Structure and sense of the seventh deduction in Prm. 164b5-165e1

Φιλοσοφία, 2022

Books M and N of the Metaphysics, which form a unity, criticize Plato and the Academy and present Aristotle's views regarding the mathematical objects. In the major part of M 1 the structure of books M and N is presented. Then, starting from M 1, 1076a32, up to M 3, Aristotle deals with the existence of the mathematical objects. At the end of M 1, Aristotle mentions four possible cases regarding the existence of mathematical objects. As he mentions, mathematical objects either a) exist in sensible objects, or b) exist as separate in substance from the sensible objects, or c) they do not exist at all, or d) they exist in some other way. In M 2, he presents arguments against the first two of the aforementioned cases. At first, in lines 1076a38-1076b11, he presents two arguments against the first case. Then, starting from line 1076b11, he presents a series of arguments against the second case. After refuting those two cases regarding the existence of mathematical objects, he proceeds, in chapter M 3, to present his own theory which falls under the fourth case, namely that the objects of mathematics exist in some other way 1. In this paper I am going to discuss and offer an interpretation to the Aristotelian argument in lines 1076b36-39 from M 2, which targets the view that the objects of arithmetic exist as separate in substance from the sensible objects. Since this argument functions in the same way as the preceding one, in lines 1076b11-36, I am first going to, briefly, present this argument and then focus on the next argument in lines 1076a36-39. The argument in lines 1076b11-36 is from the case of geometry. There Aristotle attempts to show that the view, according to which geometrical objects exist as separate in substance from sensible objects, leads to some absurd consequences. What he argues is that, if we posit geometrical objects as separate

According to current interpretations of Parmenides, he either embraces a token-monism of things, or a type-monism of the nature of each kind of thing, or a generous monism, accepting a token-monism of things of a specific type, necessary being. These interpretations share a common flaw: they fail to secure commensurability between Parmenides' alētheia and doxa. We effect this by arguing that Parmenides champions a metaphysically refined form of material monism, a type-monism of things; that light and night are allomorphs of what-is (to eon); and that the key features of what-is are entailed by the theory of material monism.

PLATO JOURNAL

The fifth “deduction” in Plato’s Parmenides (160b5-163b6) concerns the consequences that follow for a (or the) one from the hypothesis that it is not. I argue that the subject of this hypothesis is, effectively, any Form, considered just insofar as it is one Form. The hypothesis, I further argue, does not concern any essential aspect of a Form, but rather posits its contingent non-instantation (“a one is not” = “a Form is not instantiated”). The motion this deduction attributes to its one is a special type of motion: motion into and out of instantiation.

Studies in the pre-judicative hermeneutics and meontology, 2023

The aim of this article is to explore the ontological difference within Parmenides's poem "Peri physeōs," with a specific focus on line B 2.3, which reads: "exists, and it is not possible not to exist" (estin te kai hōs ouk esti mē einai). By interpreting "ouk esti" as a negative judgment and "mē einai" as a negative predication, I argue that this line already conceals the essence of the ontological difference, insofar as being is not an entity, and entities are not-being. This interpretation draws on Plato's notion of negation and difference as discussed in "The Sophist," as well as on Kantian infinite judgment. The distinction between these two negations enables the development of the concept of a meontological difference between "non-being" and "non-entities," which lies at the core of the ontological difference between being and entities, and also illuminates Heidegger's pairing of Ereignis and Enteignis. Additionally, I argue that Heidegger's interpretation of Heraclitus in light of truth as alethēia relies on a similar double-negativity. Finally, I show the illuminating potential of examining the ontological difference in Parmenides by analyzing Heidegger's 1949 preface to the third edition of the treatise "On the Essence of Ground" (1929).

Ancient Philosophy (43,2), 2023

This article argues that the second part of the Parmenides (137-166) consists not only of the well-known logical structure which has been widely studied but also of a great variety of definitions of forms. My aim is to show how these definitions depend on a specific group of closely connected primary forms (i.e. same, different, part, whole). The definitions which Parmenides provides help Socrates overcome his failure in attempting to define forms in the first part of the dialogue. In the second part of the Parmenides (137c-166c), we can distinguish two different, yet intertwined, structural principles. The first principle, according to which the second part of the dialogue is structured, is the well-known and much disputed 'logical' one, which starts with the conditional 'if the One is', 'if the One is not'. On this level Parmenides investigates if different 'attributes' belong or do not belong to

Mélanges en l’honneur du Professeur Jean-Marc Trigeaud, 2020

In this article we reconsider Parmenides' Parricide, which is notoriously thought to have been accomplished by Plato, and show that is not based on strong reasons but on the alleged undeniability of experience. Instead we think that such undeniability is only formal, being based on an extrinsic denial which requires that which is denied. Moreover we show that those who oppose the unity of being, which is its absoluteness-as Parmenides maintains-, to the multiplicity of entities do not consider that they are not disposed on the same level, so that their opposition is untenable. Since the One (Being) and the Many (non-being) are on different levels, one can understand the level of being as emerging beyond the universe of determination (finite being), which is that which Parmenides identifies with non-being.

Plato Journal, 2021

The fifth "deduction" in Plato's Parmenides (160b5-163b6) concerns the consequences that follow for a (or the) one from the hypothesis that it is not. I argue that the subject of this hypothesis is, effectively, any Form, considered just insofar as it is one Form. The hypothesis, I further argue, does not concern any essential aspect of a Form, but rather posits its contingent non-instantation ("a one is not" = "a Form is not instantiated"). The motion this deduction attributes to its one is a special type of motion: motion into and out of instantiation.

Intensional Logic, History of Philosophy, and Methodology: to Imre Ruzsa on the Occasion of his 65th Birthday, 1988

Φιλοσοφια, 2019

The current idea of what Parmenides was, did, taught and wrote is presently subject (this at least is my claim) to a substantial reassessment, since the scholarly tradition is likely to have been (and still to be today) affected by the large scale adoption of some seriously misleading assumptions. Contrary to these assumptions, Parmenides is likely to have been very different from what this community seemingly continues to believe. For the «physical» doctrines are an indisputable fact, while the allusions to the brotōn doxai have been charged with a meaning they cannot have. A number of implications follow, and the matter has been argued within the limits of a paper while two books of mine, a larger and a shorter one, dealt with basically the same topics, and were printed quite recently (in 2020). One of them is entitled "Verso la filosofia: Nuove prospettive su Parmenide, Zenone e Melisso", while the other is "Parmenide e Zenone sophoi ad Elea".

Unisinos Journal of Philosophy, 2020