Les preuves de l’immortalité de l’âme, qui sont un des thèmes cen­traux de l’enseignement de Platon, ont fait l’objet d’une réflexion d’ordre logique et formel sur la manière dont elles sont (ou devraient être) exprimées. En particulier l’argument en faveur de l’immortalité de l’âme contenu dans le Phèdre (245c5-246a2), fondé sur la notion d’âme automotrice et principe de mouve­ment, a été assidûment analysé, pour ce qui est de sa formulation, par plusieurs représentants de la tradition platonicienne (Alcinoos, Hermias d’Alexandrie), ainsi (...) qu’à l’intérieur de la tradition péripatéticienne (Alexandre d’Aphrodise). Par conséquent, il représente, à l’avis de l’auteur, un point privilégié d’observation de la façon dont les platoniciens s’approprient la logique aristotélicienne et récri­vent, à partir de l’époque impériale, certains arguments platoniciens. En outre, il apparaît qu’Alexandre d’Aphrodise, bien qu’étant de tradition péripatéticienne, a grandement contribué à la reformulation des arguments de Platon selon les canons de la logique aristotélicienne par les platoniciens contemporains et posté­rieurs. Il semble aussi qu’Hermias, dans ses scholies sur le Phèdre, réagit juste­ment à certaines affirmations d’Alexandre. Dans cet article, on montre quels sont les points de contact ainsi que les différences dans la réécriture analytico-syllogistique de l’argument du Phèdre en faveur de l’immortalité de l’âme par Alcinoos et Hermias, sans négliger l’apport d’Alexandre. (shrink)

The paper deals with the "deuteros plous", literally ‘the second voyage’, proverbially ‘the next best way’, discussed in Plato’s "Phaedo", the key passage being Phd. 99e4–100a3. The second voyage refers to what Plato’s Socrates calls his “flight into the logoi”. Elaborating on the subject, the author first (I) provides a non-standard interpretation of the passage in question, and then (II) outlines the philosophical problem that it seems to imply, and, finally, (III) tries to apply this philosophical problem to the "ultimate (...) final proof" of immortality and to draw an analogy with the ontological argument for the existence of God, as proposed by Descartes in his 5th "Meditation". The main points are as follows: (a) the “flight into the logoi” can have two different interpretations, a common one and an astonishing one, and (b) there is a structural analogy between Descartes’s ontological argument for the existence of God in his 5th "Meditation" and the "ultimate final proof" for the immortality of the soul in the "Phaedo". (shrink)

In Prior Analytics 1.15 Aristotle undertakes to establish certain modal syllogisms of the form XQM. Although these syllogisms are central to his modal system, the proofs he offers for them are problematic. The precise structure of these proofs is disputed, and it is often thought that they are invalid. We propose an interpretation which resolves the main difficulties with them: the proofs are valid given a small number of intrinsically plausible assumptions, although they are in tension with some claims found (...) elsewhere in Aristotle’s modal syllogistic. The proofs make use of a rule of propositional modal logic which we call the possibility rule. We investigate how this rule interacts and coheres with the core elements of the modal syllogistic. (shrink)

The article presents a formalization of Thomas Aquinas proof for the indestructibility of the human soul. The author of the formalization—the first of its kind in the history of philosophy—is Father Joseph Maria Bocheński. The presentation involves no more than updating the logical symbolism used and accompanies the logical formulae with ordinary language paraphrases in order to ease the reader’s understanding of the formulae. “The fundamental idea of the Thomist proof is of utmost simplicity: things which are destructible are (...) destructible either per se or per accidens; but the human soul is destructible neither per se nor per accidens: therefore the human soul is not destructible”. Bochenski’s words required him to devote considerable effort for the sake of precision of the symbolic language that would be maximally adequate to Thomas’ discourse. Moreover, I have thought it necessary to provide an ample commentary to the traditional and contemporary semantical presuppositions of Aquinas philosophical anthropology in light of Bocheński’s interpretation thereof. (shrink)

Aristotle’s modal syllogistic is his study of patterns of reasoning about necessity and possibility. Many scholars think the modal syllogistic is incoherent, a ‘realm of darkness’. Others think it is coherent, but devise complicated formal modellings to mimic Aristotle’s results. This volume provides a simple interpretation of Aristotle’s modal syllogistic using standard predicate logic. Rini distinguishes between red terms, such as ‘horse’, ‘plant’ or ‘man’, which name things in virtue of features those things must have, and green terms, such as (...) ‘moving’, which name things in virtue of their non-necessary features. By applying this distinction to the Prior Analytics, Rini shows how traditional interpretive puzzles about the modal syllogistic melt away and the simple structure of Aristotle’s own proofs is revealed. The result is an applied logic which provides needed links between Aristotle’s views of science and logical demonstration. The volume is particularly valuable to researchers and students of the history of logic, Aristotle’s theory of modality, and the philosophy of logic in general. (shrink)

I argue that Kant's refutation of Mendelssohn's proof of the immortality of the soul also refutes his own proof of the permanence of material substance. To evade this result, Kant would have had to rely on premises that can only be established empirically. This difficulty brings up deep and disturbing difficulties with Kant's theory of matter and body in his Metaphysical Foundations of Natural Science and suggests that his early Physical Monadology offered a better account, one he was (...) constrained by later commitments to abandon to the detriment of the coherence of his matter theory. (shrink)

Socrates’ second speech in the Phaedrus includes the argument (245c6–246a2) that starts “all/every soul is immortal” (“ψυχὴ πᾶσα ἀθάνατος”).1 This argument has attracted attention for its austerity and placement in Socrates’ grand speech about chariots and love. Yet it has never been identified as a deliberately fallacious argument.2 This article argues that it is. Socrates intends to confront his interlocutor Phaedrus with a dubious sequence of reasoning. He does so to show his speech-loving friend how—rather than simply to tell (...) him that—analytic as much as imagistic speech can persuade without deserving conviction.It has been shown in recent years that on four other occasions Socrates deliberately utters bad .. (shrink)

This paper argues that Augustine did not take the proof inSoliloquia2.22-4, which centers on the Aristotelian notion of ‘being in a subject’, from a single source but constructed it in a deliberately imperfect manner from several passages from Porphyry’s works on Aristotle’sCategoriesin order to supplement it with further arguments in Book Three. InDe immortalitate animaeAugustine explicitly discloses the weaknesses of the proof and repairs them by means of a Neoplatonic notion of causality.

In 1951 Lukasiewicz [[sic]] linked Aristotle's Prior Analytics with modern formal logic. This book attempts to analyze Aristotle's syllogistic theory in the light of Lukasiewcz's work and the whole tradition of classic interpretations of Aristotle's logic. The first of the book's five chapters shows that for Aristotle the syllogism is basically a relationship of terms couched in conditional form; a relationship of variables rather than concrete terms; and a relationship that sees S linked with P not by the copula but (...) by less metaphysical expressions. The classical S is P form is not Aristotelian at all but a much later renovation. The second chapter maintains that Aristotle distinguishes "relative necessity" from "absolute necessity." Aristotle himself ignores his own distinction at times and thus creates logical difficulties for himself. The oft-fought sea battle is fought again in this chapter. Chapter three deals with the controversial notions of "perfect" and "imperfect" syllogisms. The author asserts that by "perfect syllogism" Aristotle means self-evident syllogisms that serve as axioms for deducing other proofs. Chapters four and five deal with the figures of the syllogism and the syllogism as a deductive system respectively. Patzig concludes that Aristotle's syllogistic theory is purely formal in its structure and can only be properly understood if it is not tied to a metaphysics and converted into a philosophical logic. He denies that it is a universal logic, but rather sees it as a specialized theory of relations.--J. J. R. (shrink)

Aquinas's thoughts about the human soul present us with a puzzle. On the one hand, Thomas has been applauded within the analytic tradition as an anti-dualistic thinker, who emphasises the animal nature of human beings and denies that there could be disembodied human persons. Yet on the other hand he holds, as a faithful Catholic theologian, that the human soul survives death, and maintains that the post-mortem soul, prior to its reunification with the body is the subject (...) of characteristically personal intellectual activities. This paper reviews the state of the debate regarding whether these commitments of Aquinas's can be reconciled, and concludes that they cannot in his own terms. However, a recognisably thomist approach to the post-mortem survival of the soul is available, proceeding on the basis that to be rationally ensouled is to have a life-story. (shrink)

An argument in Cicero's Tusculan Disputations (Tusc. 1.39–49) defends psychic immortality by reference to the physical constitution of the soul. This article argues that this ‘Physical Argument’ should be interpreted as a reception of Plato's doctrine of the soul within the philosophical paradigm of the Hellenistic era. After analysing the argument, it is shown that Cicero's proof recasts elements of Plato's Phaedo, in particular the kinship between the soul and the heavens and the soul's essentially (...) contemplative nature, within a corporealist cosmology. The article also argues that Cicero formulates his argument to oppose the Stoic view that the soul's survival after death is only temporary. The Physical Argument emerges as a modernization of Platonic thought, putting Plato into dialogue with contemporary Hellenistic philosophy. Cicero, too, emerges as a more adept philosophical author than is often supposed. (shrink)

The paper argues that the role of ἀριθμός (i.e., a limited multitude) is important for understanding the logical form of the final proof for the immortality of the soul. Along the way, it rejects the notion that soul is a form or the particularity of a form and suggests instead that it is something like an intermediate object. It is the first paper from a set of papers in progress that analyze Plato's metaphysics with respect to the (...) ancient Greek conception of number. (shrink)

In the course of the eighteenth century, understanding human cognitive life came to be construed as something to be explored in terms of the physiology of the sensory organs, the nerves, and the brain: a form of naturalization that effectively moved cognition out of the realm of philosophy as it had traditionally been understood. Bonnet's Analytical Essay on the Faculties of the Soul was at the forefront of these developments, and this is its first English translation. Drawing on his (...) earlier work in natural history -- he was the leading entomologist of his era -- he approaches problems of the nature of the mind via the physiology and anatomy of the brain and sensory systems. His approach is one of 'reverse engineering', starting from an organic statue without faculties, and investigating how it would need to be modified to produce a human being. Bonnet takes up a position that cuts across the standard understanding of the period as a clash between materialism and dualism. While his approach was rigorously naturalistic and physiological, this did not lead him to reject the notion of a soul. Instead, he argues that, in order to make sense of their sensory abilities, we need to attribute a soul to animals as well as human beings. At the same time, he argues that if personal immortality is to be possible, it can be conceived along the lines of insect metamorphosis, which shows how different biological forms can harbour a single identity.--dust jacket. (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 article investigates the prospect of giving de dicto- and de re-necessity a uniform treatment. The historical starting point is a puzzle raised by Aristotle's claim, advanced in one of the modal chapters of his Prior Analytics, that universally privative apodeictic premises simply convert. As regards the Prior and the Posterior Analytics, the data suggest a representation of propositions of the type in question by doubly modally qualified formulae of modal predicate logic that display a necessity operator in two distinct (...) positions. Can the N-operator occurring in these positions be given a unified semantical treatment (which would justify dispensing with a notational differentiation)? A positive answer, based on a suitably shaped truth condition for N-formulae, is given, and is supported in the final section with an alternative proof theoretically based conception of a property's essential belonging to an individual. (shrink)

In Prior Analytics 1.15, Aristotle attempts to give a proof through the impossible of Barbara, Celarent, Darii, and Ferio with an assertoric first premiss, a contingent second premiss, and a possible conclusion. These proofs have been controversial since antiquity. I shall show that they are valid, and that Aristotle is able to explain them by relying on two meta-syllogistic lemmas on the nature of possibility interpreted as syntactic consistency. It will turn out that Aristotle's proofs are not of the intended (...) schemata. I shall investigate some of the results that the impact of this reconstruction on the modal syllogistic has: the relationship between Aristotle's syllogistic and the logics of relevance; the value of Aristotle's requirement that universal affirmative propositions be taken ‘absolutely’; the destruction of many Aristotelian proofs; the recovery of certain principles of modal opposition from a charge of inconsistency. (shrink)

This study offers a new analysis of the last argument of Plato's Phaedo for the immortality of the soul. Interpretations of this argument and especially of the last section have differed considerably. Judgements on its value have usually been adverse. One scholar speaks of the ‘screen of unreal argument’ which concludes the proof, and writes that ‘from the standpoint of logic the argument has petered out into futility’. Another describes the final stage of the proof as ‘a blatant (...) petitio principii’. A third remarks that the conclusion follows ‘if we do not look too closely’. (shrink)

Hegel believes that the immanent ascent of finite spirit and its immersion in its uncreated foundation-in absolute spirit-is a true transition and he cannot use the so-called proofs of the existence of God. Besides, he sees an advantage here in that this transition results in the ascent of the human spirit to the most concrete and true, to God in His absolute truth-to Absolute Spirit. In connection with this, Hegel emphasizes in the manuscript of his lectures on the philosophy of (...) religion that the speculative meaning of the religious idea of the immortality of the soul lies in attaining the absoluteness and infinity of self-consciousness, the fact that "the self-consciousness of the spiritual is itself an eternal, absolute factor.". (shrink)

This study argues both that the proofs are ultimately unconvincing and that Plato was aware of the problems. The Phaedo is shown as a truly dialectical philosophical conversation about the immortality of the soul.

Peter Geach brings the same careful attention to logical detail to these studies in the philosophy of religion and philosophy of mind as he has brought to other philosophical works. Some of the topics discussed here, however, will surprise some readers of Geach's earlier works, e.g., reincarnation, immortality, creation, praying for things to happen, and worshipping the right God. There are separate chapters on these topics as well as chapters on thought, form and existence, and the moral law. It (...) should be noted for readers who may not share Geach's interest in some of these topics that each of the chapters makes important points about issues which go beyond the topics of immediate interest. For example, Geach's two chapters on reincarnation and immortality are very interesting commentaries on the problem of personal identity, and the chapter on praying for things to happen is an interesting essay on time. The chapters on existence and thought pick up themes from Geach's earlier writing on Aquinas and Frege and mental acts. The Aristotelian roots of Geach's thought are clear in these essays from his account of existence and thought to his denial of clear sense to the idea of an immortality of a separate soul or its reincarnation. There is a helpful analytical index.--R. H. K. (shrink)

"In this essay, I wish to question the view that the distinction between medieval and early modern philosophy is primarily one of method. I shall argue that what has come to be known as the modern method in fact owes much to the natural philosophy of John Buridan (ca. 1295-1361), a secular arts master who taught at the University of Paris some three centuries before Descartes. Surrounded by conflicts over institutional governance and curricular disputes, Buridan emerged as a forceful voice (...) for the independence and autonomy of teachers in the faculty of arts, arguing that philosophy as properly practiced belonged to them, the "artists artistae", not to those who taught in the so-called 'higher' faculties of theology, law, and medicine. Now such voices had been heard before at Paris, most notably from Averroist arts masters in the late 13th and early 14th-centuries.(*) Buridan is different, however, because unlike Boethius of Dacia and John of Jandun, he knew how to make the case for artistic autonomy without denigrating the theology and thereby inviting official condemnation. His trick was not to argue that there are 'two truths', one acquired and the other revealed, which might well come into conflict with each other, or that propositions whose truth has been revealed in scripture in no way qualify as scientia. It was rather to recognize the profoundly different methods of theology and philosophy, without losing sight of the fact that what counts as evidence in a proof in natural philosophy does not work in a theological argument, even if both have the same conclusion, such as that the human soul is immortal. Buridan seems to think that if only people would respect the differences between the rules of philosophical and theological inquiry, no conflicts would arise. He is not so naive as to claim this could ever happen, of course. But it does explain why he almost always diagnoses such conflicts in terms of some logical or linguistic confusion on the part of the people who propose them. Buridan is also different because in him the secularizing sentiment already present in the Latin Averroists begins to take shape as a way of doing philosophy, i.e., as a philosophical grammar.. (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)

Essays on The Soul's Logical Life in the Work of Wolfgang Giegerich: Psychology as the Discipline of Interiority is the second collection of essays dedicated to the study and application of Psychology as the Discipline of Interiority - a new 'wave' within Analytical Psychology which pushes off from the work of C. G. Jung and James Hillman. Reflecting upon the notion of psychology developed by German psychoanalyst Wolfgang Giegerich, whose Hegelian turn sheds light on the notion of soul, (...) or the objective psyche, and its inner logic and 'thought', forming a radical new basis from which to ground a modern psychology with soul. The book explores the theme of "the soul's logical life" as it displays itself in various modern phenomena, from overwhelming anxiety, cryptocurrency, the dreams of Japanese college students, and contemporary psychoanalysis, to myth, music, social movements, and the question and relevance of truth in psychology and consciousness. The authors, comprising clinical psychologists, teachers, Jungian analysts, and international scholars, aim to reveal and convey the dialectical inner workings and speculative logic of the modern soul. Essays on The Soul's Logical Life in the Work of Wolfgang Giegerich: Psychology as the Discipline of Interiority will be essential reading for depth and clinical psychologists, Jungian psychoanalysts, and academics and students of post-Jungian studies, and for all those interested in what it means to think in the highly sophisticated and technological world of the twenty-first century. (shrink)

This paper examines the relevance and importance of the large number of examples which Aristotle uses in his "Prior Analytics." In the first part of the paper three preliminary issues are raised: First, it investigates what counts as an example in Aristotle's syllogistic, and especially whether only examples expressed in concrete terms should be considered as examples or maybe also propositions and arguments with letters of the alphabet. The second issue concerns the kinds of examples Aristotle actually uses from everyday (...) life as well as from various scientific and philosophical forms of discourse; among these, it seems that biological examples, rather than mathematical ones, have a predominant place. Finally, I discuss what Aristotle himself has to say about the use of examples, and in particular about the similarity between the use of an example and the use of induction. The second part of the paper focusses on the functions of Aristotle's logical examples. It is of course obvious that some of the examples in the Prior Analytics are used to illustrate, and thus to clarify, a definition, a logical rule, a type of argument. However, I think that Aristotle's logical examples have another function, which is philosophically more interesting, namely as integral parts of the procedure of proving something. To support this claim, I analyse three passages from the "Prior Analytics" in which examples are used either in order to prove that something is not the case, i.e. as counter-examples, or in order to prove positively that it is possible for something to be the case. At the end, I argue that for such uses of examples Aristotle uses the notion of 'ekthesis', which seems to have a wider sense than usually suggested; that is to say, it is used to refer to any proof by means of an example, and not only for the procedure which Aristotle uses to reduce imperfect to perfect syllogisms. (shrink)

Not until the early 1920’s was it possible to distinguish Aristotelian or traditional logic from Aristotle’s own ancient logic. We can now recognize many aspects of his logical investigations that are themselves modern, in the sense that modern logicians are making discoveries that Aristotle had already made or had anticipated. Here we gather five salient features of Aristotle’s logical investigations that reveal a striking philosophical modernity: 1) Aristotle took logic to be that part of epistemology used to establish knowledge of (...) logical consequence; 2) Prior Analytics is a metalogical treatise on the syllogistic deduction system; 3) Aristotle recognized the epistemic efficacy of certain elemental argument patterns, and he explicitly formulated them as rules of natural deduction in corresponding sentences; 4) Prior Analytics is a proof-theoretic treatise in which Aristotle describes a natural deduction system and demonstrates certain of the logical relationships among syllogistic deduction rules ; and finally, 5) Aristotle worked with a notion of substitution sufficient for distinguishing logical syntax and semantics. In this connection he also distinguished validity from deducibility sufficiently well to note the completeness of his logic. (shrink)

Considered in light of the reader’s expectation of a thoroughgoing criticism of the pretensions of the rational psychologist, and of the wealth of discussions available in the broader 18th century context, which includes a variety of proofs that do not explicitly turn on the identification of the soul as a simple substance, Kant’s discussion of immortality in the Paralogisms falls lamentably short. However, outside of the Paralogisms (and the published works generally), Kant had much more to say about (...) the arguments for the soul’s immortality as he devoted considerable time to the topic throughout his career in his lectures on metaphysics. In fact, as I show in this paper, the student lecture notes prove to be an indispensable supplement to the treatment in the Paralogisms, not only for illuminating Kant’s criticism of the rational psychologist’s views on the immortality of the soul, but also in reconciling this criticism with Kant’s own positive claims regarding certain theoretical proofs of immortality. (shrink)

In the recent literature on proof theory, there seems to be a new raising topic which consists in identifying those properties that characterise a good sequent calculus. The property that has received by far the most attention is the analyticity property. In this paper we propose a new argument in support of the analyticity property. We will do it by means of the example of the logic of proofs, a logic recently introduced by Artemov [1]. Indeed a detailed proof analysis (...) of this logic sheds new light on the logic itself and perfectly exemplifies our argument in favour of the analiticity. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Logic Pamphlets of Charles Lutwidge Dodgson and Related PiecesIrving H. AnellisFrancine F. Abeles, editor. The Logic Pamphlets of Charles Lutwidge Dodgson and Related Pieces. The Pamphlets of Lewis Carroll, 4. New York-Charlottesville-London: Lewis Carroll Society of North America-University Press of Virginia, 2010. Pp. xx + 271. Cloth, $75.00.Until William Bartley’s rediscovery and reconstruction of Dodgson’s lost Part II of Symbolic Logic, Lewis Carroll’s reputation in logic, when (...) taken seriously, rested upon his few published articles on logical paradoxes and puzzles, while his published books, The Game of Logic and Symbolic Logic, were regarded as suitable perhaps as pedagogical tools, but dismissed otherwise as amusements, on a par with the Alice works. Richard Braithwaite asserted (“Lewis Carroll as Logician”) that “Carroll regarded formal and symbolic logic not as a corpus of systematic knowledge about valid thought nor yet as an art for teaching a person to think correctly.” He suggested that Dodgson used his pseudonym for his popular and whimsical writings, reserving his legal name only for his serious mathematical products. Philosophers practicing linguistic analysis in their assault on nonsense deriving from misuse of language meanwhile developed an interest in Carroll (e.g. George Pitcher, “Wittgenstein, Nonsense, and Lewis Carroll”). Abeles, on the contrary, stresses the seriousness of Dodgson’s pedagogical and popularizing mission (195–99).Bartley’s discovery opened the door for reevaluating Dodgson as a serious logician, and Abeles has been in the forefront of that reevaluation. Her general introduction and introductions to the main divisions of this collection of Carroll’s publications (and additional material from his Nachlass and a handful of publications of others, composed in response to Carroll’s published articles) place his serious logical work and its significance in historical perspective, providing a deeper, more sophisticated view than found in Bartley’s “Editor’s Introduction” to Lewis Carroll’s Symbolic Logic. Abeles also offers brief introductions to the individual entries, which describe their physical characteristics and circumstances of composition.Dodgson aligned with the majority of those British logicians of his day, starting with George Boole, who understood formal logic to be Aristotelian syllogistic, and symbolic logic to be syllogistic logic expressed algebraically. His notational innovation was employing indices to terms so that, independently of the arrangement of terms, propositions could easily be read; thus, “xy0” can be read as “no x are y” or “no y are x” and “x1y0” as “all x are not y” or “no x are y”. In dealing with the classical elimination problem in the class calculus—to determine the maximum information, without duplications, obtainable from a given set of premises—Dodgson in his later work and unpublished letters anticipated several concepts of automated theorem proving.Central to both geometry and to formal logic are the rules of logical inference that establish the validity of arguments and guarantee that conclusions inferred from true [End Page 506] premises are true. The modern analytic tableaux, or tree method, is a fundamental tool in this regard, both for deriving theorems and for determining the validity or invalidity of the proofs for propositional calculus and first-order predicate calculus.Introducing his reconstruction of Part II of Symbolic Logic, Bartley noted that, along with the logic diagrams that Carroll devised, he also devised a tableau method that strongly resembled Beth’s semantic tableaux. Abeles went more deeply and convincingly into that resemblance in her earlier research. Beth’s tableaux, together with Hintikka’s model sets, were the direct ancestors of Smullyan’s analytic tableaux, which in turn are the theoretical basis for the Robinson resolution method that continues to be central to much work in programming logic.Abeles has also shown that the work in Studies in Logic by Charles Peirce and his logic students at Johns Hopkins University served as a source of inspiration for Dodgson. More critically, she demonstrated that Dodgson devised and employed the tree method for carrying out proofs of syllogisms and chains of syllogisms, or soriteses, in Part II of Symbolic Logic (see her “Lewis Carroll’s Method of Trees: Its Origins in Studies in Logic,” Modern Logic 1 [1990]: 25–34). The tree... (shrink)

In this paper, we discuss the syllogisms from both fronts : Aristotle and Boethius. We mainly focus on the differences with respect to categorical and hypothetical syllogisms in Aristotle and Boethius. Regarding Aristotle’s works on logic, it is not unusual to claim that Aristotle extensively worked on categorical syllogisms. In Prior Analytics, Aristotle gave proofs for many valid moods. However we cannot find a similar treatment for hypothetical syllogism in his works. Thus, it might be a reason for his students (...) to improve Aristotle’s theory of syllogisms by filling the gaps in hypothetical syllogisms. As Boethius already emphasized in the Book I of De Hypotheticis Syllogismis, the Peripatetic School only initiated the start. The remaining and detailed treatise was due to Boethius himself. The impression we got from Boethius’s and Aristotle’s works on syllogisms is that the categorical syllogism is almost entirely developed by Aristotle himself, whereas the extensive and the detailed study of the hypothetical syllogism was carried out by Boethius, although he was not the first figure in the history who gave concise expositions on hypothetical syllogism. Boethius’s translations of syllogisms in medieval era were the primer resource and textbook for Aristotelian logic during the early Medieval ages. Therefore, the scholars of those times had no other chance but to work from Boethius’s commentaries. So, the evident properties of Aristotelian figures were not then visible. Boethius wrote several textbooks in logic. A detailed investigation might yield significant information on Boethius’s logic compared with the influence of Aristotle on Boethius. (shrink)

The numerically definite syllogistic is the fragment of English obtained by extending the language of the classical syllogism with numerical quantifiers. The numerically definite relational syllogistic is the fragment of English obtained by extending the numerically definite syllogistic with predicates involving transitive verbs. This paper investigates the computational complexity of the satisfiability problem for these fragments. We show that the satisfiability problem (= finite satisfiability problem) for the numerically definite syllogistic is strongly NP-complete, and that the satisfiability problem (= finite (...) satisfiability problem) for the numerically definite relational syllogistic is NEXPTIME-complete, but perhaps not strongly so. We discuss the related problem of probabilistic (propositional) satisfiability, and thereby demonstrate the incompleteness of some proof-systems that have been proposed for the numerically definite syllogistic. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.4 (2003) 561-562 [Access article in PDF] Gianni Paganini, Miguel Benítez, and James Dybikowski, editors. Scepticisme, Clandestinité et Libre Pensée. Paris: Honoré Champion, 2002. Pp. 382. Cloth, €60.00. This book consists of papers from two Tables rondes held in Dublin in 1999 on the occasion of the Tenth International Congress on the Enlightenment. The contributors are: Paganini, Benítez, Dybikowski, Alan Charles Kors, Winfried (...) Schröder, José R. Maia Neto, Adam Sutcliffe, Justin Champion, Antony McKenna, Lorenzo Bianchi, Christine Berkvens-Stevelinck, Pierre Lurbe, Stephen David Snobelen, Nigel Aston, and Stuart Brown. There is remarkably little overlap among the papers and Paganini has clearly insisted on very [End Page 561] high standards. Because of space limitations, I shall focus on several of the general themes which run through the book rather than on individual contributions.Despite the phenomenal success Richard Popkin and collaborators like the late Charles B. Schmitt, Giorgio Tonelli, and Ezequiel de Olaso have had in documenting the amazing impact of skepticism in the Renaissance and in the years up to the Enlightenment, this volume demonstrates that skepticism, that many-faceted force, continued throughout the eighteenth-century Enlightenment. After Bayle, and the application of his special forms of skepticism to theological topics—forms which were often employed, contrary to Bayle's probable intentions, in defense of atheism—skepticism went "underground." A large variety of literature was circulated in manuscript form, the clandestine literature of the period. The lesson which this conference celebrates is that skepticism did not cease being a major cultural force. Thus there is, thanks to the philosophical dimension of the clandestine literature in the eighteenth century, a transition from Christian rationalism to an anti-Christian rationalism.Major figures of the Enlightenment were, of course, well-acquainted with skepticism, e.g., Berkeley, Voltaire, Hume, Crousaz, Condillac, Reid, and Kant. Not surprisingly, the major topics discussed in these papers center around skepticism, fideism and atheism, proofs for the existence of God, and the status of the "preambles" to the faith. These all receive careful attention. The tension between the arguments for Christian Pyrrhonism versus anti-Christian rationalism runs through many of these papers. And of course Bayle's points of view on both sides of the Christian debate appear in much of the clandestine literature. The matter of the immortality of the soul is carefully discussed. What is the status of this doctrine? Is it a question of Church dogma or is it another belief to be discarded in the light of reason?The connection perceived to hold between atheism and political legitimacy are explored in several papers. In the seventeenth century, Locke would exclude atheists from the body politic, in part because they were unable to truthfully swear an oath. Atheists were perceived as a danger for many eighteenth-century figures and the political need to suppress atheism was widely understood and accepted by those in the various religious establishments. Bayle's two-century-old attempt to break the putative logical tie between morality and religion failed in his own day, and despite the efforts of the authors of clandestine philosophical literature, the intimate link Bayle tried to break seems to be stronger than ever in much of the world today. It is interesting that the United States is virtually the only industrial and democratic society in which atheists are virtually precluded from being political candidates in federal, and probably most local, elections. Among other things, the papers in this volume help one to understand just how difficult breaking free from theological constraints in the interest of political freedom has proved to be. Harry McFarland Bracken Arizona State University, Tempe... (shrink)

Considered in light of the reader’s expectation of a thoroughgoing criticism of the pretensions of the rational psychologist, and of the wealth of discussions available in the broader 18th century context, which includes a variety of proofs that do not explicitly turn on the identification of the soul as a simple substance, Kant’s discussion of immortality in the Paralogisms falls lamentably short. However, outside of the Paralogisms (and the published works generally), Kant had much more to say about (...) the arguments for the soul’s immortality as he devoted considerable time to the topic throughout his career in his lectures on metaphysics. In fact, as I show in this paper, the student lecture notes prove to be an indispensable supplement to the treatment in the Paralogisms, not only for illuminating Kant’s criticism of the rational psychologist’s views on the immortality of the soul, but also in reconciling this criticism with Kant’s own positive claims regarding certain theoretical proofs of immortality. (shrink)

While there has been a resurgence in Malebranche scholarship in the anglophone world over the last twenty years, most of it has focused on Malebranche’s theory of ideas, and little attention has been paid to his philosophy of mind. Schmaltz’s book thus comes as a welcome addition to the Malebranche literature; that he has given us such a well-researched and carefully argued study is even more welcome. The focus of this work is Malebranche’s split with Descartes on the question of (...) our knowledge of the nature of the mind; the book concentrates specifically on Malebranche’s rejection of the claim that we know the nature of the mind better than we know the nature of body. Schmaltz maintains that Malebranche’s arguments for his position are, for the most part, successful against the Cartesians who opposed him, though he claims—and this is perhaps the central claim of the book—that “Malebranche took his negative thesis concerning our knowledge of the soul to involve not so much a rejection of Cartesianism as an internal correction of it”. While acknowledging that Augustine was “the primary inspiration for [Malebranche’s] view of the ideas that are the objects of perception”, Schmaltz’s interpretation of Malebranche’s theory of the soul “presents it as fundamentally Cartesian”. According to Schmaltz, not only is Malebranche closer to Descartes in this regard than is generally thought, he is closer to him than are many other Cartesians. Part 1 of the book examines Malebranche’s position that while we have certain knowledge of the soul’s existence, we have only confused knowledge of its nature. Part 2 focuses on Arnauld’s objection that if in fact we had no clear idea of the soul, we could not, despite Malebranche’s claims to the contrary, know anything of its immortality, spirituality, or freedom. (shrink)

The admissibility of Ackermann's rule γ is one of the most important problems in relevant logics. The admissibility of γ was first proved by an algebraic method. However, the development of Routley-Meyer semantics and metavaluational techniques makes it possible to prove the admissibility of γ using the method of normal models or the method using metavaluations, and the use of such methods is preferred. This paper discusses an algebraic proof of the admissibility of γ in relevant modal logics based on (...) modern algebraic models. (shrink)

David Apolloni defends a modern version of Plato's argument for the immortality of the soul and argues the soul is non-physical. The book also defends a version of Gödel's ontological argument for God's existence. Using the results, he supports accounts of the afterlife from those who have had near-death experiences.

The historical context of the philosophical work of St. Thomas Aquinas, by D. Knowles.--Form and existence, by P. Geach.--Categories, by H. McCabe.--Analogy as a rule of meaning for religious language, by J. F. Ross.--Nominalism, by P. Geach.--St. Thomas' doctrine of necessary being, by P. Brown.--The proof ex motu for the existence of God; logical analysis of St. Thomas' arguments, by J. Salamucha.--Infinite causal regression, by P. Brown.--St. Thomas Aquinas and the language of total dependence, by J. N. Deck.--Divine foreknowledge and (...) human freedom, by A. Kenny.--Intellect and imagination in Aquinas, by A. Kenny.--The immortality of the soul, by H. McCabe.--Aquinas on intentionality, by P. Sheehan.--The scholastic theory of moral law in the modern world, by A. Donagan.--The first principle of practical reason, by G. G. Grisez. (shrink)

Alexander of Aphrodisias, Aristotle’s commentator par excellence, rarely engages with Plato. In the present paper, however, we see him at work as an exegete of a passage in the _Phaedrus_ (245c5-9), in which Plato argues for the immortality of the soul based on its self-motion. In this paper, I focus on two ways in which Alexander deals with the passage. In his commentary on Aristotle’s _Prior Analytics_ (CAG II 1), Alexander employs the same approach to the _Phaedrus_ that (...) he uses with Aristotle’s treatises: he puts an informal argument expressed in ordinary language into the more formal shape of a syllogism. This does not mean that Alexander gives his approval to Plato’s theory. In fact, in his commentary on Aristotle’s _Topics_ (CAG II 2), Alexander introduces a polemical discussion of the same Platonic argument. Commenting on Aristotle’s denial that the soul is a self-moving substance (_Top_. IV 1.120b21-29), Alexander spells out the implicit reference to the _Phaedrus_ and criticizes Plato’s argument for not taking into account the difference between an accidental property of the soul and the essential characteristics by which it is defined. Plato’s theory of self-motion is partly accepted by Alexander and partly criticized. This paves the way for how the theory will be applied in the Aristotelian tradition, not to the soul, as in Plato, but to the ensouled body, either of the living being or of the heavens. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 127 les Paiens de leurs t6nebres,... de les fortifier de telle sorte contre les pr~jugez & contre les erreurs populaires qu'ils fussent incapables d'y tomber. Again, we learn that Bayle says "we do not know if a substance is by nature spiritual or corporeal, nor if the soul is immortal" with references to "Pyrrhon, B" and "Charron, O" (p. 112). Whatever Professor Mason means about substance, (...) it is not contained as far as I can see in "Pyrrhon, B"; and the point in "Charron, O" is that there is no irrefutable proof of the immortality of the soul. 2Professor Mason is following Voltaire's example more thanBayle's when he attributes to an author implications or attitudes not clearly expressed in the original. This is not to say that his conclusions are totally invalidated; on the contrary, they stand up despite his unreliability on Bayle, for his principal concern is Voltaire's reactions to the Scholar of Rotterdam. Apart from these reservations, it is good to have so important and so complicated a subject so compactly documented. CRAm B. BRVS~ Columbia University Das medizinische Weltbild des Paracelsus. Seine Zusammenhiinge mit Neuplatonismus und Gnosis. By Waiter Pagel. (Wiesbaden: Franz Steiner Verlag, 1962. "Kosmosophie", Forschungen und Texte zur Geschichte des Weltbildes, der Naturphilosophie, der Mystik und des Spiritualismus vom Sp~tmittelalter bis zur Romantik, ed. by K. Goldammer, Vol. I. Pp. xvi ~- 160. DM 24.) The new monograph series "Kosmosophie" couId not have been introduced more excellently than by Walter Pagel's work on Paracelsus which supplements and extends his earlier study Paracelsus, An Introduction to Philosophical Medicine in the Era of the Renaissance (Basel & New York: 1958). The new series is devoted to studies in the history of science, exploring the old traditions of a "sophic" understanding of the cosmos which always existed side by side with a "logical" one, i.e., the heritage from ancient mysticism, gnosticism, alchemy, and metaphysical speculation which so "disgracefully" characterizes the beginnings of modern science. In this book, Pagel tries to locate the great physician and philosopher Theophrastus of Hohenheim called Paracelsus (1493-1541) within the history of science at that turning point between the Middle Ages and the Renaissance and to understand him on the basis of the specific relationship of inheriting and modifying the traditions of neoplatonie and gnostic thought in his writings. After an introductory chapter about Paracelsus's position in the history of medicine and in contemporary times, the author investigates the neoplatonic and gnostic sources and presuppositions for the medical-physical world-view of Paracelsus. It should have been pointed out more clearly in this chapter, however, that the study of gnosticism and its effect upon the thinking of the later Hellenism is still in its beginning stages. He describes, then, Paracelsus's world of ideas as it is to be seen in the light of these neoplatonic and gnostic traditions: the doctrines of the invisible spiritual world, the astral powers, the astral body, dualism of sex, the two kinds of fire, the Logoi, the elements, primordial matter, etc. In each case, possible connections with the Hermetic writings, alchemy, gnosticism, neoplatonism, and their transmission through mysticism, cabbala, and the neoplatonic philosophers of the Renaissance (especially Marsilius Ficinus) as well as through St. Augustine have been discussed. Here are a few other distressing misrepresentations of what Bayle has to say: p. 30, on Jews; p. 30, n. 6, on the inspiration of scripture; p. 31, n. 2, on the same subject; p. 37, on miracles; p. 61, n. 1, on man's dominion over animals; p. 92, n. 4, on Christian and natural morality; p. 137, n. 4, on moral and speculative dogmas. Page 92, n. 9, refers to several pages in which Bayle's concluding remark flatly contradicts Professor Mason's interpretation. Spot checks in Moland have turned up no misrepresentations of Voltaire's thought, which is generally less qualified than Bayle's. 128 HISTORY OF PHILOSOPHY The result is that this Hellenistic-Middle Age syncretism has had a far-reaching influence upon Paracelsus's thought. Because he was in no way a systematic philosopher, his writings are full of contradictions, developments, unitarian and dualistic tendencies, theistic... (shrink)

This paper aims to achieve a better understanding of what Socrates means by "συμφωνε[unrepresentable symbol]ν" in the sections of the "Phaedo" in which he uses the word, and how its use contributes both to the articulation of the hypothetical method and the proof of the soul's immortality. Section I sets out the well-known problems for the most obvious readings of the relation, while Sections II and III argue against two remedies for these problems, the first an interpretation of (...) what the συμφωνε[unrepresentable symbol]ν relation consists in, the second an interpretation of what sorts of thing the relation is meant to relate. My positive account in Section IV argues that we should take the musical connotations of the term seriously, and that Plato was thinking of a robust analogy between the way pitches form unities when related by certain intervals, and the way theoretical claims form unities when related by explanatory co-dependence. Section V surveys the work of IV from the point of view of the initial difficulties and suggests further consequences for the hypothetical method, including the logical relation between the συμφωνν[unrepresentable symbol]ν and διαφωνε[unrepresentable symbol]ν relations, and the need for care in ordering the results of a hypothesis. (shrink)