Corrective intervention in Plato's metaphysics replacing the standard view of Plato as a metaphysical dualist with a novel and revolutionary paradigm of unitary pluralism in a single reality built on ontological diversity.

This chapter contains sections titled: Going Beyond Nature in Order to Explain it Technē, epistēmē and alēthēs doxa Mathematics, pure and applied Observation and Experimental Verification Bibliography.

I argue that in the Phaedo, Plato maintains that the soul is located in space and is capable of locomotion and of interacting with the body through contact. Numerous interpreters have dismissed these claims as merely metaphorical, since they assume that as an incorporeal substance, the soul cannot possess spatial attributes. But careful examination of how Plato conceives of the body throughout his corpus reveals that he does not distinguish it from the soul in terms of spatiality. Furthermore, assigning spatial (...) attributes to the soul plays an important role in Plato’s account of the relation of body and soul. (shrink)

Although most scholars agree that the lexicon of Sophist 232b1-236d4 is similar to that of Republic X, they leave undetermined whether they are theoretically compatible. Notably, both dialogues elucidate the art of imitation through the metaphor of the painter who deceives his pupils through φαντάσματα. I argue that Plato’s conception of imitation of the Republic is not only consistent with that presented in the Sophist, but also importantly integrates it.

The relationship between philosophy and medicine in antiquity has been extensively discussed by commentators and scholars. The objective of this article was to determine if it is possible to assert that the Hippocratic treatise De prisca Medicina is a criticism directed at Philolaus and, if possible, in what terms it could be stated. With this in mind, the work concentrates on the characterization of the position of the opponent of the author of said treatise in DM § 1. 15-21. Particular (...) emphasis will be placed on the terms “hypothesis” and “principle”. Thus, from four possible proposed interpretations of the first of these terms, namely: a proposition postulated but not affirmed sharply, a proposition whose veracity is supposed, a proposition that must be proved, and an object put to discussion or a purpose, the criticisms that could be at stake in DM in each of these will be outlined and then contrasted with the doctrine of the Pythagorean philosopher that can be reconstructed from the fragments attributed to him as authentic, as well as some testimonies about his medical and epistemological approaches. Finally, it was stated by way of conclusion that the Hippocratic treatise that is thematized in it can be, in various ways, conceived as a criticism of Philolaus. However, it is necessary to emphasize that this inquisition on this subject is not intended to be conclusive; rather, it seeks to provide relevant elements to this debate. (shrink)

The argument at Phaedo 74 B 4‐C 6 that the equal itself is ‘something different from’ sets of physical equals depends on Leibniz's Law: there is a property that perceptible equals have that the equal itself does not have. What I call the ‘epistemic interpretation’ holds that the property is an epistemic one: having appeared unequal. The ‘ontological interpretation’ holds that the property is not epistemic, but simply the property of being unequal. The most natural reading of the text favours (...) the epistemic interpretation; scholarly support for the ontological interpretation is based on the widely held view that on the epistemic interpretation the argument is manifestly invalid. But this view implicitly relies on an impoverished sense of ‘appearing’ as equivalent to ‘being thought’. Drawing on an analogy with colour perception, I elaborate an experiential sense of ‘appearing’ which makes Plato's argument on the epistemic interpretation philosophically defensible. (shrink)

En este artículo se argumenta que, para comprender las relaciones unificadas que son comúnmente predicadas de la koinōnía en las esferas ética, política y cosmológica respectivamente, uno debe apreciar primero ciertos “principios” o “reglas” que son prerrequisitos necesarios para la formación de koinōnía. Un principio que ha sido durante mucho tiempo objeto de una discusión intensa entre los intérpretes de Platón es la proporcionalidad. No obstante, en lugar de detenernos en el vínculo directo e inmediato entre proporcionalidad –en el sentido (...) más amplio posible– y las totalidades bien-ordenadas, sugiero que podemos obtener una explicación mucho más rica del interés platónico en la proporcionalidad y la formación de koinōnía si exploramos los diferentes modelos proporcionales que utiliza en diferentes contextos. Se argumentará que, para Platón, la proporcionalidad geométrica en particular es el principio vinculante par excellence para la formación de koinōnía al ser el modelo de orden más justo y permitir las totalidades complejas más duraderas. Abordar el punto desde este ángulo puede proporcionar una forma más decisiva de entender las diferencias políticas innegablemente obvias entre la República y las Leyes en términos de koinōnía. (shrink)

This paper concerns Aristotle's kind‐crossing prohibition. My aim is twofold. I argue that the traditional accounts of the prohibition are subject to serious internal difficulties and should be questioned. According to these accounts, Aristotle's prohibition is based on the individuation of scientific disciplines and the general kind that a discipline is about, and it says that scientific demonstrations must not cross from one discipline, and corresponding kind, to another. I propose a very different account of the prohibition. The prohibition is (...) based on Aristotle's scientific and metaphysical essentialism, according to which a scientific demonstration must take as its starting point a set of per se properties of a subject, if these make up a single, unitary definition. The subject of demonstration here is a kind, although not the general kind associated with a discipline, but rather the particular kind that the particular demonstration is about. (shrink)

In this paper I ask whether mathematicians should swear an oath similar to the Hippocratic oath sworn by some medical professionals as a means to foster morally praiseworthy engagement with the ethical dimensions of mathematics. I individuate four dimensions in which mathematics is ethically charged: (1) applying mathematical knowledge to the world can cause harm, (2) participation of mathematicians in morally contentious practices is an ethical issue, (3) mathematics as a social activity faces relevant ethical concerns, (4) mathematical knowledge itself (...) may be ethically charged. I present a conceptual framework for oaths and discuss some empirical results on the effectiveness of oath-taking to foster morally praiseworthy behaviour. My findings suggest that enforcing oath-taking practices in mathematics is not currently a suitable means to foster ethically praiseworthy behaviour amongst mathematicians. Oaths can, however, provide needed edifying narratives about how to act ethically when acting as a mathematician. (shrink)

In general, scholars have viewed the mathematical detail of Plato’s Divided Line discussion in Republic VI-VII as irrelevant to the substance of his epistemology.Against this stance this essay argues that this detail serves a serious and instructive purpose and makes manifest some central features of Plato’s account of human knowledge.

In Plato's Phaedrus, Socrates offers two speeches, the first portraying madness as mere disease, the second celebrating madness as divine inspiration. Each speech is correct, says Socrates, though neither is complete. The two kinds of madness are like the left and right sides of a living body: no account that focuses on just one half can be adequate. In a recent paper, Hugh Benson gives a left-handed speech about a psychic condition endemic among mathematicians: dianoia. Benson acknowledges that his account (...) is one-sided, but only hints at the virtues of right-handed dianoia. This note sketches a somewhat fuller picture. (shrink)

The literary and critical discourse about characters and characterization in Anglophone drama and fiction since the Renaissance shows a persistent but underrecognized presence of three idioms and vocabularies, two highly developed and one nascent, that either derive from the rhetoric of mathematics in classical antiquity or participate in its modern afterlife. Those discourses—which this article studies in detail—are, first, an explicitly Theophrastan one, in which taxonomies of character are constructed; second, an explicitly Euclidean one, in which characterization is discussed and (...) accomplished in relatively conventional or commonsensical geometric terms; and third, a non- or post-Euclidean one, in which characterization is discussed and inchoately accomplished in the terms of the “new geometries” that emerged during the nineteenth century. What taxonomy in the Aristotelian mode and geometry in the Euclidean mode have in common is that when their vocabularies are applied to characterization, they delimit characters in terms of established categories—whether of ideal shapes or statistically probable types—while discounting whatever features may be unique to individuals. An obliviousness to these three discourses can limit seriously what can be said about, and what can be said on behalf of, the literary and critical texts framed in their terms and also, most importantly, what can be said about the nature of literary characters. (shrink)

It is a notion commonly acknowledged that in his work Timaeus the Athenian philosopher Plato (_c_. 429–347 BC) laid down an early chemical theory of the creation, structure and phenomena of the universe. There is much truth in this acknowledgement because Plato’s “chemistry” gives a description of the material world in mathematical terms, an approach that marks an outstanding advancement over cosmologic doctrines put forward by his predecessors, and which was very influential on western culture for many centuries. In the (...) present article, I discuss inter-transformations among Plato’s four types (fire, air, water, and earth) as well as the interpretation they received in the literature. I find that scientists and scholars generally emphasized (and often misunderstood) mathematical aspects of these “reactions” over the philosophical ones. I argue that Plato’s “chemistry” in fact bears on crucial topics of his philosophical system, such as Forms, Becoming, causation and teleology. I propose that consideration of these doctrines help to understand not only the sense of his “chemical” reactions, but also the reason why their stoichiometry is by surface balance and is restricted only to types that come to be and pass away but not to those that provoke the inter-transformations. (shrink)

In this paper, I argue that Plato conceives self-motion as non-spatial in Laws X. I demonstrate this by focusing on the textual evidence and by refuting interpretations according to which self-motion either is a specific type of spatial motion or is said to require space as a necessary condition for its occurrence. Moreover, I show that this non-spatial understanding differs from the identification of the soul’s motion with locomotion in the Timaeus. Consequently, I provide an explanation for this difference between (...) the Timaeus and Laws X by considering developmentalist and contextualist viewpoints. (shrink)

Graduate Papers from the 2022 Joint Session. It is often said that Aristotle takes geometrical objects to be absolutely unmovable and unchangeable. However, Greek geometrical practice does appeal to motion and change, and geometers seem to consider their objects apt to be manipulated. In this paper, I examine if and how Aristotle’s philosophy of geometry can account for the geometers’ practices and way of talking. First, I illustrate three different ways in which Greek geometry appeals to change. Second, I examine (...) Aristotle’s ontology of geometrical objects and argue that although the truth-makers of geometrical statements are in fact unmovable because they are properties of sensible objects, geometers ‘separate them in thought’ and treat them as substances apt to be modified. Finally, I examine whether allowing for the possibility of manipulating these semi-fictional geometrical individuals creates problems for the applicability of geometry. I find that it does not, insofar as one accepts that geometry is not meant to track physical change but merely to study the instantaneous geometrical configuration of sensible bodies, and is thus only applicable at the instant. (shrink)

What is it for a judgement, action, or character state to be itself a good thing, so genuinely worth pursuing? Readers of Plato's Republic discover that that it is by standing in the right relation to the Form of the Good that other things are, or become, good. In her recent monograph, Plato's Sun-Like Good, Sarah Broadie inverts the standard interpretive strategy by focusing primarily on the role of the Good in dialectic, and drawing conclusions about its metaphysical status on (...) that basis. In this paper, I argue that the metaphysically radical features of the Good on her reading – that it is undefinable and not an object of knowledge for the guardians – are ultimately undermined by her full account of the Form, in particular of the way that it endows ‘the things known’ with their reality, as well as relating to its participants as participand. I also argue that her preferred interpretation of the guardians' objects of knowledge in the sun-analogy as action-types is conceptually and textually problematic, and should be rejected in favour of her dispreferred - yet ultimately deeply insightful - interpretation of these objects as Forms that the Good makes known and fully real. (shrink)

The article resonates Plato's ideas on education and art. In the Apology, Socrates describes his life's mission of practicing philosophy as aimed at getting the Athenians to care for virtue; in the Gorgias, Plato claims that happiness depends entirely on education and justice; in the Protagoras and the Meno, he puzzles about whether virtue is teachable or how else it might be acquired; in the Phaedrus, he explains that teaching and persuading require knowledge of the soul and its powers, which (...) requires knowledge of what objects the soul may act on and be acted on by which, in turn, requires knowledge of nature. The article also looks at musical and gymnastic education's effects on the soul using images from metallurgy and dyeing wool, saying that prerational souls are “most malleable and take on any pattern one wishes to impress on them.”. (shrink)

In this paper, I reconsider the commonly held position that the early moral education of the Republic is arational since the youths of the Kallipolis do not yet have the capacity for reason. I argue that, because they receive an extensive mathematical education alongside their moral education, the youths not only have a capacity for reason but that capacity is being developed in their early education. If this is so, though, then we must rethink why the early moral education is (...) arational. I argue that the reason is rooted in the nature of moral explanations. These sorts of explanations are rooted in the Forms and thus one can only understand those explanations when they have knowledge of the Forms. But this requires preparation – the very sort of preparation that is provided by both the mathematical and moral educations. (shrink)

In modern epistemology, one ‘value of knowledge’ problem concerns the question why knowledge should be valued more highly than mere true belief. Though this problem has a background in Plato, the present paper, focused on Philebus 55–9, is concerned with a different question: what questions might one ask about the value of knowledge, and what question does Plato ask here? The paper aims to articulate the kind of value Plato here attributes to ‘useless’ knowledge, knowledge pursued without practical object; and (...) why, according to him, there is value in being a knower. Though his answer to this question requires commitments we may resist, it has a structure of general philosophical interest. (shrink)

In his book On What Matters, Derek Parfit defends a version of moral non-naturalism, a view according to which there are objective normative truths, some of which are moral truths, and we have a reliable way of discovering them. These moral truths do not exist, however, as parts of the natural universe nor in Plato’s heaven. While explaining in what way these truths exist and how we discover them, Parfit makes analogies between morality on the one hand, and mathematics and (...) logic on the other. Moral truths “exist” in a way that numbers exist, and we discover these truths in a similar way as we discover truths about numbers. By the end of the second volume, Parfit also responds to a powerful objection against his view, an objection based on the phenomenon of moral disagreement. If people widely and deeply disagree about what is the moral truth, it is doubtful whether we have a reliable way of discovering it. In his reply, he claims that in ideal conditions for thinking about moral questions, we would all have sufficiently similar moral beliefs. However, we often find ourselves in less-than-ideal conditions due to various factors that distort our ability to agree. Therefore, differences in moral opinion can be expected. In this paper, I draw a connection between these parts of Parfit’s theory and comment on them. Firstly, I argue that Parfit’s analogy with mathematics and logic and his answer to the disagreement objection are in tension because there are important epistemic differences between morality and these fields. If one would try to account for the differences, one would have to sacrifice some measure of similarity between morality and them. Secondly, I comment on Parfit’s reply to the disagreement objection itself. I believe that, although his description of ideal conditions has some potential for reaching moral agreement, it may be difficult to tell if ideal conditions prevail. This obscurity spells further trouble for Parfit’s overall theory. (shrink)

Republic 596a introduces a One over Many principle that has traditionally been considered as an argument for the existence of Forms, according to which, one Form should be posited for each like-named plurality. This interpretation was challenged by (Smith, J. A. 1917. “General Relative Clauses in Greek.” Classical Review 31: 69–71.), who interpreted it rather as a statement that each Form is unique and correlated to a plurality of things that have the same name as it. (Sedley, D. 2013. “Plato (...) and the One-over-Many Principle”, in Chiaradonna & Galluzzo 2013, 113–37.) has offered a forceful defence of Smith’s interpretation. I argue that Sedley’s defence fails and that the traditional interpretation should be preferred. (shrink)

In this paper, I examine the problem of the so-called Mathematical Objects within the context of the Divided Line. I argue that Plato believes that there are such objects but their distinctness and the mode of cognition relative to them can only be understood in relation to the superordinate, unhypothetical first principle of all, the Idea of the Good. The objects of mathematics or διάνοια are, unlike the objects of intellection or νόησις, cognized independently of the Good.

Despite the fact that the theory of Forms is regarded as the hallmark of Plato’s philosophy, it has remained remarkably elusive, because it is more hinted at than explained in his dialogues. Given the uncertainty concerning the nature and extension of the Forms, this article makes no pretense to coming up with solutions to all problems that have occupied scholars since antiquity. It aims to elucidate only two aspects of that theory: the indication in certain dialogues that the Forms are (...) what in modern parlance are called functions or purposes, and the indication in other dialogues that such functions rely on harmonious structures. (shrink)

It may be a myth that Plato wrote over the entrance to the Academy “Let no-one ignorant of geometry enter here.” But it is a well-chosen motto for his view in the Republic that mathematical training is especially productive of understanding in abstract realms, notably ethics. That view is sound and we should return to it. Ethical theory has been bedevilled by the idea that ethics is fundamentally about actions (right and wrong, rights, duties, virtues, dilemmas and so on). That (...) is an error like the one Plato mentions of thinking mathematics is about actions (of adding, constructing, extracting roots and so on). Mathematics is about eternal relations between universals, such as the ratio of the diagonal of a square to the side. Ethics too is about eternal verities, such as the equal worth of persons and just distributions. Mathematical and ethical verities do both constrain actions, such as the possibility of walking over the seven bridges of Königsberg once and once only or of justly discriminating between races. But they are not themselves about action. In principle, neither mathematical nor ethical verities are subject to historical forces or disagreement among tribes (though they can be better understood as time goes on). Plato is right: immersion in mathematics induces an understanding of the necessities underpinning reality, an understanding that is essential for distinguishing objective ethics from tribal custom. Equality, for example, is an abstract concept which is foundational for both mathematics and ethics. (shrink)

The aim of this paper is to examine the implications of Plato’s use of the term stoicheion, since his awareness of stoicheion’s polysemy reveals his view of the origin, the complexity and, at the same time, the order of reality. Moreover, his use of stoicheion allowed him both to inherit and to detach himself from his predecessors. I begin by presenting the history of the notion of stoicheion; then, since one of the meanings of stoicheion is ‘letter of the alphabet’, (...) I focus on the Cratylus, which contains the first of several passages where Plato employs the alphabet as a paradigm for the structure of a complex system. Finally, I turn to the Theaetetus, where Plato, for the first time, uses stoicheion in the sense of ‘element’ and where, through the relation letters/syllables, Plato clarifies that enumeration and juxtaposition are not sufficient to attain the real knowledge. I will argue that only thanks to these steps can we understand the occurrences of stoicheion in the Timaeus, where Plato first states that air, earth, fire and water are not stoicheia tou pantos, and then reveals that, instead, the basic triangles are ‘the elements of the universe’. (shrink)

I examine the passages where Aristotle maintains that intellectual activity employs φαντάσματα (images) and argue that he requires awareness of the relevant images. This, together with Aristotle’s claims about the universality of understanding, gives us reason to reject the interpretation of Michael Wedin and Victor Caston, on which φαντάσματα serve as the material basis for thinking. I develop a new interpretation by unpacking the comparison Aristotle makes to the role of diagrams in doing geometry. In theoretical understanding of mathematical and (...) natural beings, we usually need to employ appropriate φαντάσματα in order to grasp explanatory connections. Aristotle does not, however, commit himself to thinking that images are required for exercising all theoretical understanding. Understanding immaterial things, in particular, may not involve employing phantasmata. Thus the connection that Aristotle makes between images and understanding does not rule out the possibility that human intellectual activity could occur apart from the body. (shrink)

Ethics and mathematics have long invited comparisons. On the one hand, both ethical and mathematical propositions can appear to be knowable a priori, if knowable at all. On the other hand, mathematical propositions seem to admit of proof, and to enter into empirical scientific theories, in a way that ethical propositions do not. In this article, I discuss apparent similarities and differences between ethical (i.e., moral) and mathematical knowledge, realistically construed -- i.e., construed as independent of human mind and languages. (...) I argue that some are are merely apparent, while others are of little consequence. There is a difference between the cases. But it is not an epistemological difference per se. The difference, surprisingly, is that ethical knowledge, if it is practical, cannot fail to be objective in a way that mathematical knowledge can. One upshot of the discussion is radicalization of Moore’s Open Question Argument. Another is that the concepts of realism and objectivity, which are widely identified, are actually in tension. (shrink)

In Plato’s Gorgias 482c4–484c3, Callicles advances a concept of natural justice: the laws of the polis must agree with nature, that is, human nature. Since human nature is characterised by its desire to get a greater share, nature itself makes it legitimate that stronger human beings get a greater share than weaker ones. Socrates objects: Callicles’ theoretical approach to civic life poses a threat to the polis’ community, its citizens, and to the friendship amongst its citizens. However, Socrates accepts Callicles’ (...) premise, that the laws of the polis must agree with nature. Still, he disagrees with Callicles about the nature of human nature and proposes an alternative theory of human nature, eventually leading to his alternative concept of natural justice. The article explains the arguments underpinning these two concepts of natural justice, including the conflicting understandings of human nature. (shrink)

I argue that, according to Plato, the body is the sole cause of psychic disorders. This view is expressed at Timaeus 86b in an ambiguous sentence that has been widely misunderstood by translators and commentators. The goal of this article is to offer a new understanding of Plato’s text and view. In the first section, I argue that although the body is the result of the gods’ best efforts, their sub-optimal materials meant that the soul is constantly vulnerable to the (...) body’s influences. In the second section, I argue that every psychic disorder is a disruption of the motions of the inner psychic circles by the body; moreover, I defend my translation of 86b. In the final section, I argue that the goal of education is to restore the circles to their original orbits, and I disarm a possible objection that bad education is also a cause of psychic disorder. (shrink)

I argue that Plato thinks that the soul has location, surface, depth, and extension, and that the Timaeus’ composition of the soul out of eight circles is intended literally. A novel contribution is the development of an account of corporeality that denies the entailment that the soul is corporeal. I conclude by examining Aristotle’s objection to the Timaeus’ psychology and then the intellectual history of this reading of Plato.

This paper presents a new interpretation of the objects of dianoia in Plato’s divided line, contending that they are mental images of the Forms hypothesized by the dianoetic reasoner. The paper is divided into two parts. A survey of the contemporary debate over the identity of the objects of dianoia yields three criteria a successful interpretation should meet. Then, it is argued that the mental images interpretation, in addition to proving consistent with key passages in the middle books of the (...) Republic, better meets those criteria than do any of the three main positions. (shrink)

At least since Sachs' well-known essay, readers of Plato's Republic have worried that there is a gap between the challenge posed to Socrates--to show that it is always in one's interest to act justly--and his response--to show that it is always in one's interest to have a just soul. The most popular response has been that Socrates fills this gap in Books Five through Seven by supposing that knowledge of the Forms motivates those with just souls to act justly. I (...) offer some complaints about this gap-filling strategy and offer an alternative account, according to which there was never a gap. On my account, Socrates assumes that no one can have a just soul unless they have been raised well and that anyone who is raised well will act justly. On this view, the account of moral education in Books Two through Four is the key to understanding the connection between psychological and practical justice. I argue that this account makes better sense of what the Republic says, and that it attributes to Plato a more plausible moral psychology. (shrink)

I argue against a formidable interpretation of Plato’s Divided Line image according to which dianoetic correctly applies the same method as dialectic. The difference between the dianoetic and dialectic sections of the Line is not methodological, but ontological. I maintain that while this interpretation correctly identifies the mathematical method with dialectic, ( i.e. , the method of philosophy), it incorrectly identifies the mathematical method with dianoetic. Rather, Plato takes dianoetic to be a misapplication of the mathematical method by a subset (...) of practicing mathematicians. Thus, Plato’s critique of dianoetic is a not a critique of mathematics, as such, but of mathematicians. (shrink)

The conceptualisation of numbers is culturally bound. This may seem like a counterintuitive claim, but one illustration thereof is the limitations of the resemblance of the ancient Greek concept of number to that in modern mathematics.

One of the hardest questions to answer for a (Neo)platonist is to what extent and how the changing and unreliable world of sense perception can itself be an object of scientific knowledge. My dissertation is a study of the answer given to that question by the Neoplatonist Proclus (Athens, 411-485) in his Commentary on Plato’s Timaeus. I present a new explanation of Proclus’ concept of nature and show that philosophy of nature consists of several related subdisciplines matching the ontological stratification (...) of nature. Moreover, I demonstrate that for Proclus philosophy of nature is a science, albeit a hypothetical one, which takes geometry as its methodological paradigm. I also offer an explanation of Proclus’ view of what is later called the mathematization of physics, i.e. the role of the substance of mathematics, as opposed to its method, in explaining the natural world. Finally, I discuss Proclus’ views of the discourse of philosophy of nature and its iconic character. (shrink)

This dissertation is a study of the relation between Aristotle’s ethics and the crafts (or technai). My thesis is that Aristotle’s argument is at key points shaped by models proper to the crafts, this shaping being deeper than is generally acknowledged, and philosophically more problematic. Despite this, I conclude that the arguments I examine can, if revised, be upheld. The plan of the dissertation is as follows – Preface: The relation of my study to the extant secondary literature; Introduction: The (...) pre-Platonic concept of technē, as evidenced in Greek philosophical and literary sources, in particular the early Hippocratic corpus; Chapter one: The Platonic concept of technē, followed by an investigation of whether Plato affirms a virtue-technē in the Protagoras and Republic; Chapter two: Aristotle’s concept of technē, followed by scrutiny of his arguments in NE VI.5 against a virtue-technē, and of his analyses of slavery and deliberation; Chapter three: An exposition of Aristotle’s function argument, followed by a dominantist interpretation of it, and an explanation of dominantism as in part a technē-influenced doctrine; Chapter four: An examination of Aristotle’s ethical mean and its problems, with a diagnosis of these in terms of influence by the Philebus, and by paradigms derived from the crafts; Chapter five: Argument that Aristotle’s theory of habituation suffers from two significant opacities, these being a function of influence both by the Republic, and by models of craft-learning; Conclusion: Response to key objection; Aristotle’s ethics revised, defended. (shrink)

Plato seems to countenance both positive and negative Forms, that is to say, both good and bad ones. He may not say so outright, but he invokes both and rejects neither. The apparent finality of this impression creates a lack of direct interest in the subject: Plato scholars do not give negative Forms much thought except as the prospect relates to something else they happen to be doing. Yet when they do give the matter any thought, typically for the sake (...) of a prior concern, they try either to support the textual evidence or to contradict it, indicating that the evidence does not stand on its own. The purpose of this paper is to determine why they tend to affirm or deny the obvious, how they try to confirm or dispute it, and what this says about Plato’s position. The strategic vehicle is a comparative case study. The confirmation comes from Debra Nails (2013), who needs to embrace negative Forms to demonstrate that the unhypothetical first principle of the all is not identical to the Form of the good, something she cannot do unless Plato recognizes negative Forms. The contradiction comes from Holger Thesleff (2013), who needs to reject negative (Ideal) Forms because the defining feature of his (Ideal) Forms is the possession of positive intrinsic value, which cannot be predicated of anything negative. Despite defending opposite views, or perhaps because of this, they jointly make up for any lack of interest in the scholarly community. I appreciate both yet side with Thesleff. (shrink)

One of the questions regarding the Parmenides is whether Plato was committed to any of the arguments developed in the second part of the dialogue. This paper argues for considering at least one of the arguments from the second part of the Parmenides, namely the argument of the generation of numbers, as being platonically genuine. I argue that the argument at 142b-144b, which discusses the generation of numbers, is not deployed for the sake of dialectical argumentation alone, but it rather (...) demonstrates key platonic features, such as the use of the greatest kinds and the generation principle. The connection between the argument for the generation of numbers and Plato’s philosophy of mathematics is strengthened by the exploration of a possible reference in Aristotle’s Metaphysics A6. Taken as a genuine platonic theory, the argument could have significant impact on how we understand Plato’s philosophy of mathematics in particular, and the ontology of the late dialogues in general – that numbers can be reduced to more basic entities, i.e the greatest kinds, in a way similar to the role the greatest kinds are assigned in the Sophist. (shrink)

At 435c-d and 504b ff., Socrates indicates that there is a "longer and fuller way" that one must take in order to get "the best possible view" of the soul and its virtues. But Plato does not have him take this "longer way." Instead Socrates restricts himself to an indirect indication of its goals by his images of sun, line, and cave and to a programmatic outline of its first phase, the five mathematical studies. Doesn't this pointed restraint function as (...) a provocation, moving us to want to begin the "longer way" and to make use of its conceptual resources to rethink Socrates' images? I begin by finding a double movement in the complex trajectory of the five studies: they both guide the soul in the "turn away from what is coming to be ... [to] what is" (518c) and, at the same time, lead the soul back, albeit in the medium of pure intelligibility, to the sensible world; for the pure figures and ratios that they disclose constitute the core structures of sensible things. I then draw on what Socrates says about geometry and harmonics to address three fundamental questions that he leaves open: the nature of the Good in its responsibility for truth and for the being of the forms; the relations of forms, mathematicals, and sensibles as these are disclosed by dialectic; and the bearing of the philosopher's discovery of the Good on his disposition towards his community and the task of ruling. I close by marking six sets of further questions that these reflections bequeath for dialogues to come. (shrink)