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)

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)

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)

There is agreement neither concerning the point that is being made in Posterior analytics 96b15–25 nor the issue Aristotle intends to address. There are two major lines of interpretation of this passage. According to one, sketched by Themistius and developed by Philoponus and Eustratius, Aristotle is primarily concerned with determining the definitions of the infimae species that fall under a certain genus. They understand Aristotle as arguing that this requires collating definitional predictions, seeing which are common to which species. Pacius, (...) on the other hand, takes Aristotle to be saying that a genus is studied scientifically through first determining the infimae species that fall under that genus. This interpretation attributes to Aristotle a distinction between primary and derivative subjects. I argue for Pacius’s interpretation, defending it against Barnes’s objections.Author Keywords: Demonstration; Definition; Aristotle; Species; Principles. (shrink)

In Aristotle's biological works, there is an apparent conflict between passages which seem to insist that only hypothetical necessity (anagk ex hypotheses) operates in the sublunary world, and passages in which some biological phenomena are explained as simply (hapls) necessary. Parallel to this textual problem lies the claim that explanations in terms of simple necessity render teleological explanations (in some of which Aristotle puts hypothetical necessity to use) superfluous. I argue that the textual conflict is only apparent, and that Aristotle's (...) notion of coincidental sameness allows him to avoid the superfluity problem. (shrink)

At the end of Republic 5, Plato distinguishes epistêmê from doxa, knowledge from belief. In Posterior Analytics 1.33, Aristotle provides his own distinction between epistêmê and doxa. I explore his way of distinguishing them and compare it with Plato's.

The question as to what makes a perfect Aristotelian syllogism a perfect one has long been discussed by Aristotelian scholars. G. Patzig was the first to point the way to a correct answer: it is the evidence of the logical necessity that is the special feature of perfect syllogisms. Patzig moreover claimed that the evidence of a perfect syllogism can be seen for Barbara in the transitivity of the a-relation. However, this explanation would give Barbara a different status over the (...) other three first figure syllogisms. I argue that, taking into account the role of the being-contained-as-in-a-whole formulation, transitivity can be seen to be present in all four first figure syllogisms. Using this wording will put the negation sign with the predicate, similar to the notation in modern predicate calculus. (shrink)

The paper rejects Michael Wolff's claim that Aristotle offers proofs for the validity of his perfect syllogisms.

Scholars often assert that Plato and Aristotle share the view that discursive thought is internal speech. However, there has been little work to clarify or substantiate this reading. In this paper I show Plato and Aristotle share some core commitments about the relationship of thought and speech, but cash out TIS in different ways. Plato and Aristotle both hold that discursive thinking is a process that moves from a set of doxastic states to a final doxastic state. The resulting judgments (...) can be true or false. Norms govern these final judgments and, in virtue of that, they govern the process that arrives at those judgments. The principal norm is consistency. However, the philosophers differ on the source of this norm. For Plato, persuasiveness and accuracy ground non-contradiction because internal speech is dialogical. For Aristotle, the Principle of Non-Contradiction grounds a Doxastic Thesis that no judgment can contradict itself. For Aristotle, metaphysics grounds non-contradiction because internal speech is monological. (shrink)

This article aims at elucidating the logic of Arist. SE 22, 178b36–179a10 and, in particular, of the sophism labelled "Third Man" discussed in it. I suggest that neither the sophistic Walking Man argument, proposed by ancient commentators, nor the Aristotelian Third Man of the , suggested by modern interpreters, can be identified with the fallacious argument Aristotle presents and solves in the passage. I propose an alternative reconstruction of the Third Man sophism and argue that an explanation of the lines (...) regarding the identity of Coriscus and Coriscus the musician (178b39–179a3) is indispensable for its correct understanding, since they hint at another sophism in some important aspects analogous. Finally, I show that two contradictions concerning spotted by scholars in the passage are only apparent and can be dissolved once the assumption that the anti-Platonic Third Man argument is at stake here is discarded, and once the passage is read in the light of its agonistic context. (shrink)

This is a translation, made by myself, of the paper to be published in Portuguese in the journal Discurso, 2020, in honour of the late professor Oswaldo Porchat. I discuss what Aristotle was trying to encode when he said that the object of scientific knowledge is necessary, or that what we know (scientifically) cannot be otherwise etc. The paper is meant as a continuation of previous papers—orientated towards a book on the Posterior Analytics—and thus does not discuss in much detail (...) key passages, as the very definition of scientific knowledge in APo I.2, or passages from APo I.4 and I.6 (for these, I refer to my previous papers). This paper is mainly focused on Aristotle’s references to his notion of scientific knowledge both in other passages from the APo and in other treatises. I intend to show that there is a progressive, intrinsic relation between the two requirements by which scientific knowledge is defined. It is not true that each of these requirements stems from a different source. The Causal-Explanatory requirements gives Aristotle the general heading. Then, the Necessity Requirement ranges over the explanatory relation between explanans and explanandum and thereby specifies what sort of cause is sctricly required for having scientific knowledge of a given explanandum. Now, Aristotle was also concerned with the necessary truth of the elemental predications that constitute a demonstration. My claim that the Necessity Requirement ranges over the explanatory relation does not ignore that concern, and does not deny it. My claim is that Aristotle’s main focus, and main concern, consists in stressing that the explanatory factor to be captured in scientific knowledge of a given explanandum is such that cannot be otherwise. (shrink)

Through a detailed analysis of the various modes of argumentation employed by Aristotle throughout his natural scientific works, I aim to contribute to the growing scholarship on the relation between Aristotle’s theory of science and his actual scientific practice. I challenge the standard reading of Aristotle as a methodological empiricist and show that he permits a variety of non-empirical arguments to support controversial theses in properly scientific contexts. Specifically, I examine his use of logical (logikôs) argumentation in the discussion of (...) mule sterility in Generation of Animals II 8, rational (kata ton logon) argumentation in his discussion of cardiocentrism throughout the biological works, and the method of division in Posterior Analytics II 13. (shrink)

I present Aristotle’s theory of causation in a way that privileges a comparison with contemporary discussion on causation. I do so by selecting in Aristotle’s theory points that are interesting to contemporary discussion and by translating Aristotle in the contemporary philosophical terminology. I compare Aristotle’s views with Mackie’s (1993/1965) and Sosa’s (1993/1980). Mackie is a humean regularist regarding the metaphysics of causal necessity, but his theory postulates some formal aspects of the causal relation which are similar to the Aristotelian theory. (...) By introducing the notion of causal field as a third causal relatum – a sample in which the cause must be picked out as a explanation coextensive to the effect –, Mackie holds a point very similar to Aristotle, inasmuch as both defend that the causal relation is triadic and both have the extensional desideratum. Sosa (1993/1980) defends that every cause necessitates its effect, arguing against classical Humeanism, and he also proposes a causal pluralism. Both these theses are clearly Aristotelian. Aristotle comprehends that the causal relation has three relata: a subjacent C, a property of that subjacent A and a cause B that explains why such property is attributed to that subjacent. The subjacent is similar to Mackie’s notion of causal field, for in regard to it the cause must be coextensive to the property. But Aristotle also says that for each explanandum (property attributed to a subjacent of which one aims to investigate a cause) there is only one cause, which necessitates it. Sosa and Aristotle are similar because both develop a causal pluralism from a theory of causes as having intrinsic necessitation. For Aristotle, causes/explanations [aitiai] are central for attaining scientific knowledge, and its triadic structure determines the syllogistic structure of scientific demonstrations. Aristotle’s theory of causation also involves comprehending the actualisation of capacities (dispositional properties of objects) affirming that the causal relation is resultant from intrinsic properties of the objects, and the cause B is the essence of the explanandum. (shrink)

This dissertation explores Aristotle’s use of teleology as a principle of explanation, especially as it is used in the natural treatises. Its main purposes are, first, to determine the function, structure, and explanatory power of teleological explanations in four of Aristotle’s natural treatises, that is, in Physica (book II), De Anima, De Partibus Animalium (including the practice in books II-IV), and De Caelo (book II). Its second purpose is to confront these findings about Aristotle’s practice in the natural treatises with (...) the theoretical picture of the structure of teleological explanations gained from Aristotle’s theory of scientific demonstration. For this purpose a new interpretation of Analytica Posteriora II.11 is presented. This study thereby contributes to recent scholarship on the relation between Aristotle’s philosophy of science and his philosophy of nature, while at the same time adding to our knowledge of Aristotle’s notion of teleology in terms of its explanatory merits and limits. (shrink)

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 rea­ son, 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)

This chapter discusses the first part of Aristotle's Posterior Analytics A-33, 88b30-89a10. I claim that Aristotle is not concerned with an epistemological distinction between knowledge and belief in general. He is rather making a contrast between scientific knowledge (which is equivalent to explanation by the primarily appropriate cause) and some explanatory beliefs that falls short of capturing the primarily appropriate cause.

I argue that Aristotle’s account of scientific demonstrations in the Posterior Analytics is centred upon formal causation, understood as a demonstration in terms of essence (and as innocent of the distinction between form and matter). While Aristotle says that all four causes can be signified by the middle term in a demonstrative syllogism, and he discusses at some length efficient causation, much of Aristotle’s discussion is foremost concerned with the formal cause. Further, I show that Aristotle had very detailed procedures (...) for identifying the formal cause, and that he is aware of several problems which might lead one to erroneously identify the wrong form as the cause of a property. Finally, I show that Aristotle’s account can easily be adapted to material causation, and through some modifications (introduction of process universals related through parthood), hinted at in II 11-12 and 16-17, to efficient and final causation. (shrink)

The concept of “necessity of thought” plays a central role in Dag Prawitz’s essay “Logical Consequence from a Constructivist Point of View” (Prawitz 2005). The theme is later developed in various articles devoted to the notion of valid inference (Prawitz, 2009, forthcoming a, forthcoming b). In section 1 I explain how the notion of necessity of thought emerges from Prawitz’s analysis of logical consequence. I try to expound Prawitz’s views concerning the necessity of thought in sections 2, 3 and 4. (...) In sections 5 and 6 I discuss some problems arising with regard to Prawitz’s views. (shrink)

Epicureans and Stoics reject the independent existence of the Platonic Ideas. This paper assesses what both schools put forward as substitutes for universals. Both Epicureans and Stoics appeal to an a posteriori mental capacity for generalisation but that is where their shared commitments end. the divergences are mapped out, against a tendency in historiography to assimilate the two strategies, and both theories are then analysed independently.

Although the theory of the assertoric syllogism was Aristotle's great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was that a syllogism is (...) a conditional proposition deduced from a set of axioms. There is even unclarity about what the basis of syllogistic validity consists in. Returning to Aristotle's text, and reading it in the light of commentary from late antiquity and the middle ages, we find a coherent and precise theory which shows all these claims to be based on a misunderstanding and misreading. (shrink)

This article outlines a method of collaboration that will manifest a high probability of cumulative and progressive results in science. The method will accomplish this through a division of labour grounded in the order of occurrence of human cognitional operations. The following article explores the possibility of a method known as functional specialization, distinct tasks presently operative in neuroscience. Functional specialization will enhance collaboration within a science as well as initiate implementation of generalized empirical method. Implementation of generalized empirical method (...) will be achieved through the focus of individual specialties on specific mental operations. (shrink)

We can now recognize Aristotle's many accomplishments in logical theory, not the least of which is treating the deduction process itself as a subject matter and thus establishing the science of logic. Aristotle took logic to be that part of epistemolo gy used to establish knowledge of logical consequence. Prior Analytics is a metalogical treatise on his syllogistic system in which Aristotle modelled his deduction system to demonstrate certain logical relationships among its rules. Aristotle's n otion of substitution distinguishes logical (...) syntax from semantics and enabled him to distinguish validity from deducibility sufficiently to note the completeness of his logic. (shrink)

Aristotle's cognitive ideal is a form of understanding that requires a sophisticated grasp of scientific first principles. At the end of the Analytics, Aristotle tells us that we learn these principles by induction. But on the whole, commentators have found this an implausible claim: induction seems far too basic a process to yield the sort of knowledge Aristotle's account requires. In this paper I argue that this criticism is misguided. I defend a broader reading of Aristotelian induction, on which there's (...) good sense to be made of the claim that we come to grasp first principles inductively, and show that this reading is a natural one given Aristotle's broader views on scientific learning. (shrink)

En este artículo se discute la relación entre silogismo y demostración con respecto al concepto aristotélico del conocimiento científico formulado en los Analíticos segundos. La argumentación sigue tres líneas principales: (i) se ofrecen razones para rechazar la relegación de la sistematización silogística a la instancia postrera de justificación y exposición didáctica del conocimiento previamente adquirido. Como respuesta alternativa, (ii) se muestra que una explicación aristotélica necesita la silogística en virtud del papel que desempeña la causa como término medio silogístico. En (...) consecuencia, debería estar en condiciones de (iii) sostener que no resulta factible establecer firmemente los principios propios como premisas explicativas sin construir silogismos. This article focuses on the relation between syllogism and demonstration, as related to Aristotle's concept of scientific knowledge in his Posterior Analytics. Three main lines of argumentation are followed: (i) reasons are given to reject that syllogistic systematization plays a unique role as a skill for justification and didactic proof of a body of knowledge previously acquired. Alternatively, (ii) it is showed that an Aristotelian explanation requires syllogistic as to the role of cause as middle syllogistic term. Thus, it should be feasible (iii) to sustain that it is not possible to firmly establish proper principles as explanative premises without constructing syllogisms. (shrink)

Aristotle was the first thinker to articulate a taxonomy of scientific knowledge, which he set out in Posterior Analytics. Furthermore, the “special sciences”, i.e., biology, zoology and the natural sciences in general, originated with Aristotle. A classical question is whether the mathematical axiomatic method proposed by Aristotle in the Analytics is independent of the special sciences. If so, Aristotle would have been unable to match the natural sciences with the scientific patterns he established in the Analytics. In this paper, I (...) reject this pessimistic approach towards the scientific value of natural sciences. I believe that there are traces of biology in the Analytics as well as traces of the Analytics’ theory in zoological treatises. Moreover, for a lack of chronological clarity, I think it’s better to unify Aristotle’s model of scientific research, which includes Analytics and the natural sciences together. (shrink)