Plato: Forms

This paper shows how the universals of category theory in mathematics provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. The paper also shows how the always-self-predicative universals of category theory provide the "opposite bookend" to the never-self-predicative universals of iterative set theory and thus that the paradoxes arose from having (...) one theory (e.g., Frege's Paradise) where universals could be either self-predicative or non-self-predicative (instead of being always one or always the other). (shrink)

We propose the concepts of philomatics and psychomatics as hybrid combinations of philosophy and psychology with mathematics. We explain four motivations for this combination which are fulfilling the desire of analytical philosophy, proposing science of philosophy, justifying mathematical algorithms by philosophy, and abstraction in both philosophy and mathematics. We enumerate various examples for philomatics and psychomatics, some of which are explained in more depth. The first example is the analysis of relation between the context principle, semantic holism, and the usage (...) theory of meaning with the attention mechanism in mathematics. The other example is on the relations of Plato's theory of forms in philosophy with the holographic principle in string theory, object-oriented programming, and machine learning. Finally, the relation between Wittgenstein's family resemblance and clustering in mathematics is explained. This paper opens the door of research for combining philosophy and psychology with mathematics. (shrink)

Sut Jhally begins his essay “Advertising at the Edge of the Apocalypse” with the following provocative claim: “Advertising is the most powerful and sustained system of propaganda in human history and its cumulative effects, unless quickly checked, will be responsible for destroying the world as we know it.” Jhally argues that the advertising industry, in fostering an association between human aspiration and desire for consumable goods, creates an artificial demand for such goods that is, at once, far in excess of (...) what is needed for human flourishing and catastrophic to the global environment. Jhally sees capitalism as the ultimate culprit. In a system in which wealth is defined as a “vast collection of commodities” (Marx, Capital), those who produce such commodities have no other choice but to promote excess consumption. Hence the advertising industry emerges as the propaganda arm of capitalism. My paper argues that, though Jhally’s analysis of the problem is both compelling and alarming, his diagnosis fails to reach its heart. Indeed, it is not Marx but Plato who provides us with the terms needed both to understand and respond to the problem Jhally cites. My paper provides a Platonic analysis of these issues and concludes with some suggestions as to how to address them. (shrink)

One of the ways in which Plato has captured the popular imagination is with the claim that the philosopher can feel erôs, passionate love, for the objects of knowledge. Why should Plato make this claim? In this chapter, I explore Plato’s treatment of philosophical erôs along three dimensions. First, I consider the source of philosophical erôs. I argue that it is grounded in our mortality and imperfection, which give rise to a desire for immortality and the immortal. Second, I turn (...) to the object of philosophical erôs. I suggest that it is an arresting response to beauty, through which we come to value the ideal properties of the forms. Finally, I address the nature of erôs. I claim that it is a focusing desire, that overrides other concerns and causes us to overwhelmingly focus on its object. I conclude the chapter by considering the problem Vlastos famously raises for Plato’s account of erôs: can it do justice to disinterested, interpersonal love? In agreement with Vlastos, I claim that one who comes to grasp the forms will cease to feel interpersonal love; however, I also suggest that erôs can give rise to philia, beneficent concern with the wellbeing of others. (shrink)

The paper proposes (1.) a non-standard interpretation of the proverbial expression “deuteros plous” by giving a fresh look to Phaedo, 99c9-d1. Then (2.) it proceeds to the philosophical problem raised in this passage according to this interpretation, that is, the problem of the “hypothesis” or the “unproved principle”. It indicates finally (3.) the kernel of truth contained in the standard Interpretation and it concludes with some remarks on the “weakness of the logoi”.

This is a revised short overview of Plato’s “greatest thing to be learned” or the “greatest lesson” (megiston mathêma) – the Idea of the Good.

The so-called Final Ranking of the Philebus offers Socrates’ final evaluation of the relative merits of pleasure and reason in the best life. I begin by examining two common lines of interpretation as they address the criterion according to which the final ranking is organized. I then discuss the role ‘similarity’ has in organizing the investigation throughout the dialogue, from the initial comparison of the two lives (of reason and pleasure singly) down through the final ranking. I then consider the (...) thematic discussions of pleasure and reason separately, arguing that their treatments display an intriguing structural similarity. Next, I propose my own reading of the final ranking, whereby the ‘dependence’ relation at work in those two specific discussions may be see as the through-line of all (now five) tiers of the final ranking. I conclude by suggesting that this interpretation is able to preserve what is worthwhile in the two traditional lines of interpretation, while avoiding the pitfalls that tend to accompany them. (shrink)

This paper examines how Plato’s rejection of the friends of the forms at 248a–249b in the Sophist is continuous with the arguments that he develops shortly after this part of the dialogue for the interrelatedness of the forms. I claim that the interrelatedness of the forms implies that they are changed, and that this explains Plato’s rejection of the friends of the forms. Much here turns on the kind of change that Plato wants to attribute to the forms. I distinguish (...) my view of the sort of change that the forms experience from other kinds of change—such as ‘Cambridge change’—that scholars have believed Plato has in mind in rejecting the friends of the forms. On the view that I advance, a form experiences a change (which I call ‘perfect change’) in its association with another form that distinguishes it as the distinctive being that it is—that is, through its possession of its distinctive properties. (shrink)

Plato often depicts Socrates inquiring together with an interlocutor into a thing/concept by trying to answer the “What is it?” question about that thing/concept. This typically involves Socrates requesting that his discussion partner answer the question, and usually ends in failure. There are, however, instances in which Socrates provides the sort of answer, in relation to a more familiar thing/concept, that he would like to receive in relation to a more obscure thing/concept, thus furnishing his interlocutor with an example of (...) how he would like him to answer. This chapter considers this dialectical tool by focusing on three instances of its use (Meno 73e3–76e4; Laches 191e9–192b3; Theaetetus 146e7–147c6). It argues, first, that in these instances Socrates provides true and adequate definitions of the things/concepts in question. It further argues that dialectic, for Plato, is just as much about the essences everyday things/concepts as it is about the essences of more obscure things/concepts; and that it is just as much about the meanings of the words we use to designate things, as it is about the essences of those things. (shrink)

The third deduction in Plato’s Parmenides is often given a constructive reading on which Plato’s Parmenides, or even Plato himself, presents us with a positive account of the relation between parts and wholes. However, I argue that there is a hitch in the third deduction which threatens to undermine the mereology of the third deduction by the lights of the dialogue. Roughly, even if the Others partake of the One, the account of the third deduction leads to an ontology of (...) gunk, that is, an ontology on which there are no mereological atoms (except for the One). Hence, it is unclear whether the participation relation between the Others and the One is sufficient to impose the sort of structure on the Others which, in the context of this deduction, Parmenides (or Plato) seems to hope for. Instead of the constructive reading of the third deduction, I therefore offer an aporetic reading on which the third deduction raises further difficulties for the participation relation at the heart of young Socrates’ theory of Forms. (shrink)

As Socrates recounts his search for causes (aitiai) in the Phaedo, he identifies the following as genuine causes: intelligence (nous), seeming best, choice of the best, and the forms. I argue that these causes should be understood as norms prescribing the conditions their effects must meet if those effects are to be produced. Thus, my account both explains what Socrates’ causes are and the way in which they cause what they cause.

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 paper deals with the deuteros plous, literally ‘the second voyage’, proverbially ‘the next best way’, discussed in Plato’s Phaedo, the key passage being Phd. 99e4-100a3. I argue that (a) the ‘flight into the logoi’ can have two different interpretations, a standard one and a non-standard one. The issue is whether at 99e-100a Socrates means that both the student of erga and the student of logoi consider images (‘the standard interpretation’), or the student of logoi does not consider images but (...) that “consistency should suffice for truth” (‘the non-standard interpretation’); (b) the non-standard one implies the problem of the hypothesis, a problem analogous to the problem of the elenchus; (c) there is a structural analogy between Descartes’ ontological argument for the existence of God in his 5th Meditation and the final proof for the immortality of the soul in the Phaedo. (shrink)

This paper aims to argue for, else illustrate the epistemological significance of the use of non transitive similarity relations, mapping only to "types", as methodologically being on a par with the use of transitive similarity relations (equivalence relations), mapping as well to "predicates". -/- In this paper the sketch of an exact but simple geometrical model of the above construct is followed by mentioning respective use cases for non transitive similarity relations from science and humanities. A well known metaphysics example (...) is elaborated along these lines to some extent. (shrink)

Empleando procedimientos de la lógica simbólica, se intenta contribuir a una mejor comprensión del ejercicio dialéctico llevado a cabo en el Parménides. La interpretación de las formas del ser y el no ser a partir de la oposición entre el objeto de conocimiento y el pensamiento acerca del mismo, abre la puerta a una manera original de enfocar el problema de la verdad en Platón. Puede resultar interesante, asimismo, la solución que se propone a la aporía planteada en Parménides 132b-c, (...) relativa a la confusión del pensamiento o el no ser con otras formas. (shrink)

In this article I seek to come to some understanding of the interlocutors in the first book of Plato’s Republic, particularly Cephalus. A more complete view of Cephalus not only provides some interesting ways to think about Plato and the Republic, but also suggests an interesting alternative to Plato’s view of justice. The article will progress as follows: First, I discuss Plato’s allegory of the cave. I, then, critique the cave allegory by applying the same kind of reasoning that O. (...) K. Bouwsma used to criticize Descartes’ evil genius. Next, I present what I think is a fruitful way to understand Cephalus. Finally, I draw some important conclusions regarding justice and offer some interesting critiques of Plato and Platonism. (shrink)

Conceptualism—the view that universals are mental entities without an external, independent, or substantial reality—has enjoyed popularity at various points throughout the history of philosophy. While Plato’s Theory of Forms is not a conceptualist theory of universals, we find at Parmenides 132b–c the startling conceptualist suggestion from a young Socrates that each Form might be a noēma, or a mental entity. This suggestion and Parmenides’ cryptic objections to it have been overshadowed by their placement directly after the notoriously difficult Third Man (...) Argument, and before the Likeness Regress. However, in the background of 132b–c, we find illuminating assumptions behind Parmenides’ arguments against the Theory of Forms in the first half of the dialogue. We also find in this text a set of implied criteria for Platonic concepthood. While in the Platonic corpus, Forms are explanantia for many of the phenomena explained by concepts in contemporary philosophy, concepts do seem to have an important epistemic role in Plato’s philosophy. An account of Platonic concepthood therefore opens the door for new ways of understanding the Platonic corpus as a whole. My focus in this paper is to uncover these assumptions and criteria through a close reading of Socrates’ conceptualist suggestion and Parmenides’ truncated objections to it at Parmenides 132b–c. (shrink)

This paper compares two influential but conflicting contemporary models of politics as an activity: those of Hannah Arendt and Alain Badiou. It discovers the fundamental difference between their approaches to politics in their opposing evaluations of the contemporary political significance of the legacy of Plato, Platonism, and the Platonic Idea. Karl Popper’s and Arendt’s analyses of the inherently ideological nature of totalitarianism are contrasted with Badiou’s vindication of an ideological “politics of the Idea.” Arendt and Badiou are shown to share (...) an understanding of politics as a realm for the human deployment of novelty and world-transformation. Their key disagreement concerns the form of activity that accomplishes this deployment. For Arendt, political activity has the basic form of noninstrumental and nonteleological action (praxis), devalued by the Platonic tradition of political philosophy. Badiou, by contrast, follows Plato in regarding politics essentially as a process of production (poiēsis) oriented to an ideal end. (shrink)

This paper provides a rational reconstruction of a Platonic trope bundle theory that is a live alternative to contemporary bundle theories. According to the theory, Platonic particulars are composed of what Plato calls images of Forms; contemporary metaphysicians call these tropes. Tropes are dependent on Forms and the Receptacle, while trope bundles are structured by natural kinds using the Phaedo's principles of inclusion and exclusion and the Timaeus’ geometrised elements, as well as by co-location in the Receptacle. Key elements of (...) discussion include persistence and abundance of Plato's tropes. The resulting theory is compared with contemporary trope bundle theories. (shrink)

Augustine’s accounts of his so-called mystical experiences in conf. 7.10.16, 17.23, and 9.10.24 are puzzling. The primary problem is that, although in all three accounts he claims to have seen “that which is,” we have no satisfactory account of what “that which is” is supposed to be. I shall be arguing that, contrary to a common interpretation, Augustine’s intellectual “seeing” of “being” in Books 7 and 9 was not a vision of the Christian God as a whole, nor of one (...) of the divine persons, each of whom is equally God, according to Augustine. This becomes clear when we attend to the fact that Augustine is appropriating a specific meaning of “that which is” or “being” used by Plotinus in his account of the lover of Beauty. This resolution, however, leads to a second question. Is there anything distinctively Christian about any, or all, of Augustine’s ascents? On the one hand, it would be odd if there were not, given that the Confessions are addressed to the Christian God. On the other hand, upon close inspection we find that the allegedly specific “Christian” characteristics that modern commentators have identified in the ascents of conf. 7 and 9 also occur in the Neoplatonists. I will argue that there is in fact one important difference between Augustine and the Neoplatonists here that has not been pointed out in these prior interpretations. (shrink)

In this paper, our intention is to present the main aspects of the understanding of the logos in Philo of Alexandria. Philo’s reception of this notion is especially important because his insights significantly influenced the development of patristic philosophy, and these influences, through the mediation of scholasticism, reached the modern age. Philo has a very important role in creating the Judeo-Christian heritage, and represents an important link for understanding the formation of the basic matrices of this worldview. For the first (...) time, a thorough synthesis of Semitic and Hellenic heritage was performed with him. The use of the term logos in that synthesis proves to be one of the key ones, since it is precisely this term, which has never lost its philosophical significance, partly and thanks to Philo, that is identified with the Son of God of the Christian tradition. (shrink)

This article defends three claims. First, that collection and division in the Phaedrus are described as procedures that underlie human speaking and thinking in general, as well as philosophical inquiry, and are not identified with either. Second, that what sets the dialectical use of these procedures apart from their ordinary use are philosophical suppositions independent of the procedures of collection and division themselves; for that reason, collection and division cannot be identified with dialectic as such. Third, that the second part (...) of the Phaedrus is concerned with the broader question how noble or beautiful speaking, in general, may be said to depend on dialectic as much as it is concerned with the question how rhetoric, as a kind of expertise, is related to dialectic. (shrink)

Plato’s Sophist and Statesman stand out from many other Platonic dialogues by at least two features. First, they do not raise a ti esti question about a single virtue or feature of something, but raise the questions what sophist, statesman, and philosopher are, how they differ from each other, and what worth each should be accorded. Second, a visitor from Elea, rather than Socrates, seeks to addressed these questions and does so by employing what is commonly referred to as the (...) method of collection and division. Some scholars have argued that this so-called method is value neutral and therefore unable to address the question how philosophy differs from sophistry and statesmanship according to worth. This article contends that the procedures of collection and division does not preclude the visitor from taking considerations of worth into account, but rather helps establish an objective basis for settling the main questions of the dialogue. (shrink)

In this paper, I argue that Plato's views on Forms play a central role in his educational philosophy. In response to what certain commentators have recently written, I contend that this interpretation not only is accurate but also is advantageous because of how it can help philosophy of education. I also address the view, proposed by one philosopher of education, that Plato believes that the most valuable sort of knowledge cannot be fully expressed in words and that the objects of (...) this knowledge are something other than transcendent Forms. Preferable to that view, I argue, is the idea that Plato wants knowledge of Forms which is nonrepresentational. (shrink)

In this work I propose a theory of evolution as a process of unfolding. This theory is based on four logically concatenated principles. The principle of evolutionary order establishes that the more complex cannot be generated from the simpler. The principle of origin establishes that there must be a maximum complexity that originates the others by logical deduction. Finally, the principle of unfolding and the principle of actualization guarantee the development of the evolutionary process from the simplest to the most (...) complex. These logical principles determine the existence of a virtual ideological matrix that contains the sequence of the preformed and folded morphogenetic fields. In this manner, the evolutionary process consists of the sequential unfolding and actualization of these fields, which is motorized by a process of teleologization carried out by the opening consciousness of the forms included in the fields of the ideological matrix. This theory leads to a radical change of perspective regarding the materialist worldview, and places life at the center of the evolutionary process as an activity carried out by a consciousness that seeks to fulfill a purpose by actualizing its own potentialities. (shrink)

The article treats again the question of whether «the Idea of the Good is a Reality in the Universe, or beyond it. Is it immanent or transcendent ?» (Rufus Jones, 1863 1948). Plato scholars such as Matthias Baltes (1940 2003) and Luc Brisson have defended the thesis that Plato’s Idea of the Good is, on the one hand, beyond being (epekeina tês ousias) in dignity and power, but on the other, is nevertheless not transcendent over being. The article delivers first (...) (I.) the most important arguments for the thesis of Baltes and Brisson. Then (II.), it gives two counterarguments against the thesis. Third (III.), it concludes with some general questions concerning the deflationist interpretation of Plato’s Republic 509b9 10 and defends again the transcendence of the Idea of the Good. (shrink)

The paper analyzes the final proof with Greek mathematics and the possibility of intermediates in the Phaedo. The final proof in Plato’s Phaedo depends on a claim at 105c6, that μονάς, ‘unit’, generates περιττός ‘odd’ in number. So, ψυχή ‘soul’ generates ζωή ‘life’ in a body, at 105c10-11. Yet commentators disagree how to understand these mathematical terms and their relation to the soul in Plato’s arguments. The Greek mathematicians understood odd numbers in one of two ways: either that which is (...) not divisible into two equal parts, or that which differs from an even number by a unit. Plato uses the second way in the final proof. This paper argues that a proper understanding of these mathematical terms within Greek mathematics shows that the argument for the final proof is better than previously thought. Such an interpretation of the final proof lends credence to Platonic intermediates. (shrink)

This is a study of the correspondence between Forms and particulars in Plato. The aim is to determine whether they exhibit an ontological symmetry, in other words, whether there is always one where there is the other. This points to two questions, one on the existence of things that do not have corresponding Forms, the other on the existence of Forms that do not have corresponding things. Both questions have come up before. But the answers have not been sufficiently sensitive (...) to the intricacies of the questions. Nor have they been adequately resourceful with what little evidence there is in the original sources. The intention here is to make up for that deficiency, not just with better answers but also with better insight into the questions. (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)

The article again treats the question of whether ≪the Idea of the Good is a Reality in the Universe, or beyond it. Is it immanent or transcendent?≫. Plato scholars such as Matthias Baltes and Luc Brisson have defended the thesis that Plato’s Idea of the Good is, on the one hand, beyond being in dignity and power, but, on the other, is nevertheless not transcendent over being. The article delivers first the most important arguments for the thesis of Baltes and (...) Brisson. Then, it gives two counterarguments against the thesis. Third, it concludes with some general questions concerning the deflationist interpretation of Plato’s Republic 509b9‑10, and defends again the transcendence of the Idea of the Good. (shrink)

What distinguishes the Socrates of the early from the Socrates of the middle dialogues? According to a well-known opinion, the “dividing line” lies in the difference between the Socratic and the Platonic theory of action. Whereas for the Platonic Socrates of the early dialogues, all desires are good-dependent, for the Platonic Socrates of the middle dialogues, there are good-independent desires. The paper argues first that this “dividing line” is blurred in the "Symposium", and second that we have in the "Symposium" (...) a more distinctive dividing line, namely the introduction of the separate existence of the idea of beauty. This introduction by Diotima/Plato of separate ideas and the lack of understanding of separate ideas – here the idea of beauty – by Socrates may have been the limit not only of the Socrates of the early Platonic dialogues, but of the historical Socrates as well. (shrink)

Y a-t-il des Idées et peut-on démontrer qu’elles existent ? Parmi les protagonistes anciens de la controverse qui a opposé partisans et adversaires des Idées, Aristote mérite une attention toute particulière. De fait, si – au moment où Aristote intervient dans le débat autour de l’hypothèse des Idées – ce débat a déjà une histoire, c’est avec lui que cette histoire atteint une maturité qui est à la fois d’ordre doctrinal et doxographique. De fait, non seulement Aristote est le premier (...) à avoir défini certaines au moins des propriétés de ce qui est et se dit en commun de plusieurs, mais encore a-t-il pris soin d’inscrire ces définitions dans la continuité de l’héritage socratique dont il s’est explicitement revendiqué tout en dénonçant sa dérive aux mains des successeurs de Socrate. L’objectif principal du cycle de conférences a été d’étudier les objections qu’Aristote a formulées à l’encontre des partisans des Idées en prenant comme fil conducteur la notion de substance que sa discussion des Formes platoniciennes tantôt présuppose, tantôt mobilise explicitement. Pour ce faire, nous avons procédé à une lecture détaillée d’un certain nombre de documents, tirés aussi bien de ses écrits d’école que des vestiges de ses traités perdus, où Aristote rejette la notion d’un universel substantiel (autant dire, en l’occurrence, séparé) et s’efforce de mettre à mal les arguments que ses partisans avançaient pour prouver son existence. (shrink)

Many assume that Plato's Form of the Good is a final cause. This might be true if one assumes an Aristotelian definition of final cause; however, I argue that if one adopts Plato's conception of final causation as evidenced in the Phaedo and Timaeus, the claim that the Form of the Good is a final cause for Plato is untenable.

A commentary on "Philebus" of PLato.

The essay consists in the analysis of the problem of the evil in the man and in the analysis of the remedies which the man can find against the evil. Plato affirms the presence of an active principle of evil in the soul of every man, which coincides with some instincts of the appetitive soul; the opposite principle to the evil is the reason, which needs, though, a correct education in order to be able to fight efficiently against the evil (...) in us. The man can be seen as a battle field of these opposite forces. Plato describes the presence of the evil in us in some passages of Republic Book 9, where he compares the appetitive part of the soul with a monster. The destiny of every person in her earthly existence consists in the continuing control of the appetitive part of the soul, if the status of ethical education is to be reached and maintained. The man who remains in the realm of the opinion, that is, in the realm of the doxa is an individual who only disposes of unstable opinions and who as a consequence do not have authentic remedies against the appetitive part. On the contrary, the individual who can ascend to the realm of being through the hard education represented by arithmetic, geometry, stereometry, astronomy, harmony and, finally, dialectic is really able to contrast the force of the evil within the individual. Ethics is really possible only through the complete education which passes through these disciplines: the more the individuals is theoretically educated, the more the individual is ethically educated. The knowledge of ideas is the only authentic therapy against the evil in us. (shrink)

Plato is commonly considered a metaphysical dualist conceiving of a world of Forms separate from the world of particulars in which we live. This paper explores the motivation for postulating that second world as opposed to making do with the one we have. The main objective is to demonstrate that and how everything, Forms and all, can instead fit into the same world. The approach is exploratory, as there can be no proof in the standard sense. The debate between explaining (...) Plato’s ontology with a single world and requiring a two-world model to make sense of the same thing is typically about scouring the Platonic corpus for evidence and turning to Aristotle for help where we need it. The aim here is to dig deeper than what either of them, or anyone else, has said or implied about the number or worlds, searching instead for any insight that might be gained from the way Forms are supposed to exist versus what we ourselves might understand by existence. Although the paper is, at its most basic level, about the existence of the Forms, the intention is not to prove that they exist, nor to evaluate the proofs and objections already on record, but to consider how they might exist and what follows if they do. Dialogue toward consensus on why we think the Forms exist, and why we think they do not, could perhaps provide a smoother “second sailing” in waters where we have been unable to agree whether they do and where they would if they did. (shrink)

The paper argues that Motion and Rest are “greatest kinds” and not just convenient examples, since they are all-pervading. Thus Motion and Rest can be jointly predicated of a single subject and can be predicated of each other, just as Sameness and Otherness can. While Sameness and Otherness are opposites, a single subject may be the same in one respect, namely, the same as itself, and other in another respect, namely, other than other things. Thus they can be predicated of (...) a single subject, and they can be predicated of each other, as well, since Sameness is other than other things and Otherness is the same as itself. The same explanation applies to Motion and Rest, as the paper demonstrates: a given subject may be in motion in one respect while being at rest in another respect. This distinction is made in the Sophist itself, right in the passage concerning the greatest kinds. Thus Motion and Rest should be considered greatest kinds on par with Being, Sameness, and Otherness, and each of these kinds pervades all other kinds. (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)

The article tries to prove that the famous formula "epekeina tês ousias" has to be understood in the sense of being beyond being and not only in the sense of being beyond essence. We make hereby three points: first, since pure textual exegesis of 509b8–10 seems to lead to endless controversy, a formal proof for the metaontological interpretation could be helpful to settle the issue; we try to give such a proof. Second, we offer a corollary of the formal proof, (...) showing that not only self-predication of the form of the Good, but of any form is not possible, that is: no form of F has the form of F. Third, we apply Spinoza’s distinction between an ens imaginarium and a chimaera to Plato’s Idea of the Good. (shrink)

This paper is a critical evaluation of Holger Thesleff’s thinking on Plato’s Forms, especially of his “rethinking” of the matter, as he puts it in the title of his most recent contribution. It lays out a broadly sympathetic perspective through dialectical engagement with the main lines of his interpretation and reconstruction of Plato’s world. The aim is to launch the formal academic reception of that reconstruction (rethinking), which Thesleff cautiously and modestly presents as a “proposal” — his teaser to elicit (...) a reaction, positive or negative. The exegetical focus is on tracing the inspiration and reasoning behind his “two-level” model of Plato’s ontology, which, in turn, supports his tripartite classification of Forms. The critical focus is on identifying potential areas of misunderstanding and supplying any explanations, analyses, or arguments that may enhance the clarity of the respective positions. (shrink)

Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic treatment of concrete universals (...) along with a new concept to abstractly model the functions of a brain. (shrink)

Few arguments from the past have stirred up as much interest as Aristotle’s “Third man” and not so many texts have received as much attention as its account in chapter 22 of the Sophistici elenchi. And yet, several issues about both remain highly controversial, starting from the very nature of the argument at stake and the exact signification of some of its features. The essay provides a close commentary of the text, dealing with its main difficulties and suggesting an overall (...) interpretation of Aristotle’s discussion of the “Third Man” argument. (shrink)

This is a proposal for rethinking the main lines of Plato’s philosophy, including some of the conceptual tools he uses for building and maintaining it. Drawing on a new interpretive paradigm for Plato’s overall vision, the central focus is on the so-called Forms. Regarding the guiding paradigm, we propose replacing the dualism of a world of Forms separated from a world of particulars, with the monistic model of a hierarchically structured universe comprising interdependent levels of reality. Regarding the tools of (...) the trade, we distinguish between three constructs that have come, one and all, and largely indiscriminately, to be regarded as Forms: Ideal Forms, Conceptual Forms, and Relational Forms. This recalibration of what we know of Plato’s outlook, tools, and methods, together with a realignment of these with his general aims, will also help restore the philosopher’s emphasis on that which is good, a perspective often blurred in the structure of two worlds. (shrink)

It is argued that the analysis by which the gene are differentiated in the dialogue is an exercise in studied ambiguities informed by an Eleatic logic of strict dichotomy that was the underpinning of the Sophist's method of division. By this dialectical drill, Plato shows that the metaphysics underlying the Visitor's method fails to adequately distinguish what it means to have a character from what it means to be a character, and therefore remains inadequate to track down the sophist or (...) to distinguish him from the philosopher: Eleaticism, as critically examined by Plato, proves to be means to disguise, not to discover the sophist. (shrink)