Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does (...) not discuss many other historically and philosophically important aspects of Boole’s book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole’s contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology. (shrink)

In Prior Analytics I.30, Aristotle seems too much optmistic about finding out the principles of sciences. For he seems to say that, if our empirical collection of facts in a given domain is exhaustive or sufficient, it will be easy for us to find out the explanatory principles in the domain. However, there is a distance between collecting facts and finding out the explanatory principles in a given domain. In this paper, I discuss how the key expression in (...) the sentence at 46a25 should be interpreted: “the true characteristics of things” (“τῶν ἀληθῶς ὑπαρχόντων τοῖς πράγμασιν”). I argue that, on a more accurate interpretation of the expression, Aristotle’s point would cease to look like a piece of naïve or even silly optimism. (shrink)

Since at least late antiquity, Aristotle’s Prior Analytics B 23 has been misread. Aristotle does not think that an induction is a syllogism made good by complete enumeration. The confusion can be eliminated by considering the nature of the surviving text and watching very closely Aristotle’s moving back and forth between “induction” and “syllogism from induction.” Though he does move freely between them, the two are not synonyms.

The word pro-tasis is etymologically a near equivalent of pre-mise, pro-position, and ante-cedent—all having positional, relational connotations now totally absent in contemporary use of proposition. Taking protasis for premise, Aristotle’s statement (24a16) -/- A protasis is a sentence affirming or denying something of something…. -/- is not a definition of premise—intensionally: the relational feature is absent. Likewise, it is not a general definition of proposition—extensionally: it is too narrow. This paper explores recent literature on these issues.

In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. It consists of a deductive system (I.4-22), meta-logical results (I.23-26), and a method for finding and giving deductions (I.27-29) that can apply in “any art or science whatsoever” (I.30). After this, Aristotle compares this method with Plato’s method of division, a procedure designed to find essences of natural kinds through systematic classification. This critical comparison in APr I.31 (...) raises an interpretive puzzle: how can Aristotle reasonably juxtapose two methods that differ so much in their aims and approach? What can be gained by doing so? Previous interpreters have failed to show how this comparison is legitimate or what important point Aristotle is making. The goal of this paper is to resolve the puzzle. In resolving this puzzle we not only learn more about the relationship be- tween division and the syllogistic in Aristotle. We will also learn something about the motivation for the syllogistic itself, by seeing the role that it plays in his philosophy of science. (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)

In this paper, I argue that, if ‘the overrepresentation of Christian theists in analytic philosophy of religion is unhealthy for the field, since they would be too much influenced by prior beliefs when evaluating religious arguments’ (De Cruz and De Smedt (2016), 119), then a first step toward a potential remedy is this: analytic philosophers of religion need to restructure their analytical tasks. For one way to mitigate the effects of confirmation bias, which may be influencing how analytic philosophers (...) of religion evaluate arguments in Analytical Philosophy of Religion (APR), is to consider other points of view. Applied to APR, this means considering religious beliefs, questions, and arguments couched in non-Christian terms. In this paper, I focus on Islam in particular. My aim is to show that Islam is a fertile ground of philosophical questions and arguments for analytic philosophers of religion to engage with. Engaging with questions and arguments couched in non-Christian terms would help make work in APR more diverse and inclusive of religions other than Christianity, which in turn would also be a first step toward attracting non-Christians to APR. (shrink)

In this dissertation, I explore the work of Donald Davidson, reveal an inconsistency in it, and resolve that inconsistency in a way that complements a debate in philosophy of science. In Part One, I explicate Davidson's extensional account of meaning; though not defending Davidson from all objections, I nonetheless present his seemingly disparate views as a coherent whole. In Part Two, I explicate Davidson's views on the dualism between conceptual schemes and empirical content, isolating four seemingly different arguments that Davidson (...) makes against the dualism; I demonstrate that, though the arguments fail, each is ultimately meant to rely on his account of meaning. ;In Part Three, I show that Davidson's extensional account of meaning gives rise to the analytic-synthetic distinction, while simultaneously needing to reject it. I then propose a resolution to Davidson's dilemma. Rather than treating interpretation of meaning as continuous with the holistic enterprise of science, as Quine treats translation, one should treat it as conceptually prior to science, as Kant treats epistemology. Nonetheless I recognize four reasons why Davidson himself would reject doing so. I therefore propose a view called 'transcendental semantics', based on Davidson's, that accepts my resolution. Further, transcendental semantics, like Kant's own transcendental idealism, posits a single conceptual scheme; nonetheless Kant's is concerned with Newtonian physics, transcendental semantics' with interpretation. ;Finally, in Part Four, I show how positing such a scheme allows transcendental semantics to complement a promising neo-Carnapian account of theory confirmation in science proposed by Michael Friedman. Scientists are first and foremost interpreters, a fact that allows transcendental semantics to help Friedman establish the possibility of rational continuity through scientific revolutions. In fact, transcendental semantics, by complementing Friedman's project, reunites two of Carnap's own concerns, philosophy of language and philosophy of science. I conclude that philosophy of language without philosophy of science is empty , while philosophy of science without philosophy of language is blind. (shrink)

Visual analytics (VA) combines the strengths of human and machine intelligence to enable the discovery of interesting patterns in challenging datasets. Historically, most attention has been given to developing the machine component—for example, machine learning or the human-computer interface. However, it is also essential to develop the abilities of the analysts themselves, especially at the beginning of their careers. -/- For the past several years, we at the University of British Columbia (UBC)—with the support of The Boeing Company—have experimented (...) with various ways of preparing undergraduate students for VA. Although inspired by the need to prepare students to become visual analysts, the result turned out to be fairly general in scope, applicable to other analytical approaches, as well as more general research. In hindsight, this makes considerable sense. Although the visual component of VA is necessary, it is insufficient; many analytical activities at the human end involve nonvisual skills, such as effective decision-making and the ability to quickly focus on the relevant parts of a problem. -/- The result of this experimentation is a third-year undergraduate course titled Cognitive Systems 303 (COGS 303) that focuses on “VA unplugged”—that is, on developing investigative abilities prior to training on the VA systems themselves. It was felt that if students focused on developing basic analytical habits of thought prior to learning VA systems, these habits would be reinforced by subsequent practice on “live” systems. (shrink)

ABSTRACTThis paper is concerned with the reasons for the emergence and dominance of analytic philosophy in America. It closely examines the contents of, and changing editors at, The Philosophical Review, and provides a perspective on the contents of other leading philosophy journals. It suggests that analytic philosophy emerged prior to the 1950s in an environment characterized by a rich diversity of approaches to philosophy and that it came to dominate American philosophy at least in part due to its effective (...) promotion by The Philosophical Review’s editors. Our picture of mid-twentieth-century American philosophy is different from existing ones, including those according to which the prominence of analytic philosophy in America was basically a matter of the natural affinity between American philosophy and analytic philosophy and those according to which the political climate at the time was hostile towards non-analytic approaches. Furthermore, our reconstruction suggests a new perspective on the nature of 1950s analytic philosophy. (shrink)

Meaning without Analyticity draws upon the author’s essays and articles, over a period of 20 years, focused on language, logic and meaning. The book explores the prospect of a non-behavioristic theory of cognitive meaning which rejects the analytic-synthetic distinction, Quinean behaviorism, and the logical and social-intellectual excesses of extreme holism. Cast in clear, perspicuous language and oriented to scientific discussions, this book takes up the challenges of philosophical communication and evaluation implicit in the recent revival of the pragmatist tradition—especially those (...) arising from its relation to prior American analytic thought. This volume continues the work of Callaway’s 1993 book, Context for Meaning and Analysis, building on the “turn toward pragmatism.” . (shrink)

This paper is a reply to a prior work by C. J. F. Williams in which he criticised David Kaplan's account of the contingent analytic. In this paper, I take myself to be defending Kaplan's views against Williams' attack.

The article explains on the two-year experiment after the author’s finalization of dissertation. The thesis of the dissertation was hidden in the last chapter with analytical linguistics. It was done so with the fascist development of the Chinese Communist regime with neo- Nazi characteristics. Since numerous prior warnings on the political downshifts & coup d’état in China was willfully ignored by the university, the linguistic innovations in dissertation found a balance between multilateralism and outer space (security). The experiments were (...) conducted with a combination of physical unit analysis & thermonuclear dynamics analysis. It describes the experiment process in terms of gravitation as gravitational singularity and Bekenstein-Penrose singularity. Detailed research process is elaborated in the article concerning the sociopolitical interactions the research involved. (shrink)

At the beginning of the first book of Posterior Analytics, Aristotle‟s feature of demonstrative knowledge involves a certain concept of “necessity”. The traditional interpretation tends to associate this concept with modal necessity, which is found in the Prior Analytics and De interpretatione. The present article aims to show in which way the sixth chapter of book A of Posterior Analytics presupposes a set of essentialist theses that claims to base the necessity of scientific knowledge on predicative (...) relations of essential character. To acknowledge this essentialist background and simultaneously support a modal interpretation of scientific necessity urges us to attribute serious drawbacks to Aristotle‟s theory of demonstration, forcing us to reassess this interpretative tendency. (shrink)

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient logic texts. A renaissance in ancient (...) logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (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)

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)

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)

ABSTRACT: This paper traces the earliest development of the most basic principle of deduction, i.e. modus ponens (or Law of Detachment). ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call any (...) arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)

The goal of this paper is to present a new reconstruction of Aristotle's assertoric logic as he develops it in Prior Analytics, A1-7. This reconstruction will be much closer to Aristotle's original...

This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and (...) his understanding of modern logical theory. In the process Corcoran and Scanlan present new, previously unpublished results. Corcoran regards this review as an important contribution to contemporary study of PRIOR ANALYTICS: both the book and the review deserve to be better known. (shrink)

How does Aristotle think about sentences like ‘Every x is y’ in the Prior Analytics? A recently popular answer conceives of these sentences as expressing a mereological relationship between x and y: the sentence is true just in case x is, in some sense, a part of y. I argue that the motivations for this interpretation have so far not been compelling. I provide a new justification for the mereological interpretation. First, I prove a very general algebraic soundness (...) and completeness result that unifies the most important soundness and completeness results to date. Then I argue that this result vindicates the mereological interpretation. In contrast to previous interpretations, this argument shows how Aristotle’s conception of predication in mereological terms can do important logical work. (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)

We reconstruct as much as we can the part of al-Fārābī's treatment of modal logic that is missing from the surviving pages of his Long Commentary on the Prior Analytics. We use as a basis the quotations from this work in Ibn Sīnā, Ibn Rushd and Maimonides, together with relevant material from al-Fārābī's other writings. We present a case that al-Fārābī's treatment of the dictum de omni had a decisive effect on the development and presentation of Ibn Sīnā's (...) modal logic. We give further evidence that the Harmonisation of the Opinions of Plato and Aristotle was not written by al-Fārābī. (shrink)

ABSTRACT: Alexander of Aphrodisias’ commentaries on Aristotle’s Organon are valuable sources for both Stoic and early Peripatetic logic, and have often been used as such – in particular for early Peripatetic hypothetical syllogistic and Stoic propositional logic. By contrast, this paper explores the role Alexander himself played in the development and transmission of those theories. There are three areas in particular where he seems to have made a difference: First, he drew a connection between certain passages from Aristotle’s Topics and (...) Prior Analytics and the Stoic indemonstrable arguments, and, based on this connection, appropriated at least four kinds of Stoic indemonstrables as Aristotelian. Second, he developed and made use of a specifically Peripatetic terminology in which to describe and discuss those arguments – which facilitated the integration of the indemonstrables into Peripatetic logic. Third, he made some progress towards a solution to the problem of what place and interpretation the Stoic third indemonstrables should be given in a Peripatetic and Platonist setting. Overall, the picture emerges that Alexander persistently (if not always consistently) presented passages from Aristotle’s logical œuvre in a light that makes it appear as if Aristotle was in the possession of a Peripatetic correlate to the Stoic theory of indemonstrables. (shrink)

Logic is the systematic study of patterns of correct inference. The first treatise on logic is Aristotle's Prior Analytics , written around 350 B.C. and there are remarkable similarities between the way he presented his theory of valid arguments and the way it is still taught today. He analyzes the form of various inferences and then illustrates them with concrete examples. He begins with very simple cases.

Aristotle's syllogistic theory, as developed in his Prior Analytics, is often regarded as the birth of logic in Western philosophy. Over the past century, scholars have tried to identify important precursors to this theory. I argue that Platonic division, a method which aims to give accounts of essences of natural kinds by progressively narrowing down from a genus, influenced Aristotle's logical theory in a number of crucial respects. To see exactly how, I analyze the method of division as (...) it was originally conceived by Plato and received by Aristotle. I argue that, while Plato allowed that some divisions fail to rigorously investigate the essence, he began a program continued by Aristotle (and others in antiquity and the middle ages) of seeking norms for division that would apply in any domain whatsoever. This idea of a rigorous, general method was taken up and developed by Aristotle in his syllogistic. Aristotle also used Plato's conception of predication as parthood in his semantics for syllogistic propositions. As part of my argument, I prove that a semantics based on Platonic divisional structures is sound and complete for the deduction system used in the literature to model Aristotle's syllogistic. (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)

The premise-fact confusion in Aristotle’s PRIOR ANALYTICS. -/- The premise-fact fallacy is talking about premises when the facts are what matters or talking about facts when the premises are what matters. It is not useful to put too fine a point on this pencil. -/- In one form it is thinking that the truth-values of premises are relevant to what their consequences in fact are, or relevant to determining what their consequences are. Thus, e.g., someone commits the premise-fact (...) fallacy if they think that a proposition has different consequences were it true than it would have if false. C. I. Lewis said that confusing logical consequence with material consequence leads to this fallacy. See Corcoran’s 1973 “Meanings of implication” [available on Academia. edu]. -/- The premise-fact confusion occurs in a written passage that implies the premise-fact fallacy or that suggests that the writer isn’t clear about the issues involved in the premise-fact fallacy. Here are some examples. -/- E1: If Abe is Ben and Ben swims, then it would follow that Abe swims. -/- Comment: The truth is that from “Abe is Ben and Ben swims”, the proposition “Abe swims” follows. Whether in fact Abe is Ben and Ben swims is irrelevant to whether “Abe swims” follows from “Abe is Ben and Ben swims”. -/- E1 suggests that maybe “Abe swims” wouldn’t follow from “Abe is Ben and Ben swims” if the latter were false. -/- E2: The truth of “Abe is Ben and Ben swims” implies that Abe swims. -/- E3: Indirect deduction requires assuming something false. -/- Comment: If the premises of an indirect deduction are true the conclusion is true and thus the “reductio” assumption is false. But deduction, whether direct or indirect, does not require true premises. In fact, indirect deduction is often used to determine that the premises are not all true. -/- Anyway, the one-page paper accompanying this abstract reports one of dozens of premise-fact errors in PRIOR ANALYTICS. In the session, people can add their own examples and comment on them. For example, is the one at 25b32 the first? What is the next premise-fact error after 25b32? Which translators or commentators discuss this? -/- . (shrink)

Flannery’s volume looks in two directions. On the one hand, as Flannery announces in the book’s introduction, the chapters in the volume were intended to shed light on three specific ‘background’ issues in contemporary ethics and the interpretation of Thomas Aquinas, namely, Aquinas’ notion of ethical theory (as articulated especially in Summa Theologica 1-2.6-21), the ramifications of physical actions on moral evaluation in contemporary ethics (for instance, whether the fact that an abortion consists specifically in the crushing of a fetus’ (...) skull rather than some other form of terminating the fetus has moral relevance), and the understanding of Aquinas’ ‘principle of double effect’ (Summa Theologica 2-2.64.7). On the other hand, the eight chapters (and two appendices) are all devoted to the exegesis of passages in Aristotle’s corpus (primarily the ethical treatises, but with substantial discussions of passages from the Prior Analytics, the Physics, and the Metaphysics insofar as they shed light on passages in the eth-ical corpus). Although the exegetical chapters are motivated by contemporary and Thomistic background issues, the exegesis appears entirely grounded in Aristotle’s (rather than Aristotelian) texts. (shrink)

The purpose of this paper is to give an account and a rational reconstruction of the heuristic advice provided by Aristotle in the Topics and Prior Analytics in regard to the difficulty or ease of strategic planning in the context of a dialectical dialogue. The general idea is that a Questioner can foresee what his refutational syllogism would have to look like given the character of the thesis defended by the Answerer, and therefore plan accordingly. A rational reconstruction (...) of this advice will be attempted from three perspectives: strategic planning based on the acceptability of Answerer’s thesis, strategic planning based on the predicational form of the thesis, strategic planning based on the logical form of the thesis. In addition, we will provide an illustration of the potential of this heuristic advice as we apply it to the interpretation of a fragment from Plato, presuming that, in a similar way, a reading of this kind might be more generally applicable in the interpretation of the Platonic dialogues. (shrink)

Groarke is surely right that Aristotle believed the cognitive hierarchy he described in Posterior Analytics B 19 is central to, and not antithetical to, validating the syllogism described in Prior Analytics B 23. But did Aristotle really believe induction ultimately relies on what Groarke calls “a stroke or leap of understanding,” “immediate illumination,” “moment of immediate cognition,” “a direct insight,” “moment of illumination,” and so on? . . . Overall, what Groarke says here is provocative and inviting, (...) even if not definitive. (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)

This article is intended to examine specific passages from the section of Metaphysics IV 3-4 to be found between 1005a19-1006b34 in the light of the discussions made by Aristotle in the Prior Analytics. The aim is to understand better the argumentative strategies directed at proving the Principle of Non-Contradiction adopted in the above- mentioned section, based on the logic structured by Aristotle.

Analytical philosophy is ruled by the alliance of logic, linguistics and mathematics since its beginnings in the syllogistic calculus of terms and premises in Aristotle's Analytica protera, in the theories of medieval logic that dealt with what are Proprietatis Terminorum (significatio, suppositio, appellatio), in the theological apologetics of argumentation with the combinatorics of symbols by Raymundus Llullus in the work Ars Magna, Generalis et Ultima (1305-08), in what is presented as Theologia Combinata (cf. Tomus II.p.251) in Ars Magna Sciendi sive (...) Combinatoria by Athanasius Kircher (1669), in analytical combinatorics based in Leibniz's dissertation Ars Combinatoria (1666), where language is understood as a lingua characteristica and as a calculus ratiocinator, in the combinatorics of classes that have the meanings 1 or 0 given in the idea of Boolean functions (1854), in Frege's work Begriffschrift, eine der arithmeticeschen nachgebildete Fomelsprache des reinen Denkens (Concept letter, the language of formulas of pure thought made according to the model in arithmetical language), in Cantor's study of set theory / Grundlagen einer allgemeinen Mannigfaltigkeitstheorie (1883) and up to algorithms of fuzzy logic as a "means of approximate thinking that is in the human prior" (Zadeh, 1990) and fuzzy linguistics in computer semantics (Burghard B. Rieger, 1993). These are all the philosophical ideas of mathematicians and logicians that founded what we call logical pragmatism here as a demand that logic be absolutely used in every way in which it will dominate the grammar of language until logic itself becomes the philosophical grammar of the mind!!! (shrink)

Aristotle's General Definition of the Syllogism may be taken as consisting of two parts: the Inferential Conditions and the Final Clause. Although this distinction is well known, traditional interpretations neglect the Final Clause and its influence on syllogistic. Instead, the aforementioned tradition focuses on the Inferential Conditions only. We intend to show that this neglect has severe consequences not just on syllogistic but on the whole exegesis of Aristotle's Prior Analytics I. Due to these consequences, our objective is (...) to analyse the General Definition's Final Clause and its consequences on syllogistic. We propose a reading of the Final Clause as an additional criterion for distinguishing some arguments as properly syllogistic ones and as a main theme which connects all parts of the Prior Analytics I into one coherent piece of work. (shrink)

Recent decades have seen a surge in interest in metaphilosophy. In particular there has been an interest in philosophical methodology. Various questions have been asked about philosophical methods. Are our methods any good? Can we improve upon them? Prior to such evaluative and ameliorative concerns, however, is the matter of what methods philosophers actually use. Worryingly, our understanding of philosophical methodology is impoverished in various respects. This article considers one particular respect in which we seem to be missing an (...) important part of the picture. While it is a received wisdom that the word “ intuition ” has exploded across analytic philosophy in recent decades, the article presents evidence that the explosion is apparent across a broad swathe of academia. It notes various implications for current methodological debates about the role of intuitions in philosophy. (shrink)

This essay presents a fully inferentialist-expressivist account of scientific representation. In general, inferentialist approaches to scientific representation argue that the capacity of a model to represent a target system depends on inferences from models to target systems. Inferentialism is attractive because it makes the epistemic function of models central to their representational capacity. Prior inferentialist approaches to scientific representation, however, have depended on some representational element, such as denotation or representational force. Brandom’s Making It Explicit provides a model of (...) how to fully discharge such representational vocabulary, but it cannot be applied directly to scientific representations. Pursuing a strategy parallel to Brandom’s, this essay begins with an account of how surrogative inference is justified. Scientific representation and the denotation of model elements are then explained in terms of surrogative inference by treating scientific representation and denotation as expressive, analogous to Brandom’s account of truth. The result is a thoroughgoing inferentialism: M is a scientific representation of T if and only if M has scientifically justified surrogative consequences that are answers to questions about T. (shrink)

I address the question of whether phenomenology is "prior to" all intentionality. I also sketch a version of David Lewis's interpretationism in which phenomenal intentionality plays the role of source intentionality.

I give an interpretation according to which Meno’s paradox is an epistemic regress problem. The paradox is an argument for skepticism assuming that acquired knowledge about an object X requires prior knowledge about what X is and any knowledge must be acquired. is a principle about having reasons for knowledge and about the epistemic priority of knowledge about what X is. and jointly imply a regress-generating principle which implies that knowledge always requires an infinite sequence of known reasons. Plato’s (...) response to the problem is to accept but reject : some knowledge is innate. He argues from this to the conclusion that the soul is immortal. This argument can be understood as a response to an Eleatic problem about the possibility of coming into being that turns on a regress-generating causal principle analogous to the regress-generating principle presupposed by Meno’s paradox. (shrink)

People are motivated by shared social values that, when held with moral conviction, can serve as compelling mandates capable of facilitating support for ideological violence. The current study examined this dark side of morality by identifying specific cognitive and neural mechanisms associated with beliefs about the appropriateness of sociopolitical violence, and determining the extent to which the engagement of these mechanisms was predicted by moral convictions. Participants reported their moral convictions about a variety of sociopolitical issues prior to undergoing (...) functional MRI scanning. During scanning, they were asked to evaluate the appropriateness of violent protests that were ostensibly congruent or incongruent with their views about sociopolitical issues. Complementary univariate and multivariate analytical strategies comparing neural responses to congruent and incongruent violence identified neural mechanisms implicated in processing salience and in the encoding of subjective value. As predicted, neuro-hemodynamic response was modulated parametrically by individuals’ beliefs about the appropriateness of congruent relative to incongruent sociopolitical violence in ventromedial prefrontal cortex, and by moral conviction in ventral striatum. Overall moral conviction was predicted by neural response to congruent relative to incongruent violence in amygdala. Together, these findings indicate that moral conviction about sociopolitical issues serves to increase their subjective value, overriding natural aversion to interpersonal harm. (shrink)

In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and (...) skill. Several attributions of shortcomings and logical errors to Aristotle are shown to be without merit. Aristotle's logic is found to be self-sufficient in several senses: his theory of deduction is logically sound in every detail. (His indirect deductions have been criticized, but incorrectly on our account.) Aristotle's logic presupposes no other logical concepts, not even those of propositional logic. The Aristotelian system is seen to be complete in the sense that every valid argument expressible in his system admits of a deduction within his deductive system: every semantically valid argument is deducible. (shrink)

I reconstruct the notion of significance [_Sinnhaftigkeit_] in the later Husserl, with attention to his conceptions of judgment and transcendental logic. My analysis is motivated by the idea that an account of significance can help to connect analytic, Anglo-American conceptions of meaning as a precise, law-governed phenomenon investigated via linguistic analysis and Continental European conceptions of meaning in a broader “existential” sense. I argue that Husserl’s later work points to a transcendental-logical conception of a founding level of _significance_ [_Sinnhaftigkeit_] (...) class='Hi'>prior to language, and that this conception meets characteristically analytic demands for precision and governance by logical constraints. At the same time, since it is based in descriptions of perceptual intentionality at the level of essential possibility, it leaves room for an account of meaning as a partially undetermined phenomenon of lived experience, and not just of our language and concepts, and thereby meets the characteristically Continental demand to take at face value meaning’s vagueness and indeterminacy in everyday human life. (shrink)

how does one inquire into the truth of first principles? Where does one begin when deciding where to begin? Aristotle recognizes a series of difficulties when it comes to understanding the starting points of a scientific or philosophical system, and contemporary scholars have encountered their own difficulties in understanding his response. I will argue that Aristotle was aware of a Platonic solution that can help us uncover his own attitude toward the problem.Aristotle's central problem with first principles arises from the (...) fact that they cannot be demonstrated in the same way as other propositions. Since demonstrations proceed from prior and better-known principles, if the principles themselves were in need of... (shrink)

This chapter considers Kant's relation to Hume as Kant himself understood it when he wrote the Critique of Pure Reason and the Prolegomena. It first seeks to refine the question of Kant's relation to Hume's skepticism, and it then considers the evidence for Kant's attitude toward Hume in three works: the A Critique, Prolegomena, and B Critique. It argues that in the A Critique Kant viewed skepticism positively, as a necessary reaction to dogmatism and a spur toward critique. In his (...) initial statement of the critical philosophy Kant treated Hume as an ally in curbing dogmatism, but one who stopped short of what was really needed: a full critique of reason, to establish the boundaries of metaphysical cognition. Kant found fault with Hume's analyses of cognition and experience, and specifically his failure to see the crucial importance of synthetic a priori cognition in metaphysics. In particular, he held that Hume's empiricist account of cognition could neither explain the synthetic a priori cognition actually found in mathematics and natural science, nor provide a principled account of the limits on what can be known--and what can be thought--through the pure concepts of the understanding. According to Kant, Hume therefore failed in his attempt to determine the limits of metaphysics, whereas he was able to succeed because his transcendental philosophy provided a thorough account of cognition, its structure and limits. In the Prolegomena and the B Critique Kant distinguished his position more sharply from Hume's. He also adopted a more negative attitude toward "skeptical idealism" than before; but he attributed such skepticism to Descartes, not Hume. Prior to the B Critique Kant did not see Hume as attacking natural science or ordinary cognition. In none of the three works was Kant's main aim to "answer the skeptic." His primary aim was to firmly establish the boundary of metaphysics, by discovering the elements of human cognition and fixing its proper domain. His purported discoveries about the limits of metaphysical cognition meant that the traditional objects of metaphysical knowledge, God, the soul, and the world as it is in itself, are unknowable, hence that traditional metaphysics itself is impossible. Besides settling the possibility or impossibility of metaphysics, his findings would also prevent the illegitimate extension of principles of sensibility to God and the noumenal self, an extension that would threaten the metaphysics of morals by incorrectly denying the thinkability of noumenal freedom, and that might otherwise lead to "materialism, fatalism, atheism, and freethinking unbelief" (B xxxiv). (shrink)

This essay claims that a rupture between two languages permeates human rights discourse in contemporary Anglo-American legal thought. Human rights law is no exception. The one language is written in the sense that a signifying relation inscribed by institutional authors represents concepts. Theories of law have shared such a preoccupation with concepts. Legal rules, doctrines, principles, rights and duties exemplify legal concepts. One is mindful of the dominant tradition of Anglo-American conceptual jurisprudence in this regard. Words have been thought to (...) copy ready-made concepts. Acts of intellectualisation and the accompanying analytic technique have excluded a consideration of a very different sense of legal language. The second sense of a language concentrates upon unwritten acts of meaning which lack a discrete and assignable author. This essay aims to unconceal the importance of an unauthored language. Drawing from Edmund Husserl’s early writings, particularly his Logical Investigations, I shall argue that an unwritten language embodies the written language with acts of meaning. An act of meaning confers one’s experiential body into the content of a concept signified in a written language. In order to understand the importance of such pre-legal acts of meaning in human rights laws, I begin by outlining how universal human rights have been signified as universal by virtue of their content-independence. I then raise the problem of the exclusion of social-cultural phenomena as elements of human rights laws. The clue to this exclusionary character of human rights law rests in the analytic leap from an unwritten to a written legal language. The essay then addresses the effort to link legality with the social world: namely, the effort of grounding legality in a social convention. I examine how a social convention itself is conceptualized, leaving the remainder of acts of meaning. This failure of social conventions to access social-cultural phenomena encourages me to turn to acts of meaning as such acts were understood by Edmund Husserl in his earlier works. Meaning-constituting acts exist prior to intuitions and prior to social conventions. This priority exists analytically as well as phenomenologically. In order to exemplify this prior character of acts of meaning, I retrieve Antigone’s experiential knowledge in Sophocles’ Antigone. Antigone’s unwritten laws are characterized by an absence of mediating concepts. I then identify several elements of an act of meaning in an unwritten language: the experiential body as the source of the acts of meaning, praeiudicia (prejudgements), collective memories, the act character of meaning, and the act of interpretation of social behaviour. My final section raises the prospect of whether human rights can be considered universal if acts of meaning are that important in the identity of a law. (shrink)

In 2004 Jürgen Habermas and Joseph Ratzinger participated in a debate on the ‘pre-political moral foundations of the free-state’. Their contributions showed broad agreement on the role of religion in today’s Western secular state and on areas of collaboration and mutual enrichment between Modernity and Christianity in Europe and the West. They diverged regarding the need or not of a common cultural background prior to the existence of the polity. Their diverging point becomes all the more fascinating to the (...) extent that the matter requires wider empirical, analytical and normative research before it can be settled. Nevertheless, the implications that derive from one or the other possibility are very different in terms, for instance, of immigration and citizenship policies. This is already clear in Europe and is becoming more evident in general in Western democracies. (shrink)

Mass shootings constitute a recurrent and most violent phenomenon in the U.S. and elsewhere. This paper challenges the ready-made, solipsistically contained metanarratives on offer by mainstream media and formal institutions with regard to the psychological antecedents of the perpetrating social actors, while theorizing mass shootings as acts of violence that are systemically inscribed in the foundations of communities. These foundations abide by the logic of sacrifice which is propagated in instances of collective traumatism. It is argued that the cultural trauma (...) that emanates from events of mass shootings, inasmuch as the commemorative events that are performed on regular occasions, constitute re-enactments of the death drive that sustains communities. The cultural analytic deploys against a CDA reading of longitudinal studies on mass shootings, coupled with psychoanalytic discourse analysis, prior to submitting mass shootings to a deconstructive line of reasoning as systemically necessary transcendental violence. Ultimately, it is shown that the intertextual institutional chain that informs the mediatized representation of this social phenomenon merely attains to obliterate and, hence, to propagate cultural traumatism and the sacrificial logic that underpins it. The terms micrometanarrative, parafunction and expropriating ipseity are introduced and operationalized in this context. (shrink)

This paper develops the situational model of primate beliefs from the Prior-Lurz line of thought. There is a strong skepticism concerning primate beliefs in the analytic tradition which holds that beliefs have to be propositional and non-human animals do not have them. The response offered in this paper is twofold. First, two arguments against the propositional model as applied to other animals are put forward: an a priori argument from referential opacity and an empirical argument from varieties of working (...) memory. Second, the Prior-Lurz situational model based on state of affairs as opposed to propositions is introduced and defended with two significant modifications. With this model of primate beliefs we can make progress in understanding how other primates can have certain mindreading capacity. (shrink)

From the beginning of the 16th century to the end of the 18th century, there were not less than ten philosophers who focused extensively on Venn’s ostensible analytical diagrams, as noted by modern historians of logic (Venn, Gardner, Baron, Coumet et al.). But what was the reason for early modern philosophers to use logic or analytical diagrams? Among modern historians of logic one can find two theses which are closely connected to each other: M. Gardner states that since the Middle (...) Ages certain logic diagrams were used just in order to teach “dull-witted students”. Therefore, logic diagrams were just a means to an end. According to P. Bernhard, the appreciation of logic diagrams had not started prior to the 1960s, therefore the fact that logic diagrams become an end the point of research arose very late. The paper will focus on the question whether logic resp. analytical diagrams were just means in the history of (early) modern logic or not. In contrast to Gardner, I will argue that logic diagrams were not only used as a tool for “dull-witted students”, but rather as a tool used by didactic reformers in early modern logic. In predating Bernhard’s thesis, I will argue that in the 1820s logic diagrams had already become a value in themselves in Arthur Schopenhauer’s lectures on logic, especially in proof theory. (shrink)