Weak Alternating Timed Automata

Alternating timed automata on infinite words are considered. The main result is a characterization of acceptance conditions for which the emptiness problem for these automata is decidable. This result implies new decidability results for fragments of timed temporal logics. It is also shown that, unlike for MITL, the characterisation remains the same even if no punctual constraints are allowed

Zeno's Paradoxes. A Cardinal Problem 1. On Zenonian Plurality

In this paper the claim that Zeno's paradoxes have been solved is contested. Although no one has ever touched Zeno without refuting him (Whitehead), it will be our aim to show that, whatever it was that was refuted, it was certainly not Zeno. The paper is organised in two parts. In the first part we will demonstrate that upon direct analysis of the Greek sources, an underlying structure common to both the Paradoxes of Plurality and the Paradoxes of Motion can be exposed. This structure bears on a correct - Zenonian - interpretation of the concept of division through and through. The key feature, generally overlooked but essential to a correct understanding of all his arguments, is that they do not presuppose time. Division takes place simultaneously. This holds true for both PP and PM. In the second part a mathematical representation will be set up that catches this common structure, hence the essence of all Zeno's arguments, however without refuting them. Its central tenet is an aequivalence proof for Zeno's procedure and Cantor's Continuum Hypothesis. Some number theoretic and geometric implications will be shortly discussed. Furthermore, it will be shown how the Received View on the motion-arguments can easely be derived by the introduction of time as a (non-Zenonian) premiss, thus causing their collapse into arguments which can be approached and refuted by Aristotle's limit-like concept of the potentially infinite, which remained - though in different disguises - at the core of the refutational strategies that have been in use up to the present. Finally, an interesting link to Newtonian mechanics via Cremona geometry can be established.Comment: 41 pages, 7 figure

Do Zeno\u27s Arguments Challenge Aristotle\u27s Account of Motion?

What is the relationship between the arguments that Aristotle and Simplicius attribute to Zeno of Elea, and the account of motion that Aristotle presents in the Physics? Do the considerations that Aristotle raises in Physics Z.9 overcome the arguments about motion that he attributes to Zeno? Do they show the Zenonian arguments to be inapplicable or ill formed? Or do considerations that Zeno raises in the discussions attributed to him instead undermine Aristotle\u27s account of motion? Do they undermine the possibility of physics as epistëmë? And why does Aristotle not treat Zeno\u27s arguments about magnitude and plurality in his account of motion? After all, motion involves distances and multiple positions and times. What is at stake here is phusikë as epistëmë: If it can be shown that his conception of motion is incoherent or self-contradictory, then there is for Aristotle small prospect of a science of physics, an account of phusis through its archai. If it can be shown that problems of the sort Zeno raised with respect to plurality and magnitude will surface in the account of motion that Aristotle proposes, then we shall need to ask whether or to what extent this undermines the possibility of an epistëmë of phusis

Anaxagoras\u27 Theory of Change: A Response to Parmenides

Assuming that Anaxagoras was responding to Parmenides, I shall examine the nature of his response. I aim to show that the fragments and other evidence can and should be interpreted as belonging to a system whose main purpose is to provide an apparatus for explaining change without coming to be or perishing

To Tell the Truth: \u3cem\u3eDissoi Logoi\u3c/em\u3e 4 & Aristotle\u27s Response

Roll 121a. Quad Wall being demolished. Image 3 of 33. (6 April, 1954) [PHO 1.121a.3]The Boleslaus Lukaszewski (Father Luke) Photographs contain more than 28,000 images of Saint Louis University people, activities, and events between 1951 and 1970. The photographs were taken by Boleslaus Lukaszewski (Father Luke), a Jesuit priest and member of the University's Philosophy Department faculty

The Tradition about Zeno of Elea Re-Examined

Acceptance of Plato\u27s testimony in the Parmenides raises more problems than has commonly been realized. Plato\u27s divinatio may have hit the truth, but to have this confidence involves an act of faith. If anyone wonders what other theory we may put forward regarding Zeno\u27s treatise, he may take notice of the fact that in the Phaedrus Plato mentions Zeno in the company of rhetoricians like Thrasymachus, Theodorus, and Gorgias. In the devising of new methods and argumentative techniques he remains a pioneer

The stoics on nature and truth

First, this thesis outhnes part of the thought of some pre-Socratic thinkers, particularly Heraclitus. In doing this, I explore the historical provenance of certain ideas which came to be important in Stoicism. It then moves on to look at the Stoic view of 'physics', including some comparison with Epicurus and Aristotle, and with a focus on the concept of the continuum. The third chapter attempts to synthesise a common problem arising from a belief in the continuum, namely a problem of indeterminacy. In the fourth chapter, certain characterisations of Stoic epistemology are considered, along with an overview of recent interpretations of the Stoic theory of impressions. It concludes with the thought that at certain crucial points - such as whether impressions themselves are to be thought of as true and false - the Stoic position is underdetermined with respect to the evidence. Pursuing this thought into the fifth chapter, we see the evidence as being equivalently consistent with a 'two-tier’ theory of perception, where impressions themselves are understood as neither true nor false in any sense, but iu which 'the true' arises as a result of the transformative effect of reason. This theory is shown to connect with verbalisation through the 'rational impression'. This leads to the suggestion that the Stoics had a linguistic diagnosis for some problems in philosophy, arrived at by their reflections on ambiguity and etymology. In the final chapter, an account of intersubjectivity is explored, which preserves for the Stoics the claim that their truth has an objective character and is thus appropriate for a 'dogmatic' philosophy