Hupo in the Prior Analytics: a note on Disamis XLL

This is a brief note that looks at the problem presented by the traditional rendering of the modal syllogism Disamis XLL. In two recent articles, I argue that we should not attribute Disamis XLL to Aristotle. The purpose of this note is to provide textual support for my claim.     

Proof by Assumption of the Possible in Prior Analytics, 1.15; How Not to Blend Modal Frameworks

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.     

Aristotle's Endoxa and Plausible Argumentation

Aristotle's conception and use of ta endoxa are key points to our understanding of Aristotelian dialectic. But, nowadays, they are not of historical or hermeneutic importance alone, as, in Aristotle's treatment of endoxa, we still see a relevant contribution to the modern study of argumentation. I propose here an interpretation of endoxa to that effect: namely, as plausible propositions. This version is not only defensible in the Aristotelian context, it may also shed new light on some of his assumptions and methodological shortcomings – e.g. concerning the 'plausible/implausible' pair –; finally, it will even enable us to show certain basic hints and guidelines, advanced by Aristotle's study of endoxa, which still serve nowadays to orientate our studies of argumentation from the angle of a theory of plausible argument currently under construction. These hints and guidelines suggest a pragmatic, gradual and comparative discursive concept of plausibility, and point, in particular, towards the reasonable dealing with, and weighing up of, differences of opinion within this frame of reference.     

Statistical inference and Aristotle's Rhetoric

Formal logic operates in a closed system where all the information relevant to any conclusion is present, whereas this is not the case when one reasons about events and states of the world. Pollard and Richardson drew attention to the fact that the reasoning behind statistical tests does not lead to logically justifiable conclusions. In this paper statistical inferences are defended not by logic but by the standards of everyday reasoning. Aristotle invented formal logic, but argued that people mostly get at the truth with the aid of enthymemes—incomplete syllogisms which include arguing from examples, analogies and signs. It is proposed that statistical tests work in the same way—in that they are based on examples, invoke the analogy of a model and use the size of the effect under test as a sign that the chance hypothesis is unlikely. Of existing theories of statistical inference only a weak version of Fisher's takes this into account. Aristotle anticipated Fisher by producing an argument of the form that there were too many cases in which an outcome went in a particular direction for that direction to be plausibly attributed to chance. We can therefore conclude that Aristotle would have approved of statistical inference and there is a good reason for calling this form of statistical inference classical.     

Computation of Aristotle's and Gergonne's syllogisms

A connection between Aristotle's syllogistic and the calculus of relations is investigated. Aristotle's and Gergonne's syllogistics are considered as some algebraic structures. It is proved that Gergonne's syllogistic is isomorphic to closed elements algebra of a proper approximation relation algebra. This isomorphism permits to evaluate Gergonne's syllogisms and also Aristotle's syllogisms, laws of conversion and relations in the square of oppositions by means of regular computations with Boolean matrices.     

Aristotle's Syllogistic and Core Logic

I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain how the syllogistic is a fragment of my (constructive and relevant) system of Core Logic. Then I introduce my main innovation: the use of binary quantifiers, governed by introduction and elimination rules. The syllogisms in all four figures are re-proved in the binary system, and are thereby revealed as all on a par with each other. I conclude with some comments and results about grammatical generativity, ecthesis, perfect validity, skeletal validity and Aristotle's chain principle.     

亚里士多德的心灵哲学

亚里士多德是一个广义的物活论者(Animist),与其他物活论者不一样,他不认为灵魂存在于万物中,而认为灵魂只存在于有生命的活的事物中.他的灵魂概念与我们现在的观点也不一样,他认为植物是有灵魂的.灵魂(soul)在希腊语中是"psyche",即生命的原则或生命的原理,在拉丁语中被转译为"anima',它是使活的事物与非活的事物相区别的东西.他又把它叫做"生命的原理"(entelechy).     

Aristotle's Thesis between paraconsistency and modalization

If the arrow → stands for classical relevant implication, Aristotle's Thesis ¬(A→¬A) is inconsistent with the Law of Simplification (AB)→B accepted by relevantists, but yields an inconsistent non-trivial extension of the system of entailment E. Such paraconsistent extensions of relevant logics have been studied by R. Routley, C. Mortensen and R. Brady. After examining the semantics associated to such systems, it is stressed that there are nonclassical treatments of relevance which do not support Simplification. The paper aims at showing that Aristotle's Thesis may receive a sense if the arrow is defined as strict implication endowed with the proviso that the clauses of the conditional have the same modal status, i.e. the same position in the Aristotelian square. It is so grasped, in different form, the basic idea of relevant logic that the clauses of a true conditional should have something in common. It is proved that thanks to such definition of the arrow Aristotle's Thesis subjoined to the minimal normal system K yields a system equivalent to the deontic system KD.     

Aristotle's Four Causes of Action

Aristotle's typical procedure is to identify four causes of natural changes. Intentional action, a natural change, has standardly 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.