In Laws book X Plato tries to give us conclusive evidence that there are at least two gods (one good and the other bad). The reasoning depends crucially on the idea of ‘self moving motion.’ In this paper I try to show that the ‘evidence’ is not persuasive. (Nevertheless, the idea of ‘self – moving motion is interesting.).

In Metaphysics Λ.6-7 Aristotle argues that an unmoved substance causes the outermost sphere to rotate. His argument has puzzled and divided commentators from ancient Greece to the present. I offer a novel defense of Aristotle's argument by highlighting the logic of classification that Aristotle deploys. The core of Aristotle's argument is the identification of the unmoved substance on the 'table of opposites' as simple and purely actual. With this identification in place, Aristotle argues that the outermost sphere activates its capacity (...) to relocate its body by rotating because this is how it can be a simple and actual substance. But unlike traditional attempts to rehabilitate Aristotle's argument, I argue that the sphere does not rotate in order to imitate the Prime Mover. Rather, the sphere rotates because that is good for it to do, and the Prime Mover is a metaphysically necessary source of simple and actual substantial being, which the sphere acts for the sake of. (shrink)

This paper elaborates some of the conceptual implications of Derrida’s call for “another thinking of life” in Voyous: Deux essais sur la raison. The paper first argues that Derrida’s deconstruction of the opposition between metaphorical and literal uses of the discourse of life in La vie la mort is radicalized in Voyous when he argues that democracy’s “autoimmunitary suicide” should be the point of departure for rethinking life in general. To understand further these autoimmune-suicidal tendencies, the paper turns to Derrida’s (...) engagement with Aristotle’s conceptual figure of the prime mover in Voyous. The paper argues that Derrida turns to Aristotle because the prime mover illustrates the ways in which the concept of life remains historically and structurally informed by the philosophical value of ipseitocratic sovereignty, which is allergic to the disseminatory, proliferating, and improper qualities that the philosophical tradition has always ascribed to democracy. Autoimmunity thus provides a way for thinking of a democratic life that is not entirely determined by the teleological power of any divinely good life. (shrink)

If the prime mover must be considered as efficient cause and not only as a final cause, then one must ask: why does God move the heavens? We hold the position that the anthropocentrism which Aristotle maintains is able to sufficiently justify the thesis that God moves the spheres so that human beings may exist. This provides an additional motive for accepting providence, which is manifestly ordered specifically towards man.

Argues that Aristotle regarded the universe, or Totality, as a single substance with form and matter, and that he regarded this substance together with the Prime Mover as a self-mover.

It is commonly assumed that Aristotle denies any real existence to infinity. Nothing is actually infinite. If, in order to resolve Zeno’s paradoxes, Aristotle must talk of infinity, it is only in the sense of a potentiality that can never be actualized. Aristotle’s solution has been both praised for its subtlety and blamed for entailing a limitation of mathematic. His understanding of the infinite as simply indefinite (the “bad infinite” that fails to reach its accomplishment), his conception of the cosmos (...) and even its prime mover as finite (in the sense of autarchic/self-contained) have been contrasted with the subsequent claim of God as ens infinitum (understood as a “positive” infinity). The goal of this essay is to reexamine the major texts (notably De caelo) and to demonstrate that (1) Aristotle’s claim according to which there is no actual infinite concerns only substances, not processes. (2) That Aristotle does not deny an actual infinite as such. (3) That when considering time and God (qua eternal) Aristotle acknowledges an actual infinite. (shrink)

The transitory and ever-evolving process of law making plays a role of primal importance in the regulation of human conduct of society. It goes without saying that in this entire process, judges have a participation. The power entrusted by law and the nature of judicial process, make judges the prime mover of the development of law. It matters how judges decide cases. It matters most to people unlucky or litigious or wicked or saintly enough to find themselves in (...) court... The effect emanating from the decision of a case affects the life of a person in many ways that at times has far reaching impact...When the law in question happens to be criminal law, it requires a cautious consideration to see how the interpretive tools used by judges affect the life of a litigant in ways both seen and unseen... Several areas concerning adjudication and judicial interpretation have been the subject matter of study. This paper includes a discussion on the principle of non- retrospectivity in light of judicial adjudication in criminal matters. (shrink)

In Aristotle's cosmology, the nature of the elements is defined by their place in the Totality. Their cosmic motions keep the whole in motion, and this is their nature. Thus, the cosmos is an organized whole, a single substance directed to the good; this body constitutes together with its Prime Mover a composite substance that can be regarded as a self-mover.

The Eleventh Aporia results from the breakup of the entire Greek philosophy previous to Aristotle in two manners of conceiving and proposing the first principles (archai), specially the One (to hen): (i) the manner by which Physiologoi conceived the One as a principle, namely, assuming an underlying nature, different from the One in itself, not adequately characterized by the simple fact of being one and which is denoted by the concept of One, and (ii) the manner inaugurated by the Pythagoreans (...) and later endorsed by Plato, marked by the abandonment of the appeal to an underlying nature and by conceiving the One in itself (auto to hen) as a principle, depriving it of any connection with some reality not strictly characterized by being one. Aristotle faces this aporia in Metaphysics Iota 2 and, according to the interpretation I propose: (a) refuses the Pythagorean-Platonic manner of conceiving and proposing principles, (b) endorses the course of action of the Physiologoi, and, in doing so, (c) steps back and retakes the “project” of the Physiologoi at the point where it was interrupted, namely, during the search for a principle of motion. From this scenario, I will try to show that the final outcome of the Eleventh Aporia can be the introduction of the Prime Mover as the properly Aristotelian (and cosmological) candidate to the title of One between the principles. (shrink)

This work in metaphysics adheres to the critical demands of Immanuel Kant for what Kant would call a science of metaphysics, in that it consits strictly of a priori principles that, while from pure reason, can help make sense of our phenomenal world (Kant's criterion for objective validity). The work has an Appendix quoting Kant's most relevant remarks with regard to a science, and offers parallel quotes from David Hume's "Treatise of Human Nature". The work advances the explanation of a (...) causal process that accounts for the origination of the universals: space, time, mass (or substance), and mind (or consciousness), and it necessitates the existence of God as Absolute Being and Absolute Mind. Hegel's 'Science of Logic' is quoted wherein Hegel makes an analogous claim. The causal process is defined with both a definite beginning and a definite end and agreement can be found with the statement found in the book of Revelation, final chapter: "I am the Alpha and the Omega, the first and the last, the beginning and the end." The statement suggests a movement that is not in conflict with the science, and seems to reflect Hegel's own thoughts. The science does not conflict with, but it further finds agreement with the science of big bang cosmology, but it goes further in necessitating a 'singularity' at the beginning of time. The causal process defined has a Formative Phase and a Creative Phase, with the former preceding the big bang and the latter following after the big bang. (shrink)

Moeser suggested participants default to linear ordering elements but they can be primed to impose either linear or partial ordering. This study seems problematic insofar as ‘greater than’ might be understood to incline participants to favor linear orderings. Recent follow-up studies strongly suggest participants do not default to linear ordering. It seems plausible, moreover, that the observed priming effect is far more pervasive than Moeser countenanced. The present work explores the extent to which priming for linear or partial orders conflicts (...) with the construction of linear or partial ordering lists. Our two experiments suggest friction between priming and task, and also show once the priming tasks are cleared of potentially confounding semantic content, participants perform equally with respect to constructing linear or partial orders under similar priming conditions. (shrink)

I argue that the empirical literature on priming effects does not warrant nor suggest the conclusion, drawn by prominent psychologists such as J. A. Bargh, that we have no free will or less free will than we might think. I focus on a particular experiment by Bargh – the ‘elderly’ stereotype case in which subjects that have been primed with words that remind them of the stereotype of the elderly walk on average slower out of the experiment’s room than control (...) subjects – and I show that we cannot say that subjects cannot help walking slower or that they are not free in doing do. I then illustrate how these cases can be reconciled and normalized within a Davidsonian theory of action to show that, in walking slower, subjects are acting intentionally. My argument applies across various experiments, including those of goal priming. In the final section I argue that the only cases in which priming effects are efficacious are so-called Buridan cases. (shrink)

It is often assumed that believing that p for a normative reason consists in nothing more than (i) believing that p for a reason and (ii) that reason’s corresponding to a normative reason to believe that p, where (i) and (ii) are independent factors. This is the Composite View. In this paper, we argue against the Composite View on extensional and theoretical grounds. We advocate an alternative that we call the Prime View. On this view, believing for a normative (...) reason is a distinctive achievement that isn’t exhausted by the mere conjunction of (i) and (ii). Its being an achievement entails that (i) and (ii) are not independent when one believes for a normative reason: minimally, (i) must hold because (ii) holds. Apart from its intrinsic interest, our discussion has important upshots for central issues in epistemology, including the analysis of doxastic justification, the epistemology of perception, and the place of competence in epistemology. (shrink)

Whether some condition is equivalent to a conjunction of some conditions has been a major issue in analytic philosophy. Examples include: knowledge, acting freely, causation, and justice. Philosophers have striven to offer analyses of these, and other concepts, by showing them equivalent to such a conjunction. Timothy Williamson offers a number of arguments for the idea that knowledge is ‘prime’, hence not equivalent to or composed by some such conjunction. I focus on one of his arguments: the requirement that (...) such conjuncts must be freely recombinable. Although there has been a great deal of discussion of Williamson's arguments, the flaw I describe has gone unnoticed. Williamson's argument is expressed in terms of conditions, and cases of the condition. Does the condition include specific information, or is the specific information only part of the case? His argument equivocates between more and less general specifications of the conditions. Once this distinction is clarified, his argument can be seen to be vitiated by this conflation. Neither option yields a sound argument for Williamson's desired conclusion. (shrink)

According to the target article authors, initial experience with a circumstance primes a relation that can subsequently be applied to a different circumstance to draw an analogy. While I broadly agree with their claim about the role of relational priming in early analogical reasoning, I put forward a few concerns that may be worthy of further reflection.

Sri Guru Granth Sahib, the holy scripture of the Sikhs, contains numerous references to the worship of the divine in Nature. The Sikh scripture declares that human beings' purpose is to achieve a blissful state and be in harmony with the Earth and all creation. Millions of Sikhs recite Gurbani daily wherein the divine is remembered using the symbolism from Nature, esp. air, water, sun, moon, trees, animals, and the Earth. The human mind loses communion with Nature and ultimately with (...) God by being self-conceited. It causes misery all around, is a repeated assertion of Sikhism. The contemporary environmental crisis is an outcome of the actions of such a self-conceited human mind. By affirming God's immanence and His presence in the creation, the Sikh religion imparts the spirit of self-righteousness to the entire subject of Nature. Sikhism is a remarkable religious and cultural phenomenon; several important themes emerge within its universe of beliefs. On the ecological front, the theology of Sikhism suggests that humans must live in harmony with Nature. The Sikh Gurus exemplified many of these teachings, and their examples continue to inspire contemporary social, religious, and environmental leaders in their efforts to protect the planet. In this presentation, the prime environmental teachings of Sikhism are shared with the community. (shrink)

The 16th and 17th centuries witnessed a philosophical shift that would help pave the way for modern science, a shift from metaphysical theories of material objects to other views embracing only the empirically-accessible parts of material things. One much-debated topic in the course of this shift was regarding prime matter. The late scholastic Jacobus Zabarella (1533-1589) arrived upon his views about prime matter via his version of the regressus method, a program for a sort of scientific reasoning. In (...) his De rebus naturalibus, Zabarella defends the position that prime matter is extended. However, it is less clear how he accounts for its extension. There is an important text where he apparently suggests that prime matter is extended in and of itself. However, there are two other texts apparently stating that matter is extended in virtue of a distinct accident in the category of quantity. I argue that a decisive reading based solely upon any particular texts is not available. Nevertheless, examining Zabarella’s writing on the topic as a whole, the trajectory of his overall argument is remarkably sympathetic to Averroes, who famously took the accidentally quantified position. Thus, from this systematic feature, the accidentally quantified reading is more reasonable. (shrink)

This paper aims to show that Selim Berker’s widely discussed prime number case is merely an instance of the well-known generality problem for process reliabilism and thus arguably not as interesting a case as one might have thought. Initially, Berker’s case is introduced and interpreted. Then the most recent response to the case from the literature is presented. Eventually, it is argued that Berker’s case is nothing but a straightforward consequence of the generality problem, i.e., the problematic aspect of (...) the case for process reliabilism (if any) is already captured by the generality problem. (shrink)

A lean hylomorphism stands as a metaphysical holy grail. An embarrassing feature of traditional hylomorphic ontologies is prime matter. Prime matter is both so basic that it cannot be examined (in principle) and its engagement with the other hylomorphic elements is far from clear. One particular problem posed by prime matter is how it is to be understood both as a principle of individuation for material substances and as pure potency. I present Thomas Aquinas’s way of squeezing (...) some intelligibility out of prime matter by modeling it on the idea of logical genus. Such a modeling provides insight into understanding prime matter as substratum, as maximally indeterminate, and as ontologically vague. One of the unusual but exciting things that fall out from this analysis of prime matter is the Entirety Thesis: “For any substance x, if x has prime matter then the prime matter of x is the same* as x,” where ‘same*’ is understood as “indeterminately identical.”. (shrink)

I argue that the science of the soul only covers sublunary living things. Aristotle cannot properly ascribe ψυχή to unmoved movers since they do not have any capacities that are distinct from their activities or any matter to be structured. Heavenly bodies do not have souls in the way that mortal living things do, because their matter is not subject to alteration or generation. These beings do not fit into the hierarchy of soul powers that Aristotle relies on to provide (...) unity to ψυχή. Their living consists in their activities, not in having a capacity for activity. (shrink)

I argue that the prime matter that Leibniz posits in every created monad is understood by him to be a mere defect or negation, and not something real and positive. Further, I argue that Leibniz’s talk of prime matter in every created monad is inspired by the thirteenth-century doctrine of spiritual matter, but that such talk is simply one way in which Leibniz frames a point that he frequently makes elsewhere—namely, that each creaturely essence incorporates a limitation that (...) is the ultimate source of an original imperfection that affects the creature from the first moment of its existence. (shrink)

The present study aimed to explore the effect of subliminal priming on team trust and the mechanism through the mediating role of perceived trustworthiness. A total of 144 participants were asked to complete a lexical decision task that was embedded with the “trust” or “suspicion” Chinese words as the subliminal stimuli. Then, they played a public good game and evaluated the perceived trustworthiness of the team. The results of the study showed that subliminal stimuli had a significant effect on team (...) trust [β = –0.99, 95% CI = (−1.64, −0.33)]. Perceived trustworthiness was found to have a significant mediating effect between the priming condition and team trust [β = −0.35, 95% CI = (−0.72, −0.02)]. The current study revealed the underlying mechanism through which subliminal priming techniques influence team trust and informed efforts by altering perceived trustworthiness. (shrink)

In a recent book and article, James Sterba has argued that there is no free will defense. It is the purpose of this article to show that, in the most technical sense, he is wrong. There is a version of the free will defense that can solve what Sterba (rightly) takes to be the most interesting and severe version of the logical problem of moral evil. However, I will also argue that, in effect (or, we might say, in practice), Sterba (...) is correct. The only working version of the free will defense requires embracing a view that entails consequences theists traditionally have not and cannot accept. Consequently, the one and only free will solution is not viable. Unless some other solution can be found (Sterba argues there is none), the logical problem of evil, as Sterba understands it, either commits one to atheism, or a version of theism that practically all theists would regard as a heresy. (shrink)

An excerpt of "The SignalGlyph Project and Prime Numbers" (a chapter of the book THE IMAGE OF LANGUAGE) that attempts to illustrate how dimensional limitations of mathematical language have obscured recognition of the system of patterning in the distribution of prime numbers.

Two very different forms of externalism about mental states appear prima facie unrelated: Williamson’s (1995, 2000) claim that knowledge is a mental state, and Clark & Chalmers’ (1998) extended mind hypothesis. I demonstrate, however, that the two approaches justify their radically externalist by appealing to the same argument from explanatory generality. I argue that if one accepts either Williamson’s claims or Clark & Chalmers’ claims on considerations of explanatory generality then, ceteris paribus, one should accept the other. This conclusion has (...) implications for philosophy of mind, epistemology, and cognitive science. (shrink)

Strategies for effectively communicating scientific findings to the public are an important and growing area of study. Recognizing that some complex subjects require recipients of information to take a more active role in constructing an understanding, we sought to determine whether it was possible to increase subjects’ intellectual effort via “priming” methodologies. In particular, we asked whether subconsciously priming “intellectual virtues”, such as curiosity, perseverance, patience, and diligence might improve participants’ effort and performance on various cognitive tasks. In the first (...) experiment, we found no significant differences in either effort or understanding between IV-primed and neutrally-primed individuals across two different priming techniques. The second experiment measured the effect of IV-priming on intellectual effort in simpler, shorter-duration puzzles and exploration activities; here, we observed an effect, but given its low strength and short duration, we do not believe that priming of IVs is a promising strategy for science communication. (shrink)

The Consequence Argument is the classic argument for the incompatibility of determinism and our ability to do otherwise. Daniel C. Dennett objects that the Consequence Argument suffers from the same error as a clearly unconvincing argument that there are no mammals. In this paper, I argue that these arguments do not suffer from the same error. The argument that there are no mammals is unconvincing as it takes the form of a sorites, whereas the Consequence Argument does not. Accordingly, Dennett's (...) objection misses its mark. (shrink)

In this short note many conjectures on partitions of integers as summations of prime numbers are presented, which are extension of Goldbach conjecture.

The importance of the prime factorization problem is very well known (e.g., many security protocols are based on the impossibility of a fast factorization of integers on traditional computers). It is necessary from a number k to establish two primes a and b giving k = a · b. Usually, k is written in a positional numeral system. However, there exists a variety of numeral systems that can be used to represent numbers. Is it true that the prime (...) factorization is difficult in any numeral system? In this paper, a numeral system with partial carrying is described. It is shown that this system contains numerals allowing one to reduce the problem of prime factorization to solving [K/2] − 1 systems of equations, where K is the number of digits in k (the concept of digit in this system is more complex than the traditional one) and [u] is the integer part of u. Thus, it is shown that the difficulty of prime factorization is not in the problem itself but in the fact that the positional numeral system is used traditionally to represent numbers participating in the prime factorization. Obviously, this does not mean that P=NP since it is not known whether it is possible to re-write a number given in the traditional positional numeral system to the new one in a polynomial time. (shrink)

No one influenced and shaped our thinking about dispositions and causal properties more than Aristotle. What he wrote about power (dynamis), nature (physis) and habit (hexis) has been read, systematised and criticised again and again during the history of philosophy. In this chapter I sketch Aristotle's thoughts about dispositions and argue that his theory can still be regarded as a good one.

In August 2002, three Indian computer scientists published a paper, ‘PRIMES is in P’, online. It presents a ‘deterministic algorithm’ which determines in ‘polynomial time’ if a given number is a prime number. The story was quickly picked up by the general press, and by this means spread through the scientific community of complexity theorists, where it was hailed as a major theoretical breakthrough. This is although scientists regarded the media reports as vulgar popularizations. When the paper was published (...) in a peer-reviewed journal only two years later, the three scientists had already received wide recognition for their accomplishment. Current sociological theory challenges the ability to clearly distinguish on independent epistemic grounds between distorted and non-distorted scientific knowledge. It views the demarcation lines between such forms of presentation as contextual and unstable. In my paper, I challenge this view. By systematically surveying the popular press coverage of the ‘PRIMES is in P’ affair, I argue--against the prevailing new orthodoxy--that distorted simplifications of scientific knowledge are distinguishable from non-distorted simplifications on independent epistemic grounds. I argue that in the ‘PRIMES is in P’ affair, the three scientists could ride on the wave of the general press-distorted coverage of their algorithm, while counting on their colleagues’ ability to distinguish genuine accounts from distorted ones. Thus, their scientific reputation was unharmed. This suggests that the possibility of the existence of independent epistemic standards must be incorporated into the new SSK model of popularization. (shrink)

Euclid's classic proof about the infinitude of prime numbers has been a standard model of reasoning in student textbooks and books of elementary number theory. It has withstood scrutiny for over 2000 years but we shall prove that despite the deceptive appearance of its analytical reasoning it is tautological in nature. We shall argue that the proof is more of an observation about the general property of a prime numbers than an expository style of natural deduction of the (...) proof of their infinitude. (shrink)

El intento de estas páginas es el de seleccionar dentro de la semántica del miedo que contribuye a organizar la imagen moderna del orden político y jurídico el elemento específico del pánico, en la hipótesis de que este último constituya una diferencia que es asimismo un recurso epistémico. Dicho de un modo directo: si el miedo se presenta como una referencia constitutiva del orden, de su constitución como de su mantenimiento, el pánico parece, en cambio, cargado de un signo contrario; (...) nos habla de la disolución de un agregado dado por supuesto y es inclusivo en el perimetrar los límites y las condiciones de posibilidad. El objetivo es aquel de repasar algunos momentos de la historia del pánico buscando argumentar que el pánico es una pasión política, en el sentido de que se refiere a aquello de lo que la político está hecha, y al mismo tiempo es expresión de un límite "pasional" de la política, en tanto que define políticamente un límite interno. Respecto a tal objetivo, esta aportación no reivindica más que los caracteres de un hilvanado necesitante de un desarrollo ulterior por lo que se refiere no solo a aquello que no se incluye (y es obviamente mucho), sino también a los nudos que de forma conscientemente provisional se indican. Además, se limita a una periodizacion histórica que es de alguna manera preliminar, deteniéndose en el umbral de la fase en la cual el pánico es una palabra de un discurso disciplinar, es parte del objeto de un saber codificado (psicología, sociología, ciencia política), incluso si no desempeña necesariamente un rol apaciguador. (shrink)

Abstract: The main purpose of this paper is to find Artin's characters table of the group (Q2n×D3)when n=p_1.p_2….p_n,and p_1,p_2,…,p_n are primes number, which is denoted by Ar(Q2n×D3) where Q2m is denoted to Quaternion group and D3 is the Dihedral group of order 6 .

Alexander of Aphrodisias understood the Aristotle´s Unmoved Mover as efficient cause only to the extent that it is the final cause of heaven, which by moving strives to imitate the divine rest. Aquinas seems to agree with him. However his interpretation is original and philosophically more satisfactory: God is the efficient cause of the world, not only as creator, but also as it´s ruler. In this way God is also the final cause.

I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what I will call the Cut-for-Formulas to Cut-for-Sets Theorem: for a set F and a binary relation |- on Power(F), if |- is finitary, monotonic, and satisfies cut for formulas, then it also satisfies cut for sets. I deduce the CF/CS Theorem from the Ultrafilter Theorem twice; each proof uses a different order-theoretic variant of the Tukey- Teichmüller Lemma. I then discuss relationships between (...) various cut-conditions in the absence of finitariness or of monotonicity. (shrink)

The present text is the revised and corrected English translation of the book published in German by the Lang Verlag, Bern 2008. Unfortunately the text still has some minor flaws (especially in the Index Locorum) but they do not concern the main thesis or the arguments. It will still be the final version, especially considering my age. It is among the most widespread and the least questioned convictions that in Metaphysics Lambda Aristotle presents a theology which has its basis in (...) a metaphysics of substance. Doubts about theological interpretation are beginning to stir in a growing number of publications, but nevertheless the majority of research literature, compendiums and histories of philosophy argues within this frame. A closer look at the facts reveals that this conviction has no basis in the text. Quite the contrary it is based on a reception with theological interests. It arised over centuries, starting from Patristic times and the Middle Ages; it was influenced by Neoplatonic texts as the Liber de Causis or the Theologia Aristotelis, texts for a long time considered as original Aristotelian books. And, if you read not translations but the Greek text, you see that the word 'god' occurs much less than in a theological book should be. In some translations we find more occurences of that word, and especially in French, Italian, English translations some words as le Bien, l'Intelligence etc. are written with capitals to inticate that it is about god. To make it even more clear, we read often the term 'First Mover' or 'Unmoved Mover' as an other name for god, but this expression is never used by Aristotle. So the reader has the impression that Aristotle speaks continuously about god. In addition, in the present book you will find arguments which clean up with the outdated concept of substance in the Aristotelian text, a concept which was developed for quite other problems than Aristotle had, namely theolgical ones. And, if there is no substance, there is no corresponding metaphysics of substance and no theology or onto-theology. If substance, metyphysics, theology play no role in Metaphysics Lambda, what else is its content and aim? That is not so difficult to say because Aristotle says it sufficiently clear in his first sentence, περὶ οὐσίας ἡ θεωρία: our inquiry is about being; its aim is to develop the Frage nach dem Sein and to state a speculative answer: being is noesis, Sein ist Gewahren. (shrink)

The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...) Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (shrink)

In this paper, we provide an account of the ontological status of Christ’s dead body, which remained in the tomb during the three days after his crucifixion. Our account holds that Christ’s dead body – during the time between his death and resurrection – was prime matter without a substantial form. We defend this account by showing how it is metaphysically possible for prime matter to exist in actuality without substantial forms. Our argument turns on the truth of (...) two theses: God is able to produce all acts of secondary causes without those secondary causes, and Substantial forms are secondary causes of the actuality of prime matter. We argue that the metaphysical possibility of matter without form is perfectly consistent with holding both there is only one substantial form in a material substance and that prime matter is pure potentiality. Moreover, we argue that the metaphysical possibility of matter without form does little-to-no damage to our natural understanding of material substances. (shrink)

Thomas Aquinas embraces a controversial claim about the way in which parts of a substance depend on the substance’s substantial form. On his metaphysics, a ‘substantial form’ is not merely a relation among already existing things, in virtue of which (for example) the arrangement or configuration of those things would count as a substance. The substantial form is rather responsible for the identity or nature of the parts of the substance such a form constitutes. Aquinas’ controversial claim can be roughly (...) put as the view that things are members of their kind in virtue of their substantial form. To put it simply, Aquinas’ claim results in the implication that, every time the xs come to compose a y, those xs have to undergo a change in kind membership. -/- This has been called the “homonymy principle,” and it follows from Aquinas’ view of substantial forms, and specifically from the position that substantial forms inform prime matter, rather than substance-parts. The aim of this paper will be to defend that the Thomistic claim that substantial forms account for the determinate actuality of every part of a substance is plausible and coherent. After defending the Thomistic account, I propose that approaching problems of material composition as a Thomist has a significant, oft-overlooked advantage of involving a thorough-going naturalistic methodology that resolves such problems by appeal to empirical considerations. (shrink)

The paper considers the philosophical component of the approach to the time as an emergent phenomenon absent at the fundamental level. The anthropic principle is shown as arising from the time emergence. Consciousness is shown as an epiphenomenon in such a model, although it is more fundamental than matter in this case. An answer to the question about the prime cause is suggested.

After an initial premise of historical contextualization, the article presents Suárez’s theory of matter, contained above all in the Disputatio metaphysica XIII, as a renewal and conceptual and terminological improvement of the Scotist theory of prime matter exposed in Lectura II, d. 12. Based on the Scotist idea of matter as aliquid (something) endowed with a positive entitas in so far as founded on the theological notion of creation, Suárez elaborates a new ontological statute of matter, of a non-Aristotelian (...) nature, on new theoretical bases: the hipostatization of the prime matter, the immediate inhesion of the quantity on matter, the loss of unity of the material substance (and the appeal of the mode of substantial union to remedy it) and the distinction between entitative extension and quantitative extension. (shrink)

Let f(1)=2, f(2)=4, and let f(n+1)=f(n)! for every integer n≥2. Edmund Landau's conjecture states that the set P(n^2+1) of primes of the form n^2+1 is infinite. Landau's conjecture implies the following unproven statement Φ: card(P(n^2+1))<ω ⇒ P(n^2+1)⊆[2,f(7)]. Let B denote the system of equations: {x_j!=x_k: i,k∈{1,...,9}}∪{x_i⋅x_j=x_k: i,j,k∈{1,...,9}}. The system of equations {x_1!=x_1, x_1 \cdot x_1=x_2, x_2!=x_3, x_3!=x_4, x_4!=x_5, x_5!=x_6, x_6!=x_7, x_7!=x_8, x_8!=x_9} has exactly two solutions in positive integers x_1,...,x_9, namely (1,...,1) and (f(1),...,f(9)). No known system S⊆B with a finite (...) number of solutions in positive integers x_1,...,x_9 has a solution (x_1,...,x_9)∈(N\{0})^9 satisfying max(x_1,...,x_9)>f(9). For every known system S⊆B, if the finiteness/infiniteness of the set {(x_1,...,x_9)∈(N\{0})^9: (x_1,...,x_9) solves S} is unknown, then the statement ∃ x_1,...,x_9∈N\{0} ((x_1,...,x_9) solves S)∧(max(x_1,...,x_9)>f(9)) remains unproven. Let Λ denote the statement: if the system of equations {x_2!=x_3, x_3!=x_4, x_5!=x_6, x_8!=x_9, x_1 \cdot x_1=x_2, x_3 \cdot x_5=x_6, x_4 \cdot x_8=x_9, x_5 \cdot x_7=x_8} has at most finitely many solutions in positive integers x_1,...,x_9, then each such solution (x_1,...,x_9) satisfies x_1,...,x_9≤f(9). The statement Λ is equivalent to the statement Φ. It heuristically justifies the statement Φ . This justification does not yield the finiteness/infiniteness of P(n^2+1). We present a new heuristic argument for the infiniteness of P(n^2+1), which is not based on the statement Φ. Algorithms always terminate. We explain the distinction between existing algorithms (i.e. algorithms whose existence is provable in ZFC) and known algorithms (i.e. algorithms whose definition is constructive and currently known). Assuming that the infiniteness of a set X⊆N is false or unproven, we define which elements of X are classified as known. No known set X⊆N satisfies Conditions (1)-(4) and is widely known in number theory or naturally defined, where this term has only informal meaning. *** (1) A known algorithm with no input returns an integer n satisfying card(X)<ω ⇒ X⊆(-∞,n]. (2) A known algorithm for every k∈N decides whether or not k∈X. (3) No known algorithm with no input returns the logical value of the statement card(X)=ω. (4) There are many elements of X and it is conjectured, though so far unproven, that X is infinite. (5) X is naturally defined. The infiniteness of X is false or unproven. X has the simplest definition among known sets Y⊆N with the same set of known elements. *** Conditions (2)-(5) hold for X=P(n^2+1). The statement Φ implies Condition (1) for X=P(n^2+1). The set X={n∈N: the interval [-1,n] contains more than 29.5+\frac{11!}{3n+1}⋅sin(n) primes of the form k!+1} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. 501893∈X. Condition (1) holds with n=501893. card(X∩[0,501893])=159827. X∩[501894,∞)= {n∈N: the interval [-1,n] contains at least 30 primes of the form k!+1}. We present a table that shows satisfiable conjunctions of the form #(Condition 1) ∧ (Condition 2) ∧ #(Condition 3) ∧ (Condition 4) ∧ #(Condition 5), where # denotes the negation ¬ or the absence of any symbol. No set X⊆N will satisfy Conditions (1)-(4) forever, if for every algorithm with no input, at some future day, a computer will be able to execute this algorithm in 1 second or less. The physical limits of computation disprove this assumption. (shrink)

In the given article the problems of choice as for the types and forms of debt and share financing on the developing and “frontier markets” with high interest rates have been considered, the definition of what kind of interest rates can be viewed as high and under which circumstances nominal interest rate and in which ones – the real interest rate is important for business. Also, the classification of debt and sharing financing is given and the comparative analysis of such (...) financing is made. Some close attention has been paid to the calculation of the real interest rate according to the inflation forecast. Recommendations concerning attracting of relatively cheap trade financing including international financial and credit organizations, development of operation factoring, financing from captive financial institutions of the exporters of the materials and equipment from the EU and the US have been grounded. The opportunity of relatively free of charge share financing through the mechanism of placing shares IPO/SPO is emphasized, exemplified by the results of placing shares on stock exchanges and their alternative platforms of issuing banks with businesses in Ukraine in 2005 – 2013. As a result, the conclusion concerning the necessity of thorough analysis of financial conditions on the developing and frontier markets before gaining such financing has been made. High interest rates within the average indicators even on the basis of prime rates do not necessarily mean absence of attractive conditions of financing. (shrink)

Several metaphysical/philosophical concepts are developed as tools by which we may further understand the essence, structure, and events/symbols of “Complex” Synchronicity, and how these differ from “Chain of Events” Synchronicity. The first tool is the concept of Astronomical vs Cultural time. This tool is to be the basis of distinguishing Simple from Complex Synchronicity as Complex Synchronicities are chunks of time that have several coincidences in common with each other. We will also look at the nature of the perspective of (...) the time being quantized. The next tool is a particular case study of two movies, The Matrix and Black Swan, that may be viewed as an example of a Complex Synchronicity in the collective conscious of popular culture (as opposed to Simple Synchronicity or a single coincidence). And the final tool is the concept of “Chain of Events” synchronicity as a separate concept from Simple or Complex synchronicities. This 3rd tool is developed using a mathematical metaphor of foreshadowing (an element of storytelling) in the seemingly random pattern of prime numbers. The purpose of this paper is to distinguish and develop these concepts and to lay a foundation for the further study of the concept of Synchronicity first illuminated by Carl Jung as an acausal connecting principle between coincidences. (shrink)

I argue that Plato thinks that a sunaition is a mere tool used by a soul (or by the cosmic nous) to promote an intended outcome. In the first section, I develop the connection between sunaitia and Plato’s teleology. In the second section, I argue that sunaitia belong to Plato’s theory of the soul as a self-mover: specifically, they are those things that are set in motion by the soul in the service of some goal. I also argue against (...) several popular and long-standing interpretations, namely, that sunaitia correspond to Aristotle’s idea of hypothetical necessity, that sunaitia are the ‘how’ in an explanation (whereas the true cause is the ‘why’), and that Plato’s causal views should be read through Aristotle’s fourfold schema. I conclude the article by surveying the history of sunaitia after Plato’s usage. (shrink)