Aristotle presents four causes in Posterior Analytics 2.11, but where we expect matter we find instead the confusing formula, ‘what things being the case, necessarily this is the case’, and an equally confusing example. Some commentators infer that Aristotle is not referring to matter, others that he is but in a non-standard way. I argue that APo. 94a20-34 presents not matter, but determination by general features or facts, including facts about something’s genus. The closest connection to matter is Aristotle’s view (...) that the relation between genus and species is analogous to that between matter and a hylomorphic compound. (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)

Aristotle frequently describes essence as a “cause” or “explanation”, thus ascribing to essence some sort of causal or explanatory role. This explanatory role is often explicated by scholars in terms of essence “making the thing be what it is” or “making it the very thing that it is”. I argue that this is problematic, at least on the assumption that “making” expresses an explanatory relation, since it violates certain formal features of explanation. I then consider whether Aristotle is vulnerable to (...) this problem by examining the explanatory role of essence in Posterior Analytics and Metaphysics Z 17. (shrink)

Aristotle’s typical procedure is to identify something's four causes. Intentional action has typically been treated as an exception: most think that Aristotle has the standard causalist account, according to which an intentional action is a bodily movement efficiently caused by an attitude of the appropriate sort. I show that action is not an exception to Aristotle’s typical procedure: he has the resources to specify four causes of action, and thus to articulate a powerful theory of action unlike any other on (...) offer. (shrink)

Modern logicians have sought to unlock the modal secrets of Aristotle's Syllogistic by assuming a version of essentialism and treating it as a primitive within the semantics. These attempts ultimately distort Aristotle's ontology. None of these approaches make full use of tests found throughout Aristotle's corpus and ancient Greek philosophy. I base a system on Aristotle's tests for things that can never combine (polarity) and things that can never separate (inseparability). The resulting system not only reproduces Aristotle's recorded results for (...) the apodictic syllogistic in the Prior Analytics but it also generates rather than assumes Aristotle's distinctions among 'necessary', 'essential' and 'accidental'. By developing a system around tests that are in Aristotle and basic to ancient Greek philosophy, the system is linked to a history of practices, providing a platform for future work on the origins of logic. (shrink)

The notion of identity is investigated through Aristotle and Hegel as supporters of two different ontological conceptions: pluralism of substances and relational holism. Through Aristotle, I examine both the thesis according to which the identity of an object is constituted by its properties and the difficulties which this thesis encounters. Aristotle easily defines the identity in species, in genus, and in number; some problems arise regarding the identity of individuals: for these, it is not enough to indicate the definition and (...) the proper qualities, but matter is needed. Matter cannot, however, be a criterion for identifying duplicate objects: in this case, it plays at most the role of a “weak individuator.” A weak individuator involves relations with other entities. The use of relations in determining the identity of an entity is extensively treated by Hegel, according to whom, in order to define the identity of an object a multiplicity of particular objects is required and, therefore, relations among entities. I conclude by proposing a notion of the object understood not as an independent, separate, and autonomous item, but as a portion of the world, which is given in a phenomenological context and identifies a dialectical context. (shrink)

From Euclid to the second half of the 17th century, mathematicians as well as philosophers continued to raise the question of the angle of contact and, generally, of the concept of angle. This article is the first essay devoted to this subject in Arabic mathematics. It deals with Greek writings translated into Arabic on the one hand, and contributions of Arabic mathematicians on the other hand: al-Nayrīzī, Ibn al-Haytham, al-Samawʾal, al-Shīrāzī, al-Fārisī, al-Qūshjī, among others. Most of these contributions are hitherto (...) unknown.Depuis Euclide jusque tard dans le xviie siècle, mathématiciens et philosophes n'ont cessé de s'interroger sur l'angle de contingence et, plus généralement, sur la notion d'angle. Cet article est le premier essai où sont examinés les écrits grecs portant sur ce thème et transmis en arabe, ainsi que les nombreux travaux, pour la plupart jusqu'ici inconnus, des mathématiciens arabes eux-mêmes: al-Nayrīzī, Ibn al-Haytham, al-Samawʾal, al-Shīrāzī, al-Fārisī, al-Qūshjī, entre autres.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.L'ANGLE DE CONTINGENCE: UN PROBLÈME DE PHILOSOPHIE DES MATHÉMATIQUESVolume 22, Issue 1Roshdi Rashed DOI: https://doi.org/10.1017/S0957423911000087Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. L'ANGLE DE CONTINGENCE: UN PROBLÈME DE PHILOSOPHIE DES MATHÉMATIQUESVolume 22, Issue 1Roshdi Rashed DOI: https://doi.org/10.1017/S0957423911000087Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. L'ANGLE DE CONTINGENCE: UN PROBLÈME DE PHILOSOPHIE DES MATHÉMATIQUESVolume 22, Issue 1Roshdi Rashed DOI: https://doi.org/10.1017/S0957423911000087Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

From Euclid to the second half of the 17th century, mathematicians as well as philosophers continued to raise the question of the angle of contact and, generally, of the concept of angle. This article is the first essay devoted to this subject in Arabic mathematics. It deals with Greek writings translated into Arabic on the one hand, and contributions of Arabic mathematicians on the other hand: al-Nayrīzī, Ibn al-Haytham, al-Samawʾal, al-Shīrāzī, al-Fārisī, al-Qūshjī, among others. Most of these contributions are hitherto (...) unknown.Depuis Euclide jusque tard dans le xviie siècle, mathématiciens et philosophes n'ont cessé de s'interroger sur l'angle de contingence et, plus généralement, sur la notion d'angle. Cet article est le premier essai où sont examinés les écrits grecs portant sur ce thème et transmis en arabe, ainsi que les nombreux travaux, pour la plupart jusqu'ici inconnus, des mathématiciens arabes eux-mêmes: al-Nayrīzī, Ibn al-Haytham, al-Samawʾal, al-Shīrāzī, al-Fārisī, al-Qūshjī, entre autres.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.L'ANGLE DE CONTINGENCE: UN PROBLÈME DE PHILOSOPHIE DES MATHÉMATIQUESVolume 22, Issue 1Roshdi Rashed DOI: https://doi.org/10.1017/S0957423911000087Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. L'ANGLE DE CONTINGENCE: UN PROBLÈME DE PHILOSOPHIE DES MATHÉMATIQUESVolume 22, Issue 1Roshdi Rashed DOI: https://doi.org/10.1017/S0957423911000087Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. L'ANGLE DE CONTINGENCE: UN PROBLÈME DE PHILOSOPHIE DES MATHÉMATIQUESVolume 22, Issue 1Roshdi Rashed DOI: https://doi.org/10.1017/S0957423911000087Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

There is a current debate about the grammar of intention: do I intend to φ, or that I φ? The equivalent question in Aristotle relates especially to choice. I argue that, in the context of practical reasoning, choice, as also wish, has as its object an act. I then explore the role that this plays within his account of the relation of thought to action. In particular, I discuss the relation of deliberation to the practical syllogism, and the thesis that (...) the conclusion of the second is an action. (shrink)

We may try to explain proofs as chains of valid inference, but the concept of validity needed in such an explanation cannot be the traditional one. For an inference to be legitimate in a proof it must have sufficient epistemic power, so that the proof really justifies its final conclusion. However, the epistemic concepts used to account for this power are in their turn usually explained in terms of the concept of proof. To get out of this circle we may (...) consider an idea within intuitionism about what it is to justify the assertion of a proposition. It depends on Heyting’s view of the meaning of a proposition, but does not presuppose the concept of inference or of proof as chains of inferences. I discuss this idea and what is required in order to use it for an adequate notion of valid inference. (shrink)

One of Etchemendy's arguments against the Tarskian and model‐theoretic notion of logical truth is based on a reduction principle according to which a universally quantified sentence is true if, and only if, all of its instances are logically true. The reduction of logical truth to mere truth reveals that the concept of validity at play in Tarski and in model‐theory relies upon extra‐logical assumptions. A similar reduction had already been put forward by Prawitz, although not with focus on extra‐logical assumptions. (...) Prawitz's reduction concerns rather the possibility of understanding the Tarskian and model‐theoretic approach as implying any epistemic modality. We take into account a possible strategy that an advocate of Tarski and model‐theory may use against Etchemendy's objection, and argue that this strategy fails with respect to Prawitz's criticism. This permits us to shed light upon a difference between Prawitz's and Etchemendy's standpoints: while Etchemendy's reduction shows that the Tarskian and model‐theoretic notion of logical truth cannot be understood as an adequate formal counterpart of truth‐preservation solely by virtue of logical form, Prawitz's reduction insists on the fact that truth‐preservation solely by virtue of logical form is insufficient for epistemic modality to obtain. (shrink)

I present the text at Posterior Analytics II.11, 94b8-26, offer a tentative translation, discuss the main construals offered in the literature, and argue for my own interpretation. Some of the general questions I discuss are the following: 1. What is the nature of the explanatory syllogisms offered as examples, especially in the case of the moving and the final cause? Are they scientific demonstrative explanations? In the case of the final cause, are they practical syllogisms? Are they productive? 2. Are (...) we to read into such examples Aristotle’s requirements from APo I.4-6 that demonstrative premisses and conclusions are universal, per se, and necessary? If so, in what way? If such requirements do not apply here, what are the implications for question 1? 3. What, if any, is the advantage of one type of causal explanation over another in cases in which there is causal competition between complementary explanations? 4. What is the relation between the thesis of this chapter, especially the section dedicated to the final cause, and the argument of II.8-10? How is essence related to causes? How is explanation/demonstration-based definition related to causal explanation in terms of the four causes? (shrink)

The subject of this article is Leibnizian interpretation of the principle of reason. Although the German philosopher called it principium grande of his philosophy, we do not find its systematic exposition in Leibniz’s works. The main aim of my paper is to present a short exposition of the principle. The article consists of three parts: in the first I present systematic exposition of the principle of reason with particular emphasis on explication of terms “principle” and “reason,” in the second, I (...) show the origins of the principle, finally, in the third part, I discuss in detail three forms of it: the principle of sufficient reason, the principle of determining reason and the principle of rendering reason. I accept two main theses: firstly, a proper interpretation of this principle requires taking into account the whole context of Leibnizian philosophy, i.e. one cannot limit oneself (as it is usually happens among researchers) to only one discipline, e.g. logic. Secondly, the ultimate methodological and heuristical foundation of the principle of reason is Leibnizian metaphysics, especially natural theology. (shrink)

The paper is devoted to Aristotle's solution to Meno's paradox: a person cannot search for what he knows -- he knows it, and there is no need to search for such a thing -- nor for what he doesn't know -- since he doesn't know what he's searching for. The autor argues that Aristotle proposes solutions of this paradox for every stage of cognition, not only for exercising available scientific knowledge as regarded by most Aristotelian scholars. He puts more focus (...) on the importance of the distinction between 'progignoskein' (pre-existing cognition) and 'proepistasthai' (pre-existong knowledge) for Aristotle's solution of this paradox. [In Russian]. (shrink)

In this paper, we provide an overview of some of the results obtained in the mathematical theory of intermediate quantifiers that is part of fuzzy natural logic. We briefly introduce the mathematical formal system used, the general definition of intermediate quantifiers and define three specific ones, namely, “Almost all”, “Most” and “Many”. Using tools developed in FNL, we present a list of valid intermediate syllogisms and analyze a generalized 5-square of opposition.

The main objective of this paper is devoted to two main parts. First, the paper introduces logical interpretations of classical structures of opposition that are constructed as extensions of the square of opposition. Blanché’s hexagon as well as two cubes of opposition proposed by Morreti and pairs Keynes–Johnson will be introduced. The second part of this paper is dedicated to a graded extension of the Aristotle’s square and Peterson’s square of opposition with intermediate quantifiers. These quantifiers are linguistic expressions such (...) as “most”, “many”, “a few”, and “almost all”, and they correspond to what are often called “fuzzy quantifiers” in the literature. The graded Peterson’s cube of opposition, which describes properties between two graded squares, will be discussed at the end of this paper. (shrink)

Both Aristotle and Ernst Mayr present theories of dual explanation in biology, with proximal, clearly physical explanations and more distal, biology-specific explanations. Aristotle’s presentation of final cause explanations in Posterior Analytics relates final causes to the necessary material, formal, and efficient causes that mediate them. Johnson and Leunissen demonstrate the problematic nature of historical and recent interpretations and open the door for a new interpretation consistent with modern evolutionary theory. Mayr’s differentiation of proximate and ultimate/evolutionary causes provides a key to (...) appropriating Aristotle for modern use, if care is taken to differentiate Mayr’s proximate/distal and mechanical/evolutionary distinctions from his intentional/non-intentional distinction. Building on Mayr, and noting his appropriation of ancient and recent commentary, a strong case can be made for nested explanation, wherein evolutionary explanations are instantiated in systems of mechanical explanations. Biological concepts of organism, gene, function, etc., are etiologically prior to mechanical explanations of function, but temporally posterior to mechanical explanations of historical adaptation. Such an analysis sheds light on recent arguments within evolutionary biology while highlighting the importance of epistemology in contemporary science. (shrink)

The relations between different areas of knowledge have been a subject of interest to philosophers as well as to scientists and mathematicians from antiquity. While recent work in this direction has been largely concerned with the question whether one branch of knowledge can be reduced to another , the questions which exercised the Greek philosophers on these matters have a different starting point. Taking for granted that there are a number of distinct areas of knowledge, they proceeded to consider a (...) variety of relations which they observed to hold among the sciences as they knew them; the question of the priority of one science to another is a recurrent theme. In fact, three sorts of orderings were noticed, and the associated conceptions of priority are interesting. Only one of them is the concern of the present paper, though, and I shall briefly describe the remaining two only for purposes of contrast. (shrink)

Arystoteles wyodrębnił w Organonie dwa rodzaje rozumowań: analityczne i dialektyczne. Badaniami rozumowań analitycznych, które podjął w Analitykach I i II, zasłużył sobie na miano ojca logiki formalnej. Według Chaima Perelmana, współczesnym logikom umknął z pola widzenia fakt, że rozważania Arystotelesa na temat rozumowań dialektycznych – podjęte w Topikach, Retoryce i O dowodach sofistycznych – czynią zeń także ojca teorii argumentacji. Niniejszy artykuł jest próbą odpowiedzi na tę diagnozę. Jego celem jest potwierdzenie tezy Perelmana o jednorodności Arystotelesowskiej koncepcji sylogizmu teoretycznego i (...) praktycznego. W tym potwierdzeniu kluczową rolę odgrywa pojęcie entymematu. W artykule odpowiadamy na pytanie, jakie miejsce zajmuje ono w teorii retoryki Arystotelesa i porównujemy je z ogólnym pojęciem sylogizmu. Szkicujemy też strukturę argumentacji przez entymemat oraz przedstawiamy dwa typy entymematów omawiane przez Arystotelesa: pozorne i obalające. (shrink)

In the Organon, Aristotle distinguished two types of reasoning: analytical and dialectical. His studies on analytical reasoning in the Prior and Posterior Analytics, earned him the title of the father of formal logic. According to Chaim Perelman, modern logicians have failed to see the fact that Aristotle’s considerations on dialectical reasoning in the Topics, the Rhetoric and the Sophistical Refutations made him also the father of the theory of argumentation. This article attempts to answer this diagnosis. Our aim is to (...) prove Perelman’s thesis on the homogeneity of Aristotle’s concept of theoretical and practical syllogism. The key concept in this proof is that of the enthymeme. In the article, we will try to answer the question of what place the enthymeme occupies in Aristotle’s theory of rhetoric and confront it with the concept of a syllogism. We will also outline the structure of argumentation that makes use of the enthymeme, and present two types of enthymemes discussed by Aristotle: the apparent enthymeme and the refutative enthymeme. (shrink)

Ever since ?ukasiewicz, it has been opinio communis that Aristotle's modal syllogistic is incomprehensible due to its many faults and inconsistencies, and that there is no hope of finding a single consistent formal model for it. The aim of this paper is to disprove these claims by giving such a model. My main points shall be, first, that Aristotle's syllogistic is a pure term logic that does not recognize an extra syntactic category of individual symbols besides syllogistic terms and, second, (...) that Aristotelian modalities are to be understood as certain relations between terms as described in the theory of the predicables developed in the Topics. Semantics for modal syllogistic is to be based on Aristotelian genus-species trees. The reason that attempts at consistently reconstructing modal syllogistic have failed up to now lies not in the modal syllogistic itself, but in the inappropriate application of modern modal logic and extensional set theory to the modal syllogistic. After formalizing the underlying predicable-based semantics (Section 1) and having defined the syllogistic propositions by means of its term logical relations (Section 2), this paper will set out to demonstrate in detail that this reconstruction yields all claims on validity, invalidity and inconclusiveness that Aristotle maintains in the modal syllogistic (Section 3 and 4). (shrink)

I reconstruct Aristotle’s analytical procedure in Prior Analytics I.45 and its metalogical implications. Aristotle’s analysis unfolds three groups of syllogisms: symmetrically analysable, asymmetrically analysable, and non-analysable syllogisms. From the first and the third group could be extracted 27 combinations of the two mutually non-derivable deductive rules. Aristotle’s reduced deductive system in APr. I.7 with the two moods in the first figure (traditionally called Barbara and Celarent) follows this pattern. I demonstrate that the deductive system with Barbara and Celarent is just (...) one of 27 possible complete deductive systems with the two mutually non-derivable syllogistic rules. On top of that, given the fact that there are two combinations of mutually non-derivable conversion rules, I conclude that Prior Analytics hides in itself 54 complete deductive systems with a minimal number of mutually non-derivable rules. Finally, it is commented what might be the role of analysis; to what extent Aristotle could be aware of possibilities presented here; why he still prefers only one deductive system to many others with the same deductive power. (shrink)

In Prior Analytics 1.27–30, Aristotle develops a method for finding deductions. He claims that, given a complete collection of facts in a science, this method allows us to identify all demonstrations and indemonstrable principles in that science. This claim has been questioned by commentators. I argue that the claim is justified by the theory of natural predication presented in Posterior Analytics 1.19–22. According to this theory, natural predication is a non-extensional relation between universals that provides the metaphysical basis for demonstrative (...) science. (shrink)

In Posterior Analytics 1.3, Aristotle advances three arguments against circular proof. The third argument relies on his discussion of circular proof in Prior Analytics 2.5. This is problematic because the two chapters seem to deal with two rather disparate conceptions of circular proof. In Posterior Analytics 1.3, Aristotle gives a purely propositional account of circular proof, whereas in Prior Analytics 2.5 he gives a more complex, syllogistic account. My aim is to show that these problems can be solved, and that (...) Aristotle’s third argument in 1.3 is successful. I argue that both chapters are concerned with the same conception of circular proof, namely the propositional one. Contrary to what is often thought, the syllogistic conception provides an adequate analysis of the internal deductive structure of the propositional one. Aristotle achieves this by employing a kind of multiple-conclusion logic. (shrink)

Building on previous scholarly work on the mathematical roots of assertoric syllogistic we submit that for Aristotle, the semantic value of the copula in universal affirmative propositions is the relation of divisibility on positive integers. The adequacy of this interpretation, labeled here ‘arithmetical dictum’, is assessed both theoretically and textually with respect to the existing interpretations, especially the so-called ‘mereological dictum’.

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

En este trabajo planteo la pregunta de si la lógica de Aristóteles es o no una lógica formal. Respondo que, aunque las doctrinas contenidas en el Organon inauguren, efectivamente, la lógica formal, hay también buenas razones para pensar que Aristóteles no creía que la lógica fuese una disciplina que pudiera prescindir por completo del contenido. In this paper I discuss the question of whether Aristotle’s logic is a formal logic or not. I answer that, although the doctrines contained in the (...) Organon inaugurate indeed formal logic, there are also good reasons to think that Aristotle did not believe that logic was a discipline that ought to prescind completely from content. (shrink)

This is my first professional philosophical essay. I wrote "The twofold meaning of being" in 1996 when I was a student of Nunzio Incardona at University of Palermo (Italy) and before my degree thesis, "The difference in Aristotle’s Metaphysics". It still waits to be published.

I will argue for the similarity between some aspects of Aristotle’s doctrine of causes and a particular kind of interventionist theory of causality. The interventionist account hypothesizes that there is a connection between causation and human intervention: the idea of a causal relation between two events is generated by the reflection of human beings on their own operating. This view is remindful of the Aristotelian concept of αἴτιον, which is linked to the figure of the αἴτιος, the person who is (...) responsible of an action. Aristotle conceives of the efficient cause as the active element which, in the φύσις, gives rise to movement and imposes the form, in analogy with the active element that in τέχνη operates the production: the craftsman. This analogy suggests that Aristotle conceives of the causation on the basis of the human ability to modify the environment with aims. Within the debate on the manipulative theory the classical accounts worked out by Collingwood, Gasking and von Wright have been recently criticized by Woodward. von Wright’s reductive account explains causation on the basis of human free action, while Woodward regards this reduction as a dangerous move which makes causal explanations too much anthropomorphic. I will show that Aristotle’s doctrine of causes is more similar to von Wright’s account and that the Aristotelian analysis of becoming supports von Wright’s reductive interventionism against Woodward’s criticism. Furthermore, I will draw a comparison between interventionism and dispositionalism, where the latter is another contemporary account of causation that claims Aristotelian roots. (shrink)

Aristotle’s treatment of mixed, first-figure, problematic-assertoric syllogisms has generated a good deal of controversy among modern commentators.I argue that W.D.Ross’s criticism of A.Becker’s cr...

(1993). Alexander of aphrodisias and others on a controversial demonstration in aristotle’s modal syllogistic. History and Philosophy of Logic: Vol. 14, No. 2, pp. 201-214.

Although there are many questions to be asked about philosophy of mathematics, the fundamental questions to be asked will be questions about what the mathematical object is in view of being and what the mathematical reasoning is in view of knowledge. It is clear that other problems will develop in parallel within the framework of the answers to these questions. For this reason, when we approach Aristotle's philosophy of mathematics over these two basic problems, we come up with the concept (...) of abstraction. In our work, I will try to explain the mathematical abstraction that Aristotle has developed to understand mathematical philosophy. (shrink)

The present paper aims to show that the reconstruction of the formal framework of the proofs in Pr. An. 1.15, as proposed by Malink and Rosen 2013 (‘Proof by Assumption of the Possible in Prior Analytics 1.15’, Mind, 122, 953-85) is due to affront a double impasse. Malink and Rosen argue convincingly that Aristotle operates with two different modal frameworks, one as found in the system of modal logic presented in Prior Analytics 1.3 and 8-22, and one occurring in many (...) of Aristotle’s works, such as the Physics, De Caelo and the Metaphysics. However, they misconstrue the latter framework. More precisely, they misconstrue the domain of significance of what they call the ‘Principle of Necessitation’. As a consequence, bringing the two frameworks into one results into a contradictory modal logic. On the other hand, if the Principle of Necessitation is rectified, the proofs put forward by Malink and Rosen in the same paper are no longer available. (shrink)

How many scientific demonstrations can a single phenomenon have? This paper argues that, according to Aristotle's theory of scientific knowledge as laid out in the Posterior Analytics, a single conclusion may be demonstrated via more than one explanatory middle term. I also argue that this model of multiple demonstration is put into practice in the biological writings. This paper thereby accomplishes two related goals: it clarifies certain relatively obscure passages of the Posterior Analytics and uses them to show how Aristotle (...) explains biological phenomena by reference to both final and material causes in the Parts of Animals. The first part of the paper explains the account of multiple demonstration present in the Posterior Analytics and distinguishes it from another kind of plural explanation rejected by Aristotle. The second part of the paper turns to the biological explanation in the Parts of Animals and shows how Aristotle's account of multiple demonstrations works in practice. The paper thus provides evidence for the claim that the ‘applied’ reasoning on display in the biological works is in harmony with the framework of the logical treatises, and thus may also shed light on questions of the unity of the Aristotelian corpus. (shrink)

In his 1910 book On the principle of contradiction in Aristotle, Jan Łukasiewicz claims that syllogistic is independent of the principle of contradiction . He also argues that Aristotle would have defended such a thesis in the Posterior Analytics. In this paper, we first show that Łukasiewicz's arguments for these two claims have to be rejected. Then, we show that the thesis of the independence of assertoric syllogistic vis-à-vis PC is nevertheless true. For that purpose, we first establish that there (...) is no possibility to account for Aristotle's original views on syllogistic without using per impossibile deductions. At last, following an idea due to Smith 1983, we prove that there is a complete reconstruction of assertoric syllogistic using ecthesis instead of reductio ad absurdum. Contrary to what is claimed in Smith 1983, we show that Smith's system SE has to be improved for such a reconstruction. This results in an ecthetic system which is complete with respect to syllogistic arguments, not explosi.. (shrink)

Fred's semantics for McCall's syntactic presentation of Aristotle's assertoric and apodeictic syllogistic is altered to free it from Thom's objections that it is unAristotelian. The altered semantics rejects Baroco-XLL and Bocardo-LXL, which Thom says Aristotle should have accepted. Aristotle's proofs that use ecthesis are formalized by using singular sentences. With one exception the (acceptance) axioms for McCall's system L-X-M are derivable. Formal proofs are shown to be sound.

We trace two logical ideas further back than they have previously been traced. One is the idea of using diagrams to prove that certain logical premises do—or don’t—have certain logical consequences. This idea is usually credited to Venn, and before him Euler, and before him Leibniz. We find the idea correctly and vigorously used by Abū al-Barakāt in 12th century Baghdad. The second is the idea that in formal logic, P logically entails Q if and only if every model of (...) P is a model of Q. This idea is usually credited to Tarski, and before him Bolzano. But again we find Abū al-Barakāt already exploiting the idea for logical calculations. Abū al-Barakāt’s work follows on from related but inchoate research of Ibn Sīnā in eleventh century Persia. We briefly trace the notion of model-theoretical consequence back through Paul the Persian and in some form back to Aristotle himself. (shrink)

How do, according to Aristotle, peirastic arguments, which are employed by nonscientists to put professed scientists to the test, work, and how do they differ from genuine scientific arguments? A peirastic argument succeeds in unmasking a would-be scientist if it establishes an inconsistency among the answers given. These answers may only comprise: propositions which are proper to the field and which everybody can know; propositions which only scientists may know; “common” propositions that everybody, including various sciences, uses in all kind (...) of arguments. On the other hand, a peirastic argument fails to do its job if it either features or presupposes in addition propositions which would justify a fallacy, or if it purports to be scientific. The latter type of bad peirastic argument crucially depend on common propositions where scientific arguments explain by reference to combinations of the primitive items of the science in question. (shrink)

Aristotle's notion of experience plays an important role in his epistemology as the link between perception and memory on the one side, and higher cognitive capacities on the other side. However, Aristotle does not say much about it, and what he does say seems inconsistent. Notably, some passages suggest that it is a non-rational capacity, others that it is a rational capacity and that it provides the principles of science. This paper presents a unitary account of experience. It explains how (...) experience grows from perception and memory into a rational capacity, and in what way it provides the principles. (shrink)