la noción de generación. Nuestra tesis es que Física I 7 es el “momento” de euporía que cierra un proceso que se inicia en 1-2 con la problematización acerca de la naturaleza y número de los principios. Para demostrar esto, dividiremos el trabajo en dos partes. En la primera intentaremos establecer por qué Aristóteles emprende esta investigación y cuál es el contexto argumentativo (...) a partir del cual postula sus principios. En la segunda parte, analizaremos los supuestos con base en los cuales sostiene que materia, forma y privación son los tres principios buscados. (shrink)

The core sense of pistis as understood in Posterior Analytics, De Anima, and the Rhetoric is not that of a logical relation in which cognitively grasped propositions stand in respect to one another, but the result of an act of socially embedded interpersonal communication, a willing acceptance of guidance offered in respect to action. Even when pistis seems to have an exclusively epistemological sense, this focal meaning of pistis is implicit; to have pistis in a proposition is to willingly accept (...) that proposition as a basis for some kind of activity (albeit possibly theoretical) as a result of some kind of communicative act. This is in accordance with Aristotle’s understanding of argumentation as a social practice, entered into in order lead others to certain actions, for certain ends. Understanding pistis in this way allows us to understand how it is that pistis admits of quantitative variation. (shrink)

How do, according to Aristotle, peirastic arguments, which are employed by nonscientists to put professed scientists to the test, work, and how do they differ from genuine scientific arguments? A peirastic argument succeeds in unmasking a would-be scientist if it establishes an inconsistency among the answers given. These answers may only comprise: propositions which are proper to the field and which everybody can know; propositions which only scientists may know; “common” propositions that everybody, including various sciences, uses in all kind (...) of arguments. On the other hand, a peirastic argument fails to do its job if it either features or presupposes in addition propositions which would justify a fallacy, or if it purports to be scientific. The latter type of bad peirastic argument crucially depend on common propositions where scientific arguments explain by reference to combinations of the primitive items of the science in question. (shrink)

In view of the current fragmentation in management and organisation studies, we argue that there is a need to elaborate techniques that help reconcile contradictory and superficially incommensurable standpoints. For this purpose, we draw on ‘pre-modern’ Aristotelian epistemological and methodological sources, particularly the idea of ‘saving the appearances’ (SA), not previously introduced into organisation studies. Using SA as our starting point, we outline a methodology that helps to develop reasonable and acceptable intermediary positions in contemporary debates between ‘modernism’ and ‘post-modernism’. (...) We illustrate the functioning of SA in the case of three issues in the philosophy of science where ‘modernist’ and ‘post-modernist’ scholars seem to have incommensurable standpoints: the nature of scientific knowledge; the conception of causality; and the epistemology of practice. We show in particular how to use the logics of ‘qualification’, ‘new conception’, and ‘complementary combination’ to form the basis for mediating positions which could then be accepted by less extreme proponents of both ‘modernism’ and ‘postmodernism’. (shrink)

Topical Themes in Argumentation Theory brings together twenty exploratory studies on important subjects of research in contemporary argumentation theory. The essays are based on papers that were presented at the 7th Conference of the International Society for the Study of Argumentation in Amsterdam in June 2010. They give an impression of the nature and the variety of the kind of research that has recently been carried out in the study of argumentation. The volume starts with three essays that provide stimulating (...) theoretical perspectives on argumentation. Subsequently, some views are explained on the intriguing topics of ‘dissensus’ and ‘deep disagreement’. After a discussion of three different approaches to the treatment of types of argumentation some classical themes from antique argumentation theory are revisited. The new research area of visual argumentation is explored in the next part. The volume concludes with three reports of experimental studies concerning argumentative discourse. The volume starts with three essays that provide stimulating theoretical perspectives on argumentation. Subsequently, some views are explained on the intriguing topics of ‘dissensus’ and ‘deep disagreement’. After a discussion of three different approaches to the treatment of types of argumentation some classical themes from antique argumentation theory are revisited. The new research area of visual argumentation is explored in the next part. The volume concludes with three reports of experimental studies concerning argumentative discourse. The volume starts with three essays that provide stimulating theoretical perspectives on argumentation. Subsequently, some views are explained on the intriguing topics of ‘dissensus’ and ‘deep disagreement’. After a discussion of three different approaches to the treatment of types of argumentation some classical themes from antique argumentation theory are revisited. The new research area of visual argumentation is explored in the next part. The volume concludes with three reports of experimental studies concerning argumentative discourse. (shrink)

Aristotle’s account of epistēmē is foundationalist. In contrast, the web of dialectical argumentation that constitutes justification for scientific principles is coherentist. Aristotle’s account of explanation is structurally parallel to the argument for a foundationalist account of justification. He accepts the first argument but his coherentist accounts of justification indicate that he would not accept the second. Where is the disanalogy? For Aristotle, the intelligibility of a demonstrative premise is the cause of the intelligibility of a demonstrated conclusion and causation is (...) asymmetric. Within the Posterior Analytics itself, Aristotle does not account for this, but elsewhere he develops the resources for doing so: the cause is what acts on a substrate to actualize a potential in that substrate, resulting in the effect. On the other hand, it may well happen that two propositions entail each other, in which case one may as well justify the one on the basis of the other as vice versa. (shrink)

In Metaphysics IV.2 Aristotle assigns a very specific role to dialectic in philosophical and scientific inquiry. This role consists of the use of the special form of dialectic which he calls peirastic. This is not a new conception of, or a new role for, dialectic in philosophy and science, but one also assigned to it in the Topics and Sophistical Refutations. In the SE Aristotle lays down multiple overlapping requirements for the premises or bases for peirastic dialectical argument. These must (...) be things known by skilled practitioners of dialectic; things in fact in accord with the science or subject of the peirastic dialectical encounter in question; things known by non-experts as well as by experts in that subject, things known even by ordinary people in general; things believed by the answerer in the given peirastic encounter and things which are as noted and accredited as possible. We can see from Aristotle’s discussion and from his, and earlier, examples that all of these various requirements can be and are met by a single identifiable set of propositions, one whose use gives a special power to peirastic, one adequate to show the falsity of particular pretensions to knowledge on specific points, in science and philosophy. (shrink)

In the present work, we are interested in establishing the possible influence of Socrates in the Aristotelian dialectic. To do this, we will divide the work into three sections. In the first, we will focus very briefly on the problem of the Aristotelian reconstruction of Socrates’ thinking. In the second part, we will analyze some aspects of the so-called Socratic method. Finally, in the third section, we will examine what aspects of this method Aristotle may have inherited. Our thesis is (...) that the Aristotelian dialectic has Socratic reminiscences that allow us to speak of an inheritance Socratic. (shrink)

A historical and philosophical reassessment of the impact of Aristotle and early-modern Aristotelianism on the development of Kant’s transcendental philosophy. Kant and Aristotle reassesses the prevailing understanding of Kant as an anti-Aristotelian philosopher. Taking epistemology, logic, and methodology to be the key disciplines through which Kant’s transcendental philosophy stood as an independent form of philosophy, Marco Sgarbi shows that Kant drew important elements of his logic and metaphysical doctrines from Aristotelian ideas that were absent in other philosophical traditions, such as (...) the distinction of matter and form of knowledge, the division of transcendental logic into analytic and dialectic, the theory of categories and schema, and the methodological issues of the architectonic. Drawing from unpublished documents including lectures, catalogues, academic programs, and the Aristotelian-Scholastic handbooks that were officially adopted at Königsberg University where Kant taught, Sgarbi further demonstrates the historical and philosophical importance of Aristotle and Aristotelianism to these disciplines from the late sixteenth century to the first half of the eighteenth century. (shrink)

(1) If a deductive argument is valid, then the conclusion is not novel. (2) If the conclusion of an argument is not novel, the argument is not useful. So, (3) if a deductive argument is valid, it is not useful. This conclusion, (3), is unacceptable. Since the argument is valid, we must reject at least one premise. So, should we reject (1) or (2)? This puzzle is usually known as the ‘scandal of deduction’. Analytic philosophers have tried to reject (1) (...) but have assumed premise (2). I argue here that Aristotle would deny (2). Aristotle thinks that at least some deductive arguments are useful, even though they present no new conclusions. Thus, Aristotle’s view contrasts with analytic philosophers of logic, who assume that all useful deductive arguments present novel conclusions. I don’t claim that Aristotle ‘solves’ the problem: it was never posed in Aristotle’s time. Rather, I suggest that Aristotle does not face the problem because he assumes deductions can be useful, without presenting novel conclusions. Aristotle’s view of deduction tames the scandal. (shrink)

La interpretación de la metodología científica de Aristóteles, desarrollada en las últimas décadas, introdujo algunas modificaciones importantes en la imagen fundacionista-axiomática que tradicionalmente se le había adjudicado a la epistemología del estagirita. Sin embargo, tales modificaciones cond..

En este trabajo planteo la pregunta de si la lógica de Aristóteles es o no una lógica formal. Respondo que, aunque las doctrinas contenidas en el Organon inauguren, efectivamente, la lógica formal, hay también buenas razones para pensar que Aristóteles no creía que la lógica fuese una disciplina que pudiera prescindir por completo del contenido. In this paper I discuss the question of whether Aristotle’s logic is a formal logic or not. I answer that, although the doctrines contained in the (...) Organon inaugurate indeed formal logic, there are also good reasons to think that Aristotle did not believe that logic was a discipline that ought to prescind completely from content. (shrink)

Me propongo ofrecer una interpretación unificada de la metodología aristotélica y mostrar que ella se integra en un empirismo híbrido en el cual se combina la doble naturaleza de los phainomena , hechos observacionales y creencias comunes. Polemizaré con la lectura coherentista de la prueba dialéctica de consistencia que se expresa en EN VII 1, y trataré de aclarar qué uso hace Aristóteles de aquella doble fuente de sus investigaciones en algunos textos de ciencia natural ( Ph . IV 4).

The main concern of this paper is the problem of method in De Caelo, which has been recently invigorated by the supposition of Aristotle’s acceptance of two standards of justification. Whereas the φυσικῶς argument comes close to demonstrative knowledge, the εὐλόγως argument relies on more general assumptions and allegedly points towards argumentative justification. With a view to better understanding how empirical criteria for theories, teleological principles, and the resolution of difficulties are laid down to provide as much causal explanations as (...) possible, we take side here in the debate about the very purpose of Aristotle’s using of justification by argument in scientific contexts. Our main claim is that although only reasonable proofs can be worked out in empirically underdetermined domains, this in no way amounts to endorsing an alternative to the norms of inquiry Aristotle upholds in natural science. (shrink)

I reconstruct the original versions of Zeno's Racetrack and Achilles paradoxes, along with Aristotle's responses thereto. Along the way I consider some of the consequences for modern analyses of the paradoxes. It turns out that the Racetrack and the Achilles were oral two-party question-and-answer dialectical paradoxes. One consequence is that the arguments needed to be comprehensible to the average person, and did not employ theses or concepts familiar only to philosophical specialists. I rely on this fact in reconstructing the original (...) dialectical versions of the paradoxes. I show that both paradoxes rely for their success on forcing the dialectical answerer to reflect on his own potentially unending experience of imagination, and show that this renders the most popular contemporary critique of each paradox unworkable in an ancient dialectical context. In responding to the Racetrack, Aristotle seeks to replace the answerer's first-person experience with something more objective, a visible diagram. He then argues that the Racetrack involves an equivocation, an equivocation resulting from the fact that one and the same visible diagram can be interpreted in two ways. He frames his charge of equivocation in standard dialectical fashion, but his use of a diagram is his own innovation. While first employing his response to the Racetrack to construct a response to the somewhat different Achilles paradox, Aristotle later proceeds to offer a revised critique of the Racetrack itself. His revised critique is heavily influenced by his reaction to a variant pre-Aristotelian version of the paradox, a version involving counting. This leads him to reflect on the possibility of mentally experiencing an infinite collection. He also reflects on his earlier diagrammatic methodology, and on the conditions that individuate points, especially halfway-points. He concludes that points which are individuated in diagrams need not represent points that are individuated in reality. His revised critique of the Racetrack hinges on the distinction between actual points and potential points, and I show that this critique maintains the dialectical form of its predecessor, while constituting a reflection on the potentially misleading nature of diagrams. (shrink)