Though Spinoza's definition of God at the beginning of the Ethics unequivocally asserts that God has infinitely many attributes, the reader of the Ethics will find only two of these attributes discussed in any detail in Parts Two through Five of the book. Addressing this intriguing gap between the infinity of attributes asserted in E1d6 and the discussion merely of the two attributes of Extension and Thought in the rest of the book, Jonathan Bennett writes: Spinoza seems to imply (...) that there are other [attributes] – he says indeed that God or Nature has “infinite attributes.” Surprising as it may seem, there are reasons to think that by this Spinoza did not mean anything entailing that there are more than two attributes. In this paper I will argue that Bennett’s claim is fundamentally wrong and deeply misleading. I do think, however, that addressing Bennett’s challenge will help us better understand Spinoza’s notion of infinity. I will begin by summarizing Bennett’s arguments. I will then turn to examine briefly the textual evidence for and against his reading. Then I will respond to each of Bennett’s arguments, and conclude by pointing out theoretical considerations which, I believe, simply refute his reading. (shrink)
An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.
The seventeenth century was an important period in the conceptual development of the notion of the infinite. In 1643, Evangelista Torricelli (1608-1647)—Galileo’s successor in the chair of mathematics in Florence—communicated his proof of a solid of infinite length but finite volume. Many of the leading metaphysicians of the time, notably Spinoza and Leibniz, came out in defense of actual infinity, rejecting the Aristotelian ban on it, which had been almost universally accepted for two millennia. Though it would be another (...) two centuries before the notion of the actually infinite was rehabilitated in mathematics by Dedekind and Cantor (Cauchy and Weierstrass still considered it mere paradox), their impenitent advocacy of the concept had significant reverberations in both philosophy and mathematics. In this essay, I will attempt to clarify one thread in the development of the notion of the infinite. In the first part, I study Spinoza’s discussion and endorsement, in the Letter on the Infinite (Ep. 12), of Hasdai Crescas’ (c. 1340-1410/11) crucial amendment to a traditional proof of the existence of God (“the cosmological proof” ), in which he insightfully points out that the proof does not require the Aristotelian ban on actual infinity. In the second and last part, I examine the claim, advanced by Crescas and Spinoza, that God has infinitely many attributes, and explore the reasoning that motivated both philosophers to make such a claim. Similarities between Spinoza and Crescas, which suggest the latter’s influence on the former, can be discerned in several other important issues, such as necessitarianism, the view that we are compelled to assert or reject a belief by its representational content, the enigmatic notion of amor Dei intellectualis, and the view of punishment as a natural consequent of sin. Here, I will restrict myself to the issue of the infinite, clearly a substantial topic in itself. (shrink)
This is a book review of Oppy's "Philosophical Perspectives on Infinity", which is of interest to those in metaphysics, epistemology, philosophy of science, mathematics, and philosophy of religion.
In this paper I present a novel supertask in a Newtonian universe that destroys and creates infinite masses and energies, showing thereby that we can have infinite indeterminism. Previous supertasks have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism. In the Nothing from Infinity paradox we will see an infinitude of finite masses and an infinitude of energy disappear entirely, and do so despite the conservation of energy in all collisions. (...) I then show how this leads to the Infinity from Nothing paradox, in which we have the spontaneous eruption of infinite mass and energy out of nothing. I conclude by showing how our supertask models at least something of an old conundrum, the question of what happens when the immovable object meets the irresistible force. (shrink)
Bowin begins with an apparent paradox about Aristotelian infinity: Aristotle clearly says that infinity exists only potentially and not actually. However, Aristotle appears to say two different things about the nature of that potential existence. On the one hand, he seems to say that the potentiality is like that of a process that might occur but isn't right now. Aristotle uses the Olympics as an example: they might be occurring, but they aren't just now. On the other hand, (...) Aristotle says that infinity "exists in actuality as a process that is now occurring" (234). Bowin makes clear that Aristotle doesn't explicitly solve this problem, so we are left to work out the best reading we can. His proposed solution is that "infinity must be...a per se accident...of number and magnitude" (250). (Bryn Mawr Classical Review 2008.07.47). (shrink)
Infinity exists as a concept but has no existence in actuality. For infinity to have existence in actuality either time or space have to already be infinite. Unless something is already infinite, the only way to become infinite is by an 'infinity leap' in an infinitely small moment, and this is not possible. Neither does infinitely small have an existence since anything larger than zero is not infinitely small. Therefore infinity has no existence in actuality.
I advance a novel interpretation of Kant's argument that our original representation of space must be intuitive, according to which the intuitive status of spatial representation is secured by its infinitary structure. I defend a conception of intuitive representation as what must be given to the mind in order to be thought at all. Discursive representation, as modelled on the specific division of a highest genus into species, cannot account for infinite complexity. Because we represent space as infinitely complex, the (...) spatial manifold cannot be generated discursively and must therefore be given to the mind, i.e. represented in intuition. (shrink)
There exists a huge number of numerical methods that iteratively construct approximations to the solution y(x) of an ordinary differential equation (ODE) y′(x) = f(x,y) starting from an initial value y_0=y(x_0) and using a finite approximation step h that influences the accuracy of the obtained approximation. In this paper, a new framework for solving ODEs is presented for a new kind of a computer – the Infinity Computer (it has been patented and its working prototype exists). The new computer (...) is able to work numerically with finite, infinite, and infinitesimal numbers giving so the possibility to use different infinitesimals numerically and, in particular, to take advantage of infinitesimal values of h. To show the potential of the new framework a number of results is established. It is proved that the Infinity Computer is able to calculate derivatives of the solution y(x) and to reconstruct its Taylor expansion of a desired order numerically without finding the respective derivatives analytically (or symbolically) by the successive derivation of the ODE as it is usually done when the Taylor method is applied. Methods using approximations of derivatives obtained thanks to infinitesimals are discussed and a technique for an automatic control of rounding errors is introduced. Numerical examples are given. (shrink)
There exist many applications where it is necessary to approximate numerically derivatives of a function which is given by a computer procedure. In particular, all the fields of optimization have a special interest in such a kind of information. In this paper, a new way to do this is presented for a new kind of a computer - the Infinity Computer - able to work numerically with finite, infinite, and infinitesimal number. It is proved that the Infinity Computer (...) is able to calculate values of derivatives of a higher order for a wide class of functions represented by computer procedures. It is shown that the ability to compute derivatives of arbitrary order automatically and accurate to working precision is an intrinsic property of the Infinity Computer related to its way of functioning. Numerical examples illustrating the new concepts and numerical tools are given. (shrink)
In order to explain Wittgenstein’s account of the reality of completed infinity in mathematics, a brief overview of Cantor’s initial injection of the idea into set- theory, its trajectory and the philosophic implications he attributed to it will be presented. Subsequently, we will first expound Wittgenstein’s grammatical critique of the use of the term ‘infinity’ in common parlance and its conversion into a notion of an actually existing infinite ‘set’. Secondly, we will delve into Wittgenstein’s technical critique of (...) the concept of ‘denumerability’ as it is presented in set theory as well as his philosophic refutation of Cantor’s Diagonal Argument and the implications of such a refutation onto the problems of the Continuum Hypothesis and Cantor’s Theorem. Throughout, the discussion will be placed within the historical and philosophical framework of the Grundlagenkrise der Mathematik and Hilbert’s problems. (shrink)
I tried to describe Infinity as a major natural conundrum known to man. The booklet also contains answers to some eternal questions, such as the meaning of life, faith, etc. I am especially proud of my Morality section.
Abstract -/- The concept of infinity is of ancient origins and has puzzled deep thinkers ever since up to the present day. Infinity remains somewhat of a mystery in a physical world in which our comprehension is largely framed around the concept of boundaries. This is partly because we live in a physical world that is governed by certain dimensions or limits – width, breadth, depth, mass, space, age and time. To our ordinary understanding, it is a seemingly (...) finite world under those dimensions and we may find it difficult to comprehend something that by definition can have no beginning and no end, no limit or boundary. The article argues that this concept can have a meaning different from that normally envisaged in science, philosophy or mathematics, a meaning that transcends all boundaries and which proceeds from a non-material or metaphysical perspective. It examines the features and implications of that concept. -/- . (shrink)
Can life be visually represented as a circle? Hegel states that true infinity, when visualized, takes the shape of a circle. The dissertation begins with a hypothesis, "does the progression to the true infinite reflect the notion of life itself?" Then, Hegel's notion of infinity is expanded and applied to the notion of life. This work is trying to explain human evolution and life itself.
Infinity and infinite sets, as traditionally defined in mathematics, are shown to be logical absurdities. To maintain logical consistency, mathematics ought to abandon the traditional notion of infinity. It is proposed that infinity should be replaced with the concept of “indefiniteness”. This further implies that other fields drawing on mathematics, such as physics and cosmology, ought to reject theories that postulate infinities of space and time. It is concluded that however indefinite our calculations of space and time (...) become, the Universe must nevertheless be finite. (shrink)
This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any of these (...) notions and proposes a more physical treatment of mathematical objects separating the objects from tools used to study them. It both offers a possibility to create new numerical methods using infinities and infinitesimals in floating-point computations and allows one to study certain mathematical objects dealing with infinity more accurately than it is done traditionally. In these notes, we explain that even though both methodologies deal with infinities and infinitesimals, they are independent and represent two different philosophies of Mathematics that are not in a conflict. It is proved that texts :539–555, 2017; Gutman and Kutateladze in Sib Math J 49:835–841, 2008; Kutateladze in J Appl Ind Math 5:73–75, 2011) asserting that the ①-based methodology is a part of non-standard analysis unfortunately contain several logical fallacies. Their attempt to show that the ①-based methodology can be formalized within non-standard analysis is similar to trying to show that constructivism can be reduced to the traditional Mathematics. (shrink)
This article discusses some of Chateaubriand’s views on the connections between the ideas of formalization and infinity, as presented in chapters 19 and 20 of Logical Forms. We basically agree with his criticisms of the standard construal of these connections, a view we named “formal proofs as ultimate provings”, but we suggest an alternative way of picturing that connection based on some ideas of the late Wittgenstein.
Is there room enough in all creation for an 'Empty Universe Theory'? How should we view the realm in which we exist? Are the natures of matter and energy, their compositions and relationships with each other the fundamental key to the understanding of everything or is it something else? A thought on the true nature of the realm we really inhabit with some basic mathematical description of the relationship between the finite and the absolute as we are capable of understanding (...) it. (shrink)
God seemingly had a duty to create minds each of infinite worth through possessing God-like knowledge. People might object that God’s own infinite worth was all that was needed, or that no mind that God created could have truly infinite worth; however, such objections fail. Yet this does not generate an unsolvable Problem of Evil. We could exist inside an infinite mind that was one among endlessly many, perhaps all created by Platonic Necessity. “God” might be our name for this (...) Necessity, or for the infinite mind inside which we existed, or for an infinite ocean of infinite minds. (shrink)
The mathematician Georg Cantor strongly believed in the existence of actually infinite numbers and sets. Cantor’s “actualism” went against the Aristotelian tradition in metaphysics and mathematics. Under the pressures to defend his theory, his metaphysics changed from Spinozistic monism to Leibnizian voluntarist dualism. The factor motivating this change was two-fold: the desire to avoid antinomies associated with the notion of a universal collection and the desire to avoid the heresy of necessitarian pantheism. We document the changes in Cantor’s thought with (...) reference to his main philosophical-mathematical treatise, the Grundlagen (1883) as well as with reference to his article, “Über die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche” (“Concerning Various Perspectives on the Actual Infinite”) (1885). (shrink)
It is often alleged that Cantor’s views about how the set theoretic universe as a whole should be considered are fundamentally unclear. In this article we argue that Cantor’s views on this subject, at least up until around 1896, are relatively clear, coherent, and interesting. We then go on to argue that Cantor’s views about the set theoretic universe as a whole have implications for theology that have hitherto not been sufficiently recognised. However, the theological implications in question, at least (...) as articulated here, would not have satisfied Cantor himself. (shrink)
Peter Walley argues that a vague credal state need not be representable by a set of probability functions that could represent precise credal states, because he believes that the members of the representor set need not be countably additive. I argue that the states he defends are in a way incoherent.
In this paper, a number of traditional models related to the percolation theory has been considered by means of new computational methodology that does not use Cantor’s ideas and describes infinite and infinitesimal numbers in accordance with the principle ‘The part is less than the whole’. It gives a possibility to work with finite, infinite, and infinitesimal quantities numerically by using a new kind of a compute - the Infinity Computer – introduced recently in [18]. The new approach does (...) not contradict Cantor. In contrast, it can be viewed as an evolution of his deep ideas regarding the existence of different infinite numbers in a more applied way. Site percolation and gradient percolation have been studied by applying the new computational tools. It has been established that in an infinite system the phase transition point is not really a point as with respect of traditional approach. In light of new arithmetic it appears as a critical interval, rather than a critical point. Depending on “microscope” we use this interval could be regarded as finite, infinite and infinitesimal short interval. Using new approach we observed that in vicinity of percolation threshold we have many different infinite clusters instead of one infinite cluster that appears in traditional consideration. (shrink)
Iterability, the repetition which alters the idealization it reproduces, is the engine of deconstructive movement. The fact that all experience is transformative-dissimulative in its essence does not, however, mean that the momentum of change is the same for all situations. Derrida adapts Husserl's distinction between a bound and a free ideality to draw up a contrast between mechanical mathematical calculation, whose in-principle infinite enumerability is supposedly meaningless, empty of content, and therefore not in itself subject to alteration through contextual change, (...) and idealities such as spoken or written language which are directly animated by a meaning-to-say and are thus immediately affected by context. Derrida associates the dangers of cultural stagnation, paralysis and irresponsibility with the emptiness of programmatic, mechanical, formulaic thinking. This paper endeavors to show that enumerative calculation is not context-independent in itself but is instead immediately infused with alteration, thereby making incoherent Derrida's claim to distinguish between a free and bound ideality. Along with the presumed formal basis of numeric infinitization, Derrida's non-dialectical distinction between forms of mechanical or programmatic thinking (the Same) and truly inventive experience (the absolute Other) loses its justification. In the place of a distinction between bound and free idealities is proposed a distinction between two poles of novelty; the first form of novel experience would be characterized by affectivites of unintelligibility , confusion and vacuity, and the second by affectivities of anticipatory continuity and intimacy. (shrink)
Totalidad e Infinito (TI) resulta ser una obra compleja. Ante el estilo de Levinas para la exposición de sus ideas, resulta oportuno contar con un apoyo para los nuevos lectores, con el objetivo de poder indagar en aspectos que podrían pasar desapercibidos. El trabajo desarrollado por James R. Mensch, profesor de Filosofía de la Charles University en República Checa y de Saint Francis Xavier University en Canadá, le permite incorporarse dentro de la lista de comentadores destacados de Levinas. El acercamiento (...) a TI desde la analítica existencial posibilita un panorama al lector de la obra a partir de la confrontación con un interlocutor ineludible: Martin Heidegger. (shrink)
It is modernly debated whether application of the free will has potential to cause harm to nature. Power possessed to the discourse, sensory/perceptual, physical influences on life experience by the slow moving machinery of change is a viral element in the problems of civilization; failed resolution of historical paradox involving mind and matter is a recurring source of problems. Reference is taken from the writing of Euclid in which a oneness of nature as an indivisible point of thought is made (...) prerequisite in criteria of interpretation to demonstrate that contemporary scientific methodologies alternately ensue from the point of empirically centered induction. A qualification for conceptualizations is proposed that involves a physically describable form bound to energy in addition to contemporary notions of energy bound to form and a visually based mathematical-physical form is elaborated and discussed with respect to biological and natural processes. (shrink)
"The definitive clarification of the nature of the infinite has become necessary, not merely for the special interests of the individual sciences, but rather for the honour of the human understanding itself. The infinite has always stirred the emotions of mankind more deeply than any other question; the infinite has stimulated and fertilized reason as few other ideas have ; but also the infinite, more than other notion, is in need of clarification." (David Hilbert 1925).
On the face of it, Locke rejects the scholastics' main tool for making sense of talk of God, namely, analogy. Instead, Locke claims that we generate an idea of God by 'enlarging' our ideas of some attributes (such as knowledge) with the idea of infinity. Through an analysis of Locke's idea of infinity, I argue that he is in fact not so distant from the scholastics and in particular must rely on analogy of inequality.
World news can be discouraging these days. In order to counteract the effects of fake news and corruption, scientists have a duty to present the truth and propose ethical solutions acceptable to the world at large. -/- By starting from scratch, we can lay down the scientific principles underlying our very existence, and reach reasonable conclusions on all major topics including quantum physics, infinity, timelessness, free will, mathematical Platonism, triple-aspect monism, ethics and religion, all the way to creation and (...) a special type of multiverse. -/- This article amounts to a summary of my personal Theory of Everything. -/- DOI: 10.13140/RG.2.2.36046.31049. (shrink)
“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)
Many philosophers have argued that the past must be finite in duration because otherwise reaching the present moment would have involved something impossible, namely, the sequential occurrence of an actual infinity of events. In reply, some philosophers have objected that there can be nothing amiss in such an occurrence, since actually infinite sequences are ‘traversed’ all the time in nature, for example, whenever an object moves from one location in space to another. This essay focuses on one of the (...) two available replies to this objection, namely, the claim that actual infinities are not traversed in nature because space, time, and other continuous wholes divide into parts only in so far as we divide them in thought, and thus divide into only a finite number of parts. I grant that this reply succeeds in blunting the anti-finitist objection, but I argue that it also subverts the very argument against an eternal past that it was intended to save. (shrink)
This paper considers whether an analogy between distance and dissimilarlity supports the thesis that degree of dissimilarity is distance in a metric space. A straightforward way to justify the thesis would be to define degree of dissimilarity as a function of number of properties in common and not in common. But, infamously, this approach has problems with infinity. An alternative approach would be to prove representation and uniqueness theorems, according to which if comparative dissimilarity meets certain qualitative conditions, then (...) it is representable by distance in a metric space. I will argue that this approach faces equally severe problems with infinity. (shrink)
Some philosophers contend that the past must be finite in duration, because otherwise reaching the present would have involved the sequential occurrence of an actual infinity of events, which they regard as impossible. I recently developed a new objection to this finitist argument, to which Andrew Ter Ern Loke and Travis Dumsday have replied. Here I respond to the three main points raised in their replies.
Friedrich Waismann, a little-known mathematician and onetime student of Wittgenstein's, provides answers to problems that vexed Wittgenstein in his attempt to explicate the foundations of mathematics through an analysis of its practice. Waismann argues in favor of mathematical intuition and the reality of infinity with a Wittgensteinian twist. Waismann's arguments lead toward an approach to the foundation of mathematics that takes into consideration the language and practice of experts.
Descartes' philosophy contains an intriguing notion of the infinite, a concept labeled by the philosopher as indefinite. Even though Descartes clearly defined this term on several occasions in the correspondence with his contemporaries, as well as in his Principles of Philosophy, numerous problems about its meaning have arisen over the years. Most commentators reject the view that the indefinite could mean a real thing and, instead, identify it with an Aristotelian potential infinite. In the first part of this article, I (...) show why there is no numerical infinity in Cartesian mathematics, as such a concept would be inconsistent with the main fundamental attribute of numbers: to be comparable with each other. In the second part, I analyze the indefinite in the context of Descartes' mathematical physics. It is my contention that, even with no trace of infinite in his mathematics, Descartes does refer to an actual indefinite because of its application to the material world within the system of his physics. This fact underlines a discrepancy between his mathematics and physics of the infinite, but does not lead a difficulty in his mathematical physics. Thus, in Descartes' physics, the indefinite refers to an actual dimension of the world rather than to an Aristotelian mathematical potential infinity. In fact, Descartes establishes the reality and limitlessness of the extension of the cosmos and, by extension, the actual nature of his indefinite world. This indefinite has a physical dimension, even if it is not measurable. La filosofía de Descartes contiene una noción intrigante de lo infinito, un concepto nombrado por el filósofo como indefinido. Aunque en varias ocasiones Descartes definió claramente este término en su correspondencia con sus contemporáneos y en sus Principios de filosofía, han surgido muchos problemas acerca de su significado a lo largo de los años. La mayoría de comentaristas rechaza la idea de que indefinido podría significar una cosa real y, en cambio, la identifica con un infinito potencial aristotélico. En la primera parte de este artículo muestro por qué no hay infinito numérico en las matemáticas cartesianas, en la medida en que tal concepto sería inconsistente con el principal atributo fundamental de los números: ser comparables entre sí. En la segunda parte analizo lo indefinido en el contexto de la física matemática de Descartes. Mi argumento es que, aunque no hay rastro de infinito en sus matemáticas, Descartes se refiere a un indefinido real a causa de sus aplicaciones al mundo material dentro del sistema de su física. Este hecho subraya una discrepancia entre sus matemáticas y su física de lo infinito, pero no implica ninguna dificultad en su física matemática. Así pues, en la física de Descartes, lo indefinido se refiere a una dimensión real del mundo más que a una infinitud potencial matemática aristotélica. De hecho, Descartes establece la realidad e infinitud de la extensión del cosmos y, por extensión, la naturaleza real de su mundo indefinido. Esta indefinición tiene una dimensión física aunque no sea medible. (shrink)
It is commonly assumed that Aristotle denies any real existence to infinity. Nothing is actually infinite. If, in order to resolve Zeno’s paradoxes, Aristotle must talk of infinity, it is only in the sense of a potentiality that can never be actualized. Aristotle’s solution has been both praised for its subtlety and blamed for entailing a limitation of mathematic. His understanding of the infinite as simply indefinite (the “bad infinite” that fails to reach its accomplishment), his conception of (...) the cosmos and even its prime mover as finite (in the sense of autarchic/self-contained) have been contrasted with the subsequent claim of God as ens infinitum (understood as a “positive” infinity). The goal of this essay is to reexamine the major texts (notably De caelo) and to demonstrate that (1) Aristotle’s claim according to which there is no actual infinite concerns only substances, not processes. (2) That Aristotle does not deny an actual infinite as such. (3) That when considering time and God (qua eternal) Aristotle acknowledges an actual infinite. (shrink)
Time may be infinite in both directions. If it is, then, if persons could live at most once in all of time, the probability that you would be alive now would be zero. But if persons can live more than once, the probability that you would be alive now would be nonzero. Since you are alive now, with certainty, either the past is finite, or persons can live more than once.
[ES] El presente artículo estudia el influjo de los tratados físicos de Aristóteles sobre la concepción tomista en torno al lugar del infinito en el cosmos creado. Se analiza la posición sostenida por el Aquinate respecto a cuatro aspectos fundamentales de la teoría aristotélica en torno al infinito: existencia de una sustancia infinita, existencia de un cuerpo infinito, existencia de un infinito en acto y la infinitud del tiempo. Asimismo se expone el empleo de la teoría aristotélica del movimiento y (...) los lugares naturales, por parte del Doctor angélico, para la refutación de toda posición que conciba el acto de creación como una mutación temporalmente sucesiva, así como su caracterización de la divinidad como sustancia perfecta cuya infinitud no puede ser comprendida bajo la noción de cantidad. [EN] This article studies the influence of Aristotle’s physical treatises on the Thomist conception on the place of infinity in the created cosmos. It analizes the position held by Aquinas on four fundamental aspects of the Aristotelian theory about infinity: existence of an infinite substance, existence of an infinite body, existence of an infinite in act and the infinity of time. Is also exposed the use of the Aristotelian theory of motion and natural places by the Angelic Doctor for the refutation of every position that presents the act of creation as a temporally successive mutation and his characterization of divinity as a perfect substance whose infinity can not be understood under the notion of quantity. (shrink)
Abstract: With all the obstacles and challenges it has suffered, the modern religion is an integral part of our society. Are the religions and the new technical developments in any form of reasonable harmony? There is nothing greater than infinity, nothing more mysterious than the infinite space or time, and nothing more mysterious than the Creator. In this way, it seems that there is a symbolic correlation connecting the concept of infinity and the transcendental vision of the mighty (...) Creator. Is the God’s inspired word from a sacred book vulnerable to the “deconstruction” prejudice so elegantly exposed by Jacques Derrida? These are some topics this essay tries to consider. Feedback: gondork@yahoo.com. (shrink)
This paper discusses an infinite regress that looms behind a certain kind of historical explanation. The movement of one barbarian group is often explained by the movement of others, but those movements in turn call for an explanation. While their explanation can again be the movement of yet another group of barbarians, if this sort of explanation does not stop somewhere we are left with an infinite regress of barbarians. While that regress would be vicious, it cannot be accommodated by (...) several general views about what viciousness in infinite regresses amounts to. This example is additional evidence that we should prefer a pluralist approach to infinite regresses. (shrink)
It is widely known that Aristotle rules out the existence of actual infinities but allows for potential infinities. However, precisely why Aristotle should deny the existence of actual infinities remains somewhat obscure and has received relatively little attention in the secondary literature. In this paper I investigate the motivations of Aristotle’s finitism and offer a careful examination of some of the arguments considered by Aristotle both in favour of and against the existence of actual infinities. I argue that Aristotle has (...) good reason to resist the traditional arguments offered in favour of the existence of the infinite and that, while there is a lacuna in his own ‘logical’ arguments against actual infinities, his arguments against the existence of infinite magnitude and number are valid and more well grounded than commonly supposed. (shrink)
Our evidence can be about different subject matters. In fact, necessarily equivalent pieces of evidence can be about different subject matters. Does the hyperintensionality of ‘aboutness’ engender any hyperintensionality at the level of rational credence? In this paper, I present a case which seems to suggest that the answer is ‘yes’. In particular, I argue that our intuitive notions of 'independent' evidence and 'inadmissible' evidence are sensitive to aboutness in a hyperintensional way. We are thus left with a paradox. While (...) there is strong reason to think that rational credence cannot make such hyperintensional distinctions, our intuitive judgements about certain cases seem to demand that it does. (shrink)
This paper is a response to David Oderberg's discussion of the Tristram Shandy paradox. I defend the claim that the Tristram Shandy paradox does not support the claim that it is impossible that the past is infinite.
This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.
The purpose of this paper is to suggest that we are in the midst of a Cantorian bubble, just as, for example, there was a dot com bubble in the late 1990’s.
At A71/B96–7 Kant explains that singular judgements are ‘special’ because they stand to the general ones as Einheit to Unendlichkeit. The reference to Einheit brings to mind the category of unity and hence raises a spectre of circularity in Kant’s explanation. I aim to remove this spectre by interpreting the Einheit-Unendlichkeit contrast in light of the logical distinctions among universal, particular and singular judgments shared by Kant and his logician predecessors. This interpretation has a further implication for resolving a controversy (...) over the correlation between the logical moments of quantity (universal, particular, singular) and the categorial ones (unity, plurality, totality). (shrink)
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