In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...) by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be proved using my 1972 (...) proof of the completeness of Aristotle’s syllogistic. (shrink)

It is tempting to think that multi premise closure creates a special class of paradoxes having to do with the accumulation of risks, and that these paradoxes could be escaped by rejecting the principle, while still retaining single premise closure. I argue that single premise deduction is also susceptible to risks. I show that what I take to be the strongest argument for rejecting multi premise closure is also an argument for rejecting single (...) class='Hi'>premise closure. Because of the symmetry between the principles, they come as a package: either both will have to be rejected or both will have to be revised. (shrink)

It’s often thought that the phenomenon of risk aggregation poses a problem for multi-premise closure but not for single-premise closure. But recently, Lasonen-Aarnio and Schechter have challenged this thought. Lasonen-Aarnio argues that, insofar as risk aggregation poses a problem for multi-premise closure, it poses a similar problem for single-premise closure. For she thinks that, there being such a thing as deductive risk, risk may aggregate over a single premise and the deduction itself. Schechter (...) argues that single-premise closure succumbs to risk aggregation outright. For he thinks that there could be a long sequence of competent single-premise deductions such that, even though we are justified in believing the initial premise of the sequence, intutively, we are not justified in believing the final conclusion. This intuition, Schechter thinks, vitiates single-premise closure. In this paper, I defend single-premise closure against the arguments offered by Lasonen-Aarnio and Schechter. (shrink)

One semantic and two syntactic decision procedures are given for determining the validity of Aristotelian assertoric and apodeictic syllogisms. Results are obtained by using the Aristotelian deductions that necessarily have an even number of premises.

Aristotle's syllogistic is extended to include denumerably many quantifiers such as 'more than 2/3' and 'exactly 2/3.' Syntactic and semantic decision procedures determine the validity, or invalidity, of syllogisms with any finite number of premises. One of the syntactic procedures uses a natural deduction account of deducibility, which is sound and complete. The semantics for the system is non-classical since sentences may be assigned a value other than true or false. Results about symmetric systems are given. And reasons are (...) given for claiming that syllogistic validity is relevant validity. (shrink)

Parry discusses an extension of Aristotle's syllogistic that uses four nontraditional quantifiers. We show that his conjectured decision procedure for validity for the extended syllogistic is correct even if syllogisms have more than two premises. And we axiomatize this extension of the syllogistic.

The multi premise closure principle states that the logical conjunction of known facts yields again a known fact. For absolute knowledge this principle holds. We show that for fallible knowledge, assuming knowing requires a minimum level of statistical certainty (whatever else it requires), and that there is a sufficient number of known facts above a given level of uncertainty, it does not hold, for simple statistical reasons. We present a modified version, the dependent conjunctive closure principle, that does (...) hold. (shrink)

This paper discusses the following question: why was the term “dunatos” (“possible”) employed by Aristotle as an alternative label for imperfect syllogisms in his discussion of assertoric syllogistic? My answer ascribes to Aristotle a bottom up perspective, in which he stresses what is necessary in the premise-pairs to attain target conclusions of a given form within a given figure. I argue that “dunatos” is employed by Aristotle to stress that an imperfect syllogism is always one of the possible (...) options to attain a conclusion of a given form within a given figure. I also argue that this picture sheds some light on Aristotle’s clarifications of the final clause in his definition of syllogism. (shrink)

Discussion of the Aristotelian syllogistic over the last sixty years has arguably centered on the question whether syllogisms are inferences or implications. But the significance of this debate at times has been taken to concern whether the syllogistic is a logic or a theory, and how it ought to be represented by modern systems. Largely missing from this discussion has been a study of the few passages in the Prior Analytics where Aristotle provides explicit guidance on how to individuate (...) syllogisms. I argue that syllogisms are individuated by unordered premise pairs and so may be fruitfully thought of as multiple-succedent sequents. I conclude by drawing a few consequences for the representation of the syllogistic. (shrink)

This document diagrams the forms OOA, OOE, OOI, and OOO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a system in (...) which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)

ABSTRACTThe Necessity of Origins is the thesis that, necessarily, if a material object wholly originates from some particular material, then it could not have wholly originated from any significantly non-overlapping material. Several philosophers have argued for this thesis using as a premise a principle that we call ‘Single Origin Necessity’. However, we argue that Single Origin Necessity is false. So any arguments for The Necessity of Origins that rely on Single Origin Necessity are unsound. We also argue that the (...) Necessity of Origins itself is false. Our arguments rely on a thesis in the ontology of art that we find plausible: Multi-Work Materialism. It is the thesis that works of art that have multiple concrete manifestations are co-located with those manifestations. (shrink)

The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic uncertainty in (...) known premises. The first strategy, while effective, retains little of the original idea—conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson’s safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson’s theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge. (shrink)

Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...) by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle's general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. (shrink)

Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on (...) the epistemic process of extracting information implicit in explicitly given information) and, second, the process of establishing knowledge that a conclusion does not follow. Despite the overwhelming tendency to interpret the syllogistic as formal epistemology, it was not until the early 1970s that it occurred to anyone to think that Aristotle may have developed a theory of deductive reasoning with a well worked-out system of deductions comparable in rigor and precision with systems such as propositional logic or equational logic familiar from mathematical logic. When modern logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle's contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotle from possible charges of psychologism. They thought they saw Aristotle applying the informal axiomatic method to formal ontology, not as making the first steps into formal epistemology. They did not notice Aristotle's description of deductive reasoning. Ironically, the formal axiomatic method (in which one explicitly presents not merely the substantive axioms but also the deductive processes used to derive theorems from the axioms) is incipient in Aristotle's presentation. Partly in opposition to the axiomatic, ontically-oriented approach to Aristotle's logic and partly as a result of attempting to increase the degree of fit between interpretation and text, logicians in the 1970s working independently came to remarkably similar conclusions to the effect that Aristotle indeed had produced the first system of formal deductions. They concluded that Aristotle had analyzed the process of deduction and that his achievement included a semantically complete system of natural deductions including both direct and indirect deductions. Where the interpretations of the 1920s and 1930s attribute to Aristotle a system of propositions organized deductively, the interpretations of the 1970s attribute to Aristotle a system of deductions, or extended deductive discourses, organized epistemically. The logicians of the 1920s and 1930s take Aristotle to be deducing laws of logic from axiomatic origins; the logicians of the 1970s take Aristotle to be describing the process of deduction and in particular to be describing deductions themselves, both those deductions that are proofs based on axiomatic premises and those deductions that, though deductively cogent, do not establish the truth of the conclusion but only that the conclusion is implied by the premise-set. Thus, two very different and opposed interpretations had emerged, interestingly both products of modern logicians equipped with the theoretical apparatus of mathematical logic. The issue at stake between these two interpretations is the historical question of Aristotle's place in the history of logic and of his orientation in philosophy of logic. This paper affirms Aristotle's place as the founder of logic taken as formal epistemology, including the study of deductive reasoning. A by-product of this study of Aristotle's accomplishments in logic is a clarification of a distinction implicit in discourses among logicians--that between logic as formal ontology and logic as formal epistemology. (shrink)

This article gives an overview over different principles of epistemic closure, their attractions and their problems.

In this fragment of Opuscula Logica it is displayed an arithmetical treatment of the aristotelic syllogisms upon the previous interpretations of Christine Ladd-Franklin and Jean Piaget. For the first time, the whole deductive corpus for each syllogism is presented in the two innovative modalities first proposed by Hugo Padilla Chacón. A. The Projection method (all the possible expressions that can be deduced through the conditional from a logical expression) and B. The Retrojection method (all the possible valid antecedents or (...) premises conjunction for an expression proposed as a conclusion). The results are numerically expressed, with their equivalents in the propositional language of bivalent logic. (shrink)

This paper discusses the possible classification of Aristotle’s syllogistic as a non-classical logical system, positing Aristotle himself as a non-classical logician. Initially, we find compelling arguments for this thesis, particularly regarding the expressive power and the rules governing logical inference inherent in Aristotle’s approach. My analysis nevertheless addresses two significant counterarguments. The first, the special case objection, posits that Aristotle’s syllogistic can be framed as a classical logic which deals with canonical syllogistic forms. I argue that this objection is insufficient, (...) as it is possible to point cases in which his system seems to differ from classical logic. The second counterargument, the formalisation gap objection, highlights that Aristotle’s syllogistic resists straightforward modern logical interpretations. This latter objection is evaluated as more compelling and substantial. In particular, a distinction between two concepts is proposed which could help us understand what Aristotle was aiming at in his theory of inference: the notions of ‘to follow from’ and ‘to be a conclusion of’. While the former aligns with the usual sense formal validity, the second requires an inferential structure connecting the premises to the conclusion, explaining why Aristotle excluded inferences like from A ⊢ A syllogisms despite acknowledging that A follows from A. (shrink)

Cloud computing has revolutionized the way businesses and individuals access and utilize computing resources. With its rapid adoption over the last few decades, it has become the backbone of many IT services across industries. This paper explores the evolution of cloud computing, highlighting key trends and identifying future directions that will shape the landscape. It discusses the evolution from traditional on-premise systems to the cloud-first approach, current advancements such as multi-cloud and hybrid cloud environments, and the growing integration (...) of artificial intelligence (AI) and machine learning (ML) into cloud services. Furthermore, the paper examines the challenges organizations face, including security concerns and regulatory compliance. Finally, the future directions of cloud computing are explored, focusing on edge computing, quantum cloud services, and the potential for deeper AI integration. (shrink)

This mainly historical paper provides a comprehensive discussion of the (heretoforth neglected) evidence of Peripatetic syllogistic in Sextus Empiricus. The paper sets out to show that it is likely that in Sextus (and Apuleius) there is valuable evidence of a transitional period in later ancient logic that is marked out as such by a number of characteristics, which include the following: (i) A Peripatetic term ‘categorical syllogism’ is newly in use, but no term ‘hypothetical syllogism’ has been established yet. (ii) (...) Stoic and Peripatetic logic are treated as complementing each other. (iii) The reversion of quantified propositions from predicate-subject to subject-predicate formulation is still fairly new. (iv) The so-called crocodile example is used to show that induction lacks the feature of concluding by necessity that is a defining mark of Aristotelian syllogisms. (v) The use of the expression katholikê protasis for categorical universal premise-propositions is distinctive of the period. (vi) The argument forms displayed by Sextus’ three examples appear to be indirectly related to the soon-to-appear Platonist hypothetical syllogistic. (vii) There are parallels that suggest that Sextus’ source belongs to the same historical period of logic as Apuleius’ source and as some probably recent source of Alexander of Aphrodisias’ Prior Analytics commentary (that is presented along with some later views and arguments, which may include Alexander’s own). Small differences between the three authors show that Sextus did not draw from the Greek handbook that was Apuleius’ source. (shrink)

This paper sets out to evaluate the claim that Aristotle’s Assertoric Syllogistic is a relevance logic or shows significant similarities with it. I prepare the grounds for a meaningful comparison by extracting the notion of relevance employed in the most influential work on modern relevance logic, Anderson and Belnap’s Entailment. This notion is characterized by two conditions imposed on the concept of validity: first, that some meaning content is shared between the premises and the conclusion, and second, that the premises (...) of a proof are actually used to derive the conclusion. Turning to Aristotle’s Prior Analytics, I argue that there is evidence that Aristotle’s Assertoric Syllogistic satisfies both conditions. Moreover, Aristotle at one point explicitly addresses the potential harmfulness of syllogisms with unused premises. Here, I argue that Aristotle’s analysis allows for a rejection of such syllogisms on formal grounds established in the foregoing parts of the Prior Analytics. In a final section I consider the view that Aristotle distinguished between validity on the one hand and syllogistic validity on the other. Following this line of reasoning, Aristotle’s logic might not be a relevance logic, since relevance is part of syllogistic validity and not, as modern relevance logic demands, of general validity. I argue that the reasons to reject this view are more compelling than the reasons to accept it and that we can, cautiously, uphold the result that Aristotle’s logic is a relevance logic. (shrink)

This review places this translation and commentary on Book A of Prior Analytics in historical, logical, and philosophical perspective. In particular, it details the author’s positions on current controversies. The author of this translation and commentary is a prolific and respected scholar, a leading figure in a large and still rapidly growing area of scholarship: Prior Analytics studies PAS. PAS treats many aspects of Aristotle’s Prior Analytics: historical context, previous writings that influenced it, preservation and transmission of its manuscripts, editions (...) of its manuscripts, interpretations, commentaries, translations, and its influence on subsequent logic, philosophy, and mathematics. All this attention is warranted because Prior Analytics marks the origin of logic: the field that, among other things, asks of a given proposition whether it follows from a given set of propositions; and, if it follows, how we determine that it follows; and, if it does not follow, how we determine that it does not follow. This translation and commentary is not suitable for use in an undergraduate course. It has too many quirks that the teacher would want to warn against. A copy editor should have dealt with these things and with other matters such as incorrect punctuation and improper end-of-line divisions. The prose is heavily laden with glaring clichés. The one-page preface contains “longer than I care to remember”, “more than I can possibly list here”, “first and foremost”, and “last and by no means least”—a sentence later is devoted to thanking the “incredibly meticulous and helpful copy-editor”. A few pages later the translator reveals the need “to find a path between the Scylla … and the Charybdis …”. Moreover, the index is far from meeting the needs of undergraduate students. The attention to scholarly detail is not what one hoped for from Oxford University Press. At 26b10-15, this translation reads “let swan and white be chosen as white things” for what Smith correctly translates “let swan and snow be selected from among those white things”. At 41b16, “angles AB and CD” should read “angles AC and BD”. Despite this book’s flaws, it will be found useful if not indispensable for those currently engaged in Prior Analytics studies. The alternatives suggested to Robin Smith’s translation choices are often worth consideration. It is to be emphasized, however, that this book is unsuitable for those entering Prior Analytics studies. (shrink)

Compare two conceptions of validity: under an example of a modal conception, an argument is valid just in case it is impossible for the premises to be true and the conclusion false; under an example of a topic-neutral conception, an argument is valid just in case there are no arguments of the same logical form with true premises and a false conclusion. This taxonomy of positions suggests a project in the philosophy of logic: the reductive analysis of the modal conception (...) of logical consequence to the topic-neutral conception. Such a project would dispel the alleged obscurity of the notion of necessity employed in the modal conception in favour of the clarity of an account of logical consequence given in terms of tractable notions of logical form, universal generalization and truth simpliciter. In a series of publications, John Etchemendy has characterized the model-theoretic definition of logical consequence as truth preservation in all models as intended to provide just such an analysis. In this paper, I will argue that Aristotle intends to provide an account of a modal conception of logical consequence in topic-neutral terms and so is engaged in a project comparable to the one described above. That Aristotle would be engaged in this sort of project is controversial. Under the standard reading of the Prior Analytics, Aristotle does not and cannot provide an account of logical consequence. Rather, he must take the validity of the first figure syllogisms (such as the syllogism known by its medieval mnemonic ‘Barbara’: A belongs to all B; B belongs to all C; so A belongs to all C) as obvious and not needing justification; he then establishes the validity of the other syllogisms by showing that they stand in a suitable relation to the first figure syllogisms. I will argue that Aristotle does attempt to provide an account of logical consequence—namely, by appeal to certain mereological theorems. For example, he defends the status of Barbara as a syllogism by appeal to the transitivity of mereological containment. There are, as I will discuss, reasons to doubt the success of this account. But the attempt is not implausible given certain theses Aristotle holds in semantics, mereology and the theory of relations. (shrink)

Aristotle presents a formal logic in the Prior Analytics in which the premises and conclusions are never conditionals. In this paper I argue that he did not simply overlook conditionals, nor does their absence reflect a metaphysical prejudice on his part. Instead, he thinks that arguments with conditionals cannot be syllogisms because of the way he understands the explanatory requirement in the definition of a syllogism: the requirement that the conclusion follow because of the premises. The key passage is (...) Prior Analytics I.32, 47a22–40, where Aristotle considers an argument with conditionals that we would consider valid, but which he denies is a syllogism. I argue that Aristotle thinks that to meet the explanatory requirement a syllogism must draw its conclusion through the way its terms are predicated of one another. Because arguments with conditionals do not, in general, draw their conclusions through predications, he did not include them in his logic. (shrink)

It is increasingly acknowledged that creativity cannot be fully understood without considering the setting where it takes place. Building on this premise, we use the concepts of niche construction, scaffolding, coupling, and functional integration to expound on the environmentally situated nature of painters’ studio work. Our analysis shows studios to be multi-resource niches that are customized by artists to support various capacities, states, and actions crucial to painting. When at work in these personalized spaces, painters do not need (...) to rely solely on their “inner” powers of imagination, memory, decision making, and technique to execute their paintings. Instead, with the help of carefully selected resources, they can offload elements of creative mentation and action onto the studio niche and enact different forms of a creative agency. To put more flesh on these ideas, we examine how painters use existing artworks, memory aids, and music to scaffold the creative process. Overall, our analysis illuminates underexamined aspects of environmentally situated creativity and demonstrates the broader utility of the applied concepts for future creativity research. (shrink)

In a recent article, Dawn Wilson (2021) has argued against single-stage accounts of photography by arguing against the latent photographic images upon which those accounts depend. Concomitantly, she argues that the only viable account of photography is multi-stage. Unlike single-stage accounts, multi-stage accounts do not postulate the existence of photographic images of any kind prior to development. Rather, according to multi-stage accounts, photographs are produced from “photographic registers.” In this Discussion Piece, I defend single-stage accounts by arguing (...) that Wilson’s rejection of latent photographic images is premised on an implausible view of what a latent photographic image is. Given a reasonable interpretation, the latent images described in single-stage accounts just are the photographic registers described in multi-stage accounts. (shrink)

The ramifications of existence provide the setup for a theory on civilization as a whole. This story is composed under the premise of looking at Rabbinic Judaism and the Old/New Testaments as contextual clues for an overview of civilization and existence in general. This includes a mathematical model for prior to the existence of time i.e. QSOPR Theorem: Quantum Similarity Origin Point References, MDQBT: Multi-Dimensional Quantum Breakpoint Theorem, and QSICT: Quantum Simulated Informational Consciousness Theory. As well as tracing (...) back ancient lineages such as Coptic DNA and the e1b1b haplogroup, FGC8712, or tribal lineages such as Berbers, the Quarashi, and ancient Mesopotamian groups. Next, we will look at history and philosophy through religious texts which include mythology, Quranic text and hadiths, and any related archaeological evidence in relationship to the Shashu, Temple 0, or contextual geological clues. This will provide a premise for human nature, civilization, world religions, societal falls, and history through correlative patterns, universal truth, linguistics, ethics and morality. (shrink)

John Corcoran and George Boger. Aristotelian logic and Euclidean geometry. Bulletin of Symbolic Logic. 20 (2014) 131. -/- By an Aristotelian logic we mean any system of direct and indirect deductions, chains of reasoning linking conclusions to premises—complete syllogisms, to use Aristotle’s phrase—1) intended to show that their conclusions follow logically from their respective premises and 2) resembling those in Aristotle’s Prior Analytics. Such systems presuppose existence of cases where it is not obvious that the conclusion follows from the (...) premises: there must be something deductions can show. Corcoran calls a proposition that follows from given premises a hidden consequence of those premises if it is not obvious that the proposition follows from those premises. By a Euclidean geometry we mean an extended discourse beginning with basic premises—axioms, postulates, definitions—1) treating a universe of geometrical figures and 2) resembling Euclid’s Elements. There were Euclidean geometries before Euclid (fl. 300 BCE), even before Aristotle (384–322 BCE). Bochenski, Lukasiewicz, Patzig and others never new this or if they did they found it inconvenient to mention. Euclid shows no awareness of Aristotle. It is obvious today—as it should have been obvious in Euclid’s time, if anyone knew both—that Aristotle’s logic was insufficient for Euclid’s geometry: few if any geometrical theorems can be deduced from Euclid’s premises by means of Aristotle’s deductions. Aristotle’s writings don’t say whether his logic is sufficient for Euclidean geometry. But, there is not even one fully-presented example. However, Aristotle’s writings do make clear that he endorsed the goal of a sufficient system. Nevertheless, incredible as this is today, many logicians after Aristotle claimed that Aristotelian logics are sufficient for Euclidean geometries. This paper reviews and analyses such claims by Mill, Boole, De Morgan, Russell, Poincaré, and others. It also examines early contrary statements by Hintikka, Mueller, Smith, and others. Special attention is given to the argumentations pro or con and especially to their logical, epistemic, and ontological presuppositions. What methodology is necessary or sufficient to show that a given logic is adequate or inadequate to serve as the underlying logi of a given science. (shrink)

This dissertation focuses on teleology and functions in biology. More precisely, it focuses on the scientific legitimacy of teleofunctional attributions and explanations in biology. It belongs to a multi-faceted debate that can be traced back to at least the 1970s. One aspect of the debate concerns the naturalization of functions. Most authors try to reduce, translate or explain functions and teleology in terms of efficient causes so that they find their place in the framework of the natural sciences. Our (...) approach here is radically different, as we question the premise that teleological explanations are disguised causal explanations. On the contrary, we defend that they are acceptable in natural sciences and in biology in particular. We challenge the idea that teleological explanations are immature causal explanations, as well as the idea that teleology and functions are some sort of intentional explanations. We therefore reject the accusations of anthropomorphism, vitalism and finalism. On the contrary, we defend that teleology, causality and intentionality correspond to different, autonomous and complementary modes of representation of the outside world. -/- ———[FRANÇAIS]——— -/- Ce travail de thèse porte sur la téléologie et les fonctions en biologie. Plus précisément, il porte sur la légitimité scientifique des attributions et des explications téléofonctionnelles en biologie. Il s’inscrit dans le cadre d’un débat à plusieurs facettes que l’on peut faire remonter au moins jusqu’aux années 1970 et qui est encore très actif aujourd’hui. L’un des aspects du débat porte sur la naturalisation des fonctions, c’est-à-dire sur la manière de les réduire, de les traduire ou de les expliciter en termes de causes efficientes de sorte qu’elles trouvent leur place dans le cadre des sciences de la nature. Notre approche ici est radicalement différente, car nous remettons en question la prémisse selon laquelle les explications téléologiques seraient des explications causales déguisées. Nous défendons au contraire qu’elles sont acceptables en tant que telles aussi bien de façon générale que dans le domaine scientifique et en particulier en biologie. De façon générale, nous remettons en question l’idée selon laquelle la pensée téléologique serait une pensée causale immature, ainsi que sa dépendance présumée vis-à-vis de la psychologie, c’est-à-dire de l’intentionnalité. Nous rejetons donc les accusations d’anthropomorphisme, de vitalisme et de finalisme formulées contre elle. Nous défendons au contraire que la téléologie, la causalité et l’intentionnalité correspondent à des modes différents, autonomes et complémentaires de représentation du monde extérieur. (shrink)

Transformed RAVAL NOTATION solves Syllogism problems very quickly and accurately. This method solves any categorical syllogism problem with same ease and is as simple as ABC… In Transformed RAVAL NOTATION, each premise and conclusion is written in abbreviated form, and then conclusion is reached simply by connecting abbreviated premises.NOTATION: Statements (both premises and conclusions) are represented as follows: Statement Notation a) All S are P, SS-P b) Some S are P, S-P c) Some S are not P, S / (...) PP d) No S is P, SS / PP (- implies are and / implies are not) All is represented by double letters; Some is represented by single letter. No S is P implies No P is S so its notation contains double letters on both sides. -/- RULES: (1) Conclusions are reached by connecting Notations. Two notations can be linked only through common linking terms. When the common linking term multiplies (becomes double from single), divides (becomes single from double) or remains double then conclusion is arrived between terminal terms. (Aristotle’s rule: the middle term must be distributed at least once) -/- (2)If both statements linked are having – signs, resulting conclusion carries – sign (Aristotle’s rule: two affirmatives imply an affirmative) -/- (3) Whenever statements having – and / signs are linked, resulting conclusion carries / sign. (Aristotle’s rule: if one premise is negative, then the conclusion must be negative) -/- (4)Statement having / sign cannot be linked with another statement having / sign to derive any conclusion. (Aristotle’s rule: Two negative premises imply no valid conclusion) Syllogism conclusion by Tranformed Raval’s Notation is in accordance with Aristotle’s rules for the same. It is visually very transparent and conclusions can be deduced at a glance, moreover it solves syllogism problems with any number of statements and it is quickest of all available methods. By new Raval method for solving categorical syllogism, solving categorical syllogism is as simple as pronouncing ABC and it is just continuance of Aristotle work on categorical syllogism. It’s believed that Boole's system could handle multi-term propositions and arguments, whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, it’s claimed that Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle". Above conclusion is reached at a glance with Raval's Notations (Symbolic Aristotle’s syllogism rules). Premise: "No (square that is a quadrangle) is a (rhombus that is a rectangle)" Raval's Representations: S – Q, S – Q / Rh – Re, Rh – Re Premise: "No (rhombus that is a rectangle) is a (square that is a quadrangle)". Raval's Representations: Rh – Re, Rh – Re / S – Q, S - Q Conclusion: "No (quadrangle that is a square) is a (rectangle that is a rhombus)" Raval’s Representations: Q – S, Q – S / Re – Rh, Re – Rh As “ Q – S” follows from “S – Q” and “Re – Rh” from “Rh – Re”. Given conclusion follows from the given premises. Author disregards existential fallacy, as subset of a null set has to be a null set. -/- . (shrink)

This book is written for those who wish to learn some basic principles of formal logic but more importantly learn some easy methods to unpick arguments and assess their value for truth and validity. -/- The first section explains the ideas behind traditional logic which was formed well over two thousand years ago by the ancient Greeks. Terms such as ‘categorical syllogism’, ‘premise’, ‘deduction’ and ‘validity’ may appear at first sight to be inscrutable but will easily be understood with (...) examples bringing the subjects to life. Traditionally, Venn diagrams have been employed to test arguments. These are very useful but their application is limited and they are not open to quantification. The mid-section of this book introduces a methodology that makes the analysis of arguments accessible with the use of a new form of diagram, modified from those of the mathematician Leonhard Euler. These new diagrammatic methods will be employed to demonstrate an addition to the basic form of syllogism. This includes a refined definition of the terms ‘most’ and ‘some’ within propositions. This may seem a little obscure at the moment but one will readily apprehend these new methods and principles of a more modern logic. (shrink)

From antiquity to date, communal clashes, inter tribal even to global crisis of war is antecedented by penetration of ill-will, unfair sharing formula of human and natural resources by a privileged few resulting in high social, economic and political acrimony hence, the growing calls to reframe the politics of poverty reduction and social protection in particular, in terms of extending the ‘social contract’ to the poorest groups as people are getting increasingly aware of injustice. This premise is on the (...) widening gap between the rich and poor on daily bases. With the increase of awareness, knowledge, technology and the advent of post-modernist era, the quest for social justice has heightened. Even communism and democracy attempt to offer social justice to its natives. Communism states that humans are free to engage in any kind of occupation and express ourselves freely without government interference, unlike the alienated labour society of the capitalist industry: this for communism is social Justice, while democracy thinks equality before law and power to its natives is social justice. All through the era of Philosophy, Philosophers differ on the definition, and what constitute social justice. Until now, there is no unifying explanation on what social justice is and consists of. This paper tends to look into the history of social Justice and different philosophers from different epochs. It also tried to expose the problems inherent in the definition and what constitute social justice, and cautioned that complimentary imperative should be employ to curtail human egoistic tendency that aids social injustice. (shrink)

The possibility of multi-location—of one entity having more than one exact location—is required by several metaphysical theories such as the immanentist theory of universals and three-dimensionalism about persistence. One of the most pressing challenges for multi-location theorists is that of making sense of exact location—in that extant definitions of exact location entail a principle called ‘functionality’, according to which nothing can have more than one exact location. Recently in a number of promising papers, Antony Eagle has proposed and (...) defended a definition of exact location in terms of weak location that does not entail functionality. This paper provides the first thorough assessment of Eagle’s proposal. In particular, we argue that it cannot account for the location of immanent universals, the multi-location of mereologically changing three-dimensional objects, the multi-location of mereologically complex objects, and that it makes extended simples impossible. (shrink)

In this paper I examine how Aristotle thinks syllogisms establish existence. I argue against the traditional "Instantiation" reading and in favor of an alternative "causal" or "structural" account of existential syllogisms. On my interpretation, syllogisms establish the existence of kinds by revealing that they are per se unities whose features are causally underwritten by a single cause/essence. They do so by tracing correlations between propria--peculiar, coextensive features--of the kind in question.

ABSTRACT: In antiquity we encounter a distinction of two types of hypothetical syllogisms. One type are the ‘mixed hypothetical syllogisms’. The other type is the one to which the present paper is devoted. These arguments went by the name of ‘wholly hypothetical syllogisms’. They were thought to make up a self-contained system of valid arguments. Their paradigm case consists of two conditionals as premisses, and a third as conclusion. Their presentation, either schematically or by example, varies in (...) different authors. For instance, we find ‘If (it is) A, (it is) B; if (it is) B, (it is) C; therefore, if (it is) A, (it is) C’. The main contentious point about these arguments is what the ancients thought their logical form was. Are A, B, C schematic letters for terms or propositions? Is ‘is’, where it occurs, predicative, existential, or veridical? That is, should ‘A esti’ be translated as ‘it is an A’, ‘A exists’, ‘As exist’ or ‘It is true/the case that A’? If A, B, C are term letters, and ‘is’ is predicative, are the conditionals quantified propositions or do they contain designators? If one cannot answer these questions, one can hardly claim to know what sort of arguments the wholly hypothetical syllogisms were. In fact, all the above-mentioned possibilities have been taken to describe them correctly. In this paper I argue that it would be mistaken to assume that in antiquity there was one prevalent understanding of the logical form of these arguments - even if the ancients thought they were all talking about the same kind of argument. Rather, there was a complex development in their understanding, starting from a term-logical conception and leading to a propositional-logical one. I trace this development from Aristotle to Philoponus and set out the deductive system on which the logic of the wholly hypothetical syllogisms was grounded. (shrink)

The adoption of multi-cloud environments has become a strategic necessity for organizations seeking scalability, flexibility, and operational efficiency. However, distributing workloads across multiple cloud providers introduces significant security challenges, including authentication vulnerabilities, inconsistent security policies, data breaches, and compliance risks. Traditional security approaches often fail to address the complexity of multi-cloud ecosystems, requiring a more comprehensive risk mitigation strategy. This paper analyses key security risks in multi-cloud architectures and evaluates industry-standard risk assessment frameworks to prioritize effective countermeasures. (...) Our findings indicate that authentication, access control, and secure cloud networking are the most critical areas requiring immediate attention. Threats such as identity mismanagement, insecure data transfers, and lack of unified monitoring further escalate security concerns. To mitigate these risks, we propose a combination of zero-trust architecture, robust identity and access management (IAM), encryption protocols, and AI-driven threat detection. Implementing these strategies can enhance data integrity, regulatory compliance, and overall cloud security posture. By adopting a proactive approach, IT leaders can optimize cybersecurity investments and ensure the resilience of multi-cloud environments. This study provides actionable insights to strengthen security in distributed cloud architectures, enabling organizations to defend against evolving cyber threats. (shrink)

In the recent literature, it has been shown that the wave function in the de Broglie–Bohm theory can be regarded as a new kind of field, i.e., a "multi-field", in three-dimensional space. In this paper, I argue that the natural framework for the multi-field is the original second-order Bohm’s theory. In this context, it is possible: i) to construe the multi-field as a real-valued scalar field; ii) to explain the physical interaction between the multi-field and the (...) Bohmian particles; and iii) to clarify the status of the energy-momentum conservation and the dynamics of the theory. (shrink)

It is a familiar point that many ordinary dispositions are multi-track, that is, not fully and adequately characterisable by a single conditional. In this paper, I argue that both the extent and the implications of this point have been severely underestimated. First, I provide new arguments to show that every disposition whose stimulus condition is a determinable quantity must be infinitely multi-track. Secondly, I argue that this result should incline us to move away from the standard assumption that (...) dispositions are in some way importantly linked to conditionals, as presupposed by the debate about various versions of the ‘conditional analysis’ of dispositions. I introduce an alternative conception of dispositionality, which is motivated by linguistic observations about dispositional adjectives and links dispositions to possibility instead of conditionals. I argue that, because of the multi-track nature of dispositions, the possibility-based conception of dispositions is to be preferred. (shrink)

Gottfried Leibniz embarked on a research program to prove all the Aristotelic categorical syllogisms by diagrammatic and algebraic methods. He succeeded in proving them by means of Euler diagrams, but didn’t produce a manuscript with their algebraic proofs. We demonstrate how key excerpts scattered across various Leibniz’s drafts on logic contained sufficient ingredients to prove them by an algebraic method –which we call the Leibniz-Cayley (LC) system– without having to make use of the more expressive and complex machinery of (...) first-order quantificational logic. In addition, we prove the classic categorical syllogisms again by a relational method –which we call the McColl-Ladd (ML) system– employing categorical relations studied by Hugh McColl and Christine Ladd. Finally, we show the connection of ML and LC with Boolean algebra, proving that ML is a consequence of LC, and that LC is a consequence of the Boolean lattice axioms, thus establishing Leibniz’s historical priority over George Boole in characterizing and applying (a sufficient fragment of) Boolean algebra to effectively tackle categorical syllogistic. (shrink)

Numerous problems arising in engineering applications can have several objectives to be satisfied. An important class of problems of this kind is lexicographic multi-objective problems where the first objective is incomparably more important than the second one which, in its turn, is incomparably more important than the third one, etc. In this paper, Lexicographic Multi-Objective Linear Programming (LMOLP) problems are considered. To tackle them, traditional approaches either require solution of a series of linear programming problems or apply a (...) scalarization of weighted multiple objectives into a single-objective function. The latter approach requires finding a set of weights that guarantees the equivalence of the original problem and the single-objective one and the search of correct weights can be very time consuming. In this work a new approach for solving LMOLP problems using a recently introduced computational methodology allowing one to work numerically with infinities and infinitesimals is proposed. It is shown that a smart application of infinitesimal weights allows one to construct a single-objective problem avoiding the necessity to determine finite weights. The equivalence between the original multi-objective problem and the new single-objective one is proved. A simplex-based algorithm working with finite and infinitesimal numbers is proposed, implemented, and discussed. Results of some numerical experiments are provided. (shrink)

The problem of multi-peer disagreement concerns the reasonable response to a situation in which you believe P1 … Pn and disagree with a group of ‘epistemic peers’ of yours, who believe ∼P1 … ∼Pn, respectively. However, the problem of multi-peer disagreement is a variant on the preface paradox; because of this the problem poses no challenge to the so-called ‘steadfast view’ in the epistemology of disagreement, on which it is sometimes reasonable to believe P in the face of (...) peer disagreement about P. After some terminology is defined (§1), Peter van Inwagen's challenge to the steadfast view will be presented (§2). The preface paradox will then be presented and diagnosed (§3), and it will be argued that van Inwagen's challenge relies on the same principle that generates the preface paradox (§4). The reasonable response to multi-peer disagreement will be discussed (§5), and an objection addressed (§6). (shrink)

Do multi-level selection explanations of the evolution of social traits deepen the understanding provided by single-level explanations? Central to the former is a mathematical theorem, the multi-level Price decomposition. I build a framework through which to understand the explanatory role of such non-empirical decompositions in scientific practice. Applying this general framework to the present case places two tasks on the agenda. The first task is to distinguish the various ways of suppressing within-collective variation in fitness, and moreover to (...) evaluate their biological interest. I distinguish four such ways: increasing retaliatory capacity, homogenising assortment, and collapsing either fitness structure or character distribution to a mean value. The second task is to discover whether the third term of the Price decomposition measures the effect of any of these hypothetical interventions. On this basis I argue that the multi-level Price decomposition has explanatory value primarily when the sharing-out of collective resources is `subtractable'. Thus its value is more circumscribed than its champions Sober and Wilson (1998) suppose. (shrink)

McCall's system for contingent syllogisms is modified. A semantics for the resulting system is provided.

Much attention has been devoted recently to cases where a controversial speaker is invited to speak on campus and subsequently some members of the university seek to have that speaker disinvited. Debates about such scenarios often blur together legal, normative, and empirical considerations. I seek to help clarify issues by separating key legal, normative, and empirical questions. Central to my examination is the idea of the university as a multi-forum institution—i.e. a complex public institution whose parts contain different types (...) of forums. I conclude that it is sometimes legally and normatively permissible (1) for universities to disinvite speakers, and (2) for students to seek to get speakers they consider unacceptable disinvited. I also suggest that my arguments sometimes extent to shouting down speakers. (shrink)

Although written in Japanese, 実践的三段論法について（On Practical Syllogisms）pursues a logical form of the practical syllogism.

I show that a generalization of premise semantics allows for a new set of solutions to the problems posed by anankastic conditionals.

The banking sector faces growing challenges in identifying and managing risks due to the complexity of financial transactions and increasing fraud. This research presents a framework that combines multiple agents with deep learning to improve risk prediction in banking. Each agent focuses on specific tasks like cleaning data, selecting important features, and detecting unusual activities, ensuring a detailed risk assessment. A deep learning model is used to analyze large amounts of transaction data and identify patterns that may signal potential risks. (...) Tests on real-world banking data show that this approach is more accurate, faster, and effective than traditional methods. By combining the strengths of multi-agent systems and deep learning, this study offers a reliable and flexible solution to help banks manage and adapt to changing risks more effectively. (shrink)

Where does agency lie in musical performance? How is it expressed? Recent music scholarship has highlighted an increasingly prominent tendency to conceive of agency as not confined to any one individual or type of individual, instead being distributed across diverse individuals that can be found occupying performance situations. . This article uses two ‘percussion’ works from the 1970s by the composer John Cage, Child of Tree (1975) and its multi-performer elaboration Branches (1976), as a foil for engaging with these (...) practical and theoretical musical concerns, and for suggesting some heretofore underappreciated distinctions within the ongoing work on multi-agential performance. (shrink)

Property and Casualty (P&C) insurers are adopting multi-cloud environments as a strategic imperative because of their increasing data volumes and complexities in regulatory compliance, customer expectations and technological advancements. This paper discusses how Snowflake’s cloud-agnostic, unified platform enables insurers to create resilient, efficient, and compliant multi cloud data strategies. Using Snowflake’s elastic scalability, real-time analytics, secure data sharing and seamless cloud interoperability, insurers can optimize claims processing, augment fraud detection, and support customer engagement. The study offers core design (...) principles for multi cloud data architectures and sheds light on problems in data fragmentation, latency, and security risks. It points to how Snowflake enables data resilience, including data replication, encryption, GDPR, and CCPA compliance. Details are provided. Practical implementation strategies of phased data migration ETL pipelines and integration with existing enterprise system to ensure a smooth deployment. Snowflake is seen as a clear win through a cost-benefit analysis with metrics like RTO and RPO that define how well Snowflake performs disaster recovery and business continuity. Additionally, the paper also looks at the emergence of tech like AI, blockchain and edge computing which could additionally bolster multi-cloud strategies even further. Finally, Snowflake enables the journey for P&C insurers through cloud ecosystem pitfalls, enabling operational resilience, regulatory compliance, along competitive advantage in a data-driven industry. (shrink)

The article summarizes the software tool on astrophysical analysis with multi-wavelength space telescope data. It recaps the evidence analysis conducted on the Kerr-Newman black hole (KNBH). It was written prior to the article Research on the Kerr-Newman Black Hole in M82 Confirms Black Hole and White Hole Juxtapose not soon after the experiment. The conducted analysis suggested Hawking radiation is caused by the movement of ergosurfaces of the BH and serves as the primal evidence for black hole and white (...) hole juxtapose. A later data exploration was conducted with the radiation trails in the multi-wavelength data. The evidences produced corroborates with Yale professor Priyamvada Natarajan's black hole seeds theory. It implies that the electromagnetic dynamic of fusion and fission temperature determines the pressure of surface tension on the macro particles, and the mass density of the BH is determined by the electromagnetic tension between the outer ergosurface and inner ergosurface. The ring singularity of the BH and the Penrose-Hawking singularity of the BH determine the spin and gravitational singularity of the BH. Inside the ergosurfaces, the BH singularities' backward inflow causes the vicinity's rate on feeding the BH. It makes the active galactic nuclei (AGN) a semi-closed system. The density pressure is released on threshold. During the mass exchange observed by energy momentum upon the AGN's open, the macroparticle composition of the BH changes with the galactic event. This causes the expansion rate of the galaxy and contraction rate of the BH. AGN types and their relative motions determine the expansion rate of the cosmic universe in a generalized quantitative thinking. The article concludes that BH spin is caused by the asymmetric motions of AGN in the BH system. A set of the nuclear resonance caused by BH and white hole (WH) oscillation is processed with the same set of data. (shrink)