Citations of:
Add citations
You must login to add citations.


I discuss in this paper the six requirements Aristotle advances at Posterior Analytics A2, 71b2033, 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. 

We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, observationalism, (...) 



The syllogistic mnemonic known by its first two words Barbara Celarent introduced a constellation of terminology still used today. This concatenation of nineteen words in four lines of verse made its stunning and almost unprecedented appearance around the beginning of the thirteenth century, before or during the lifetimes of the logicians William of Sherwood and Peter of Spain, both of whom owe it their lasting places of honor in the history of syllogistic. The mnemonic, including the theory or theories it (...) 

In this paper we provide an interpretation of Aristotle's rule for the universal quantifier in Topics Θ 157a34–37 and 160b1–6 in terms of Paul Lorenzen's dialogical logic. This is meant as a contribution to the rehabilitation of the role of dialectic within the Organon. After a review of earlier views of Aristotle on quantification, we argue that this rule is related to the dictum de omni in Prior Analytics A 24b28–29. This would be an indication of the dictum’s origin in (...) 

I argue that, in the Prior Analytics, higher and above the wellknown ‘reduction through impossibility’ of figures, Aristotle is resorting to a general procedure of demonstrating through impossibility in various contexts. This is shown from the analysis of the role of adunaton in conversions of premises and other demonstrations where modal or truthvalue consistency is indirectly shown to be valid through impossibility. Following the meaning of impossible as ‘nonexistent’, the system is also completed by rejecting any invalid combinations of terms (...) 

Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the ExistentialImport Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existentialimport predicate (...) 

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 prooftheoretically 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 firstorder logic, and the usual formalizations of Aristotle's sentenceforms. I explain how the syllogistic is (...) 



This expository paper on Aristotle’s prototype underlying logic is intended for a broad audience that includes nonspecialists. It requires as background a discussion of Aristotle’s demonstrative logic. Demonstrative logic or apodictics is the study of demonstration as opposed to persuasion. It is the subject of Aristotle’s twovolume Analytics, as its first sentence says. Many of Aristotle’s examples are geometrical. A typical geometrical demonstration requires a theorem that is to be demonstrated, known premises from which the theorem is to be deduced, (...) 