The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz (...) and developed by his student Słupecki, the pioneers of the method, which becomes relevant in modern approaches to logic. (shrink)

The idea of rejection of some sentences on the basis of others comes from Aristotle, as Jan Łukasiewicz states in his studies on Aristotle's syllogistic [1939, 1951], concerning rejection of the false syllogistic form and those on certain calculus of propositions. Short historical remarks on the origin and development of the notion of a rejected sentence, introduced into logic by Jan Łukasiewicz, are contained in the Introduction of this paper. This paper is to a considerable extent a summary (...) of papers which are not easily available, even to the Polish reader: (1) J. Słupecki, Funkcja Łukasiewicza (Łukasiewicz’s function), Zeszyty Naukowe Uniwersytetu Wrocławskiego, Seria B, nr 3 (1959), 33-40; (2) U. Wybraniec-Skardowska, Teoria zdań odrzuconych (Theory of Rejected Sentences), (doctoral dissertation under the supervision of Jerzy Słupecki, published as a monograph), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Monografie, Nr 22 (1969), 5-131; (3) G. Bryll, Kilka uzupełnień teorii zdań odrzuconych (Some supplements to the theory of rejcted sentences), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Mnografie, Nr 22 (1969), 153-154. The paper also contains a good number of results which have not been published yet. Chapter I contains results presented in the papers (1)-(3). It provides an extension of Alfred Tarski’s theory of deductive systems presented by him in the papers [1930]: Fundamentale Begriffe der Methodologie der deduktiven Wssenschaften, I and Über einige fundamentale Begriffe der Metamathematik. The enriched theory is marked with T. The most essential new concept in T is the function Cn-1, whose definition was given by Słupecki in (1) on the basis of the so-called Tarski’s general theory of deductive systems. It has the form: y e Cn-1X iff Ex e X (x e Cn {y}), where Cn is Tarski’s consequence operation. In accordance with the definition: A sentence y is rejected on the basis of the sentences of the set X iff at least one of sentences of X is a consequence of y (is deducible from y). The intuitive meaning of the rejection function Cn-1: on the basis of false sentences we can reject false sentences only (while by means of the consequence operation Cn on the basis of true sentences we can deduce true sentences only). The function Cn-1 is a generalization of the notion of rejected sentences which was introduced into logic by Łukasiewicz. The essential property of the rejection function Cn-1 is that it satisfies the axioms of general Tarski’s consequence Cn, so it is a consequence operation, called the rejection consequence. In addition, it is an additive and normal operation. In Chapter I, there are given notions analogous to those of the theory of deductive systems, but they are written down by means of the symbol ‘Cn-1’ and not ‘Cn’. There are established the properties of introduced notions and differences and analogies taking place between them and properties of respective notions of the theory T. There are also given generalizations of the notions of ‘decidable system’ and ‘consistent system’ used by Łukasiewicz. The short Chapter II contains axioms of the system T’ which is equivalent to the system T. The only difference between sets of primitive notions of these systems consists in the appearance of the function Cn-1 in the system T’ instead of the function Cn. This chapter reproduces the results given in (2), but they are partially simplified. (shrink)

The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz (...) and developed by his student Słupecki, the pioneers of the method, which becomes relevant in modern approaches to logic. (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 (...) class='Hi'>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)

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)

In lieu of an abstract, here is a brief excerpt of the content:Rhetoric and AngerKenneth S. Zagacki and Patrick A. Boleyn-FitzgeraldSince most believe anger can be either good or bad, rhetors face a moral problem of determining when anger is appropriate and when it is not. They face a corresponding rhetorical problem in deciding when and how to express anger and determining the role that it might play in public discourse, with specific audiences and in particular rhetorical situations. (...) Rhetorical scholars have catalogued whole genres of angry rhetoric—apocalyptic genres, jeremiads, the demonizing rhetoric of religious and political leaders—wherein the rhetorical display of anger is explained in terms of situational conventions and cultural norms.1 Yet these scholars have not easily resolved the moral problems associated with angry rhetoric. Aristotle suggested the earliest and most obvious solutions to these problems. In the Nicomachean Ethics, he outlines a typology for discerning the moral limits of anger and, by implication, angry rhetoric. And in Book II of the Rhetoric he asserts that the orator needs to know the structure of emotions like anger and how to intensify and dissipate them. Or, in other words, the orator must know how to make it reasonable to be angry. Some contemporary philosophers have gone further, suggesting that a failure to feel and express anger in public betrays an insufficient concern for justice and self respect.In this essay, we follow Aristotle in arguing that anger is sometimes the emotion we expect people to feel or the rhetorical response we expect them to display and evoke in others. But we also challenge part of Aristotle's argument by asking: "Even when angry rhetoric would appear to be a reasonable, morally appropriate response, is there a way in which rhetors might manage anger in their public discourse in order to achieve ends which are both morally and pragmatically productive?" The answer, we propose, lies in what we call "non-angry" rhetoric, which involves transforming and reflecting upon anger in public discourse. Because such rhetoric often promotes noble ends such as reconciliation and forgiveness, it is at least morally permissible and more likely morally virtuous.2 In order to establish these claims, our analysis focuses on the case of Nelson Mandela and his "Address to the Interfaith Commissioning Service for the Truth and Reconciliation Commission."3 In this speech, Mandela, as our [End Page 290] analysis demonstrates, managed anger and turned it into an object of reflection, thereby illustrating what opportunities for reconciliation and democratic deliberation would look like during the difficult period attending the political transition in South Africa in general and the Truth and Reconciliation Commission (TRC) hearings in particular. His "Address" exemplified a unique moment when the rhetoric and the ethics of anger came together in a public performance. While acknowledging the understandable anger of blacks, Mandela (who may in fact have harbored considerable anger himself) simultaneously suggested that by engendering a less hostile social-political context, in which participants maintained their self-respect without necessarily sacrificing justice, a new democratic community could emerge. This would be a community where, as he described it, individuals began to reconcile with and no longer persecute one another. As Aristotle might explain, the purpose of Mandela's speech was to manage the anger of blacks, so that they would then be able to deliberate properly about the issues before the TRC and about the larger democratic transition. As the philosopher Eugene Garver says, the particular passions Aristotle chooses to explore in the Rhetoric serve a role necessary for the kind of public, political decision making he assigns to rhetoric. These emotions serve to integrate—or segregate, as the case may be—"distinct individuals into a deliberative or judging body, or demos" (1994, 131).What we are recommending, then, is that rhetoric encompasses both considerations of moral desert as well as broader moral concerns. While there are times when individuals seem to deserve our angry rhetoric, it may not be justified from a broader moral perspective, especially when the goal is the good of the state or the community—viz., if angry rhetoric leads to the violent dissolution of democratic community. Ultimately, we argue that the moral constitution of political, deliberative communities must be viewed in terms... (shrink)

Arthur Madigan presents a clear, accurate new translation of the third book of Aristotle's Metaphysics, together with two related chapters from the eleventh book. Madigan's accompanying introduction and commentary give detailed guidance to these texts, in which Aristotle sets out what he takes to be the main problems of metaphysics or 'first philosophy' and assesses possible solutions to them; he takes his starting-point from the work of earlier philosophers, especially Plato and some of the Presocratics. These texts serve as a (...) useful introduction both to Aristotle's own work on metaphysics and to classical metaphysics in general; they are also a good example of Aristotle's dialectical method, which reasons not from known truths but from reputable opinions. (shrink)

Aristotle's theory of human action is an impressive achievement that has served philosophy well for more than two thousand years. In every philosophical era it is explored anew--and with great profit. As a contribution to contemporary efforts in this regard, the present dissertation aims to lay out, lucidly and in detail, the various components of Aristotle's action theory. ;Since actions, according to Aristotle, constitute a sub-class of "the voluntary", the dissertation begins by examining Aristotle's account of voluntary activities. It discusses (...) the chief characteristics shared by all such activities, and compares the Nicomachean and Eudemian accounts. ;Perception is examined next, because percepts and their lingering traces , according to Aristotle, are the triggers of desire. And desire provides the impetus for animal behavior and human action. Aristotle's analysis assumes a rich array of desire-types, including appetites, passions, emotions, and wishes, all of which are analyzed in the dissertation. ;The keys to adult human action--distinguishing it from animal and child behavior--are deliberation, "choice" and the so-called "practical syllogism". The dissertation examines these in some detail and produces a model of the practical syllogism. ;Once the practical syllogism has been examined, the dissertation considers the question of whether Aristotle's theory of action provides a successful resolution of the so-called "problem of free will". It is argued that Aristotle--despite common misconceptions to the contrary--was aware of the problem and had a promising philosophical basis for its solution. (shrink)

This is an examination of Aristotle's notion of an "accidental being" -- something intermediate between a substance and a property. An accidental being (sometimes called "accidental compound" or "kooky object") is an ephemeral object, typically the compound of a substance and a property, that exists for only as long as its components are united. I set out the role that accidental beings play in Aristotle's solutions to several philosophical problems. I also investigate the similarity between these beings and the individual (...) non-substances of Aristotle's Categories. Finally, I propose that accidental beings can be assimilated into a more contemporary conceptual scheme as events -- the states or conditions that substances are in or undergo. (shrink)

The author sets a goal to show the specificity of the formulation of universal prescriptive judgments about a virtuous act in the framework of Aristotelian ethical doctrine. To achieve this goal, Aristotle’s philosophy concept of practical wisdom is analyzed. It shows a necessity to distinguish the use of practical wisdom in a personal experience of the act and for forming the inter-subjective practical knowledge about making of a virtuous act. The specificity of ethics as practical knowledge and its difference (...) from individual moral experience are defined by means of the distinction of the use of practical wisdom. It also shows the limitations of practical syllogism as the main rational mechanism for the formation of inter-subjective practical knowledge. Additionally, the universal prescriptive judgments are divided into informative and functional: the former reveals the content of the action, the latter – its structure, that is, the former defines what a person must do, the latter defines what an action should be to comply with the right purpose, consequently, the right content. At the same time, the right content is recognized only in individual experience and can not be expressed universally, without losing its practical value. The author concludes that the formulation of informative universal prescriptive judgments is impossible within the framework of Aristotelian ethical doctrine. It is impeded by the unsolvable problem of the correlation between the general and the particular, the transition from descriptive judgments to prescriptive judgments. However, it is possible to formulate functional universal prescriptive judgments. They also constitute the methodological basis for criticism of the accepted in society moral norms, which are based on the past positive experience of actions. (shrink)

"It is an interesting and largely unexplored question whether Aristotle is in practice faithful to the general idea of science, and to the rules of method, sketched in his Analytics".It is this issue, "the Problem of Demonstration," which this study is concerned to explore. The objective of this study is not so much to render a detailed and definitive solution to the problem, but rather to suggest a context within which such a solution may be reached. (...) Further, this study is intended not as an historical critique of an historical question in a classical author but as a philosophical enquiry into the roots, in Aristotle, of a perennial philosophical question. The structure of the study is as follows: In the first chapter the problem is stated, and the possible modes of response to the problem are briefly canvassed, in order to set the framework of the response to be offered here. The second chapter attempts, through an examination of certain texts from the Posterior Analytics and elsewhere, to specify and to raise objections to the particular elements in the traditional inter¬ pretation of Aristotle's methodological intentions which have generated the problem of demonstration. Aristotle's teachings concerning the nature of knowledge include reference both to the distinctive object of knowledge and to the psychology of knowing. At one time Aristotle gives a more subjective and psychological, at other times a more object-based account of what is essential to knowledge. In the third chapter it is suggested that we must examine the manner in which Aristotle accommodates these two aspects when he comes to design a methodology of science. Aristotle's views on the aim of science are, therefore, examined as a source of insight into the balance struck between these two aspects in his writings. It is here argued that when we attempt to understand Aristotle's methodological intentions concerning the apodeictic syllogism we must not underestimate the importance in Aristotle's thought of the doctrine. It is this doctrine which, chiefly, enables Aristotle to produce a methodological doctrine which is consistent with his accounts of the nature of knowledge. Chapter four considers the evidence for understanding the Analytics as a training in critical technique, and why Aristotle feels that the apodeictic syllogism is unsuited to the task of communicating findings. The principal theme of this chapter is an examination of the Aristotelian doctrine which holds that the logical training as provided by the Analytics constitutes a and, as such, is unsuited to the task of publication. Chapter five draws together the results of the discussion, and attempts to reconstruct the specific Aristotelian context which renders Aristotle's theory and practice coherent, and which may make it possible to determine the degree of consistency operative throughout his works. A model is presented which, it is suggested, reflects the position intended by Aristotle for those bodies of demonstrated judg¬ ments prefigured in the Posterior Analytics within the economy of Aristotle's methodological theory and practice in science and philosophy. (shrink)

Arthur Madigan presents a clear, accurate new translation of the third book of Aristotle's Metaphysics, together with two related chapters from the eleventh book. Madigan's accompanying introduction and commentary give detailed guidance to these texts, in which Aristotle setsout what he takes to be the main problems of metaphysics or 'first philosophy' and assesses possible solutions to them; he takes his starting-point from the work of earlier philosophers, especially Plato and some of the Presocratics. These texts serve as a useful (...) introduction both to Aristotle's ownwork on metaphysics and to classical metaphysics in general; they are also a good example of Aristotle's dialectical method, which reasons not from known truths but from reputable opinions. (shrink)

The hypothesis of a theoretical unity between On Sophistical Refutations and Prior Analytics presents a major challenge to scholars attempting to unify the criteria of analysis. This paper examines this problem and proposes a middle ground between the perspectives of Woods and Boger to address this crucial question: If a unitary and coherent theory of deduction exists, why does not the technical apparatus of syllogistic modes for analyzing fallacies appear in SE? This paper makes useful contributions to the (...) discussion on the internal unity of Aristotle's logical writings on around categorical syllogistics and the doctrine of sophistical refutations. (shrink)

This is another contribution to the unending controversy over the two Barbaras. My approach to the problem is hopefully quite new: I wish to view the issue through the prism of modal upgrading. Modal upgrading occurs when a subject term that has only been predicated of assertorically in the premises is predicated of apodictically either: i) in the conclusion of a given syllogism, or; ii) in some proposition that is derived from either the premises of the given syllogism alone (...) or the premises in combination with other propositions that do not refer to the proposition’s subject term. I call the proposition after it has been upgraded the upgraded proposition. When a conclusion is the upgraded proposition, it is obviously a different predicate being predicated than was predicated in the premises. Aristotle endorses this kind of upgrading; it is effectively what happens in any valid mixed modal syllogism when the minor premise is not apodictic (e.g., Barbara LXL). In other cases the upgraded proposition is not a conclusion but still follows from the premises alone. In these cases it is the same predicate being predicated in the upgraded proposition as in the premises, although the quantity of the propositions are different (one is universal, another particular). Aristotle rejects this kind of upgrading and takes its occurrence as sufficient to deny the validity of the given syllogism (e.g., Barbara XLL). I will describe a third type where both the predicate remains the same and the quantity of the proposition remains the same as in the premise, e.g., the upgrading of “All C are B” to “All C are necessarily B”. In these cases it will turn out that the upgraded proposition is not derived from the premises alone, or at least, not syllogistically from the premises alone. This kind of upgrading too is reason for denying the validity of any syllogism from which the upgraded proposition follows as a consequence. I will show that Barbara LXL entails this kind of modal upgrading and should be rejected for this reason. Armed with this notion of modal upgrading I want to attack the problem of the two Barbaras in Aristotle’s apodictic syllogistic. Aristotle himself endorses mixed modal Barbara when the major is necessary and the minor is assertoric, thereby endorsing the first kind of modal upgrading, but rejects Barbara when the minor is necessary and the major is assertoric on the grounds that it leads to the second kind of modal upgrading. Theophrastus endorses the peioram rule which rejects both Barbaras on the grounds that the conclusion can only be as strong as the weakest premise. Łukasiewicz endorses both Barbaras. I will argue that both Barbaras lead to unacceptable modal upgrading and should be taken to be invalid for that reason. Hence, I agree with Theophrastus about the two Barbaras; however, I do not endorse the peioram rule because I think that the negative mixed modal syllogisms generally avoid this problem and is mostly correct. (shrink)

Penelope Maddy has attempted to develop a form of realism in mathematics that is not plagued by the sort of epistemological problems that beset traditional Platonism. Maddy advances the radical doctrine that we can and do causally interact with sets. We can see them, feel them, smell them, and even taste them. This chapter raises a series of objections to Maddy's version of realism.

In Nicomachean Ethics VII Aristotle describes akrasia as a disposition. Taking into account that it is a disposition, I argue that akrasia cannot be understood on an epistemological basis alone, i.e., it is not merely a problem of knowledge that the akratic person acts the ways he does, but rather one is akratic due to a certain kind of habituation, where the person is not able to activate the potential knowledge s/he possesses. To stress this point, I focus on (...) the gap between potential knowledge and its activation, whereby I argue that the distinction between potential and actual knowledge is at the center of the problem of akrasia. I suggest that to elaborate on this gap, we must go beyond the limits of Nicomachean Ethics to Metaphysics IX, where we find Aristotle’s discussion of the distinction between potentiality and actuality. I further analyze the gap between potential and actual knowledge by means of Aristotle’s discussion of practical syllogism, where I argue that akrasia is a result of a conflict in practical reasoning. I conclude my paper by stressing that for the akratic person the action is determined with respect to the conclusion of the practical syllogism, where the conclusion is produced by means of a ‘conflict’ between the universal opinion which is potential and the particular opinion which is appetitive. (shrink)

Classical results of additive number theory lead to the undecidability of the existence of solutions for diophantine equations in given special sets of integers. Those sets which are images of polynomials are covered by a more general result in the second section. In contrast, restricting diophantine equations to images of exponential functions with natural bases leads to decidable problems, as proved in the third section.

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

This paper explores the tension between Aristotle’s definition of the citizen and his conception of good and bad political regimes. Aristotle’s definition of the citizen as one with a share in the offices of the city produces the paradoxical result that in a monarchy, only one person, the monarch, is a citizen. The paper argues that this reveals a serious problem for Aristotle’s theory. Seven solutions are offered to repair this problem, though revisions that involve (...) broadening Aristotle’s notion of the citizen fail on multiple grounds. What Aristotle should have put forward is a theory of degrees of citizenship on which one can satisfy the conditions of citizenship to varying degrees depending on one’s participation in the life of one's city. (shrink)

In the paper we examine the method of axiomatic rejection used to describe the set of nonvalid formulae of Aristotle's syllogistic. First we show that the condition which the system of syllogistic has to fulfil to be ompletely axiomatised, is identical to the condition for any first order theory to be used as a logic program. Than we study the connection between models used or refutation in a first order theory and rejected axioms for that theory. We show (...) that any formula of syllogistic enriched with classical connectives is decidable using models in the domain with three members. (shrink)

In De Anima Book III, Aristotle subscribed to a theory of formal identity between the human mind and the extra-mental objects of our understanding. This has been one of the most controversial featu...

In this paper, we will defend a particular version of the timeless solution to the problem of divine foreknowledge and human freedom. Our strategy is grounded on a particular temporal framework, which models the flow of time and a libertarian understanding of freedom. The propositions describing a certain act by an agent have an indeterminate truth value until the agent makes her choice; therefore, they become true or false when a decision is made. In order to account for (...) this change of truth value, a multiple frame structure is introduced in which every frame presents a privileged time, with its past and the possible alternative futures, which are still open. God atemporally knows all the frames and the truth values of propositions with respect to each one. Since divine knowledge of what an agent decides in a certain temporal frame depends on the agent’s act itself, divine knowledge does not conflict with the agent’s free will. (shrink)

In the Neoplatonic schools, introductions to logic, and the Categories in particular, would begin with a list of ten different questions relating to Aristotle's philosophy and his ideal interpreter and student. Olympiodorus' own introduction to logic follows this pattern; he expands on the remarks of his own teacher Ammonius of Alexandria, and closely models his discussion on his predecessor's work. In the standard list of ten questions that must be discussed in an introductory philosophy course, the third relates to the (...) subject with which the student is to start his or her philosophical education. Which of logic, ethics, natural science and mathematics is the proper starting-point for philosophy? (shrink)

This dense book consists of an Introduction, a list of Abbreviations of Aristotle’s Works, ten chapters subdivided into numbered parts, a bibliography, index locorum, and general index. In pursuit of the solution to what Reeve calls the Primacy Dilemma, he pursues a number of notorious problems in Aristotle, including scientific knowledge, essence, substance, God, the science of being qua being, and the historical problem of Aristotelianism.

It is argued that, in the traditional subject-predicate sentence, two interpretations of the subject term coexist, one intensional and the other extensional, which explains the superficial difference between the traditional S-P relation and the predication of predicate logic. Data from psychological studies of syllogistic reasoning support the view that the contrast between predicate and argument is carried over to the traditional S-P sentence.

Contemporary philosophical discourse has deeply problematized the possibility of absolute existence. Hegel’s Foundation Free Metaphysics demonstrates that by reading Hegel’s Doctrine of the Concept in his Science of Logic as a form of Absolute Dialetheism, Hegel’s logic of the concept can account for the possibility of absolute existence. Through a close examination of Hegel’s concept of self-referential universality in his Science of Logic, Moss demonstrates how Hegel’s concept of singularity is designed to solve a host of metaphysical and epistemic paradoxes (...) central to this problematic. He illustrates how Hegel’s revolutionary account of universality, particularity, and singularity offers solutions to six problems that have plagued the history of Western philosophy: the problem of nihilism, the problem of instantiation, the problem of the missing difference, the problem of absolute empiricism, the problem of onto-theology, and the third man regress. Moss shows that Hegel’s affirmation and development of a revised ontological argument for God’s existence is designed to establish the necessity of absolute existence. By adopting a metaphysical reading of Richard Dien Winfield’s foundation free epistemology, Moss critically engages dominant readings and contemporary debates in Hegel scholarship. Hegel’s Foundation Free Metaphysics will appeal to scholars interested in Hegel, German Idealism, 19th- and 20th-century European philosophy, metaphysics, epistemology, and contemporary European thought. (shrink)

This paper intends to explain key differences between Aristotle’s understanding of the relationships between nous, epistêmê, and the art of syllogistic reasoning(both analytic and dialectical) and the corresponding modern conceptions of intuition, knowledge, and reason. By uncovering paradoxa that Aristotle’s understanding of syllogistic reasoning presents in relation to modern philosophical conceptions of logic and science, I highlight problems of a shift in modern philosophy—a shift that occurs most dramatically in the seventeenth century—toward a project of construction, (...) a pervasive desire for rational certainty, and a general insistence on the reducibility of the sciences. The major motivation of this analysis is my intention to show that modern attempts to reduce science/epistêmê to a single science/method of inquiry occlude dialectical and ethico-political dimensions of “reason” and, hence, also impoverish philosophy’s critical capacities. (shrink)

Polish philosopher Kazimierz Ajdukiewicz’s survey of epistemological and metaphysical problems, taken from a positivist orientation, is notable for its brief, clear characterizations of philosophical problems and its well placed, simplified expositions of the theories of Plato, Aristotle, Descartes, Berkeley, Hume, Kant, Hegel, Bergson and Husserl. He focusses on the logical limitations of the solutions for clearly defined problems. Any lack of depth in this book is compensated for by the accurate outlines which encourage the reader to question the foundations of (...) classical positions. In the first part of the book, the theory of truth is given logical priority to epistemology. We "... should define truth as agreement of thought with final and irrevocable criteria," to avoid the contradiction of extreme skepticism which could not be formulated without, at least, tacit reference to "reality." Because of this positive but stipulative orientation, a priorism in epistemology is given a thorough exposition. Realism, "... we can know reality only on the basis of experience," is proposed to balance the abstractness of a priorism. (shrink)

Aristotle not only formulates the problem of intentionality explicitly, he makes a solution to it a requirement for any adequate theory of mind. His own solution, however, is not to be found in his theory of sensation, as Brentano and others have thought. In fact, it is precisely because Aristotle regards this theory as inadequate that he goes on to argue for a distinct new ability he calls "phantasia." The theory of content he develops on this basis (...) (unlike Brentano's) is profoundly naturalistic: it is a representational theory, formulated in terms of the causal powers and physical magnitudes of the body. (shrink)

Ackrill’s Problem is a tension between Aristotle’s alleged view that the matter of a living being is a body that is essentially ensouled, and his view that the matter of a substance preexists its generation. Most interpreters solve the tension by claiming that the subject of substantial generation is not the organic body of the living being, but its non-organic matter. I defend a different solution by showing that the embryological theory ofOn the Generation of Animalsimplies that (...) the organic body of a living being already exists before acquiring the soul in actuality. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Abailard and the Problem of Universals JOHN F. BOLER ABAILARD t IS A CLEVERman, but in one respect he is just like the rest of us: Given one clear idea of which he is convinced, he tends to become intolerant, thinking the worst of everyone else. Abailard's clear idea goes something as follows. In what does universality consist? It consists, says Abailard, in the signifying of many things (...) by one sign? Abailard's predecessors had been searching for some thing which was universal. But a sign must signify many things to be universal; and furthermore, the sign itself, as a thing--a noise, gesture, or statue--is individual. ~ It may help to describe the model which crops up here and there in Abailard's examples and which, I think, dominates his analysis. Consider, then, a statue which is not meant to stand for any one particular individual: for example, the Minute Man at Concord, Massachusetts.* First of all, the statue is an individual thing. Second, just as a piece of metal, it need not stand for anything--anymore than a bird bath would, had the town council decided to build that instead. What is more, it is information from other sources which leads us to take the statue as "general" rather than as depicting some individual (like Nathan Hale). And even though the statue stands for "all" minute men, not only is the statue an individual thing but all those things for which it stands are (or were) individuals. And finally, we might also point out that the statue must be taken as signifying; it does not have "representative" qualities in quite the same way that it has properties like weight and shape. t The text of Abailard to which I have referred is: Peter Abaelards Philosophische Schrqte, herausgegeben yon Dr. Bernhard Geyer, I Die Logica "Ingredientibus,'" II Die Logica "'Nostrorum Petitioni Sociorum" which is to be found in Beitraege zur Geschichte der Philosophie und Theologie des Mittelalters, Band XXI (1933). A partial translation of this text appears in R. McKeon, Selections from Medieval Philosophers (New York: Scribners, 1929), II, 208-258. Hereafter I shall refer to the latin text as "G" followed by the page number and lines; and to the translation, where possible, as "'M" with the page number. 9Abailard feels that when Aristotle says that a universal is what is fitted for being predicated of many things, it is the signifying of many things which is at stake; and he chides Aristotle for seeming to ascribe universality to things as well as to words. G ~ (M 221). The reference to Aristotle is On Interpretation, 17a (38-40). *See note 7, below. 9I have interpolated on two passages: G 22t~-~ (M 241-242), and G 522*t-=. [37] 38 HISTORY OF PHILOSOPHY The upshot of Abailard's insight is that universality pertains to the interpretation of signs: the effort to locate universal things is misguided. Some want to say that the universal is a collection; but do collections signify their members? ~ Some want to say that the universal is a substance of which individuals are accidents; but is a substance predicated of its accidents? e And some want to say that universals are words--that is noises; but noises are also individual things. ~ In short, to signify or to show ("monstrare") pertains to words; to be signified or shown pertains to things. 8 And to transfer the properties of one to the other leads to hopeless difficulties. ~ One can understand Abailard's exultation (and exaltation) at having shown both sides of a seething controversy to be equally misguided? ~ But what then remains as the problem of universals? It is this: one would expect that every sign would have some subject which it signifies; but universals seem to lack a proper subject. And does this not mean that universals are fictions (like goat-stag or chimera)? = Having thus set out rather baldly what I take to be Abailard's "clear idea," let me now try to show more fully how he goes about establishing the problem and providing for a solution. Abailard's position on universals is set forth in his two logic books, both of which begin... (shrink)

In order to explain the contemporary relevance of Aristotle’s thought, the following discussion explores various examples of Aristotelian theories, concepts, and distinctions which remain at the centre of the philosophical debate. From the domain of logic we consider the notion of category, which was developed by G. Ryle, the distinction between apophantic and semantic discourse, that was stressed by J. Austin, the debate on the principle of non- contradiction, and the theory of fallacies; from the domain of physics, we (...) examine the concepts of substrate, form, continuum, and time, which have been discussed by I. Prigogine and R. Thom; from the field of biology, we consider the function of form in animal generation, which M. Delbrück has compared to the role of DNA; from the field of psychology, we look at the notion of soul as a complex of dispositions, which has been identified by many philosophers as a solution of the “Mind-Body Problem;” from the realm of ethics, we investigate the distinction between action and production, an approach developed by H. Arendt, and the virtue of phronesis, which has been developed by H. G. Gadamer and A. McIntyre. In particular, we discuss the Aristotelian theory of the ambiguity of the concept of being, the notion of “focal meaning,” that has been developed by G. E. L. Owen, and the function of form in the identification of individuals, which has been pursued by M. Frede. (shrink)

Alexander's views on universals are, it seems, quite important in the history of western philosophy. When Boethius gives in his second commentary on Porphyry's Isagoge his solution to the problem of universals as he conceived it, he claims to be adopting Alexander's approach. If true, this means that the locus classicus for all western medieval thinkers on this topic is really a rendering of Alexander's teaching. Alexander commented Aristotle’s statement in his On the Soul “The universal animal (...) either is nothing at all or is posterior if it exists”, and this commentary has been translated into Arabic several times in the classical period. In this study the anonymous Arabic translations of Alexander’s commentary has been translated into English. (shrink)

Die Suche nach historischen Quellen für die Leibniz’sche Philosophie scheint zunächst unerschöpflich. Durch alle in diesem Band versammelten Arbeiten wird der Einfluss der Philosophie des Aristoteles auf das Leibniz’sche Denken näher umrissen. Ein wesentliches Ziel ist es hierbei, einen Beitrag zur Analyse dieser philosophischen Beziehung zu leisten und zu zeigen, dass auch Aristoteles’ Philosophie nach Ansicht unserer Autoren entscheidend zum Verständnis des Leibniz’schen Denkens beiträgt. Die Texte befassen sich mit wesentlichen Themen der Leibniz’schen Logik und Metaphysik, z. B. mit den (...) Grundbegriffen „Monade“ (und deren „Körperhaftigkeit“), „Entelechie“, „Nous“, mit dem Problem der Individuation (Individuum, Atomismus, Einheit), mit den substanziellen Formen, mit der Wissenschaft im Allgemeinen und der Technik, mit der Transformation der Logik, mit den Prinzipien (nämlich denjenigen des zureichenden Grundes, der Individuation und der Notwendigkeit), mit Zukunft und Kontingenz sowie Vergänglichkeit, mit der Theorie der syllogistischen Folgerung, usw. Diese Themen werden stets in der Gegenüberstellung von Leibniz und Aristoteles behandelt – sie zeigen daher, wie Leibniz aristotelische Thesen übernahm, veränderte oder kritisierte. The search for the historical sources of Leibniz’s philosphy initially seems to be unending. All the essays in this volume outline more clearly the influence of Aristotle’s philosophy on Leibniz’s thought. In this context a fundamental aim is to contribute to the analysis of this philosophical relationship and to demonstrate that Aristotle’s philosophy, in the opinion of our authors, plays a decisive role in the understanding of Leibniz’s thought. The texts address fundamental themes of Leibniz’s logic and metaphysics, e.g. the basic concepts of ‘monads’ (and their ‘corporality’), ‘entelechy’ and ‘nous; the problem of individuation (individual, atomism, unity); substantial forms; knowledge in general, and technology; the transformation of logic; principles (namely those of sufficient grounds, of individuation and of necesssity); future and contingency and transientness; the theory of syllogistic deduction, etc. These themes are regularly considered in the comparison between Leibniz and Aristotle – they demonstrate how Leibniz took over, treated or criticised Aristotelian theses. (shrink)

Aristotle’s solution to Zeno’s arrow paradox differs markedly from the so called at-at solution championed by Russell, which has become the orthodox view in contemporary philosophy. The latter supposes that motion consists in simply being at different places at different times. It can boast parsimony because it eliminates velocity from the ontology. Aristotle, by contrast, solves the paradox by denying that the flight of the arrow is composed of instants; rather, on my reading, he holds that the (...) flight is a unity which is ontologically prior to the temporal parts that may be abstracted from it. I label this position temporal holism; and an entity that is ontological prior to its temporal parts lasting. Lasting, I argue, is the key to Aristotle’s solution to the arrow paradox, but it has received insufficient attention in the relevant literature. I therefore set out here to investigate lasting and highlight its major role in Aristotle’s metaphysics more broadly, and in his solution to other problems of change. I show, too, how lasting within a contemporary context underwrites a parsimonious and intuitive solution to the arrow paradox that retains instantaneous velocity, and hence solves a problem for those who think velocity is required within the ontology to underwrite certain causal roles. (shrink)

This volume is the product of a pair of conferences on book I of Aristotle’s Physics at Sapienza University of Rome in 2013 and 2015. Each chapter of book I receives a philosophical commentary by a prominent specialist in ancient philosophy. The contributions offer systematic and thorough exegesis, as well as new and interesting solutions to interpretative problems. In what follows, I will focus chiefly on the latter.Diana Quarantotto begins the volume with a discussion of the overall structure, role, (...) and status of book I, and offers a number of considerations in favor of viewing it as “introductory.” Perhaps her most interesting claim is that the principles introduced there are “not distinctly physical,” which... (shrink)

This edition of Zerah yah's Hebrew translation of "De Anima," Aristotle's monograph on the soul, is of major importance for the history of transmission of Aristotle's text in the Middle Ages. Zerah yah's translation is based on the same lost Arabic translation as Averroes' long commentary, and the solution which it provides for the question of the authorship of this lost Arabic translation thus also holds good for Averroes' text.

In recent decades, it has been argued that the modern concept of forgiveness is absent from Aristotle’s conception of συγγνώμη as it appears in his Rhetoric and Nicomachean Ethics. In this paper, I argue that Aristotle’s view is more modern than it might appear. I defend the idea that Aristotle’s treatment of συγγνώμη, when seen in conjunction with his theory of ethical decision, involuntary action, and character alteration, commits him to a cognitive and emotional theory of forgiveness (...) that is both well-grounded and thoroughly modern. I go on to claim that Aristotle’s view of συγγνώμη helps to solve at least four controversial problems about the nature of forgiveness raised by modern philosophers: how one can forgive a wrong without condoning it, whether forgiveness is a duty, whether moral luck requires us to forgive more widely, and whether forgiveness ought to be unconditional. (shrink)

A revised version of the author’s Göttingen doctoral dissertation, this book is as much an independent essay in modal logic as it is an interpretation of Aristotle’s modal syllogistic. In chapter 1 the author develops what he calls a "rich framework" including speech-act operators as well as epistemic and alethic modal operators, all expressed in a notation of his own devising; for example, "Pc if ENj Pc RNc S, Rc ENj Pa Rp S" translates as "The speaker claims (...) that if he is not justified in claiming that it is not certain that S, it is certain that he is not justified in allowing that it is possible that S." A dual system of quantification is then introduced, with and without existential import for both universal and particular propositions. In chapters 2 and 3 the author uses his framework as a model for discussing various difficulties in Aristotle’s assertoric and modal logic, insisting that his results are relevant to Aristotle’s even when they do not "correspond" to them. An appendix takes up the famous sea-battle of De interpretatione 9. The author is at his best when examining particular problems in Aristotle’s logic; in this regard his criticism of the operation of conversion stands out as especially effective. He is at his worst when pursuing the "intrinsic interest" of his model above and beyond its usefulness in studying Aristotle and when making unwarranted claims of originality for his objectives. One such objective is to stress what he calls the "teleological" character of Aristotle’s logic, a character which he says "is lost sight of in modern accounts" of Aristotle’s work. He appears to be unaware of Ernst Kapp’s classic Greek Foundations of Traditional Logic, which repeatedly calls attention to just this character. The author acknowledges the existence of twentieth century modal logic only once, in a one page criticism of Prior’s defense of the distinction between de dicto and de re modalities. This occurs within a curious argument, based on a premise taken from Ammonius and Abelard, that the concept of logical necessity is "bogus."—J.D. (shrink)

Aristotle not only fonnulates the problem of intentionality explicitly, he makes a solution to it a requirement for any adequate theory of mind. His own solution, however, is not to be found in his theory of sensation, as Brentano and others have thought. In fact, it is precisely because Aristotle regards this theory as inadequate that he goes on to argue for a distinct new ability he calls “phantasia.” The theory of content he develops on this basis (...) (unlike Brentano’s) is profoundly naturalistic: it is a representational theory, formulated in tenns of the causal powers and physical magnitudes of the body. (shrink)

I give a brief precis of Lyons' book. I discuss the problem of delineating basic from non-basic beliefs. I argue that one of Lyons' possible solutions doesn't work - his definition of a perceptual module does not allow us to decide which beliefs are basic. And I argue that another possible solution undermines some of Lyons' motivation. The intuitive understanding of belief may not generate the Clairvoyancy troubles he fears.

One concern bothering ancient and medieval philosophers is the logical worry discussed in Aristotle's De Interpretatione 9, that if future contingent propositions are true, then they are settled in a way that is incompatible with freedom. Another is if we grant God foreknowledge of future contingent events then God's foreknowledge will determine those events in a way precluding freedom. ;I begin by discussing the standard compatibilist solution to these problems as represented in Boethius's Consolation of Philosophy and then examine (...) theories that allegedly deviate from the Boethian solution. Boethius's solution to these separate problems involves showing that both problems operate on an ambiguity in the scope of the modal operator 'necessarily' present in the articulation of the problem. Once the ambiguity is removed we see that both disambiguations fail to offer a sound argument against the compatibility of free action with either God's omniscience or future contingent proposition's being true. The only difference between the solutions is that before executing the scope distinction strategy in the theological problem, Boethius reminds us that God knows future contingents rather than foreknowing them, since God is timeless. ;The rest of my discussion examines positions that allegedly deviate from the Boethian solution: positions held by Peter de Rivo, William Ockham and Plotinus. I argue that Ockham doesn't in fact deviate from the Boethian solution to the theological problem as is commonly held. Instead of offering a compatibilist position where God's omniscience includes foreknowledge, Ockham denies that God foreknows the future advocating instead a more sophisticated Boethian position. The other two philosophers, Rivo and Plotinus, deviate from Boethius, but unfortunately neither position appears philosophically plausible. Rivo's incompatibilist solution to the logical problem is inconsistent with his retention of the Boethian solution to the theological problem and is probably implausible on its own. Plotinus's compatibilist account fails not because it claims that necessity and freedom are compatible, but because the account of moral responsibility Plotinus offers to justify the compatibility fails. (shrink)

Citizens have two mutually exclusive options: they can exile, or even execute, a god among men, or they can submit to superhuman monarchy. Aristotle thinks any state would choose the former, but finds the latter option superior and argues the citizenry should submit to the superhuman monarch because that is precisely what ideal citizens would do if such a being appeared in their society. This problem appears in great cinema and nowhere more powerfully than in J. J. Abrams's Star (...) Trek and Star Trek Into Darkness with the character of James T. Kirk. In his Nicomachean Ethics, Aristotle describes a man he calls the megalopsychos, the great‐souled man or proud man. Aristotle defines the two solutions to the problem of greatness, exile or monarchic rule, as mutually exclusive, but Kirk is able to progress from exile on Delta Vega to the captain's chair, the former seeming necessary for the latter. (shrink)

Keith Lehrer's notion of acceptance and its relation to the notion of belief is analyzed in a way that a person only accepts some proposition p if she decides to believe it in order to reach the epistemic aim. This view of acceptance turns out to be untenable: Under the empirical claim that we don't have the power to decide what to beheve it follows that we cannot accept anything. If reaching the truth is the epistemic aim acceptance proves ill-formed, (...) it is impossible to pursue the aim of truth by believing or accepting something because belief itself is a truth-directed attitude. If the epistemic aim is formulated in a weaker sense, combined with other aims, the danger lurks that accepting a proposition p is in the end loosing any connection with the truth of p. (shrink)

Keith Lehrer's notion of acceptance and its relation to the notion of belief is analyzed in a way that a person only accepts some proposition p if she decides to believe it in order to reach the epistemic aim. This view of acceptance turns out to be untenable: Under the empirical claim that we don't have the power to decide what to beheve it follows that we cannot accept anything. If reaching the truth is the epistemic aim acceptance proves ill-formed, (...) it is impossible to pursue the aim of truth by believing or accepting something because belief itself is a truth-directed attitude. If the epistemic aim is formulated in a weaker sense, combined with other aims, the danger lurks that accepting a proposition p is in the end loosing any connection with the truth of p. (shrink)