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)

Up to the introduction of the term and concept of incommensurability by T. S. Kuhn and P. K. Feyerabend in the early 1960s, scientific texts were supposed to pose no problem as regards their translation, unlike literature, which was thought very difficult to translate. After the introduction of the term, translation of scientific language became equally problematic because, due to conceptual and perceptual incommensurability, there was no common observation basis to ground linguistic equivalences between languages of incommensurable paradigms. This article (...) highlights the presuppositions that link incommensurability to dramatic consequences (impossibility of communication, translation, and comparative evaluation of paradigms) and tries to sketch an alternative way of understanding incommensurability and translation drawing on Kuhn’s work. From this perspective, translation is not an all-or-nothing affair for either science or literature and becomes a problem to be solved for each particular set of circumstances. (shrink)

In order to set up a dialogue the author, first, will attempt to discern similarities and differences between the ideas of Gregory Bateson and those of the so-called Pragmatist philosophers, John Dewey and William James. Second, he will address connecting points and relevance to intercultural communication training and teaching. For both sides aesthetics are of central importance, for Bateson, coming from the direction of systems, more in the observation of the pattern that connects. For Dewey, the aesthetic experience is embedded (...) in the context potentially in any situation. For both Dewey and James human and other organisms actively experiencing environments as situations are the beginning and the end of any philosophy of pragmatic significance. For Bateson, the addition of aesthetics to ecology is necessary to highlight its global significance. (shrink)

Issues of communication and the possibilities for the transformation of perspectives through an experimental dialogue resulting in a mutual, open, receptive, and non-judgmental consideration of the other are addressed in this paper from transdisciplinary theoretical and conceptual standpoints. The warrant for cultivating this type of communicative ability is based on arguments resulting from the assumption of widespread confusion and conflict in intrapersonal, interpersonal, intergroup, and ecological relations across the globe. I argue that there are two distinct classes of “reasons” for (...) this proposed practice of dialogue. First is recognition of the need for human individuals to engage in a regular and systematic “social maintenance” of embodied consciousness to forestall the continuous colonization of the past/future on the living present that embodied consciousness entails. Second is the teaching of a skill to creatively and respectfully engage with others in a mutual transformation of perspectives. This paper addresses the general problem of perspectives and reflexivity at the root of the communication phenomenon and by extension – to its scale and to its pathologies in individuals and collectives. It is argued that suspension of judgment, assumption, and habit helps interlocutors to recognize the possibility of holding one's history in a tensional abeyance and to focus on the living present independent of habitualized and reified identities and the embodied manner in which we unconsciously carry ourselves as social or “universalized selves” in social situations. (shrink)

Let’s call the sentence “why is there something rather than nothing?” the Question. There’s no consensus, of course, regarding which proposed answer to the Question, if any, is correct, but occasionally there’s also controversy regarding the meaning of the Question itself. In this paper I argue that such controversy persists because there just isn’t one unique interpretation of the Question. Rather, the puzzlement expressed by the sentence “why is there something rather than nothing?” varies depending on the ontology implicitly or (...) explicitly endorsed by the speaker. In this paper I do three things. First, I argue that other proposals according to which the Question has one uniquely adequate interpretation are false. Second, I give several examples of the way in which the meaning of the Question can vary depending on the ontology to which it is coupled. Third, I explore the implications of my thesis for the manner in which we should approach future attempts to answer the Question. (shrink)

Zeno’s paradoxes of motion, allegedly denying motion, have been conceived to reinforce the Parmenidean vision of an immutable world. The aim of this article is to demonstrate that these famous logical paradoxes should be seen instead as paradoxes of immobility. From this new point of view, motion is therefore no longer logically problematic, while immobility is. This is convenient since it is easy to conceive that immobility can actually conceal motion, and thus the proposition “immobility is mere illusion of the (...) senses” is much more credible than the reverse thesis supported by Parmenides. Moreover, this proposition is also supported by modern depiction of material bodies: the existence of a ceaseless random motion of atoms—the ‘thermal agitation’—in the scope of contemporary atomic theory, can offer a rational explanation of this ‘illusion of immobility’. Our new approach to Zeno’s paradoxes therefore leads to presenting the novel concept of ‘impermobility’, which we think is a more adequate description of physical reality. (shrink)