I defend an interpretation of Aristotle’s Posterior Analytics Book I which distinguishes between two projects in different passages of that work: (i) to explain what a given science is and (ii) to explain what properly scientific knowledge is. I present Aristotle’s theory in answer to ii, with special attention to his definition of scientific knowledge in 71b9-12 and showing how this is developed on chapters I.2-9 and I.13 into a solid Theory of Scientific Demonstration. The main point of this theory (...) is that demonstrations need to capture relevant explanations. Some formal requirements of the demonstration (as the syllogistic structure and coextension between terms) are unfoldings of the main project, i.e., to capture and present properly relevant causal-explanatory relations. (shrink)

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)

In Metaphysics M.2, 1077a9-14, Aristotle appears to argue against the existence of Platonic Forms on the basis of there being certain universal mathematical proofs which are about things that are ‘beyond’ the ordinary objects of mathematics and that cannot be identified with any of these. It is a very effective argument against Platonism, because it provides a counter-example to the core Platonic idea that there are Forms in order to serve as the object of scientific knowledge: the universal of which (...) theorems of universal mathematics are proven in Greek mathematics is neither Quantity in general nor any of the specific quantities, but Quantity-of-type-x. This universal cannot be a Platonic Form, for it is dependent on the types of quantity over which the variable ranges. Since for both Plato and Aristotle the object of scientific knowledge is that F which explains why G holds, as shown in a ‘direct’ proof about an arbitrary F (they merely disagree about the ontological status of this arbitrary F, whether a Form or a particular used in so far as it is F), Plato cannot maintain that Forms must be there as objects of scientific knowledge - unless the mathematics is changed. (shrink)

In this paper I examine how Aristotle thinks syllogisms establish existence. I argue against the traditional "Instantiation" reading and in favor of an alternative "causal" or "structural" account of existential syllogisms. On my interpretation, syllogisms establish the existence of kinds by revealing that they are per se unities whose features are causally underwritten by a single cause/essence. They do so by tracing correlations between propria--peculiar, coextensive features--of the kind in question.

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 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.

Aristotle claims that the object of scientific knowledge cannot be otherwise, and at Posterior Analytics I-8 he adds that there is no scientific knowledge of corruptible objects. These claims have been traditionally understood in terms of a strict requirement of eternal existence: objects of genuine scientific knowledge must be eternal in the sense that they must exist eternally. Sometimes the "eternal existence" is taken by scholars as equivalent to the timeless truth of universal propositions. In this paper, I offer an (...) alternative view and discuss Aristotle’s argument in Posterior Analytics I-8. (shrink)

This paper attempts to clarify the nature and the importance of a third kind of sophistic argument that is not always found in the classification of those arguments in the secondary literature. An argument of the third kind not only is a valid one, but is also constituted of true propositions. What makes it a sophistic argument is the fact that it produces a false semblance of scientific explanation: its explanation seems to be appropriate to the explanandum without being so. (...) Evidence from this kind of argument comes from Sophistic Refutations 11, and Brison’s attempt to square the circle should be counted as one of its instances. (shrink)

In a series of recent papers, Emily Katz has argued that on Aristotle's view mathematical sciences are in an important respect no different from most natural sciences: They study sensible substances, but not qua sensible. In this paper, I argue that this is only half the story. Mathematical sciences are distinctive for Aristotle in that they study things ‘from’, ‘through’ or ‘in’ abstraction, whereas natural sciences study things ‘like the snub’. What this means, I argue, is that natural sciences must (...) study properties as they occur in the subjects from which they are originally abstracted, even where they reify these properties and treat them as subjects. The objects of mathematical sciences, on the other hand, can be studied as if they did not really occur in an underlying subject. This is because none of the properties of mathematical objects depend on their being in reality features of the subjects from which they are abstracted, such as bodies and inscriptions. Mathematical sciences are in this way able to study what are in reality non-substances as if they were substances. (shrink)

Most interpretations of Aristotle’s Posterior Analytics believe that the term ‘ameson’ is used to describe the principles or foundations of a given system of justification or explanation as epistemically prior to or more fundamental than the other propositions in the system. Epistemic readings (as I shall call them) arguably constitute a majority in the secondary literature. This predominant view has been challenged by Robin Smith (1986) and Michael Ferejohn (1994; 2013), who propose interpretations that should be classified as non-epistemic according (...) to the definition above. My aim in this article is purely negative. I intend to show that these non-epistemic interpretations are liable to serious objections and are in conflict with some important features of Aristotle’s theory of demonstration. (shrink)

I show that in his De motu animalium Aristoteles proposes a teleology of the practical on the most general zoological level, i.e. on the level common to humans and self-moving animals. A teleology of the practical is a teleological account of the highest practical goals of animal and human self-motion. I argue that Aristotle conceives of such highest practical goals as goals that are contingently related to their realizations. Animal and human self-motion is the kind of action in which certain (...) state of affairs that realize values are mechanized. (shrink)

I discuss in this paper the six requirements Aristotle advances at Posterior Analytics A-2, 71b20-33, for the premisses of a scientific demonstration. I argue that the six requirements give no support for an intepretation in terms of “axiomatization”. Quite on the contrary, the six requirements can be consistently understood in a very different picture, according to which the most basic feature of a scientific demonstration is to explain a given proposition by its appropriate cause.

Three different ways in which systems of axioms can contribute to the discovery of new notions are presented and they are illustrated by the various ways in which lattices have been introduced in mathematics by Schröder et al. These historical episodes reveal that the axiomatic method is not only a way of systematizing our knowledge, but that it can also be used as a fruitful tool for discovering and introducing new mathematical notions. Looked at it from this perspective, the creative (...) aspect of axiomatics for mathematical practice is brought to the fore. (shrink)