Truth of x (independently of any description of x) that it is f. A property f which holds of x but is not per se of x is said to hold per accidens of x. The essence of an individual is the sum of its per se properties. We can formulate the following: doctrine a: concrete individuals do not have essences though abstract entities do. Doctrine b: concrete individuals have essences but they do not individuate, whereas abstract entities have essences (...) which do individuate. Assumption i: we shall say that a thing exists insofar as it has an essence. Assumption ii: we shall say that we know a thing when we know what its per se properties are. We argue that plato held doctrine a and aristotle doctrine b (with assumptions i and ii). (edited). (shrink)

In (1991), Meinwald initiated a major change of direction in the study of Plato’s Parmenides and the Third Man Argument. On her conception of the Parmenides , Plato’s language systematically distinguishes two types or kinds of predication, namely, predications of the kind ‘x is F pros ta alla’ and ‘x is F pros heauto’. Intuitively speaking, the former is the common, everyday variety of predication, which holds when x is any object (perceptible object or Form) and F is a property (...) which x exemplifies or instantiates in the traditional sense. The latter is a special mode of predication which holds when x is a Form and F is a property which is, in some sense, part of the nature of that Form. Meinwald (1991, p. 75, footnote 18) traces the discovery of this distinction in Plato’s work to Frede (1967), who marks the distinction between pros allo and kath’ hauto predications by placing subscripts on the copula ‘is’. (shrink)

A discussão nos livros dos Tópicos giram em torno dos debates dialéticos e seus elementos. Aristóteles discorre sobre os gêneros, as propriedades e os chamados acidentes e suas relações predicativas em categorias. Interessa-nos, sobretudo, compreender o papel desempenhado pela Definição e qual sua relação com os demais instrumentos para a dialética.

Investigating Plato’s ontological as well as epistemological status in each of his dialogues, this book is going to challenge the current theories of Plato’s development and suggest a new one. Regarding the relation of Plato’s early and middle period dialogues, scholars have been divided to two opposing groups: unitarists and developmentalists. While developmentalists try to prove that there are some noticeable and even fundamental differences between Plato’s early and middle period dialogues, the unitarists assert that there is no essential difference (...) in there. The main goal of the first two chapters is to suggest that some of Plato’s ontological as well as epistemological principles change, both radically and fundamentally, between the early and middle period dialogues. Though this is a kind of strengthening the developmentalistic approach corresponding the relation of the early and middle period dialogues, based on the fact that what is to be proved here is a essential development in Plato’ ontology and his epistemology, by expanding the grounds of development to the ontological and epistemological principles, it hints to a more profound development. The fact that the bipolar and split knowledge and being of the early period dialogues give way to the tripartite and bound knowledge and benig of the middle period dialogues indicates the development of the notions of being and knowledge in Plato’s philosophy before the dialogues of the middle period. The first chapter entitled “Plato’s Onto-Epistemological Principles in the Early Dialogues” tries to draw out six principles out of Plato’s early dialogues specially Euthyphro, Laches, Charmides, Hippias Major and Euthydemus. We discuss that these principles present kind of a bipolar as well as split ontology and epistemology. The second chapter, “Revision of First Socrates’ Principles in the Middle Period Dialogues”, aims to argue that the onto-epistemological principles of the early dialogues are being radically changed in three dialogues of Meno, Phaedo and Republic in the middle period dialogues. Not only the bipolar ontology and epistemology of the early dialogues give place to a tripartite ontology and epistemology but also their split being and knowledge are inclined to be replaced by bound being and knowledge. Our next step in this book is to suggest a new approach to Plato’s theory of being in Republic V and Sophist based on the notion of difference and the being of a copy. To understand Plato’s ontology in these two dialogues we are going to suggest a theory we call Pollachos Esti; a name we took from Aristotle’s pollachos legetai both to remind the similarities of the two structures and to reach a consistent view of Plato’s ontology. Based on this theory, when Plato says that something both is and is not, he is applying difference on being which is interpreted here as saying, borrowing Aristotle’s terminology, 'is is (esti) in different senses'. I hope this paper can show how Pollachos Esti can bring forth not only a new approach to Plato’s ontology in Sophist and Republic but also a different approach to being in general. Thence, chapter three, “Pollachos Esti; Plato’s Ontology in Sophist and Republic”, intends to discuss that i) the theories of ‘being as difference’ and ‘being of a copy’, considered together in what we call the theory of pollachos esti, can well be compared to the structure of pollachos legetai in Aristotle when it is attached to the theories of pros hen and substance; and ii) the ontology of Republic V-VII is based on this theory and is, thus, almost the same as the ontology of Sophist. Investigating the most famous chronologies of the last 150 years from Campbell on, the fourth chapter, “The Standard Chronology of the Dialogues”, is to argue that all of them have a somewhat fix and dogmatic arrangement of Plato’s dialogues in which Meno, Phaedo and Republic are located after some early dialogues and before Theaetetus and Parmenides, on the one hand, and all the so-called late period dialogues after Theaetetus and Parmenides on the other hand. It is also reminded that all that the stylometric evidences can show is the lateness and homogeneity of the late period dialogues and, thence, nothing about the relation between dialogues like Theaetetus, Parmenides and Republic. The standard chronology is the subject of many criticisms some of which are discussed in our fifth chapter, “Objections against the Standard Chronology”, in three groups. While the first group of objections criticizes the place of the middle period dialogues immediately after the early ones, the second group attacks the place of late dialogues after the middle ones. The third group includes objections against the place of Parmenides in the standard chronology and tries to show that it cannot be considered after the middle period dialogues. The efforts of the first five chapters lead to a new theory of Plato’s ontological as well as epistemological development in an onto-epistemological chronology of his dialogues in our sixth chapter, “An Onto-Epistemological Chronology of Plato’s dialogues”. Instead of three periods, this chronology includes four waves of dialogues, Socratic wave, ontological wave, epistemological wave and political wave, in which all the so-called middle and late period dialogues are to be interpreted based on the problems presented in Parmenides I. The main changes we suggest in the standard chronology include firstly that Theaetetus and Parmenides I must be posited before Meno and Phaedo and, secondly, Republic must be posited after Sophist. Based on this arrangement, we can find Philosophos, Plato’s promised but unwritten dialogue, inside Republic. (shrink)

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)

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)

Several difficulties that accompany Plato's theory of Forms have received considerable attention in the philosophical literature in the past half century. A great deal of discussion and controversy surrounds the dialogue Parmenides and the group of considerations commonly called the “Third Man Argument”. Our purpose here is to strike out in one direction suggested by this passage, but it can in no way be thought of as an exegesis nor a logical elucidation of the “Third Man Argument” itself. While what (...) we shall say here has an obvious affinity and connection with the Parmenides passage, the two principal questions that concern us here are of a more general nature than the specific points in the Parmenides. The first is whether Plato's theory of Forms involves a regress which is ruinous to the theory. The second is, if a self-destructive regress is a necessary consequence of the theory, what elements of Plato's theory make the regress inescapable. (shrink)

Aristotle formulates in _Metaphysics_ M.9 an aporia about Forms, according to which, those who introduce Forms make them universal substances and, at the same time, separate entities and, hence, particulars. But, he claims, it is not possible that both attributes, being a universal and being a particular, inhere in the same thing. The interpretation that scholars have offered of this objection is external, in that they hold that it derives from Aristotle’s own conception of separation: only what is particular is (...) separate. Here I defend an internal interpretation which claims that the objection derives from an assumption about the explanatory role of Forms that Aristotle attributes to the Platonists. (shrink)

I discuss Aristotle’s opening argument against Platonic Forms in _Metaphysics_ A.9, ‘the Razor’, which criticizes the introduction of Forms on the basis of an analogy with a hypothetical case of counting things. I argue for a new interpretation of this argument, and show that it involves two interesting objections against the introduction of Forms as formal causes: one concerns the completeness and the other the adequacy of such an explanatory project.

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical theory of categories, (...) dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also 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. (shrink)

Contrary to the common interpretation of Platonic art that supports the view that it is ontologically and gnoseologically irrelevant because it is mainly defined by mimetic concept as a mere imitation of the material world, and is therefore banished from the Republic, we will offer some different interpretations. Namely, it is possible to show that mimetic principle is not the reason why Plato condemns art, and that the notion of artistic mimesis in fact stems from the metaphysical notion of mimesis (...) as approximation or gradual resemblance to the paradigm. In this case artistic mimesis achieves higher ontological authenticity and imitates the ideal by means of the sensory. Parmenides’ “resemblance argument” may constitute a serious obstacle for the acceptance of, on the one hand, the idea of the relation of resemblance between Forms and particulars, that is between the paradigm and its image, and on the other hand it may question the idea of approximation in which mimetic principle has metaphysical foundation. However, when Form is seen as a synthetic unity of many things, it then represents the right standpoint for the explanation of the phenomena, and it becomes questionable when it is placed on the same level with its exemplars. If the relation of resemblance between the paradigm and its image is determined by the “dynamic”, and not by “symmetric resemblance” in which both parts are on the same level of ontological authenticity, then the view of philosophical mimesis as approximation on which relies artistic mimetic concept is legitimate. (shrink)

This chapter discusses the first part of Aristotle's Posterior Analytics A-33, 88b30-89a10. I claim that Aristotle is not concerned with an epistemological distinction between knowledge and belief in general. He is rather making a contrast between scientific knowledge (which is equivalent to explanation by the primarily appropriate cause) and some explanatory beliefs that falls short of capturing the primarily appropriate cause.

In Republic V, Plato distinguishes two different cognitive powers, knowledge and belief, which operate differently on different types of object. I argue that in Republic VI Plato modifies this account, and claims that there is a single cognitive power, which under different circumstances behaves either as knowledge or as belief. I show that the circumstances which turn true belief into knowledge are the provision of an individuation account of the object of belief, which reveals the ontological status and the nature (...) of the object. Plato explores many alternative candidates of individuation accounts of objects of true belief, which he discards. I conclude with a Platonic sketch of a teleological account of individuation which would satisfy his requirements of turning true belief into knowledge. (shrink)

Dramatic changes or revolutions in a field of science are often made by outsiders or 'trespassers,' who are not limited by the established, 'expert' approaches. Each essay in this diverse collection shows the fruits of intellectual trespassing and poaching among fields such as economics, Kantian ethics, Platonic philosophy, category theory, double-entry accounting, arbitrage, algebraic logic, series-parallel duality, and financial arithmetic.

Przedmiotem artykułu jest paradoks Zenona z Elei Korzec prosa. Wszystkie zachowane argumenty Zenona znane są z przekazów filozofów późniejszych. Korzec prosa jest zdawkowo przedstawiony przez Arystotelesa w Fizyce oraz znajduje się w Komentarzu do „Fizyki” Arystotelesa autorstwa Simplikiosa. Obydwa fragmenty, które stanowią przedmiot rozważań, zawierają częściowo odmienną terminologię oraz występują w nich rozumowania, oparte na innych schematach wnioskowania. Celem analiz zawartych w tekście jest uzasadnienie, że fragment z Fizyki Arystotelesa może sytuować omawiany paradoks jako argument przeciw ruchowi, a nie jako (...) argument przeciw wielości, jak przedstawia się go zazwyczaj w świetle przekazu Simplikiosa. W artykule zostały przedstawione obydwa fragmenty w języku greckim wraz z autorskimi tłumaczeniami oraz szczegółową analizą ich treści. -------------- Zgłoszono: 28/09/2020. Zrecenzowano: 30/10/2020. Zaakceptowano do publikacji: 18/11/2020. (shrink)

En este trabajo realizo un examen crítico del reciente libro de Silvana Gabriela Di Camillo sobre la crítica de Aristóteles a la teoría platónica de las Ideas. El libro de Di Camillo es un trabajo muy serio cuya lectura recomiendo ampliamente. Sin embargo, considero que cuatro de las principales tesis que la autora defiende tienen varias dificultades y mi objetivo aquí es presentar argumentos detallados en contra de ellas: la interpretación de la distinción entre argumentos más y menos rigurosos del (...) tratado Sobre las Ideas; la tesis de que la separación es el blanco esencial de las críticas aristotélicas a las Ideas; la interpretación de las opciones que Platón tiene para responder al argumento del tercer hombre, y la tesis de que la separación de las Ideas debe entenderse como homonimia. In this paper I examine Silvana Gabriela Di Camillo's recent book on Aristotle's criticisms of Plato's theory of Ideas. Di Camillo's book is a very serious work that I highly recommend. Nevertheless, I consider that four of the main theses that the author defends face several difficulties and my aim here is to offer detailed arguments against them: the interpretation of the distinction between more and less accurate arguments of the treatise On Ideas; the thesis that separation is the essential target of Aristotle's criticisms against Plato's Ideas; the interpretation of the options available to Plato to reply to the third man argument; and the thesis that the separation of Ideas should be understood as homonymy. (shrink)

ABSTRACTCommentators have commonly noted the metaphysical role of participation in Richard Hooker’s Of the Lawes of Ecclesiastical Polity: participation both describes how creation is suspended from God and also how believers share in Christ through grace. Yet, the role in Hooker’s thought of the attendant Platonic language of ‘between’ and ‘desire’ has not received sustained attention. Metaxu describes the ‘in-between’ quality of participation: the participant and the participated remain distinct but are dynamically related as the former originates from and returns (...) to the perfection of the latter. Within this metaxological dynamic, desire acts as the physical and psychic motor driving the move between potentiality and perfect actuality, that is to say from multiplicity to divine unity: desire aims at goodness and so ultimately tends towards that which is goodness itself, namely God’s nature. For Hooker, desire becomes couched in amorous affectivity and has an erotic register. This essay explores, then, how Hooker appeals to a language of ‘between’ and ‘desire’ within his accounts of participation. First, it examines how human beings exist between the footstool and throne of God in Hooker’s legal ontology. Here, angelic desire acts as a hierarchical pattern of and spur to erotic participation in the divine nature. Second, this essay examines how theurgy transforms desire in Hooker’s account of liturgical participation as a redemptive commerce between heaven and earth. Here, angels still act as invisible, hierarchical intermediaries within earthly worship, but soon give way to immediate grace through participation in Christ within the sacraments. (shrink)