Already in ancient philosophy, there was a transition from the implicit and hidden action of the Logical ( lógos) in nature ( phýsis) to the scientific and explicit expression of the logical structures of thought, action, the world and language. Heraclitus' heno-logic with Logos as hidden implicit principle of homologization of opposites ( tà enantía) in nature differs from Parmenides' paraconsistent logic developed in a hypothetical hemidyalectics given in the formula ''All is One'' ( hén pánta eînai). Plato's concept of (...) dia-logic (dialektikè téchne ) with a new concept of Logos as the one genus of beings ( hén tí génon toôn ontoôn) in which the word not-Being (negation) got its place enabled production of dyadic logical structure by the granulation of genera into opposite species and sub-species that it contains. Aristotle's concept of triadic-logic as syl-logistics ( syllogismós) and demonstrative science (epistéme apodeiktikê ) give a new approach by new granulation of the concept of Logos into triadic logical structure: (1) the structure of being (substratum-attributes relation), (2) the structure of thought (substance-second substances relation), and (3) the structure of propositions (subject-predicate relation). Plato's dialectic and Aristotle's syllogistic both deconstructed the implicit ontological unity of the world (pan, kosmos, sphairos ) given through the concept of Logos in Pre-Socratic philosophy in order to make that unity in explicit form given by the logical and semantical structures of the propositions about the world, about the thought and about the language. The hidden implicit of the nature, which had to be known intuitively, was transformed into unhidden explicit inferential logical structures given in the semantics and pragmatics of scientific demonstration. (shrink)

The primary interpretative challenge for understanding Parmenides’ poem revolves around explaining both the meaning of, and the relationship between, its two primary sections: a) the positively endorsed metaphysical arguments which describe some unified, unchanging, motionless, and eternal “reality”, and b) the ensuing cosmology, which incorporates the very principles explicitly denied in Aletheia. I will refer to this problem as the “A-D Paradox.” I advocate resolving this paradoxical relationship by reading Parmenides’ poem as a ring-composition, and incorporating a modified version of (...) Palmer’s modal interpretation of Aletheia. On my interpretation, Parmenides’ thesis in Aletheia is not a counter-intuitive description of how all the world must truly be, but rather a radical rethinking of divine nature. Understanding Aletheia in this way, the ensuing “cosmology” can be straightforwardly rejected as an exposition of how traditional, mythopoetic accounts have misled mortals in their understanding of divinity. Not only does this interpretative view provide a resolution to the A-D Paradox, it offers a more holistic account of the poem by making the opening lines of introduction integral to understanding Parmenides’ message. By setting forth its own unacceptable fiction, paralleling the elements of the Doxa in a ring-composition, the Proem simultaneously establishes the scope of the ensuing inquiry, and its target. Maintaining Parmenides’ historical position as the “father of metaphysics,” the narrative that he advanced a strictly secular account of all reality is challenged. Instead, Parmenides is best understood as further advancing Xenophanes’ criticisms of traditional religion, an intellectual relationship which the ancient testimonia strongly supports. (shrink)

This article discusses Heidegger’s interpretation of Parmenides given in his last public lecture ‘The Principle of Identity’ in 1957. The aim of the piece is to illustrate just how original and significant Heidegger’s reading of Parmenides and the principle of identity is, within the history of Philosophy. Thus the article will examine the traditional metaphysical interpretation of Parmenides and consider G.W.F. Hegel and William James’ account of the principle of identity in light of this. It will then consider Heidegger’s contribution, (...) his return to and re-interpretation of Parmenides in his last lecture. Heidegger will, through the Parmenidean claim that ‘Thinking and Being are one’ deconstruct the traditional metaphysical understanding of the principle of identity, and in its place offer a radically different conception of how our relationship, our ‘belonging together’ with Being can be understood. (shrink)

I offer a novel solution to Zeno’s paradox of The Arrow by introducing nilpotent infinitesimal lengths of time. Nilpotents are nonzero numbers that yield zero when multiplied by themselves a certain number of times. Zeno’s Arrow goes like this: during the present, a flying arrow is moving in virtue of its being in flight. However, if the present is a single point in time, then the arrow is frozen in place during that time. Therefore, the arrow is both moving and (...) at rest. In “Zeno’s Arrow, Divisible Infinitesimals, and Chrysippus,” White suggests using an infinitesimal value as the length of the present. Contra Zeno, this allows the arrow to be moving in the present, rather than frozen in place. In this paper, I follow the basic outline of White’s solution but argue that his solution suffers from arbitrariness and a related theoretical artificiality in relation to the system of infinitesimals he invokes, viz. in relation to the hyperreal infinitesimals of nonstandard analysis. After arguing that any solution to the paradox must satisfy certain theoretical requirements, I examine White’s solution alongside two nilpotent solutions. One of these solutions is inspired by F.W. Lawvere’s Smooth Infinitesimal Analysis and the other is inspired by Paolo Giordano’s ring of Fermat Reals. I argue that Giordano’s nilpotents supply the best answer to Zeno’s paradox. (shrink)

By convention epinician poetry claims to be both obligatory and truthful, yet in the intersection of obligation and truth lies a seeming paradox: the poet presents his poetry as commissioned by a patron but also claims to be unbiased enough to convey the truth. In Slater's interpretation Pindar reconciles this paradox by casting his relationship to the patron as one of guest-friendship: when he declares himself a guest-friend of the victor, he agrees to the obligation ‘a) not to be envious (...) of hisxenosand b) to speak well of him. The argumentation is:Xeniaexcludes envy, I am axenos, therefore I am not envious and consequently praise honestly’. Slater observes that envy may foster bias against the patron, but the problem of pro-patron bias remains: does the poet's friendship with and obligation to his patron produce praise at the expense of truth? (shrink)