Is consistency the sort of thing that could provide a guide to mathematical ontology? If so, which notion of consistency suits this purpose? Mark Balaguer holds such a view in the context of platonism, the view that mathematical objects are non-causal, non-spatiotemporal, and non-mental. For the purposes of this paper, we will examine several notions of consistency with respect to how they can provide a platon-ist epistemology of mathematics. Only a Gödelian notion, we suggest, can provide a satisfactory guide to (...) a platonist ontology. Is consistency the sort of thing that could provide a guide to mathematical ontology? If so, which notion of consistency suits this purpose? Mark Bala-guer holds such a view in the context of platonism, the view that mathematical objects are non-causal, non-spatiotemporal, and non-mental. Balaguer's version of Platonism, Full-Blooded Platonism (FBP), is the view that "there are as many abstract mathematical objects as there could be-i.e., there actually exist abstract mathematical objects of all possible kinds" (Balaguer, 2017, p. 381). He continues: Since FBP says that there are abstract mathematical objects of all possible kinds, it follows that if FBP is true, then every purely mathematical theory that could be true-i.e., that is internally consistent-accurately describes some collection of actually existing abstract objects. Thus it follows from FBP that in order to acquire knowledge of abstract objects, all we have to do is come up with an internally consistent purely mathematical theory (and know that it is internally consistent). (Balaguer, 2017, p. 381) * To be published in 43rd International Wittgenstein Symposium proceedings. (shrink)

Tras analizar sucintamente las consecuencias científicas y filosóficas de la identidad mente-cerebro, se señalan argumentos a favor y en contra de mantener el debate mente-cerebro. En particular se consideran las nuevas técnicas de exploración del cerebro como argumento en contra de tal debate. Las deficiencias e insuficiencias de tales técnicas aconsejan mantener el debate mente-cerebro y no asumir el materialismo.

A new translation and edition of Aristotle's Protrepticus (with critical comments on the fragments) -/- Welcome -/- The Protrepticus was an early work of Aristotle, written while he was still a member of Plato's Academy, but it soon became one of the most famous works in the whole history of philosophy. Unfortunately it was not directly copied in the middle ages and so did not survive in its own manuscript tradition. But substantial fragments of it have been preserved (...) in several works by Iamblichus of Chalcis, a third century A.D. neo-Pythagorean philosopher and educator. On the basis of a close study of Iamblichus' extensive use and excerption of Aristotle's Protrepticus, it is possible to reconstruct the backbone of the lost work, and then to flesh it out with the other surviving reports about the work from antiquity (for example in Alexander of Aphrodisias and other ancient commentators on Aristotle). It is also possible to identify several papyrus fragments of the work, and many references and literary allusions in later authors, especially Cicero, whose own lost dialogue Hortensius was a defense of philosophy modeleld on Aristotle's. (shrink)

Interpretations are generally regarded as the formal representation of the concept of translation.We do not subscribe to this view. A translation method must indeed establish relative consistency or have some uniformity. These are requirements of a translation. Yet, one can both be more strict or more flexible than interpretations are. In this article, we will define a general scheme translation. It should incorporate interpretations but also be compatible with more flexible methods. By doing so, we want to account for methods (...) that seem to imply a sense of translation but are not reducible to interpretations. The main example will be the relative consistent proof between ZF and NBG given by Novak (1950). Further, we will explore a way of combining interpretations. This should account for truth conditions discarded by interpretations in translated theories. (shrink)

In this article, we analyse the ontological import of adding classes to set theories. We assume that this increment is well represented by going from ZF system to NBG. We thus consider the standard techniques of reducing one system to the other. Novak proved that from a model of ZF we can build a model of NBG (and vice versa), while Shoenfield have shown that from a proof in NBG of a set-sentence we can generate a proof in ZF of (...) the same formula. We argue that the first makes use of a too strong metatheory. Although meaningful, this symmetrical reduction does not equate the ontological content of the theories. The strong metatheory levels the two theories. Moreover, we will modernize Shoenfields proof, emphasizing its relation to Herbrands theorem and that it can only be seen as a partial type of reduction. In contrast with symmetrical reductions, we believe that asymmetrical relations are powerful tools for comparing ontological content. In virtue of this, we prove that there is no interpretation of NBG in ZF, while NBG trivially interprets ZF. This challenges the standard view that the two systems have the same ontological content. (shrink)

In this article, instead of taking a particular method as translation, we ask: what does one expect to do with a translation? The answer to this question will reveal, though, that none of the first order methods are capable of fully represent the required transference of ontological commitments. Lastly, we will show that this view on translation enlarge considerably the scope of translatable, and, therefore, ontologically comparable theories.

¿Llegarán los ordenadores a sustituir a los seres humanos? Lo que hasta hace unas décadas parecía una pregunta de ciencia-ficción, es ahora defendido con seriedad por algunos especialistas en inteligencia artificial. El presente articulo dibuja las más importantes líneas de investigación en este campo y las posiciones más relevantes respecto de la relación hombre-maquina pensante. La conclusión que propone el autor supone una decidida apuesta por un humanismo en el que quepa integrar el desarrollo tecnológico sin perder de vista sus (...) innegables implicaciones éticas. (shrink)

Often ZF practice includes the use of the meta-theoretical notion of classes as shorthand expressions or in order to simplify the understanding of conceptual resources. NBG theory expresses formally the internalization of this feature in set theory; in this case, classes, before used metatheoretically, will also be captured by quantifiers of the first order theory. Never- theless there is a widespread opinion that this internalization of classes is harmless. In this context, it is common to refer to the conservativeness of (...) NBG in relation to ZF as a sufficient condition to understand those theories as “equivalent”, attributing a sense of virtuality to the use of classes quantified in NBG. We believe, however, that a technique used to estab- lish relationships between theories is not necessarily neutral in relation to its results - so a conservativeness established through models have different meaning and depth of that rela- tionship established by finitary interpretations. We believe, therefore, that the way in which relationships between theories are established influences the analysis result. In the case of the relationship between NBG and ZF, since NBG is finitely axiomatizible and ZF not, we believe that we have sufficient reasons to assert that the use of different analysis tools may re- veal differences such as expressiveness, ontological commitment and logical conservativeness. Therefore, this project aims to clarify the relationship between these two theories through triangulations between them and the different analysis tools. The use of finitary techniques, in this case, may prove greater expressiveness and ontological commitment of NBG in relation to ZF - relation obscured by an infinitary approach. We believe that, through this research, we can contribute to the debate on the basis of mathematics, denaturalizing the supposedly “equivalent” use of NBG and ZF for this purpose. (shrink)

We propose that Saussure’s signifiers must be processed in the left brain hemisphere (in right handed people) and the signified may be processed in the right. This proposition has consequences for understanding human cognitive phenomena and their pathologies, and can also be related to the passive and active process of thinking, as described by Karl Jaspers. Saussure studied signifiers and their relationships. He left the signified to be studied by psychologists, but there is no consensus about it. According to some (...) linguists, the signified, or the meaning, is the specific activity or succession of bodily states related to each signifier. Learning is the process of linking a signifier (a represented object) to a signified or meaning (a specific activity). However, human beings can represent signifiers autonomously because words and drawings are easily produced with small movements and have syntactic, referential and logical rules of combination. If they are processed in the left hemisphere, the meaning (the signified) is only found when the right hemisphere is reached. The right hemisphere can also work independently, as for instance, when we imagine a story which has to find the words in the left hemisphere. The complex relationship between the hemispheres through the corpus callosum is decisive for telling stories and having self-consciousness. (shrink)

This was a little course of 4 weeks, in which we tried to develop some basic ideas about the proofs related to the properties of logarithms.

Notes from a quick course of 4 weeks, emphasizing the importance of proofs in an introductory course on logarithm, for high school students.

A guide to the first steps into the world of Geometry, Trigonometry and their lines-of-reasoning widely used through the high school and first years of college, in the exact-sciences context.

The narrative develops itself through the perspective of someone who sees Mathematics, Physics, Geometry, etc, as a sequence of logical steps.

Aristotle contrasts episteme and doxa through the key notions of universal and necessary. These notions have played a central role in Aristotle’s characterization of scientific knowledge in the previous chapters of APo. They are not spelled out in APo I.33, but work as a sort of reminder that packs an adequate characterization of scientific knowledge and thereby gives a highly specified context for Aristotle’s contrast between episteme and doxa. I will try to show that this context introduces (...) a contrast in terms of explanatory claims: on the one hand, episteme covers those claims which capture explanatory connections that are universal and necessary and thereby deliver scientific understanding; on the other hand, doxa covers the explanatory attempts that fail at doing so. (shrink)

A predicate logic typically has a heterogeneous semantic theory. Subjects and predicates have distinct semantic roles: subjects refer; predicates characterize. A sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. Traditional term logic, by contrast, has a homogeneous theory: both subjects and predicates refer; and a sentence is true if the subject and predicate name one and the same thing. In this paper, I will examine evidence for ascribing to Aristotle (...) the view that subjects and predicates refer. If this is correct, then it seems that Aristotle, like the traditional term logician, problematically conflates predication and identity claims. I will argue that we can ascribe to Aristotle the view that both subjects and predicates refer, while holding that he would deny that a sentence is true just in case the subject and predicate name one and the same thing. In particular, I will argue that Aristotle's core semantic notion is not identity but the weaker relation of constitution. For example, the predication ‘All men are mortal’ expresses a true thought, in Aristotle's view, just in case the mereological sum of humans is a part of the mereological sum of mortals. (shrink)

Paulo Freire es una figura extraordinaria no solo para la educación brasileña, sino también para la educación latinoamericana y mundial. Sus contribuciones no se limitan a una obra escrita, mucho menos a un método, ni siquiera a un paradigma teórico; también refieren a una práctica y, de un modo más general, a una vida dedicada a la educación, una vida hecha escuela, o sea, una manera de ocupar el espacio de educador que lo llevó de viaje por el mundo (...) entero ‘haciendo escuela. Este libro es por sí mismo un símbolo de lo que un maestro puede provocarnos y del gesto material de dar una respuesta en nombre de sus efectos y afectos. (shrink)

According to Aristotle, the medical art aims at health, which is a virtue of the body, and does so in an unlimited way. Consequently, medicine does not determine the extent to which health should be pursued, and “mental health” falls under medicine only via pros hen predication. Because medicine is inherently oriented to its end, it produces health in accordance with its nature and disease contrary to its nature—even when disease is good for the patient. Aristotle’s politician understands (...) that this inherent orientation can be systematically distorted, and so would see the need for something like the Hippocratic Oath. (shrink)

This paper examines Aristotle’s analysis of unenacted capacities to show the role they play in his discovery of the concept of actuality. I first argue that Aristotle begins Metaphysics IX by focusing on active and passive capacities, after which I discuss Aristotle’s confrontation with the Megarians, the philosophers who maintain that a capacity is present only insofar as it is being enacted. Using Heidegger’s interpretation as a guide, I show that Aristotle’s rejection of the Megarian position (...) leads him to propose that presence cannot be confined to activity. I also argue that this provides the context for Aristotle to realize that the relation between capacity and activity can be generalized as the relation between two ways of being. (shrink)

Para comemorarmos o centenário do patrono da Educação Brasileira, Paulo Reglus Neves Freire, iremos neste breve estudo propor um diálogo entre a pedagogia libertária de Freire e algumas princípios filosóficos que a fundamentam. Inicialmente, investigamos a trajetória histórica do pedagogo nordestino, e os momentos mais marcantes de sua vida cosmopolita. Em segundo, apresentaremos alguns dos principais alicerces de sua metodologia pedagógica, contudo, dada a vasta obra publicada por Freire, qualquer breve revisão será fadada em apenas ser um (...) breve vislumbre da filosofia e pedagogia freireana. Por fim, iremos explorar algumas das origens filosóficas e políticas do conceito de pedagogia libertária, e como essas origens podem ser ligadas a filosofia Anarquista, dado a algumas semelhanças evidentes. A crítica a autoridade injustificada, a amorosa crença do caráter social e solidário do indivíduo humano, e um forte defesa da emancipação humana, algo que só pode ser alcançado através da busca pela liberdade e autonomia do sujeito. Tais paralelos levam à conclusão de que se a pedagogia libertária é um ato de amor, a filosofia libertária também deve ser, pois, ambas se nutrem da mesma fonte, e almejam o mesmo lugar: a emancipação humana. (shrink)

I discuss what Aristotle means when he say that scientific demonstration must proceed from necessary principles. I argue that, for Aristotle, scientific demonstration should not be reduced to sound deduction with necessary premises. Scientific demonstration ultimately depends on the fully appropriate explanatory factor for a given explanandum. This explanatory factor is what makes the explanandum what it is. Consequently, this factor is also unique. When Aristotle says that demonstration must proceed from necessary principles, he means that each (...) demonstration requires the principle that is the necessary one for the fully appropriate explanation of its explanandum. This picture also provides a key to understand Aristotle's thesis that scientific explanation depends on essences: it is the essence of the attribute to be explained that should be stated as the fully appropriate explanatory factor. (shrink)

Aristotle is said to have held that any kind of actual infinity is impossible. I argue that he was a finitist (or "potentialist") about _magnitude_, but not about _plurality_. He did not deny that there are, or can be, infinitely many things in actuality. If this is right, then it has implications for Aristotle's views about the metaphysics of parts and points.

Aristotle’s theory of human happiness in the Nicomachean Ethics explicitly depends on the claim that contemplation (theôria) is peculiar to human beings, whether it is our function or only part of it. But there is a notorious problem: Aristotle says that divine beings also contemplate. Various solutions have been proposed, but each has difficulties. Drawing on an analysis of what divine contemplation involves according to Aristotle, I identify an assumption common to all of these proposals and argue (...) for rejecting it. This allows a straightforward solution to the problem and there is evidence that Aristotle would have adopted it. (shrink)

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

I discuss the argument Aristotle ascribes to Parmenides at Physics 186a23-32. I discuss (i) the reasons why Aristotle considers it as eristic and inconclusive and (i) the solution (lusis) Aristotle proposes against it.

This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".

According to the standard and largely traditional interpretation, Aristotle’s conception of nous, at least as it occurs in the Posterior Analytics, is geared against a certain set of skeptical worries about the possibility of scientific knowledge, and ultimately of the knowledge of Aristotelian first principles. On this view, Aristotle introduces nous as an intuitive faculty that grasps the first principles once and for all as true in such a way that it does not leave any room for the (...) skeptic to press his skeptical point any further. Thus the tradi- tional interpretation views Aristotelian nous as having an internalist justificatory role in Aristotelian epistemology. In contrast, a minority (empiricist) view that has emerged recently holds the same internalist justificatory view of nous but rejects its internally certifiable infallibility by stressing the connection between nous and Aristotelian induction. I argue that both approaches are flawed in that Aristotle’s project in the Posterior Analytics is not to answer the skeptic on internalist justificatory grounds, but rather lay out a largely externalist explication of scientific knowledge, i.e. what scientific knowledge consists in, without worrying as to whether we can ever show the skeptic to his satisfaction that we do ever possess knowledge so defined. (shrink)

Aristotle is history’s most famous and influential proponent of the view that there are exactly five senses. But was he entitled to hold this view, given his other commitments? In particular, was he entitled to treat touch as a single sense, given the diversity of its correlated objects? In this paper I argue that Aristotle wished to individuate touch on the basis of its correlated objects, just as he had the other four senses. I also argue, contrary to (...) what is often supposed, that he was well-placed to do so, given his other commitments and views. (shrink)

Aristotle’s discussions of natural slavery, ‘barbarian kingship’, and the natural characteristics of barbarians or non-Greeks are usually read as calling into question the intellectual, ethical, and political accomplishments of non-Greeks. Such accounts of non-Greek inferiority or inability to self-govern also appear to presuppose a climatic or environmental account that on the whole would imply severe limitations on the possibility of political flourishing for peoples living outside the Greek Mediterranean basin. In light of such accounts, it is somewhat astounding to (...) find Aristotle praising the social and political institutions of Carthage within his discussion of the best constitution in the second book of the Politics. In the 4th century BCE, Carthage (modern day Tunis) was a Phoenician commercial empire that culturally and linguistically was Semitic and clearly non-Greek. That Aristotle contrasts Carthage, a non-Greek polis, favorably with both Sparta and Crete undermines both the claim that Aristotle embraced a categorical opposition between Greeks and non-Greeks and the claim that he was dismissive of the achievements of non-Greeks. (shrink)

I discuss an important feature of the notion of cause in Post. An. 1. 13, 78b13–28, which has been either neglected or misunderstood. Some have treated it as if Aristotle were introducing a false principle about explanation; others have understood the point in terms of coextensiveness of cause and effect. However, none offers a full exegesis of Aristotle's tangled argument or accounts for all of the text's peculiarities. My aim is to disentangle Aristotle's steps to show that (...) he is arguing in favour of a logical requirement for a middle term's being the appropriate cause of its explanandum. Coextensiveness between the middle term and the attribute it explains is advanced as a sine qua non condition of a middle term's being an appropriate or primary cause. This condition is not restricted either to negative causes or to middle terms in second‐figure syllogisms, but ranges over all primary causes qua primary. (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)

Subtractive schooling is a type of pedagogy that subtracts from the student aspects of her identity in order to assimilate and reshape her identity to fit the American mainstream. Here, I question the value of assimilation as it takes place in our public school systems. Currently, immigrant children are often made to feel inadequate for being culturally different. This is detrimental to their development as students given that at their young age they do not yet have the emotional maturity to (...) know that their experience, language and culture are legitimate and valuable. My goal is to shift the focus of subtractive schooling to one that fosters the growth of students through recognition. I suggest that John Dewey’s and Paulo Freire’s pedagogy of recognition is a helpful approach to this problem. Both Dewey and Freire’s pedagogy emphasize recognition as central to their pedagogy. (shrink)

In both Metaphysics Γ 4 and 5 Aristotle argues that Protagoras is committed to the view that all contradictions are true. Yet Aristotle’s arguments are not transparent, and later, in Γ 6, he provides Protagoras with a way to escape contradictions. In this paper I try to understand Aristotle’s arguments. After examining a number of possible solutions, I conclude that the best way of explaining them is to (a) recognize that Aristotle is discussing a number of (...) Protagorean opponents, and (b) import another of Protagoras’ views, namely the claim that there are always two logoi opposed to one another. (shrink)

Both literalism, the view that mathematical objects simply exist in the empirical world, and fictionalism, the view that mathematical objects do not exist but are rather harmless fictions, have been both ascribed to Aristotle. The ascription of literalism to Aristotle, however, commits Aristotle to the unattractive view that mathematics studies but a small fragment of the physical world; and there is evidence that Aristotle would deny the literalist position that mathematical objects are perceivable. The ascription of (...) fictionalism also faces a difficult challenge: there is evidence that Aristotle would deny the fictionalist position that mathematics is false. I argue that, in Aristotle's view, the fiction of mathematics is not to treat what does not exist as if existing but to treat mathematical objects with an ontological status they lack. This form of fictionalism is consistent with holding that mathematics is true. (shrink)

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

In De Anima II.6, Aristotle divides the objects of perception into three kinds: “special perceptibles" (idia aisthêta) such as colours, sounds and flavours, which can be perceived in their own right by only one sense; “common perceptibles" (koina aisthêta) such as shapes, sizes and movements, which can be perceived in their own right by multiple senses; and “incidental perceptibles,” such as the son of Diares, which can be perceived only “incidentally” (kata sumbebêkos). In this paper, I examine this division (...) of perceptibles and consider what it amounts to. First, I argue that Aristotle’s distinction between perceiving something in its own right (kath' hauto) and perceiving it incidentally marks a causal distinction: what is perceived in its own right causes perception as such, whereas what is perceived incidentally coincides with what is perceived in its own right. Second, I argue that for Aristotle special perceptibles, unlike common perceptibles, belong to homogeneous bodies on account of their chemical composition. Finally, I explain the primacy Aristotle assigns to special perceptibles and his claim that perception of them alone is free from error. I conclude with some brief remarks on Aristotle and the primary/secondary quality distinction. (shrink)

This study aims to provide a coherent new interpretation of the notorious anti-hedonism of Speusippus, Plato’s nephew and the second scholarch of the Academy, by reconsidering all the relevant sources concerning his attitude toward pleasure—sources that seem to be in tension or even incompatible with each other. By reassessing Speusippus’ anti-hedonism and Aristotle’s response, it also sheds new light on the Academic debate over pleasure in which he and Aristotle participated: This debate is not merely concerned with the (...) truth and credibility of the arguments for or against hedonism; there are also notable differences among the participants in their understanding of the practical significance of evaluating hedonic experiences. This new interpretation allows us to better understand Aristotle’s selective representation of the intra-school debate and some neglected features of his responses to different interlocutors. (shrink)

Authenticates approximately 500 lines of Aristotle's lost work the Protrepticus (Exhortation to Philosophy) contained in the circa third century AD work by Iamblichus of Chalcis entitled Protrepticus epi philosophian. Includes a complete English translation of the authenticated material.

This is an Editorial Note for the special volume of the journal Manuscrito (42: 4) devoted to Aristotle's theory of demonstration and its logical and metaphysical entanglements, which has been organized by me and Breno Zuppolini (as Guest Editors), with papers authored by Benjamin Morison, Owen Goldin, David Bronstein, Michail Peramatzis, Andrea Falcon, Laura Castelli, Paolo Fait, Joseph Karbowski, Adam Crager, Klaus Corcilius, Robert J. Hankinson, Raphael Zillig and Pieter Sjoerd Hasper.

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 generally ignored feature of Aristotle’s famous function argument is its reliance on the claim that practitioners of the crafts (technai) have functions: but this claim does important work. Aristotle is pointing to the fact that we judge everyday rational agency and agents by norms which are independent of their contingent desires: a good doctor is not just one who happens to achieve his personal goals through his work. But, Aristotle argues, such norms can only be binding (...) on individuals if human rational agency as such is governed by objective teleological norms.
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In Posterior Analytics 71b9 12, we find Aristotle’s definition of scientific knowledge. The definiens is taken to have only two informative parts: scientific knowledge must be knowledge of the cause and its object must be necessary. However, there is also a contrast between the definiendum and a sophistic way of knowing, which is marked by the expression “kata sumbebekos”. Not much attention has been paid to this contrast. In this paper, I discuss Aristotle’s definition paying due attention to (...) this contrast and to the way it interacts with the two conditions presented in the definiens. I claim that the “necessity” condition ammounts to explanatory appropriateness of the cause. (shrink)

This paper discusses the following question: why was the term “dunatos” (“possible”) employed by Aristotle as an alternative label for imperfect syllogisms in his discussion of assertoric syllogistic? My answer ascribes to Aristotle a bottom up perspective, in which he stresses what is necessary in the premise-pairs to attain target conclusions of a given form within a given figure. I argue that “dunatos” is employed by Aristotle to stress that an imperfect syllogism is always one of the (...) possible options to attain a conclusion of a given form within a given figure. I also argue that this picture sheds some light on Aristotle’s clarifications of the final clause in his definition of syllogism. (shrink)

Aristotle holds that individual substances are ontologically independent from nonsubstances and universal substances but that non-substances and universal substances are ontologically dependent on substances. There is then an asymmetry between individual substances and other kinds of beings with respect to ontological dependence. Under what could plausibly be called the standard interpretation, the ontological independence ascribed to individual substances and denied of non-substances and universal substances is a capacity for independent existence. There is, however, a tension between this interpretation and (...) the asymmetry between individual substances and the other kinds of entities with respect to ontological independence. I will propose an alternative interpretation: to weaken the relevant notion of ontological independence from a capacity for independent existence to the independent possession of a certain ontological status. (shrink)