Plato’s Contest: Answering the Challenge of the Parmenides (original) (raw)
Related papers
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
Parmenides had identified speech and thought with Being itself, but could not explain the contrary opposition between Non-Being inscribed in every determination of Being. Heraclitus purported to explain this opposition as the coincidence of contrary opposite properties in all beings, but could not explain the possibility of non-contradictory knowledge of beings. Socrates answered that, by exposing and rejecting false definitions, we might come to know the definitions of all beings; and Plato individuated Parmenides’ Being into a plentitude of universal Ideas, each of which perfectly unites the thought and being of some predicate-property. Plato’s logic of Ideas may re-construct Aristotle’s syllogistic logic on the basis of universal Ideas of subject and predicate terms, which flow from universal Ideas to particular instances according to the higher-order Ideas of the laws of logic. This logic of Ideas is grounded, unlike Aristotle’s formal logic, in Plato’s ‘unwritten’ ontology: the original opposition of the One and the Dyad is mixed in the Triad to generate the numerical dyad, the Idea-numbers, and all complex mathematical and geometrical forms which comprise the World-Soul. This original opposition of the Dyad motivates the division of genera into many species, as well as the exclusion, opposition, and contradiction between the various assumptions of Socratic dialectic; even as the One unites these differences into ever richer triadic mixtures.
Plato’s “Third Man” Paradox : its Logic and History
Archives Internationales d'Histoire des Sciences, 2009
In Plato's Parmenides 132a-133b, the widely known Third Man Paradox is stated, which has special interest for the history of logical reasoning. It is important for philosophers because it is often thought to be a devastating argument to Plato's theory of Forms. Some philosophers have even viewed Aristotle's theory of predication and the categories as inspired by reflection on it [Owen 1966]. For the historians of logic it is attractive, because of the phenomenon of selfreference that involves. Boche ski denies any possibility of correct logical reasoning before Aristotle. In particular, he flatly declares of Plato that " correct logic we find none in his work " [1951, 15]. In this line, many papers have been written that call attention to the violation of a metalogical principle-the type rulesbecause of the Third Man Paradox. The problem of interpretation of the paradox raised many discussions, since the 50's, and the literature devoted to this topic is today enormous. Nevertheless, many points in Plato's reasoning remain obscure. Hitherto, it is commonly believed that the paradox was simply stated by Plato in his Parmenides, but not actually solved. Even more, it is believed that it is hardly possible for Plato to have suggested a solution, because he confused the categories of substance and attribute. B. Russell has also argued that Plato violates in his arguments the restrictions imposed on language by the theory of logical types. This view is encouraged by the linguistic difficulties which Plato has faced in his attempt to formulate an ontology of abstract entities, i.e. that in Greek language abstract and concrete terms are formally indistinguishable : u (literary 'the white') may signify both 'the white thing' and 'whiteness' [Kneales 1984, 19]. In this paper, we analyse the logical structure of the argument in an attempt to give a systematic consistent reconstruction of the text appealing to methods and concepts of modern logic and semantics 1. Already in 1954, G. Vlastos had noted in his seminal paper " The 'Third Man' Argument in the Parmenides " that
SOME PLATONIC ONTOLOGICAL CLAIMS UNDER A PHENOMENOLOGICAL POINT OF VIEW
Nuova Critica, 2012
In this article I deal to a certain extent with the notions of unity-as such and of unity-substance taken in an alternative sense as phenomenological objects that necessarily imply a subject performing a phenomenological reduction. Further, commenting on the structure and meaning of certain statements in Theaetetus and Parmenides, I will point to the confusion that may result from a controversial ontological treatment of these notions. In this phenomenologically motivated view, I’ll try to show how their distinct ‘ontological’ content can lead to a deeper question which is that of two irreducibilities of a fundamentally incompatible character. That of a unity-as such taken as a unity devoid of any predicative content except for its strictly name sense and that of a unity substance taken as a bearer of various categorial attributes, with at least those of individuality and existence.
Predication and Plato's Forms: from Essence to Difference
The Black Book: The Metaphysical Society Journal of Philosophy, 2013
I use the two types of predication developed by Constance Meinwald (§1) to consider the validity of explaining Plato's forms by self-predication (§2), and then by the Forms encoding other Forms (§3-4). Both methods are concluded to be untenable: self-predication because we encounter the Third-Man argument; encoding because the essential autonomy of the Forms is undermined.
PLATO AND PARMENIDES' PARRICIDE SOME THEORETICAL REFLECTIONS 1
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.
The Greatest Difficulty at Parmenides 133c-134e and Plato’s relative terms
Oxford Studies in Ancient Philosophy, 2013
""The first part of Plato’s Parmenides bombards the theory of Forms with objections. Parmenides singles out one criticism as the ‘Greatest Difficulty’ (hereafter ‘GD’) and presents it at Parmenides 133c-134e. The argument has received some attention but scholars generally think that it does not pose a threat to the theory of Forms, either because it is not formally valid, or, if it is formally valid, because it begs the question against the Platonist. This paper aims to show that the GD is a serious challenge to the theory of Forms, neither invalid, at least for the reasons usually given, nor question- begging. To understand how the GD poses a threat, we need to understand how Plato thinks of relative terms, with which the GD is concerned. We discover that the Forms are otiose when saying in virtue of what a relative comes to be the relative that it is. Roughly put: for Plato each relative term, such as master, has a correlative to which it exclusively and exhaustively relates. So when we come to say in virtue of what a relative is the relative it is, we need to mention only its correlative and not a Form. For example, if Achilles is a master, he is a master in virtue of his relationship to Briseis, not to the Form Master. Because of a peculiarity in Plato’s view of relatives, relatives only relate to their correlative; for Plato, relative terms have a special and unique relationship to a correlative term. Thus, Achilles can only be master of things in this realm. With appropriate changes, the same considerations isolate the Form Master as master only of the Form Slave. So the GD rules out the relation of relative terms to correlatives in another realm. The difficulty is serious because it entails that we cannot know the Forms, and that the gods cannot know our affairs or be our masters. ""
The Issue of the Unity of the World in Plato's Parmenides and Sophist
IPS, 2019
In the Parmenides, the examination of the theory of Forms culminates in the ‘major difficulty’, namely Parmenides and Socrates come to the conclusion that Forms and sensible things constitute two distinct realms that are completely unrelated. As a result, the theory of Forms, in the way it has been introduced and defended by the young Socrates, threatens the view that the world is one, for on the version of the theory of Forms that has been presented, the world is not a unity but the mere sum of two unrelated kinds of entities, Forms and sensible things. The introduction of the theory of Forms thus raises the issue whether the world or the totality (to pan) is one. The question I want to raise in this paper is the following: What does it take to solve that problem? By which I mean: what does it take to overcome the challenge that if we posit Forms in addition to sensible things, then we can no longer claim that the world is one? It is often assumed that Socrates’ task is to work out an account of the theory of Forms that would allow him to circumvent that problem. In contrast to the standard reading, I argue here that Plato should first pause and ask about the the conditions of possibility of the unity of the world in the case of an ontology that recognizes that there are two kinds of things.
Midwest Studies in Philosophy, 1983
One of the goals of a certain brand of philosopher has been to give an account of language and linguistic phenomena by means of showing how sentences are to be translated into a "logically perspicuous notation" (or an "ideal language" -to use pass~ terminology). The usual reason given by such philosophers for this activity is that such a notational system will somehow illustrate the "logical form" of these sentences. There are many candidates for this notational system: (almost)ordinary first-order predicate logic (see Quine [1960]), higher-order predicate logic (see Parsons 1970]), intensional logic (see Montague [1969Montague [ , 1970aMontague [ , 1970bMontague [ , 1971), and transformational grammar (see Harrnan ), to mention some of the more popular ones. I donor propose to discuss the general question of the correctness of this approach to the philosophy of language, nor do 1 wish to adjudicate among the notational systems mentioned here. Rather, I want to focus on one problem which must be faced by all such systems -a problem that must be discussed before one decides upon a notational system and tries to demontrate that it in fact can account for all linguistic phenomena. The general problem is to determine what we shall allow as linguistic data; in this paper I shall restrict my attention to this general problem as it appears when we try to account for certain words with non-singular reference, in particular, the words that are classified by the count/ mass and sortal/non-sortal distinctions.