Throughout history, almost all mathematicians, physicists and philosophers have been of the opinion that space and time are infinitely divisible. That is, it is usually believed that space and time do not consist of atoms, but that any piece of space and time of non-zero size, however small, can itself be divided into still smaller parts. This assumption is included in geometry, as in Euclid, and also in the Euclidean and non- Euclidean geometries used in modern physics. (...) Of the few who have denied that space and time are infinitely divisible, the most notable are the ancient atomists, and Berkeley and Hume. All of these assert not only that space and time might be atomic, but that they must be. Infinite divisibility is, they say, impossible on purely conceptual grounds. (shrink)

Hume's Treatise arguments concerning space, time, and geometry, especially ones involving his denial of infinite divisibility; have suffered harsh criticism. I show that in the section "Of the ideas of space and time," Hume gives important characterizations of his skeptical approach, in some respects Pyrrhonian, that will be developed in the rest of the Treatise. When that approach is better understood, the force of Hume's arguments can be appreciated, and the influential criticisms of them can be (...) seen to miss the mark. (shrink)

This paper examines connections between concepts of space and extension on the one hand and immaterial spirits on the other, specifically the immanentist concept of spirits as present in rerum natura. Those holding an immanentist concept, such as Thomas Aquinas, typically understood spirits non-dimensionally as present by essence and power; and that concept was historically linked to holenmerism, the doctrine that the spirit is whole in every part. Yet as Aristotelian ideas about extension were challenged and an actual, (...) class='Hi'>infinite, dimensional space readmitted, a dimensionalist concept of spirit became possible—that asserted by the mature Henry More, as he repudiated holenmerism. Despite More’s intentions, his dimensionalist concept opens the door to materialism, for supposing that spirits have parts outside parts implies that those parts could in principle be mapped onto the parts of divisible bodies. The specter of materialism broadens our interest in More’s unconventional ideas, for the question of whether other early modern thinkers, including Isaac Newton, followed More becomes a question of whether they too unwittingly helped usher in materialism. This paper shows that More’s attack upon holenmerism fails. He illegitimately injects his dimensionalist concept of spirit into the doctrine, failing to recognize it as a consequence of the non-dimensionalist concept of spirit, which in itself secures indivisibility. The interpretive consequence for Newton is that there is no prima facie reason to suppose that the charitable interpretation takes him to deny holenmerism. (shrink)

Despite its central role in his important theories of self and external world, Hume’s account of numerical identity has been neglected or misunderstood. The account is designed as a response to a difficulty concerning identity apparently original with Hume. I argue that the problem is real, crucial, and remains unresolved today. Hume’s response to the difficulty enlists his idiosyncratic, empiricist views on time: time consists of discrete, partless moments, some of which coexist with successions of others. Time is more like (...) a wall of variously sized bricks than like a continuous line. Hume’s arguments that time (and space) are not infinitely divisible have met with literal contempt. I show that his unusual views are motivated and consistent. The topic of identity leads naturally to Hume’s account of personal identity and his later retraction--one of the most widely discussed topics in Hume scholarship. I give a new, straightforward explanation of the retraction, by arguing that Hume’s views on consciousness preclude his prior account of the self as a fiction. I then suggest that Hume’s fundamental problem for personal identity is his general difficulty concerning identity. Discussing Hume’s metaphysics raises perhaps the most central and difficult topic in Hume scholarship--how to reconcile the constructive, theoretical Hume with the skeptical Hume. The prevailing view for the last century has been that Hume’s skepticism is limited, leaving room for his theorizing. I argue, rather, that Hume is an unlimited Pyrrhonian skeptic in relevant respects, and that this interpretation of him best reconciles his two sides. (shrink)

In two rarely discussed passages – from unpublished notes on the Principles of Philosophy and a 1647 letter to Chanut – Descartes argues that the question of the infinite extension of space is importantly different from the infinity of time. In both passages, he is anxious to block the application of his well-known argument for the indefinite extension of space to time, in order to avoid the theologically problematic implication that the world has no beginning. Descartes concedes (...) that we always imagine an earlier time in which God might have created the world if he had wanted, but insists that this imaginary earlier existence of the world is not connected to its actual duration in the way that the indefinite extension of space is connected to the actual extension of the world. This paper considers whether Descartes’s metaphysics can sustain this asymmetrical attitude towards infinite space vs. time. I first consider Descartes’s relation to the ‘imaginary’ space/time tradition that extended from the late scholastics through Gassendi and More. I next examine carefully Descartes’s main argument for the indefinite extension of space and explain why it does not apply to time. Most crucially, since duration is merely conceptually distinct from enduring substance, the end or beginning of the world entails the end or beginning of real time. In contrast, extension does not depend on any enduring substance besides itself. (shrink)

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)

Famously, Kant describes space and time as infinite “given” magnitudes. An influential interpretative tradition reads this as a claim about phenomenological presence to the mind: in claiming that space and time are given, this reading holds, Kant means to claim that we have phenomenological access to space and time in our original intuitions of them. In this paper, I argue that we should instead understand givenness as a metaphysical notion. For Kant, space and time are (...) ‘given’ in virtue of three related facts: (i) they are necessary grounds of the existence of all other spatial and temporal possibilities; (ii) in virtue of being such grounds, they are metaphysically linked to all other represented spatiotemporal things; and (iii) as representations, space and time issue from the nature of our faculty of sensibility rather than from an arbitrary act of choice. Understanding givenness in this non-epistemological way helps us recover what is plausible in both ‘intellectualist’ and ‘anti-intellectualist’ readings of the Transcendental Aesthetic. Anti-intellectualists are correct that space and time are given in mere sensibility, but intellectualists are correct that we depend on the understanding for consciousness of space and time. (shrink)

This essay explores the role of God’s omnipresence in Newton’s natural philosophy, with special emphasis placed on how God is related to space. Unlike Descartes’ conception, which denies the spatiality of God, or Gassendi and Charleton’s view, which regards God as completely whole in every part of space, it is argued that Newton accepts spatial extension as a basic aspect of God’s omnipresence. The historical background to Newton’s spatial ontology assumes a large part of our investigation, but with (...) attention also focused on the details of Newton’s unique approach to these traditional Scholastic conceptions. (shrink)

Kant's account of space as an infinite given magnitude in the Critique of Pure Reason is paradoxical, since infinite magnitudes go beyond the limits of possible experience. Michael Friedman's and Charles Parsons's accounts make sense of geometrical construction, but I argue that they do not resolve the paradox. I argue that metaphysical space is based on the ability of the subject to generate distinctly oriented spatial magnitudes of invariant scalar quantity through translation or rotation. The set (...) of determinately oriented, constructed geometrical spaces is a proper subset of metaphysical space, thus, metaphysical space is infinite. Kant's paradoxical doctrine of metaphysical space is necessary to reconcile his empiricism with his transcendental idealism. (shrink)

Draft for presentation at the 14th International Kant-Congress, September 2024. -/- Abstract: Kant claims we intuit infinite space. There’s a problem: Kant thinks full awareness of infinite space requires synthesis—the act of putting representations together and comprehending them as one. But our ability to synthesize is finite. Tobias Rosefeldt has argued in a recent paper that Kant’s notion of decomposing synthesis offers a solution. This talk criticizes Rosefeldt’s approach. First, Rosefeldt is committed to nonconceptual yet determinate (...) awareness of (potentially) infinite space, but I argue that such awareness is (1) prima facie implausible, as well as contravened by textual evidence from Kant’s (2a) definitions of ‘infinity’ and (2b) account of geometrical construction. Second, scrutiny of how Kant thinks awareness of potential infinity is afforded by geometrical construction (e.g., extending a line segment ad indefinitum) indicates no essential role for decomposing synthesis. Familiar synthesis from parts to wholes is sufficient. (shrink)

In the Treatise of Human Nature, David Hume mounts a spirited assault on the doctrine of the infinite divisibility of extension, and he defends in its place the contrary claim that extension is everywhere only finitely divisible. Despite this major departure from the more conventional conceptions of space embodied in traditional geometry, Hume does not endorse any radical reform of geometry. Instead Hume espouses a more conservative approach, claiming that geometry fails only “in this single point” – (...) in its purported proofs of infinite divisibility – while “all of its other arguments” remain intact. -/- In this paper, after laying out the prima facie case for Hume’s radical challenge to traditional geometry, I consider five strategies for blocking the arguments for infinite divisibility while conserving most of geometry. I show that each of these interpretive strategies suffers from serious substantive problems, and so none of them delivers an interpretation of Hume’s account that provides him with a way of blocking the geometric arguments for infinite divisibility while sustaining his geometric conservatism. (shrink)

Given an infinite set of finite-sized spheres extending in all directions forever, a finite-sized (relative to the spheres inside the set) observer within the set would view the set as a space composed of discrete, finite-sized objects. A hypothetical infinite-sized (relative to the spheres inside the set) observer would view the set as a continuous space and would see no distinct elements within the set. Using this analogy, the mathematics of infinities, such as the assignment of (...) a cardinality to a set, depends on the reference frame of the observer thinking about them (the mind of the mathematician) relative to the infinite set. This reasoning may also relate to the differing views of space in relativity as continuous and in quantum mechanics as discrete. (shrink)

This introduction to the roles infinity plays in metaphysics includes discussion of the nature of infinity itself; infinite space and time, both in extent and in divisibility; infinite regresses; and a list of some other topics in metaphysics where infinity plays a significant role.

Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions – amongst them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform. (...) In this paper, I will show that something very like Douven and Williamson’s argument can in fact survive with much weaker structural assumptions – and, in particular, can apply to infinite probability spaces. (shrink)

This paper argues that all of the standard theories about the divisions of space and time can benefit from, and may need to rely on, parsimony considerations. More specifically, whether spacetime is discrete, gunky or pointy, there are wildly unparsimonious rivals to standard accounts that need to be resisted by proponents of those accounts, and only parsimony considerations offer a natural way of doing that resisting. Furthermore, quantitative parsimony considerations appear to be needed in many of these cases.

For Kant, a body fills out space by means of its causal efficacy. The essential properties of matter are hence dependent on underlying forces and it is one task of the Opus postumum (OP) to reconstruct the system of forces. In order to avoid an infinite regress of causal explanations, this system of forces needs to account for a primitive origin of all mechanical moving forces in something that is constitutive of forces, yet radically different - this is (...) the ether that fills all space that constantly moves or vibrates all the parts of the material bodies internally. I argue that we can read Kant’s argument for the existence of the ether through the lens of dispositions: essential properties of matter, such as ponderability, coercibility, cohesibility, and exhaustibility, should be understood as dispositions. These dispositions are ‘physically conditioned,’ as Kant calls it, on the ether. To display their manifest and perceivable properties, the ether acts as the ubiquitous and universal ‘activation stimulus’ of the dispositions that make up material bodies. He causes them to constantly display their manifest properties that make them continuously perceivable and causally efficient. Thereby Kant offers a solution to a problem formulated by Simon Blackburn, namely that purely dispositional matter would lead us into skepticism. (shrink)

In contrast to other ancient philosophers, Epicurus and his followers famously maintained the infinity of matter, and consequently of worlds. This was inferred from the infinity of space, because they believed that a limited amount of matter would inevitably be scattered through infinite space, and hence be unable to meet and form stable compounds. By contrast, the Stoics claimed that there was only a finite amount of matter in infinite space, which stayed together because of (...) a general centripetal tendency. The Roman Epicurean poet Lucretius tried to defend the Epicurean conception of infinity against this Stoic alternative view, but not very convincingly. One might suspect, therefore, that the Epicureans’ adherence to the infinity of matter was not so much dictated by physical arguments as it was motivated by other, mostly theological and ethical, concerns. More specifically, the infinity of atoms and worlds was used as a premise in several arguments against divine intervention in the universe. The infinity of worlds was claimed to rule out divine intervention directly, while the infinity of atoms lent plausibility to the chance formation of worlds. Moreover, the infinity of atoms and worlds was used to ensure the truth of multiple explanations, which was presented by Epicurus as the only way to ward off divine intervention in the realm of celestial phenomena. However, it will be argued that in all of these arguments the infinity of matter is either unnecessary or insufficient for reaching the desired conclusion. (shrink)

I argue that Descartes' Second Causal Proof of God in the Third Meditation evidences, and commits him to, the belief that time is "strongly discontinuous" -- that is, that there is actually a gap between each consecutive moment of time. Much of my article attempts to reconcile this interpretation, the "received view," with Descartes' statements about time, space, and matter in his other writings, including his correspondence with various philosophers.

The human eyes and brain, which have finite boundaries, create a ‘‘virtual’’ space within our central nervous system that interprets and perceives a space that appears boundless and infinite. Using insights from studies on the visual system, we propose a novel fast processing mechanism involving the eyes, visual pathways, and cortex where external vision is imperceptibly processed in our brain in real time creating an internal representation of external space that appears as an external view. We (...) introduce the existence of a three-dimension default space consisting of intrapersonal body space that serves as the framework where visual and non-visual sensory information is sensed and experienced. We propose that the thalamus integrates processed information from corticothalamic feedback loops and fills-in the neural component of 3D default space with an internal visual representation of external space, leading to the experience of visual consciousness. This visual space inherently evades perception so we have introduced three easy clinical tests that can assist in experiencing this visual space. We also review visual neuroanatomical pathways, binocular vision, neurological disorders, and visual phenomenon to elucidate how the representation of external visible space is recreated within the mind. (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.

Every time we perceive the scent of an end, we are summoned to position ourselves, to express what has been, what is our condition and what is to come. Ours is, certainly the time of the end of times. A time in which the end has become the void center around which we revolve. Philosophy only speaks when there is a limit at stake: a beginning, an end, a border, a frontier. And yet, there is no measure anymore to determine (...) what is actuality or the present, what is contemporary. Time is fragmented as well as space. There is a multiplicity of time scales (cosmic, planetary, human, cultural, personal) and velocities (the human body, our cars and trains, information), but also of subjective appropriations (what is urgent, what should come first, how much time do we have left). There is no “fundamental” difference between life-time and clock-time. There are several clocks and several lives. There is also a multiplicity of space scales (elemental particles, molecules, living organisms, living collectives, all living-species), different modes (continuous, discontinuous, with borders, infinite, homogeneous, non-trivially connected), different subjective relationships to it (earth as our space -be it in terms of Husserl or of Galilei-, the cultural world-worlds, my city, my house, my body). Far is the possibility of fixing a last instance or a fundamental scale, the possibility of a whole in which we could univocally place the particulars, or the chance of finding the last constituents of being (the atoms: physical, logical, metaphysical, social, etc.). (shrink)

Understanding Hume’s theory of space and time requires suspending our own. When theorizing, we think of space as one huge array of locations, which external objects might or might not occupy. Time adds another dimension to this vast array. For Hume, in contrast, space is extension in general, where being extended is having parts arranged one right next to the other like the pearls on a necklace. Time is duration in general, where having duration is having parts (...) occurring one aft er another like the notes of a song. Hume’s diff erent view stems from his empiricism, his reliance on experience and observation as the foundation of our concepts. Nothing in our experience suggests a single vast array of locations. Rather, we simply notice that bodies are similar insofar as they have lengths that can be compared. Likewise, nothing in our experience suggests a single dimension of time. Rather, we simply notice that diff erent successions are similar insofar as they have durations that can be compared. Th eorizing that these observations show there to be a single multidimensional array goes well beyond the evidence for Hume. As a skeptic, he fi nds himself unable to assent to theories that stray too far beyond the deliverances of the senses. For Hume, the ideas of space and time are each a general idea of simple—partless— objects arrayed in a certain manner. He argues that the structures of the ideas of space and time refl ect the structures of space and time. Th erefore, space and time are not infi - nitely divisible, and they are ways simple objects are arrayed. Consequently, there is no such thing as empty space nor time without change. (shrink)

In her last known piece of work Lady Mary Shepherd’s Metaphysics (1832), Mary Shepherd writes that “mind, may inhere in definite portions of matter […] or of infinite space” (LMSM 699). Shepherd thus suggests that a mind – a “capacity for sensation in general” (e.g., EPEU 16) – may have a spatial location. This is prima facie surprising given that she is committed to the view that the mind is unextended. In this paper, we argue that Shepherd can (...) consistently honor both of these commitments. We argue, first, that even though finite minds, due to their unextendedness cannot, to use Shepherd’s term, ‘occupy’ space as material bodies do, such minds can nonetheless be said to have a spatial location in virtue of what we call their presence, or what Shepherd calls ‘inherence’, in a material body. Second, we argue that, in a similar way, the divine mind is present throughout the whole of space and is thus omnipresent. We then argue that, in contrast to finite minds, the divine mind does not require a body to be present in space. Rather, we contend, God’s omnipresence might be best understood in a ‘holenmerist’ sense, where the divine mind is wholly present in every part of creation. (shrink)

The incompleteness of set theory ZFC leads one to look for natural extensions of ZFC in which one can prove statements independent of ZFC which appear to be "true". One approach has been to add large cardinal axioms. Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski- Grothendieck set theory TG [1]-[3] It is a non-conservative extension of ZFC and is obtaineed from other axiomatic set theories by the inclusion of Tarski's axiom which implies the existence (...) of inaccessible cardinals [1].Non-conservative extension of ZFC based on an generalized quantifiers considered in [4]. In this paper we look at a set theory NC_{∞^{#}}^{#},based on bivalent gyper infinitary logic with restricted Modus Ponens Rule [5]-[8]. In this paper we deal with set theory NC_{∞^{#}}^{#} based on gyper infinitary logic with Restricted Modus Ponens Rule. Set theory NC_{∞^{}}^{} contains Aczel's anti-foundation axiom [9]. We present a new approach to the invariant subspace problem for Hilbert spaces. Our main result will be that: if T is a bounded linear operator on an infinite-dimensional complex separable Hilbert space H,it follow that T has a non-trivial closed invariant subspace. Non-conservative extension based on set theory NC_{∞}^{#} of the model theoretical nonstandard analysis [10]-[12] also is considered. (shrink)

We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown (...) to be represented by a linear transformation of the representations of the individual preorders. Further Pareto conditions on the social preorder correspond to positivity conditions on the transformation. When all the Pareto conditions hold and the population is finite, the social preorder is represented by a sum of individual preorder representations. We provide two applications. The first yields an extremely general version of Harsanyi's social aggregation theorem. The second generalizes a classic result about linear opinion pooling. (shrink)

Une preuve est pure si, en gros, elle ne réfère dans son développement qu’à ce qui est « proche » de, ou « intrinsèque » à l’énoncé à prouver. L’infinité des nombres premiers, un théorème classique de l’arithmétique, est un cas d’étude particulièrement riche pour les recherches philosophiques sur la pureté. Deux preuves différentes de ce résultat sont ici considérées, à savoir la preuve euclidienne classique et une preuve « topologique » plus récente proposée par Furstenberg. D’un point de vue (...) naïf, il semblerait que la première soit pure et la seconde impure. Des objections à cette vue naïve sont ici considérées et réfutées. Concernant la preuve euclidienne, la question relève de la logique, notamment de la définissabilité arithmétique de l’addition en termes de successeur et de divisibilité telle que démontrée par Julia Robinson, tandis qu’en ce qui concerne la preuve topologique, la question relève de la sémantique, notamment pour tout ce qui touche au problème de savoir ce qui est « inclus » dans le contenu d’énoncés particuliers.A proof is pure, roughly, if it draws only on what is « close » or « intrinsic » to the statement being proved. The infinitude of prime numbers, a classical theorem of arithmetic, is a rich case study for philosophical investigation of purity. Two different proofs of this result are considered, namely the classical Euclidean proof and a more recent « topological » proof by Furstenberg. Naively the former would seem to be pure and the latter to be impure. Objections to these naive views are considered and met. In the case of the former the issue rests on logical matters, specifically the arithmetic definability of addition in terms of successor and divisibility shown by Julia Robinson, while in the case of the latter the issue rests on semantic matters, specifically with respect to what is « contained » in the content of particular statements. (shrink)

We present a new approach to the invariant subspace problem for complex Hilbert spaces.This approach based on nonconservative Extension of the Model Theoretical NSA. Our main result will be that: if T is a bounded linear operator on an infinite-dimensional complex separable Hilbert space H,it follow that T has a non-trivial closed invariant subspace.

The purpose of this paper is to explore infinite sets and classes by mean hyperoperations. With ideal notion, the idea of extending infinite sets is as large as those objects. In this paper, extensions with hyperoperations are realized, like factorial, derivative, integral and operations between vector spaces. The ideas about infinite and count are enlarged.

There are few notions in philosophy seen more clearly, and in parallel so laden with confusion, than that of space and time. The subjective nature of analyses is most likely to blame. As it stands, a universal agreement has not yet been reached. My position is simply that the mind, when passive, has no qualms with space and time itself, nor is it concerned with its principles. It is only when our passions are ignited, and our judgment is (...) utilized, i.e. when we begin to actively think about space and time, that the notion becomes confounded. Any further digression into semantics of the issue by trying to give a ‘say all end all’ explanation will always lead to a dead end. Both space and time are ideas of an infinite nature and can never be visited manifestly since the mind itself is undeniably finite. (shrink)

How should we think about the role of visual spatial awareness in perception and perceptual knowledge? A common view, which finds a characteristic expression in Kant but has an intellectual heritage reaching back farther than that, is that an account of spatial awareness is fundamental to a theory of experience because spatiality is the defining characteristic of “outer sense”, of our perceptual awareness of how things are in the parts of the world that surround us. A natural counterpart to this (...) idea is to treat self-consciousness as residing in a kind of sense that is fundamentally “inner”, such as introspection or whatever else gives one privileged access to his own mental states as well as the proprioceptive and kinesthetic awareness of bodily position. This division is compatible, of course, with the idea that inner sense provides an awareness of a distinctive kind of “body space”, but it treats that as importantly different from the awareness of the worldly space around one. -/- In contrast to such a picture, this dissertation proposes an account of visual spatial awareness according to which it is no less a source of self-consciousness than of the awareness of the objects around us, and an account of self-awareness in which visual experience is essentially implicated. I begin by arguing that we should think of visual spatial awareness not as necessary for the individuation of visual sensations but rather as an essential element in the awareness of an experientially objective world. In the subsequent chapters, I argue that in being visually aware of the egocentric positions of the worldly objects around us we are often aware also of our own spatial locations with respect to them, and that the visual experience of the world around one and one’s own situation in it is often an essential component in the knowledge that a human agent will have of his own intentional actions. (shrink)

The purpose of this writing is to propose a frame of view, a form as the eternal world element, that is compatible with paradox within the history of ideas, modern discovery as they confront one another. Under special consideration are problems of representation of phenomena, life, the cosmos as the rational facility of mind confronts the physical/perceptual, and itself. Current topics in pursuit are near as diverse and numbered as are the possibilities for a world composed strictly of uniqueness able (...) to fill infinite space; it is assumed that not all of the paths chosen in contemporary pursuits will produce coherent determinations in an appropriate frame able to accommodate a world of nominals in motion, containing motion, and is commensurate with basic physical law and the propagation of form, change from within. Intended as a potential guiding post for the aim of reason seeking to select, define and capture topics, chosen as special examples are the works of logistician/mathematician Lewis Carroll as he presents a paradox of actuality verses the reality of perception in Alice in Wonderland, the theory of relativity of Albert Einstein as he fails to elaborate a mathematics to communicate an inertial frame of reference, and the reconstruction ideas of Jacques Derrida as he refers for contrast with the scientific world view constructed of dualisms, monisms that are conceived to have no opposites. Supporting discussion is evolved from the works of Bertrand Russell, Erwin Schrodinger, Jurgen Habermas, Bronislaw Malinowski, Michel Foucault. (shrink)

Not much attention has been paid to Malebranche’s philosophy of time. Scholars who have written on it have typically written about it only in passing, and by and large discuss it only in relation to his philosophy of religion. This is appropriate insofar as Malebranche doesn’t discuss his views of time in isolation from his religious metaphysics. I argue that Malebranche’s conception of how created beings have their properties commits him to saying that God is omnitemporal rather than atemporal. For (...) just as bodies get their spatiality by participating in God’s omnipresence, so all creatures get their temporality by participating in God’s omnitemporality. Moreover, Malebranche is a substantivalist about space and time: infinite space and time are one and the same divinely simple substance, God (partially considered), who contains the world. My exploration of Malebranche’s metaphysics sheds light on his views of eminent containment, participation, and causation. (shrink)

General Relativity’s Schwarzschild solution describes a spherically symmetric gravitational field as an utterly static thing. The Space Generation Model describes it as an absolutely moving thing. The light propagation time-delay experiment of Shapiro-Reasenberg [1] and the falling atomic clock experiment of Vessot-Levine [2] provide the ideal context for illustrating how, though the respective world views implied by these models are radically di fferent, they make nearly the same prediction for the results of these experiments.

Abstract: Standing half wave particles at light speed twice in expansion-contraction comprise a static universe where two transverse fields 90° out of phase are the square of distance from each other. The universe has a static concept of time since the infinite universe is a static universe without a beginning or end. The square of distance is a point of reversal in expansion-contraction between the fields as a means to conserve energy. Photons on expansion in the electric field create (...) matter energy while photons on contraction in the magnetic field create light energy and gravitational pull toward the higher frequency energy. Also, the universe with matter has a moving physical concept of time from gravitational pull on expansion-contraction. (shrink)

Although being widely considered as only a Western tradition, individualism is not absent in traditional Chinese philosophy and culture. In some of the classic Chinese philosophic works such as Zhuangzi, we can clearly identify some elements which can be appropriately attributed to “individualism”, such as the awareness of individual “self” as an independent and unique existence, advocating individual freedom and liberty, emphasizing on the value and dignity of individual life, favoring individuals’ autonomy and privacy, pursuing unconstrained development in personality and (...) spirituality. However, due to its particular pre-Qin social cultural background and its unique Daoist philosophic origin, this kind of individualism in Zhuangzi has its own unique characteristics, which has made it distinguishable from the variety of other individualist thoughts emerged in different times and places in the West. Zhuangzi has a dynamic and open view on individual or “self”, he does not consider individuals as fixed and interchangeable “atoms” but as dynamic, changing and unique beings, he set the unlimited and indefinable Dao as the only and ultimate source for individuals to conform to, thus to release individual mind into an realm of infinite openness and freedom. Zhuangzian individualism is “inward” rather than “outward”, which means while concentrating on individuals’ freedom of spirit and innate nature, it cares less about individuals’ outside material interests and rights in social reality, and does not encourage competition and rivalry among individuals. The special type of individualism in Zhuangzi has a profound influence on Chinese culture, providing a spiritual space for the development of individuality and personality in ancient China. It also provides an alternative understanding of individual as an existence. (shrink)

The success of a few theories in statistical thermodynamics can be correlated with their selectivity to reality. These are the theories of Boltzmann, Gibbs, end Einstein. The starting point is Carnot’s theory, which defines implicitly the general selection of reality relevant to thermodynamics. The three other theories share this selection, but specify it further in detail. Each of them separates a few main aspects within the scope of the implicit thermodynamic reality. Their success grounds on that selection. Those aspects can (...) be represented by corresponding oppositions. These are: macroscopic – microscopic; elements – states; relational – non-relational; and observable – theoretical. They can be interpreted as axes of independent qualities constituting a common qualitative reference frame shared by those theories. Each of them can be situated in this reference frame occupying a different place. This reference frame can be interpreted as an additional selection of reality within Carnot’s initial selection describable as macroscopic and both observable and theoretical. The deduced reference frame refers implicitly to many scientific theories independent of their subject therefore defining a general and common space or subspace for scientific theories (not for all). The immediate conclusion is: The examples of a few statistical thermodynamic theories demonstrate that the concept of “reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another. Still a few more general suggestions referring the scientific realism debate can be added: One can admit that reality in scientific theories is some partially shared common qualitative space or subspace describable by relevant oppositions and rather independent of their subject quite different in general. Many or maybe all theories can be situated in that space of reality, which should develop adding new dimensions in it for still newer and newer theories. Its division of independent subspaces can represent the many-realities conception. The subject of a theory determines some relevant subspace of reality. This represents a selection within reality, relevant to the theory in question. The success of that theory correlates essentially with the selection within reality, relevant to its subject. (shrink)

Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of (...) class='Hi'>space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. (shrink)

There is an apparent tension in Shepherd’s accounts of space and time. Firstly, Shepherd explicitly claims that we know that the space and time of the unperceived world exist because they cause our phenomenal experience of them. Secondly, Shepherd emphasizes that empty space and time do not have the power to effect any change in the world. My proposal is that for Shepherd time has exactly one causal power: to provide for the continued existence of self-same or (...) changing objects. Because Shepherd takes causation to be a relation whereby two objects combine to form a third, their effect, whenever we perceive a continually existing object, since time is a proper part of such objects, our perception of time is caused by time itself. Likewise, space’s causal power is to provide for the possibility of the motion or rest of objects, and so when we perceive objects with space as a proper part, we come into causal contact with space. (shrink)

A Monograph Dealing With Unification In Relation To Dark Energy, Dark Matter, Cosmic Expansion, E=mc2, Quantum Gravity, "Imaginary" Computers, Creation Of The Infinite And Eternal Universe Using Electronic BITS + PI + "Imaginary" Time, Earthly Education, Science-Religion Union, The Human Condition, Superconductivity, Planetary Fields, How Gravitation Can Boost Health, Space-Time Propulsion From The Emdrive To The Brouwer Fixed-Point Theorem, "Light Matter", Etc. These Effects Were Originally Discussed In Several Short Internet Articles. Table Of Contents Introduction Superconductivity And Planetary (...) Magnetic / Electric Fields Co-Movement Of Photons And Graviton General Relativity Deletes Dark Energy, Dark Matter And Universal Expansion The Relation Of The Higgs Field To Gravity Spin Interactions And Making Bosons Or Fermions The Final Missing Steps In E=mc2 What Will Education Be Like In 2049? Learn By Holographic Teachers Using Quantum Mechanics, "Imaginary" Computers And A Unification Of Physics That Will Bring Education To Everyone, Everywhere Hypotheses Supporting Gravitation As A Push - (1) M-Sigma, The Non-Fundamental Nuclear Forces (2) Geysers On Saturn's Moon Enceladus (3) Gravity, Falling Bodies (4) Earth's Tides, Astronomical Unit, Cosmic Backgrounds A Proposal For The True Human Condition That Reconciles Science With Religion Back To The Moon And On To The Stars Normalising Patients With Gravitation. (shrink)

Nietzsche has a surprisingly significant and strikingly positive assessment of mathematics. I discuss Nietzsche's theory of the origin of mathematical practice in the division of the continuum of force, his theory of numbers, his conception of the finite and the infinite, and the relations between Nietzschean mathematics and formalism and intuitionism. I talk about the relations between math, illusion, life, and the will to truth. I distinguish life and world affirming mathematical practice from its ascetic perversion. For Nietzsche, math (...) is an artistic and moral activity that has an essential role to play in the joyful wisdom. (shrink)

Between 1653 and 1655 Margaret Cavendish makes a radical transition in her theory of matter, rejecting her earlier atomism in favour of an infinitely-extended and infinitely-divisible material plenum, with matter being ubiquitously self-moving, sensing, and rational. It is unclear, however, if Cavendish can actually dispense of atomism. One of her arguments against atomism, for example, depends upon the created world being harmonious and orderly, a premise Cavendish herself repeatedly undermines by noting nature’s many disorders. I argue that her supposed difficulties (...) with atomism expose a deeper tension in her work between two fundamental metaphysical commitments each of which has substantial philosophical support: her monist theory of the material world (which maintains that there exists just one natural substance which is the single principal cause) and her occasional theory of causation (which requires multiple finite principal causes in nature -- causes that might be considered individual substances). Her monism undermines atomism while her theory of occasional cause seems to rest on a conception of nature that would be especially friendly to atomism. I argue further that we can solve this tension within a Cavendishian framework in such a way as to preserve her theory of causation and her monism, but that this solution depends upon our taking her monism in a particular (and weak) form. I finally note that we can best make sense of her unique and interesting form of monism by acknowledging her social-political motivations in addition to her motivations in natural philosophy. (shrink)

Quantum mechanics involves a generalized form of information, that of quantum information. It is the transfinite generalization of information and re-presentable by transfinite ordinals. The physical world being in the current of time shares the quality of “choice”. Thus quantum information can be seen as the universal substance of the world serving to describe uniformly future, past, and thus the present as the frontier of time. Future is represented as a coherent whole, present as a choice among infinitely many alternatives, (...) and past as a well-ordering obtained as a result of a series of choices. The concept of quantum information describes the frontier of time, that “now”, which transforms future into past. Quantum information generalizes information from finite to infinite series or collections. The concept of quantum information allows of any physical entity to be interpreted as some nonzero quantity of quantum information. The fundament of quantum information is the concept of ‘quantum bit’, “qubit”. A qubit is a choice among an infinite set of alternatives. It generalizes the unit of classical information, a bit, which refer to a finite set of alternatives. The qubit is also isomorphic to a ball in Euclidean space, in which two points are chosen. (shrink)

Tschumi believes that the quality of architecture depends on the theoretical factor it contains. Such a view led to the creation of architecture that would achieve visibility and comprehensibility only after its interpretation. On his way to creating such an architecture he took on a purely philosophical reflection on the basic building block of architecture, which is space. In 1975, he wrote an essay entitled Questions of Space, in which he included several dozen questions about the nature of (...) space. The questions he formulated could be regarded as analogous to the situation in the philosophy of the time, in which the interest in questioning the most obvious forms of understanding the world and intellectual categories increased. The research on space is an area common to many fields of natural sciences, humanities and artistic creation, but it also deals with other problems, such as issues of experience. The concept of space-time continuum proposed by Hermann Minkowski drew attention to the identity of time and space with the events taking place. Probably regardless of the postulates of physicists commenting on Einstein’s discoveries, also in philosophy it increased the importance of the concept of the event which became dominant in Heidegger’s latest work Contributions of Philosophy. Of the event. Furthermore, Tschumi’s reflections on space entered into relation with the problem of experience, which aroused the interest of a group of French philosophers trying to assimilate Georges Bataille’s concept of “inner experience”. Both Tschumi and Derrida referred to Bataille because his views could be used not only to modify the concept of the subject, but also to change the understanding of what constitutes the area of architecture. The discussion on experience has led to the recognition that the subject is not sovereign, but actually a form of what is on their outside. Such insights make it possible to treat the area of the Parc de La Villette as existing mainly when it is organised by its users. The decisive features of the Park are its assumptions, according to which it is a variety of active void that leads to agreeing new social relations with it. The park does not force to participate in already existing moral or political communities, but tries to move into an unknown future in which the scope of free functioning of individuals will be increased. Doubts about the principles of functioning of the individual self and its discovery as a whole composed of non-coherent parts, as well as its dependence on its own depth full of disordered forces, influenced the understanding of architecture as a set of contradictions whose source is a fundamental void anticipating the empty phenomenal space. The use of this phenomenal void in architecture, as well as the rejection of the whole and unity, had a specific political purpose and drew its inspiration from political analyses. In the Parc de La Villette, metaphysics and politics were brought closer together because the philosophy of void was used to create new conditions for community action. It can be argued that the source of this philosophy was the perception of errors in existing societies dependent on the shortcomings of traditional metaphysics. Spacing (espacement) was one of the key terms in Derrida’s philosophy, which was also combined with the concepts of différance and chôra. The study of the nature of space, especially its transition from the level of pure possibility to the level of sensual phenomenon, also contributes to understanding how well designed space can have an impact on its audience. This explanation is based on Tschumi’s assumption that the space of the Parc de La Villette contradicts the integrating approaches and instead exposes contradictions, but it does so in a way that combines incompatible properties into a single piece of architecture. The specificity of such integration is similar to the invention of a musical phrase, which is an ideological message: moral and political. Such a thesis may raise doubts, however, if both the clearly adopted assumptions and those deduced from the work allow for their ↪Quart Nr 2(52)/2019 logically ordered presentation then to a limited extent it may be assumed that the work has achieved a connection between a specific philosophy of space and its practical application. Derrida combined the problem of spatiality with the problem of transcendental imagination in Kant’s philosophy, who in the first version of Critique of Pure Reason assumed that pure imagination precedes the appearance of time and space, even in their transcendental forms. The imagination in such a situation can be described as a factor activating time and space, which indicates what function is played by movement in this activity. This leads us to recognize that the ultra originary source of pure forms of sensual intuition is movement, which in early Greek philosophy was identified with void and its lack of resistance to phenomena occurring in it. Derrida’s philosophy in search of a certain super-transcendental source of time and space pointed to différance which, like void or the chôra, does not have material features or even any other form of being. Différance is the primary cause of the disruption of motionlessness and the introduction of activity into motionless time and space, thus its activity can be described as spacing (espacement). Derrida’s discoveries in this respect are not entirely original, because Hegel already pointed out when examining the present that it is primarily a differential relation (differente Beziehung), which, being seemingly neutral, influences the present with supernatural force and makes it unidentifiable with itself. Differente Beziehung must similarly influence the originary space, negating its initial character by multiplying its divisions and expanding its boundaries. Différance acts by revealing contradictions wherever there is apparent undifferentiation. Tschumi, composing the Parc de La Villette as a variety of void and a set of incompatible layers, followed the rules of différance or the chôra: he made void visible together with its saturation with contradictions. If space can be considered to be the result of the activity of difference, such activity has a certain regularity, which influences the behaviour of its observers. Differences or contradictions fall into a certain rhythm, which can be considered a manifestation of transcendent order. The problem is that what can be considered the source of such order, namely the logos or God, is partly disorder and error. According to descriptions contained in Timaeus, the world is a combination of forces that drive to order with forces of erroneous necessity that resounds in every order and forces it to return to disorder. Derrida denied the possibility of understanding différance as a theological value, even if it were a negative or apophatic theology, but no categorical denial could be perfect. The assumption that différance or the chôra are not endowed with any substance properties cannot deny their activity, and thus a certain force. Already since Democritus, philosophy has multiplied the names of such a force and the contradictory variety of its manifestations, never forgetting also the necessity for reason to withdraw from the possibility of giving its correct characteristics. Such a withdrawal may be interpreted as an expression of respect and, in certain situations, as a cult of the force that precedes reasonableness. The Parc de La Villette, which is an artistic divagation about the contradictions and forces behind them, can be considered as a place of their sublimation, and therefore as a variation of the temple of what differs from order and disorder. (shrink)

In this paper I intend to present the Dilemma of Continuity of Matter and a possible solution to it. This dilemma consists in choosing between two misfortunes in explaining the continuity of matter: or to say that material objects are infinitely divisible and not explain what constitutes the continuity of some kind of object, or to say that there is a certain kind of indivisible object and not explain what constitutes the continuity of such an object. The solution we provide (...) is precisely the thesis that material objects consists of points, a thesis we try to make clearer, although we have not developed it much. (shrink)

Predication is a lingual relation. We have this relation when a term is said (λέγεται) of another term. This simple definition, however, is not Aristotle’s own definition. In fact, he does not define predication but attaches his almost in a new field used word κατηγορεῖσθαι to λέγεται. In a predication, something is said of another thing, or, more simply, we have ‘something of something’ (ἓν καθ᾿ ἑνὸς). (PsA. , A, 22, 83b17-18) Therefore, a relation in which two terms are posited (...) to each other in a way that one is said (predicated) of the other is a predication. The term of which the other term is said is called a subject (ὑποκειμένον) and the other, which is said about the subject, is called the predicate. Thus, in a predication the predicate is predicated of the subject; given that being predicated is almost as the same as being said. The relation between being said and being predicated is so close that ‘if something is said of a subject both its name and its definition are necessarily predicated of the subject.’ (Cat., 5, 2a19-26) This, however, is true only about the second genera and not the accidents. a) Nature of relation in predication What is Aristotle’s theory about the nature of the relation in a predication? How does he fundamentally understand this relation? Phil Corkum distinguishes between predication logic and traditional term logic and argues that the relation between subject and predicate in Aristotle is of the latter kind. While in predicate logic, subjects and predicates have distinct roles, they have the same role in traditional term logic. In predication logic, subjects refer, but predicates characterize. Thereupon, a sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. In traditional term logic, both subjects and predicates refer and a sentences expresses a truth if both name one and the same thing. He concludes that Aristotle ‘problematically conflates prediction and identity claims’ because while he thinks both subjects and predicates refer, he would deny that a sentence is true just in case the subject and the predicate name one and the same thing. Based on this, Corkum believes that Aristotle’s core semantic is not identity but the weaker relation of constitution, which is a mereological interpretation: ‘All men are mortal’ is true just in case the mereological sum of humans is part of the mereological sum of mortals. b) Aristotle’s theory of predication: one or two theories? Frank Lewis finds an inconsistent gap between the theory of predication in the Categories and that in the later books of the Metaphysics VII, 6. So too Joan Kung, Terry Irwin, Daniel Graham. c) Distinction of ‘being said of’ and ‘being in’ Owen enumerates the texts in which Aristotle’s distinction between ‘being said of’ and ‘being in’ is asserted: OI. 11b38-12a17; To., 127b1-4; Cat. 1a20-b9; 2a11-14; 2a27-b6; 2b15-17; 3a7-32; 9b22-24 d) Predication in Aristotle and the standard ‘S is P’ Marie De Rijk Lambertus thinks that the ‘S is P’ pattern is misleading when it comes to express predication in Aristotle. In his view, ‘The Aristotelian procedure should be described in terms of appositively assigning an attribute (κατηγορούμενον) to a substrate (ὑποκείμενον), rather than ascribing a predicate to a subject by means of a copula…. The comment should be considered an attribute which is said to fall to a substrate, without understanding this procedure in terms of sentence predication.’ e) Aristotle’s predication: bipartite or tripartite? It is a difficulty to make Aristotle’s theories of name-verb predication and tripartite predication consistent. The reason is that tripartite is not consistant with his name-verb structure based on which he says that the predicate term is the ‘verb.’ (20a31; 20b1-2; 16a13-5) The problem is that in a tripartite form like ‘Socrates is white’ we cannot take ‘is white’ as the verb because, based on Aristotle himself, no part of a verb can be significant itself. (16b6-7) However, his assertions about the equivalences between the two structures (OI. 12, 21b9-10; PrA. 51b13-16; Met., 1017b22-30) must mean that they are not inconsistent in his own view. Thus, as Allen Bāck points, ‘Aristotle seems to think that he has a single, consistent theory.’ The sense of saying or speaking as the root sense of rhema makes the relation between predication (saying something of something) and verb more interesting. The use of rhema in the sense of a long expression approves this. In Plato’s work (399ac) where Socrates claims that the name anthropos derives from anthron ha opopen (‘he who examines what he has seen’) we have an onoma from, or in place of, a rhema. 1) Subject The subject (ὑποκειμένον) is that of which another term is said or predicated. Aristotle’s own definition is of a much more philosophical value: ‘By subject I mean that which is expressed by an affirmative term (λέγω δὲ ὑποκείμενον τὸ κάταφάσει δηλούμενον).’ (Met., K, 1067b18) Throughout Aristotle’s work, three kinds of subjects can be found: possible, prime and absolute subject. a) Possible subject Those things that can take the position of a subject in a predication we call possible subjects, no matter they can or cannot take the position of predicate in any predication. All terms except the ultimate predicates are possible subjects because they can take the position of subject. b) Prime subject Those that in any predication can only take the position of a subject and not the position of a predicate are prime subjects. (Cat., 5, 3a36-b2; Met., Z, 1028b36-1029a1) This is the truest sense of subject and belongs only to substances. (Met., Z, 1029a1-2) In fact, ‘that which is not predicated of a subject, but of which all else is predicated’ is a substance. (Met., Z, 1029a7-9) In Categories, besides primary substances (Cat., 2, 1b3-6), individual qualities are also said not to be able to be said of anything else. (Cat., 2, 1a23-29) Aristotle’s examples are a certain ‘knowledge-of-grammar’ (τὶς γράμματικὴ) and ‘an individual white’ (τὸ τὶ λευκὸν). Thus, although substances are indeed in the truest sense individuals and, thereby, in the truest sense primary subjects, other individuals can take the position of subject as well. c) Absolute subject While substances are prime subjects of all other things, there is still something of which substances can be predicated and this predication is not an accidental predication: matter. (Met., Z, 1029a21-24) This predication is, indeed, the predication of a ‘form or this’ on matter and material substance. (Met., Θ, 1049a34-36) The only thing that is absolutely a subject, therefore, and can be a predicate is prime matter (πρώτη ὓλη). (Met., Θ, 1049a24-27) d) Subject and substance The most important thing in being a substance is being a subject: ‘It is because the primary substances are subjects for all the other things and all the other things are predicated of them or are in them, that they are called substances most of all.’ (Cat., 5, 2b15-17) And what is nearer to this position is more a substance as a species is more a substance than a genus.’ (Cat., 5, 2b7-8) e) Primary versus accidental subject A subject is a primary subject in a predication when the predicate is predicated of it as itself. In such a case, the subject is the subject of the predicate qua itself and not qua something else. A subject, on the one hand, is an accidental subject when it is not the primary subject of the predicate that is predicated on it. It means that a subject is an accidental subject when the predicate is predicated of it not qua itself but qua something else. An accidental subject is, therefore, anything other than a substance. 2) Predicate as universal It is evident from our discussion of kinds of subjects that except matter, primary substances (if we ignore both accidental predication and cases of absolute subjects) and other individuals, everything else can take the position of a predicate. Since primary substances are individuals, it results that everything except matter and individuals are capable to take the position of predicate. The immediate consequence of this is that the predicate must be a universal. When individuals cannot take the position of predicate, this position cannot be taken by any particular. Therefore, only universals can be predicated of others. Moreover, albeit universals can be a simple subject (for another universal), they are not prime subjects. The closeness of universal and predicate is to the extent that Aristotle differentiates universal from subject. (Met., Θ, 1049a27-30) 3) Categories or classes of predicates Aristotle distinguishes ten highest classes into one of which each predicate must necessarily fall: substance (or what a thing is), quality, quantity, relation, place, time, position, state, activity and passivity. (Cat., 4, 1b25-27; To., I, 9, 103b20- ; PsA., A, 22, 83b13-23) The substance counted among predicates must refer to secondary and not primary substances not only because Aristotle insists that primary substances cannot be predicated but also from his own examples of the category of substance: man and animal. (To., I, 9, 103b25) However, if a predicate be asserted of itself or its genus be asserted of it, the predicate signifies substance or what is; but if ‘one kind of predicate is asserted of another kind,’ it signifies one of the other nines. (To., I, 9, 103b30) These categories are so comprehensive that no predicate can remain outside them so that even non-being has as many senses as categories. (Met., M, 1089a26-30) a) That whether Aristotle’s categories are merely linguistic or fundamentally ontological is a so much controversial dispute. Some like G. E. R. Lloyd believe that ‘categories are primarily intended as a classification of reality … rather than of the signifying terms themselves.’ b) Although Aristotle’s categories have been historically regarded as a classification of predications, there are some recent commentators like Jonathan Barnes that think it is classifying predicates and not predications. 4) Kinds of predicates In his introduction of Categories, as J. W. Thorp truly points out , Aristotle distinguishes between the category of substance and the other categories using μὲν ... δὲ construction. This construction illustrates that beside tenfold classification of categories, there is an even more crucial differentiation between two kinds of predicates: substance or what is on the one hand and the other nine ones on the other hand: the distinction between what is predicated of the subject as what it is and what is predicated of it as an accident. Therefore, we have three kinds of classification - a twofold, a fourfold and a tenfold-complicatedly classifying the same thing, viz. the predicate. Predicates can be divided also to four kinds: property, definition, genus and accident. (To., I, 4, 101b11-20) A property is that predicate that is convertible with its subject and does not signify its essence. A definition is that predicate that is convertible with its subject and signifies its essence. It is a genus if it is not predicated convertibly and is contained in the definition of its subject. And it is an accident if it is neither convertible nor contained in the definition of its subject. (To., I, 8, ^103b3) All of these four kinds are among categories. (To., I, 9, 103b20) It seems that there might be some kind of relation between the twofold and the fourfold distinction: whereas genus and definition are predicated as what it is, accidents are not so predicated. There seems to be some rules that determine to each of these four kinds each predicate belongs. At To., IV, 123b30ff. Aristotle asserts: ‘If B has a contrary and A does not, then B does not belong to A as its genus.’ There is a dispute around per se accidents (τὰ καθ’ αὑτὰ συμβεβηκότα) (Topics., 102a18) whether they must be regarded as either of the four kinds or as a fifth kind. Barnes (1970) argued that they ‘do not fit at all neatly into the fourfold classification.’ He argues that based on the definition of accidents at A, 5, 102b4-5, they must be accidents but based on another definition, A, 5, 102b6-7, they cannot be accidents. He also defends the view that they are not properties. Barnes concludes: ‘This shows that the two definitions are not equivalent, and hence that the ‘predicables’ are not well-defined.’ Demetris J. Hadgopoulos defends the view that the two definitions of accidents are equivalent and per se accidents are properties. 5) Five types of predications We have five kinds of predications based on our division of subjects and our discussion of predicates: simple, primary (itself divided to substantial and accident), accidental (itself divided to primary and secondary), aoincidental and absolute predication. a) Simple predication. This is a predication in which a universal is predicated of either a particular or a universal subject. This sense of predication includes all other senses except the first kind of accidental predication. b) Primary predication. This is a predication in which a universal is predicated of a primary subject, namely a substance. A primary predication is of two kinds: i) Substantial predication. A primary predication in which the predicate is part of, or is included in, the definition of the subject. The universal that is the predicate here is the definition or the genus or the species or the diferentia of the subject. It is this predication that Aristotle calls a unity: ‘A statement may be called a unity … because it exhibits a single predicate as inhering not accidentally in a single subject.’ (PsA., B, 10, 93b35-37) It is only substantial predicates that can be predicated of each other: ‘Predicates which are not substantial are not predicated of one another.’ (PsA., A, 22, 83b18-19) Aristotle defines a substantial predication also in another way. A predication in which a higher genus is predicated on a lower genus, species, a substance or an individual, (or a species is predicated on an individual) is a substantial predication. Therefore, a substantial predication is a predication in a series that has individuals on one of its ends and a general category on its other end. In fact, only substantial predicates can be predicated of one another. (PsA., A, 22, 83b17-19) This series cannot be an infinite series because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) -/- ii) Accident predication. A primary predication in which the predicate is not part of, or is not included in, the definition of its subject. The universal that is the predicate here is the property or the accident of the subject. c) Accidental predication. This is a predication in which the subject is not a primary subject and its predicate is a substance. This predication is of two kinds: i) Primary accidental predication. This is a predication in which an accident is predicated of substance. Such a predication can go ad infinitum, which is inferable from Aristotle’s assertion that the secondary accidental predication cannot go ad infinitum. ii) Secondary accidental predication. It is a predication in which an accident is predicated of another accident. Such a predication, Aristotle asserts, cannot go ad infinitum because even more than two accidents cannot be combined. Now what is the meaning of Aristotle’s assertion that we cannot continue this ad infinitum? Does it mean that we cannot continue the predication ‘The musician is white’ and say ‘The white is Athenian?’ But why not? Or maybe he means that by adding any predication, we are still in a condition of predicating two accidents of a substance on each other. -/- As primary subjects, substances can also take the position of predicate though not essentially but accidentally. In propositions like ‘the white is a log’ or ‘That big thing is a log’ we observe substance taking the position of predicate but this is only accidentally: ‘When I affirm ‘the white is a log,’ I mean that something which happens to be white is a log- not that white is the subject in which log inheres (οὐχ ὡς τὸ ὑποκείμενον τῷ ξύλῳ τὸ λευκόν ἐστι), for it was not qua white or qua a species of white that the white (thing) came to be a log (οὔτε λευκὸν ὄν οὔθ᾿ ὃπερ λευκόν τι ἐγἐνετο ξύλον), and the white (thing) is consequently not a log except incidentally.’ (PsA., 22, 83a3-9) Aristotle compares this accidental use of substance in the position of predicate with the substantial use of it in the place of a subject: ‘On the other hand, when I affirm ‘the log is white,’ I do not mean that something else, which happens to be a log, is white (οὐχ ὃτι ἓτερόν τί ἐστι λευκόν, ἐκείνῳ δὲ συμβέβηκε ξύλῳ εἶναι), (as I should if I said ‘the musician is white,’ which would mean ‘The man who happens also to be a musician is white’); on the contrary, log is here the subject- the subject which actually came to be white, and did so qua wood or qua a species of wood and qua nothing else.’ (PsA., 22, 83a8-14) Aristotle asks us not to call propositions like ‘The white is a log’ a predication at all or at least call them accidental predication instead of simple (ἁπλως) predication. (PsA., A, 22, 83a14-17) An accidental predication, in which we have a substance in the place of predicate, is different from an essential predication in that while the subject of an accidental predication is said to be the predicate not by itself but as something different with which it coincides, the subject of an essential predicate is said to be the predicate by itself and not because it is something else: ‘Since there are attributes which are predicated of a subject essentially and not accidentally- not, that is, in the sense in which we say ‘That white (thing) is a man,’ which is not the same mode of predication as when we say ‘The man is white’: the man is white not because he is something else but because he is man, but the white is man because ‘being white’ coincides with ‘humanity’ within one subject. Therefore, there are terms such as are essentially subjects of predicates. (PsA., A, 19, 81a24-29) This capability of ‘non-essentially and only accidentally’ being a subject does belong, in fact, to all sensible things. (PsA., A, 27a32-36) d) Coincidental predication. this is a predication in which none of the subject and predicate are a substance or an individual. In this predication, one of the accidents of a substance or individual is predicated of one of the other accidentals of the same substance or individual. For example, when it is said that ‘The white is musical,’ there is an individual, say Socrates, for which both of white and musical are accidents. e) Absolute predication. This is a predication in which a form or a substance is predicated of a matter or a material substance. Some commentators like Loux and Lewis regarded this predication as close to accident predication, both based on inherence. As R.M. Dancy points out, these predications make Aristotle’s theory of predication immanentist: not only accident predications are explained by the immanence of accidents in substances, some of the substantial predications, which were not explained in Categories, are also explained by the immanence of form in matter. It is interesting that in this kind of predication, it is the predicate and not the subject, which is in the strictest sense substance. As the central books of Metaphysics claim, the form is the substance. Thus, in this predication, substance gets away from the sense of ὑποκείμενον. Corkum mentiones 68a19 as the only instance where Aristotle explicitly claims that a term may be predicated of itself, a passage that is, in Corkum’s view, problematic. 6) Demonstrable predicates Those predicates are demonstrable that are so related to their subjects that there are other predicates prior to them predicable of their subjects (ἔτι δ᾿ ἄλλος, εἰ ὧν πρότερα ἄττα κατηγορεῖται). (PsA., A, 22, 83b32-34) 7) Series of predications Since it is possible for a predicate to be itself the subject of another predication, we can have a series of predications in which the predicate of a predication is the subject of the next predication. This series has the following features: a) It has a limit (in number) (PsA., A, 22, 83b14-16) on the side of subjects: there are subjects that cannot themselves be predicated (PsA., A, 27, 43a39-41), which are, as we noted, prime subjects: particulars, i.e. prime substances and other individuals. (PsA., A, 19-22) Aristotle calls them ultimate (ὓστατον). (PsA., 21, 82a36-b1) b) It has a limit (in number of kinds) (PsA., A, 22, 83b14-16) also on the side of predicates: there must be predicates that cannot be subjects. (PsA., A, 19-22; PsA., A, 27, 43a36-39) Aristotle calls them primary (πρῶτον). (PsA., A, 21, 82b1-4) These are the highest categories or the highest genera of categories. (PsA., A, 22, 83b14-16) c) The series has an escalating shape from mere subjects at its downside to mere predicates at its upside. It is Aristotle himself whos uses the words up and down in this sense. (e.g. PsA., A, 22, 83b2-3) d) The predications that lie between lowest and highest ones must be finite in number. (PsA., A, 19-22 especially: 20, 82a21-35) These have subjects and predicates, each capable of both of the roles of being subject and being predicated. A result of this fitness is that neither demonstration can go to infinity nor everything is demonstrable, the two points Aristotle always insist on. e) The upward side includes the more universal ones and the downward the more particular ones. (PsA., 20, 82a21-23) f) It follows from the above features that ‘neither the ascending nor the descending series of predications … are infinite.’ (PsA., A, 22, 83b24-25) g) Reciprocation and convertibility. Except in case of terms (i.e. subjects and predicates) that are at each of the ends of series of predications, namely ultimates and primaries, it is possible to reciprocate (ἀντιστρέφειν) terms and convert the predication. (PsA., A, 19, 82a15-20) h) Antipredication. Antipredication means that in a predication (S is P), the subject becomes the predicate of its predicate (P is S) in the same category its predicate was predicated on it. For example, if P is in the category of quality, antipredication means that S be predicated of P in the category of quality. In other words, P is a quality of S and S is a quality of P. Aristotle rejects this. (PsA., A, 22, 83a36-b3) i) Self-predication versus other-predication. Aristotle distinguishes between a predication in which a term is said of itself and a predication in which a term is said of another. (Phy., Δ, 2, 209a31-33) j) Predicablity (Cat., 5, 3a36-b2): 1) Primary substances and individuals are not predicable. 2) Secondary substances are of two kinds: genus and species i) Genus is predicable able both of the species and of the individuals. ii) Species is predicable of the individual. 3) Differentiae are predicable both of the species and of the individuals. 8) Predication as classification a) Richard Patterson believes that Aristotle’s so repeated construction using hoper (estin A hoper B) in Topics (120a23 sq., 122b19, 26sq., 123a, 124a18, 125a29, 126a21, 128a35. Also in Posterior Analytics (83a24-30) (Brunschwig’s list. ‘expresses the fact that A is a kind of B (esti A B tis), that A is a species of the genus B.’ 9) Universal predication Aristotle defines universal predication (κατὰ παντὸς κατηγορεῖσθαι) as such: ‘wherever no instance of the subject (τῶν τοῦ ὑποκειμέμνου) can be found of which the other term cannot be asserted.’ (PrA., A, 24b27-29) In this predication, the subject is included in another as in a whole (ἐν ὃλῳ εἶναι) and the predicate is predicated of all of the subject (κατὰ παντὸς κατηγορεῖσθαι). (PrA., A, 24b26-27) Attach another discussion we had about ἐν ὃλῳ here. 10) Quantity of predication A predication, truly stated, has a quantity, which is the number of objects under the name of the subject of which the predicate is predicated. The quantity of subject can be stated in four ways: a. Indefinite: when the predicate belongs or does not belong to the subject without any mark to show to haw many of the particulars under the name of the subject it does or does not belong. E.g. ‘Man is white’; ‘Man is not white.’ (PrA., A, 24a20; OI., I, 7, 17b8-12) b. Universal quantity: When the predicate belongs to all or none of the subject. E.g. ‘Every man is animal’; ‘No man is animal.’ (PrA., A, 24a18-19; OI., I, 7, 17b5-6) The contrary of a predication of a universal quality is a predication of a universal quality. E.g. the contrary of ‘Every man is white’ is ‘No man is white.’ (OI., I, 7, 17b20-23) c. Particular quantity: When the predicate belongs (or does not belong) to some of the subject. E.g. ‘Some men are white’; ‘Some men are not white.’ (PrA., A, 24a19-20) d. Single quantity: when the subject is a proper name of only one object. E.g. ‘Socrates is white’; ‘Socrates is not white.’ The contrary of this predication is of a single quantity: ‘Socrates is not white.’ (OI., I, 7, 17b38-18a4) 11) Convertibility of predication. Some predications are convertible, that is, it is possible to change the place of subject and predicate in a true proposition so that the converted proposition remains true. This is supposed to mean that given the truth of a predication, the truth of the converted predication is inferable. The convert form of a predication depends on its quantity. a. Indefinite quantity: This predication has no strictly true convert because its quantity is not stated. b. Universal quantity: It can be converted in two ways: i) A negative universal can be converted to a negative universal in which the terms are changed. E.g. ‘No pleasure is good’ can be converted to ‘No good is pleasure.’ (PrA., A, 2, 25a5-8 and a14-19) ii) An affirmative universal can be converted to an affirmative particular in which the terms are changed. E.g. ‘Every pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a7-9) c. Particular quantity: If it is negative, it cannot be converted but if it is affirmative, it can be converted to an affirmative predication with particular quantity. E.g. ‘Some pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a10-13 and a20-24) d. Single quantity: It cannot be converted. 12) Characteristics of relations between subject and predicate 1. A predicate is of a wider range than its subject. It is based on this fact that Aristotle: a) Prevents individuals to be predicate because there is nothing of which an individual be of a wider range. In other words, it is due to the fact that since an individual is only ‘one particular’ thing and, thus, cannot be of a wider extent than anything that Aristotle prevents them of being a predicate. Matthews, however, thinks we cannot use Socrates, a substance and an individual, in the place of predicate and say it of Socrates because ‘Socrates does not classify Socrates: it names him.’ b) Prevents differentia, species and things under species to be predicated of genus. (To., Z, 6, 144a27-) c) Prevents the species and the things under it to be predicated of the differentia. (To., Z, 6, 144b1-4) d) Also about the effect because it is wider than its subject. (PsA., B, 17, 99a) e) Each attribute is wider than every individual it is predicated on, though several attributes, collectively considered, might not be wider but exactly the substance of a thing. (PsA., B, 13, 96a32-b1) 2. The predicate of a predicate of a subject will be predicated of the subject too: ‘whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject too.’ (Cat., 3, 1b10-15) In fact, it is due to its predication of the subject that it is predicated of its predicate. (Cat., 5, 2a36-b1) Moreover, what is not predicated of the predicate of a subject cannot be predicated of it as well. (PrA., A, 27, 43b22-27) Thus, what, for example, is not predicated of animal, cannot be predicated of man. 3. The predicate of a subject can be predicated of its predicates as well. (Cat., 5, 3a1-6) For example, you call the individual man grammatical and, thence, you call both a man and an animal grammatical. Nonetheless, the predicate of a subject belongs to it more properly than to its higher predicates. (PrA., A, 27, 43a27-32) 4. It is only the subject that can be distributed and not the predicate. (PrA., A, 27, 43b16-22; OI, I, 7, 17b12-16) Therefore, we can say e.g. ‘Every man is animal’ but we cannot say ‘Every man is every animal.’ 5. It is the reason of the relation between subjects and predicates, that is the reason of predication, which is the subject of inquiry. (Met., Z, 1041a20-24) In other words, since it is a meaningless inquiry to ask why a thing is itself (Met., Z, 1041a14-15), the only remaining meaningful inquiry is to ask why something is something else, i.e. to ask about the reason of predication. 6. A subject cannot categorize its predicate in the same category in which it is categorized by it. If e.g. A is a quality of B, B cannot be a quality of A. Therefore, there is no reciprocation in the same category. (PsA., A, 22, 83a36-39) 13) Characteristics of series of predications 1. A series of secondary accidental predication cannot go ad infinitum for not even more than two terms can be comnbined. For an accident is not an accident of an accident, unless it be because both are accidents of the same subject. (Met., Γ, 1007b1-4) 2. Infinite series cannot be traversed in thought. (PsA., A, 22, 83b6-7) 3. The predications of genera on each other must be ended and cannot go to infinity because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) Therefore, a series of predication of genera on each other must be limited on both sides. There must be an upward limit in general categories as well as a downward limit in individual because they cannot be predicated of others. Whatever lies between these limits can both be predicated of others and others be predicated of them. (PrA., A, 27, 43a36-43) 4. The order of predicates matters: it makes a difference whether the series be ABC or BAC. (PsA., B, 13, 96b25-32) . (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 is one of the best popular cosmology books ever written and Guth is now (2016) a top physics Professor at MIT. He tells the extremely complex story of inflation and related areas of particle physics in such an absorbing style that it reads like a detective novel-in fact, it is a detective novel-how he and others found out how the universe started! The interweaving of his personal story and that of many colleagues along with their photos and many wonderfully (...) clear diagrams allows just the right amount of relaxation from the intensity of the physics. In places the style reminds one of Watson´s famous book ``The Double Helix``. He tells how his work on magnetic monopoles and spontaneous symmetry breaking led to the discovery of the inflationary theory of the very early universe (ca. 10 to minus 35 seconds!). -/- Along the way you will learn many gems that should stay with you a long time such as: the observed universe(e.g., everything the Hubble telescope etc. can see out to ca. 15 billion light years when the universe began) is likely just a vanishingly tiny part of the entire inhomogeneous universe which is about 10 to the 23rd times larger; the big bang probably took place simultaneously and homogeneously in our observed universe; there probably have been and will continue to be an infinite number of big bangs in an infinite number of universes for an infinite time; when a bang happens, everything(space, time, all the elements) from the previous universe are destroyed; the stretching of space can happen at speeds much greater than the speed of light; our entire observed universe lies in a single bubble out of an endless number so there may be trillions of trillions just in our own entire(pocket) universe(and there may be an endless number of such); none of these infinite number of universes interact-i.e., we can never find out anything about the others; each universe started with its own big bang and will eventually collapse to create a new big bang; all this implies that the whole universe is fractal in nature and thus infinitely regresses to ever more universes(which can lead one to thinking of it as a giant hologram); disagreements between the endless(hundreds at least) variations of inflation are sometimes due to lack of awareness that different definitions of time are being used; some theories suggest that there was a first big bang but we can never find out what happened before it; nevertheless it appears increasingly plausible that there was no beginning but rather an eternal cycle of the destruction and creation, each being the beginning of spacetime for that universe; to start a universe you need about 25g of matter in a 10 to minus 26cm diameter sphere with a false vacuum and a singularity(white hole). -/- He deliberately spends little time on the endless variants of inflation such as chaotic, expanded and supernatural inflation or on dark matter´, supersymmetry and string theory, though they were well known at the time as you can find by reading other books such as Michio Kaku´s `Hyperspace` (see my review) and countless others. Of course much has happened since this book appeared but it still serves as an excellent background volume so cheap now it’s free for the cost of mailing. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

This paper uses a schema for infinite regress arguments to provide a solution to the problem of the infinite regress of justification. The solution turns on the falsity of two claims: that a belief is justified only if some belief is a reason for it, and that the reason relation is transitive.

The book aims to examine how a Trinitarian Theism can be formulated through the elaboration of a Relational Ontology and a Trinitarian Metaphysics, in the context of a hyperphatic epistemology. This metaphysics has been proposed by some supporters of the so-called Open Theism as a solution to the numerous dilemmas of Classical Theism. The hypothesis they support is that the Trinitarian nature of God, reflected in a world of multiplicity, relationality, substance and relations, demands that we think of God as (...) dynamic, internally multiple and relational. However, if the expression «God is love» – understood as the formula of the Trinity – is the key to a new theism, it leaves a problem open: how can it be translated philosophically? The research develops on two different levels: first, it assesses whether the expression should be translated into the Trinitarian paradigm, and the aporias it generates; secondly, it tries to assess whether this paradigm (eminently relational) has a correspondence in ontology: is there a satisfactory Relational Metaphysics already available? The suspicion is that such Trinitarian-Relational Ontology, invoked by many as a solution to the incongruities of classical theism, has yet to be formulated in a satisfactorily manner, despite the existence of various attempts to formulate Relational Ontologies. In order to provide an evaluation of all these attempts and to outline some possible new perspectives, the thesis consists of five chapters. It is the aim of the present dissertation to evaluate such attempts, and to outline some possible new solutions. In the chapters some points have been established: 1. there must be at least one irreducible real relation (non-reductionist realism); 2. the relation must be equally fundamental to the substance: this means that it is both external and internal; 3. this relation must be able to account for contingent causality; 4. holism is a plausible position; 5. the Trinity is a good theistic model of the divine, apophatic but rational. The last chapter then returns to ontological questions: several Relational Ontologies are examined – including ontic structural realism and process (or eventist) ontology – together with their applications in philosophy of religion (e.g.: the Relational God, Process Trinitarianism, the Entangled God). This assessment shows how all these ontologies postulate real transcendental relations (subsistent relations), inside the substances or inside the powers, inside the tropes or the structures, describing them as monads or processes (or actual occasions). These relations are the same we need to describe the Trinity. Therefore, they are either possible for both domains – ontology and theology – or they are both impossible. It has been opted for the second conclusion. But they are both impossible and inevitable: the fundamental entities of the world and their interactions (causation) must be described as real transcendental relations because each ontology transforms entities or relations into real transcendental relationships at some point. Thus, neither relationalism nor substantialism are convincing: from the fall of these two dogmas (or, rather, from the fall of their naive interpretations) we can realise that the fundamental reality is something that lies between processism (relationalism) and substantialism. It is impossible to completely substitute the notion of substance with the notion of event, process, structure or relation, both in speaking of God and in speaking about the entities of fundamental ontology. Neither monism nor pluralism can be affirmed in their pure forms. The hypothesis proposed, then, is that the notion of gunk-junk is the only one that can translate the relationality hitherto sought in an ontological model. The central part of the chapter describes the merits and defects of an eventist-infinitive ontology (EIO) based on the concept of gunk, and its potentiality to generate new theistic accounts. Through the notion of infinityings it seems to be possible to find some solutions for the questions left open by the causal relation, and therefore to defend at least the existence of one relation (external and internal). Each fundamental entity is described, in this ontology, through four transcendentals: ‘entity’, ‘relation’, ‘unity’ and ‘multiplicity’. The co-primarity between substance and relations (borrowed from the notion of relatio subsistens) differentiates EIO from the process philosophies precisely because it does not pretend to eliminate the substantial principle, or the category of substance, but wants to think of it with the transcendental of relationality. Of course, EIO poses a challenge to the role, the method and the explicative capacity of metaphysics, because what we can state of the fundamental reality is antinomic. EIO tries to assume the antinomy as a result, to make it the basis of a kind of apophatic ontology. If our best ontology is gunky, then it is possible to confirm what has been said in chap. 4: the ‘how’ of individual substances is unknown to us at least as much as the ‘how’ of God. Even in the world we have the mystery of a distinction that is not division. However, the convergence of these antinomies can find an ultimate explanation in a theistic metaphysics (EIM): God creates inside of Himself and his Trinitarian substance is “contracted” into the worldly entities. They are made contingent and ontologically different by this self-limitation, but it is still the infinity of God that makes space in Himself for something new, even though He is totally present in every entity. It is not absurd to think that the substances of the world keep track of the divine nature, even in His “contraction”. Among the characteristics of the divine nature that each created entity maintains we have the subsistent relationality, the pericoretic indwelling (the infinite gunk-junk), the fact of being always one-and-many. If EIO and EIM are accepted as a good compromise between relationalism and substantialism, even in their apophaticity, then, on this basis, a Trinitarian Philosophy is possible. The picture of reality that emerges represents the world as multiple, substantial, contingent and intrinsically relational, forcing us to postulate the transcendental of relationality and multiplicity. Such transcendental leads us to think of the world and God (and their relations) in a Trinitarian way – With the necessary acknowledgement that this is a reasonable but apophatic discourse. (shrink)

In this paper, I aim to show that a certain form of immortality, without the need for any intervention from a supernatural being, is almost inevitable for human beings. I take a physicalist starting point: I am a certain configuration of physical particles. Thus, if these particles were reassembled in the same configuration, I would necessarily come back into existence. I address a number of objections raised against this prospect by Eric T. Olson, who argues that the reassembly of such (...) particles following their dispersal after death would be simply impossible, and that if it did occur, it would necessarily be a mere replica rather than the real ‘me’. I suggest that the random redistribution of particles can be thought of as the throw of cosmic ‘dice’. With any specific throw, the likelihood that it yields the particular configuration that constitutes ‘me’ is vanishingly small. But over infinite spans of time, this likelihood increases until it becomes a near certainty. I show that even if this reconfiguration lacks the same causal features as those that gave rise to the original me, this cannot imply that the reassembled me is a mere replica. I acknowledge that my conjectured form of immortality may be unappealing to theists and non-theists alike. I also note that it rests on a linear conception of time, which may not harmonise with current thinking in physics. However, these issues notwithstanding, my conjectured version of immortality is at least as inexorable as many other things we take for granted, which also rest on potentially flawed beliefs about the nature of time and space. (shrink)