In the first argument of Metaphysics Μ.2 against the Platonist introduction of separate mathematical objects, Aristotle purports to show that positing separate geometrical objects to explain geometrical facts generates an ‘absurd accumulation’ of geometrical objects. Interpretations of the argument have varied widely. I distinguish between two types of interpretation, corrective and non-corrective interpretations. Here I defend a new, and more systematic, non-corrective interpretation that takes the argument as a serious and very interesting challenge to the Platonist.

The opening argument in the Metaphysics M.2 series targeting separate mathematical objects has been dismissed as flawed and half-hearted. Yet it makes a strong case for a point that is central to Aristotle’s broader critique of Platonist views: if we posit distinct substances to explain the properties of sensible objects, we become committed to an embarrassingly prodigious ontology. There is also something to be learned from the argument about Aristotle’s own criteria for a theory of mathematical objects. I hope to (...) persuade readers of Metaphysics M.2 that Aristotle is a more thoughtful critic than he is often taken to be. (shrink)

Both literalism, the view that mathematical objects simply exist in the empirical world, and fictionalism, the view that mathematical objects do not exist but are rather harmless fictions, have been both ascribed to Aristotle. The ascription of literalism to Aristotle, however, commits Aristotle to the unattractive view that mathematics studies but a small fragment of the physical world; and there is evidence that Aristotle would deny the literalist position that mathematical objects are perceivable. The ascription of fictionalism also faces a (...) difficult challenge: there is evidence that Aristotle would deny the fictionalist position that mathematics is false. I argue that, in Aristotle's view, the fiction of mathematics is not to treat what does not exist as if existing but to treat mathematical objects with an ontological status they lack. This form of fictionalism is consistent with holding that mathematics is true. (shrink)

This paper is a criticalexamination of the development of thephilosophy of medicine as a discipline. Ithighlights two major themes in the contemporarydebate about the philosophy of medicine: thescope of the discipline and the relation of thediscipline to its cognate disciplines. A broadview of the philosophy of medicine is defendedand the philosophy of medicine is seen as aphilosophical sub-discipline. These viewsdepend in important ways on three factors: ageneral metaphysical world view, particularunderstandings of the cognate disciplines, andthe perspective from which one asks (...) thequestions about the nature of the discipline. It is proposed that the future of thephilosophy of medicine may follow thephilosophy of science in that philosophical,sociological and historical studies may combinein a mutually enriching way to form ‘‘medicinestudies.’‘. (shrink)

There is little agreement about Aristotle’s philosophy of geometry, partly due to the textual evidence and partly part to disagreement over what constitutes a plausible view. I keep separate the questions ‘What is Aristotle’s philosophy of geometry?’ and ‘Is Aristotle right?’, and consider the textual evidence in the context of Greek geometrical practice, and show that, for Aristotle, plane geometry is about properties of certain sensible objects—specifically, dimensional continuity—and certain properties possessed by actual and potential compass-and-straightedge drawings qua quantitative and (...) continuous. For their part, the objects of stereometry are potential sensible three-dimensional figures qua quantitative and continuous. (shrink)

This is a close scrutiny of De Anima II 5, led by two questions. First, what can be learned from so long and intricate a discussion about the neglected problem of how to read an Aristotelian chapter? Second, what can the chapter, properly read, teach us about some widely debated issues in Aristotle's theory of perception? I argue that it refutes two claims defended by Martha Nussbaum, Hilary Putnam, and Richard Sorabji: that when Aristotle speaks of the perceiver becoming like (...) the object perceived, the assimilation he has in mind is ordinary alteration of the type exemplified when fire heats the surrounding air, that this alteration stands to perceptual awareness as matter to form. Claim is wrong because the assimilation that perceiving is is not ordinary alteration. Claim is wrong because the special type of alteration that perceiving is is not its underlying material realisation. Indeed, there is no mention in the text of any underlying material realisation for perceiving. The positive aim of II 5 is to introduce the distinction between first and second potentiality, each with their own type of actuality. In both cases the actuality is an alteration different from ordinary alteration. Perception exemplifies one of these new types of alteration, another is found in the acquisition of knowledge and in an embryo's first acquisition of the power of perception. The introduction of suitably refined meanings of 'alteration' allows Aristotle to explain perception and learning within the framework of his physics, which by definition is the study of things that change. He adapts his standard notion of alteration, familiar from Physics III 1-3 and De Generatione et Corruptione I, to the task of accounting for the cognitive accuracy of perception and second potentiality knowledge: both are achievements of a natural, inborn receptivity to objective truth. Throughout the paper I pay special attention to issues of text and translation, and to Aristotle's cross-referencing, and I emphasise what the chapter does not say as well as what it does. In particular, the last section argues that the textual absence of any underlying material realisation for perceiving supports a view I have defended elsewhere, that Aristotelian perception involves no material processes, only standing material conditions. This absence is as telling as others noted earlier. Our reading must respect the spirit of the text as Aristotle wrote it. (shrink)

This review-essay looks at three texts from, or about, the early days of the Situationist International. The first volume of Guy Debord’s Correspondence reveals the SI’s internal discussions during their decisive first three years; Bernstein’s book represents an example of the continued relevance of the technique of détournement; while Wark’s text demonstrates both the breadth of the Situationist project and that, despite being continually mined by the academy, activists, the creative industries, and other more sinister recuperators, their work has not (...) been depleted of its vitality. Taken together, the three books undermine a series of preconceptions about the SI, namely in terms of Debord’s role at the centre of the group and the SI’s engagement with the forces of the ‘spectacled’. (shrink)

I offer a new interpretation of Aristotle's philosophy of geometry, which he presents in greatest detail in Metaphysics M 3. On my interpretation, Aristotle holds that the points, lines, planes, and solids of geometry belong to the sensible realm, but not in a straightforward way. Rather, by considering Aristotle's second attempt to solve Zeno's Runner Paradox in Book VIII of the Physics , I explain how such objects exist in the sensibles in a special way. I conclude by considering the (...) passages that lead Jonathan Lear to his fictionalist reading of Met . M3,1 and I argue that Aristotle is here describing useful heuristics for the teaching of geometry; he is not pronouncing on the meaning of mathematical talk. (shrink)

In this paper, I argue that the different understandings of “harmony”, which are rooted in ancient Greek and Chinese thought, can be recapitulated in the name of “dialectic harmony” and “ambiguous harmony” regarding the representation of the beautiful. The different understandings of the concept of harmony lead to at least two kinds of aesthetic value as well as ideality – harmony in conciliation and harmony in diversity. Through an explication of the original meaning and relation between the concept of harmony (...) and beauty, we can learn more about the cosmo-metaphysical origins in Western and Eastern aesthetics, with which we may gain insights for future aesthetics discourse. (shrink)

Sextus’ interpretation of Xenophanes’ scepticism in M 7.49–52 is often cited but has never been subject to detailed analysis. Such analysis reveals that Sextus’ interpretation raises far more complex problems than has been recognised. Scholars invariably assume one of two ways of construing his account of Xenophanes B34, without observing that the choice between these two alternatives poses an interpretive dilemma. Some scholars take it that Sextus ascribes to Xenophanes the view that one may have knowledge without knowing that one (...) has knowledge. Others take it that he ascribes to Xenophanes the view that one may have true belief without knowing that one has true belief. A close examination of Sextus’ paraphrase exposes a crucial but overlooked complication. Sextus elides Xenophanes’ pivotal distinction between knowing “the clear and certain” and believing “what has been fulfilled” . He eliminates altogether tetelesmenon from his analysis of B34, and expands the role of to saphes. I demonstrate that, as a result, Xenophanes B34, as interpreted by Sextus, does not consistently and straightforwardly express either view or view . Sextus, I argue, in fact develops a fundamentally incoherent interpretation of Xenophanes B34. On Sextus’ interpretation, Xenophanes justifies the proposition “No human knows” by arguing that, even if a human does, in fact, know, he does not know that he knows. Finally, I argue that Sextus’ incoherent account reflects not unthinking negligence, but a sophisticated if ultimately doomed attempt to interpret the logical structure of Xenophanes B34 in line with later models of second-order scepticism. (shrink)

I argue that Mumford and Anjum’s recent theory of simultaneous causation among powerful meso-level objects is problematic in several respects: it is based on a false dichotomy, it is incompatible with standard meso-level physics, it is explanatory deficient, and it threatens to render the powers metaphysics incoherent. Powers theorists are advised, therefore, to adopt a purely sequential conception of causation.

Gregory Vlastos claims that in the Gorgias Socrates is confident that the elenchos is the only and the final arbiter of moral truth. Traditionally, the object of elenchos has been viewed as not one of moral truth, but one of simply revealing to Socratic interlocutors confusions and muddles within themselves, thereby jarring their unquestioning adherence to some moral dogma. On Vlastos' view, however, Socrates claims that he proves by elenchos that an interlocutor's thesis is false. How can he, when in (...) point of logic all he has proved is that the thesis is inconsistent with the agreed-upon premises in that argument whose truth Socrates does not undertake to establish? While Vlastos attempts to solve what he calls "the problem of elenchos" with all the ingenuity that we have come to expect from him, I argue that there are two major obstacles in his way. First, elenchos is not the only arbiter of moral truth in the Gorgias Socrates has a number of other reasons for believing certain things, but according to Vlastos, Socrates looks to elenchos, and to nothing but that, for the truth of his beliefs. I argue that, first, Vlastos' characterization of elenchos is unsatisfactory, for on his criteria it is difficult to distinguish it from other kinds of arguments. This in turn seriously hampers a proper evaluation of elenctic arguments. I then show that at least in this dialogue Socrates has certain religious beliefs that he holds without relying on elenchos, and so elenchos is not the only avenue for acquiring moral knowledge. ;Under Vlastos' correcting lenses, Socrates emerges also as a morally upright philosopher who would never knowingly conduct fallacious arguments. I argue that Socrates cheats at elenchos, and he does so in order to win over his interlocutors. I conclude that because of certain assumptions Vlastos makes about the character of the model philosopher and the model method, he exaggerates the strength of elenchos. If I am right, the Gorgias is witness to, not the power of elenchos as Vlastos would have us believe, but its limitations. (shrink)

This article focusses on the generality of the entities involved in a geometric proof of the kind found in ancient Greek treatises: it shows that the standard modern translation of Greek mathematical propositions falsifies crucial syntactical elements, and employs an incorrect conception of the denotative letters in a Greek geometric proof; epigraphic evidence is adduced to show that these denotative letters are ‘letter-labels’. On this basis, the article explores the consequences of seeing that a Greek mathematical proposition is fully general, (...) and the ontological commitments underlying the stylistic practice. (shrink)

Este artículo subraya la incidencia de un componente temporal en la doctrina aristotélica de la sustancia y las categorías en la medida en que la distinción sustancia-accidentes se refiere no sólo a la oposición lógica entre el sujeto y el predicado, sino también a la oposición real entre el sujeto de cambio y sus determinaciones. El argumento se basa en la interpretación de importantes pasajes de Cat. 5, Phys. I, 7 y IV 10-14.