The debate over whether we should believe that mathematical objects exist quickly leads to the question of how to determine what we should believe to exist. Indispensabilists claim that we should believe in the existence of mathematical objects because of their ineliminable roles in scientific theory. Eleatics argue that only objects with causal properties exist. Mark Colyvan’s recent defenses of Quine’s indispensability argument present an intriguing attempt to provide reasons to favor the indispensabilist’s criterion against some contemporary eleatics. I show (...) that Colyvan’s argument is not decisive against the eleatic and then sketch a way to capture some of the important intuitions behind both views. (shrink)
The Eleatic Principle or causal criterion is a causal test that entities must pass in order to gain admission to some philosophers’ ontology.1 This principle justifies belief in only those entities to which causal power can be attributed, that is, to those entities which can bring about changes in the world. The idea of such a test is rather important in modern ontology, since it is neither without intuitive appeal nor without influential supporters. Its supporters have included David Armstrong (...) (1978, Vol 2, 5), Brian Ellis (1990, 22) and Hartry Field2 (1989, 68) to name but a few. (shrink)
There is a tradition according to which Parmenides of Elea endorsed the following set of counterintuitive doctrines: (a) There exists exactly one material thing. (b) What exists does not change. (g) Nothing is generated or destroyed. (d) What exists is undivided. For convenience, I will use the label ‘Eleatic monism’ to refer to the conjunction of a–d.
The debate over whether we should believe that mathematical objects exist quickly leads to the question of how to determine what we should believe. Indispensabilists claim that we should believe in the existence of mathematical objects because of their ineliminable roles in scientific theory. Eleatics argue that only objects with causal properties exist. Mark Colyvan’s recent defenses of Quine’s indispensability argument against some contemporary eleatics attempt to provide reasons to favor the indispensabilist’s criterion. I show that Colyvan’s argument is not (...) decisive against the eleatic and sketch a way to capture the important intuitions behind both views. (shrink)
The debate over whether we should believe that mathematical objects exist quickly leads to the question of how to determine what we should believe to exist. Indispensabilists claim that we should believe in the existence of mathematical objects because of their ineliminable roles in scientific theory. Eleatics argue that only objects with causal properties exist. Mark Colyvan’s recent defenses of Quine’s indispensability argument present an intriguing attempt to provide reasons to favor the indispensabilist’s criterion against some contemporary eleatics. I show (...) that Colyvan’s argument is not decisive against the eleatic and then sketch a way to capture some of the important intuitions behind both views.El debate sobre si deberíamos creer en la existencia de los objetos matemáticos conduce rápidamente a la cuestión de cómo determinar lo que deberíamos creer que existe. Los indispensabilistas declaran que deberíamos creer en la existencia de los objetos matemáticos por sus funciones ineliminables en la teoría científica. Los eleáticos argumentan que sólo existen los objetos que tienen propiedades causales. La defensa reciente de Mark Colyvan del argumento de la indispensabilidad de Quine representa un interesante intento de proporcionar razones a favor del criterio indispensabilista, en contra de algunos eleáticos contemporáneos. Mostraré que el argumento de Colyvan en contra de los eleáticos no es decisivo y esbozaré a continuación una manera de capturar algunas de las importantes intuiciones que se encuentran tras ambos puntos de vista. (shrink)
Presocratic atomism was one of the most influential of the early theories: both Plato and Aristotle thought of it as a major competing theory, and it was an important source for post-Aristotelian Hellenistic theories. It has been commonplace that the atomism developed first by Leucippus of Abdera and then by Democritus of Abdera was a reaction to the Eleatic arguments of Zeno and Melissus, but the details of that influence have sometimes seemed rather hazy. This article brings them into (...) sharper focus. This article considers the Eleatic foundations of atomism, especially the question of the importance of Zeno and Melissus for Democritus. By concentrating on some of the less-studied aspects of atomism and especially of the development of the concept of the unlimited into the notion of the infinite, it furthers the understanding of not only the development of early atomism but also the Eleatics Zeno and Melissus. (shrink)
I present a formal ontological theory where the basic building blocks of the world can be either things or events. In any case, the result is a Parmenidean worldview where change is not a global property. What we understand by change manifests as asymmetries in the pattern of the world-lines that constitute 4-dimensional existents. I maintain that such a view is in accord with current scientific knowledge.
“Why did God create the World?” is one of the traditional questions of theology. In the twentieth century this question was rephrased in a secularized manner as “Why is there something rather than nothing?” While creation - at least in its traditional, temporal, sense - has little place in Spinoza’s system, a variant of the same questions puts Spinoza’s system under significant pressure. According to Spinoza, God, or the substance, has infinitely many modes. This infinity of modes follow from the (...) essence of God. If we ask: “Why must God have modes?,” we seem to be trapped in a real catch. On the one hand, Spinoza’s commitment to thoroughgoing rationalism demands that there must be a reason for the existence of the radical plurality of modes. On the other hand, the asymmetric dependence of modes on the substance seems to imply that the substance does not need the modes, and that it can exist without the modes. But if the substance does not need the modes, then why are there modes at all? Furthermore, Spinoza cannot explain the existence of modes as an arbitrary act of grace on God’s side since Spinoza’s God does not act arbitrarily. Surprisingly, this problem has hardly been addressed in the existing literature on Spinoza’s metaphysics, and it is my primary aim here to draw attention to this problem. In the first part of the paper I will present and explain the problem of justifying the existence of infinite plurality modes in Spinoza’s system. In the second part of the paper I consider the radical solution to the problem according to which modes do not really exist, and show that this solution must be rejected upon consideration. In the third and final part of the paper I will suggest my own solution according to which the essence of God is active and it is this feature of God’s essence which requires the flow of modes from God’s essence. I also suggest that Spinoza considered radical infinity and radical unity to be roughly the same, and that the absolute infinity of what follow from God’s essence is grounded in the absolute infinity of God’s essence itself. (shrink)
: Given Descartes's conception of extension, space and body, there are deep problems about how there can be any real motion. The argument here is that in fact Descartes takes motion to be only phenomenal. The paper sets out the problems generated by taking motion to be real, the solution to them found in the Cartesian texts, and an explanation of those texts in which Descartes appears on the contrary to regard motion as real.
It’s well known that one way to cure a hangover is by a “hair of the dog” — another alcoholic drink. The drawback of this method is that, so it would appear, it cannot be used to completely cure a hangover, since the cure simply induces a further hangover at a later time, which must in turn either be cured or suffered through.
A novel way of making a non-stick frying pan using a topologically open surface is described. While the article has a slight humorous element to it, it is also intended to contain some serious philosophical points concerning the nature of infinitely divisible matter and the kind of contact that must occur between objects in order for them to interact.
Parmenides of Elea was the most important and influential philosopher before Plato. He rejected as impossible the scientific inquiry practiced by the earlier Presocratic philosophers and held that generation, destruction, and change are unreal and that only one thing exists. In this book, Patricia Curd argues that Parmenides sought to reform rather than to reject scientific inquiry, and she offers a more coherent account of his influence on later philosophers._ _The Legacy of Parmenides_ examines Parmenides' arguments, considering his connection to (...) earlier Greek thought and how his account of what-is could have served as a model for later philosophers. Curd also explores the theories of his successors, including the Pluralists, the Atomists, the later Eleatics, and the later Presocratics. She concludes with a discussion of the importance of Parmenides' work to Plato's _Theory of Forms._ _The Legacy of Parmenides_ challenges traditional views of early Greek philosophy and provides new insights into the work of Parmenides. "_The Legacy of Parmenides_ represents a milestone... of Parmenides' interpretation. It is full of ideas and tells a coherent story about Parmenides and early Greek thought." --_ Alexander Nehamas, Princeton University___ "Professor Curd offers a genuinely original and possibly correct interpretation of the core thesis of the poem of Parmenides in a field so well worked over that saying something both new and true is profoundly difficult, this is a notable achievement." --_ Thomas M. Robinson, University of Toronto___ "This will be a substantial book in the story of early Greek philosophy, and future writers on the tradition from Thales through Plato will not be able to ignore it without missing an important interpretive alternative. It will be of value to students of Presocratic philosophy or the Greek tradition, as well as to students of the scientific revolution, cosmology, the origins of logic, or comparative mysticism." --_ Scott W. Austin, Texas A&M University___ PATRICIA CURD_ is professor at Purdue University where she works primarily in Ancient Philosophy. She is a co-editor of _Readings in Ancient Greek Philosophy_, and is the editor of _A Presocratics Reader._. (shrink)
The following suggestions for the interpretation of Parmenides and Melissus can be grouped for convenience about one problem. This is the problem whether, as Aristotle thought and as most commentators still assume, Parmenides wrote his poem in the broad tradition of Ionian and Italian cosmology. The details of Aristotle's interpretation have been challenged over and again, but those who agree with his general assumptions take comfort from some or all of the following major arguments. First, the cosmogony which formed the (...) last part of Parmenides' poem is expressly claimed by the goddess who expounds it to have some measure of truth or reliability in its own right, and indeed the very greatest measure possible for such an attempt. Second, the earlier arguments of the goddess prepare the ground for such a cosmogony in two ways. For in the first place these arguments themselves start from assumptions derived from earlier cosmologists, and are concerned merely to work out the implications of this traditional material. And, in the second place, they end by establishing the existence of a spherical universe: the framework of the physical world can be secured by logic even if the subsequent introduction of sensible qualities or ‘powers’ into this world marks some decline in logical rigour. (shrink)
I argue that the paradoxes attributed to the Megarians, namely the Liar, the Sorites, presupposition ("Have you stopped beating your father,") and failure of substitution of co-referential terms in psychological verbs ("The Electra") were intended to be reasons to accept Parmenides view that non-being is an incoherent notion and that there is exactly One Being. That is, Eubulides and others were akin to Zeno, in indirectly supporting Parmenidean monism.