The square of opposition and many other geometrical logical figures have increasingly proven to be applicable to different fields of knowledge. This paper seeks to show how Blanché generalizes the classical theory of oppositions of propositions and extends it to the structure of opposition of concepts. Furthermore, it considers how Blanché restructures the Apuleian square by transforming it into a hexagon. After presenting G. Kalinowski’s formalization of Blanché’s hexagonal theory, an illustration of its applicability to mathematics, to modal logic, and (...) to the logic of norms is depicted. The paper concludes by criticizing Blanché’s claim according to which, his logical hexagon can be considered as the objective basis of the structure of the organisation of concepts, and as the formal structure of thought in general. It is maintained that within the frame of diagrammatic reasoning Blanché’s hexagon keeps its privileged place as a “nice” and useful tool, but not necessarily as a norm of thought. (shrink)

This article is intended to examine the structure and scope of the argumentation drawn in Metaphysics Γ 4, 1006a18-b34. As we shall see, though this passage does not bring a complete proof of the Principle of Non-Contradiction, it corresponds to its first step, which consists in determining the conditions of meaning necessary for discourse. That passage encloses in nuce the reasons which underlie Aristotelian conviction con- cerning the conventional nature of names and also brings to light the way this conven- (...) tional nature of names must be understood according to Aristotle. (shrink)

The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz (...) and developed by his student Słupecki, the pioneers of the method, which becomes relevant in modern approaches to logic. (shrink)

تقریباً قاطبة فلاسفة اسلامی به صورت مستقیم یا غیرمستقیم به مسئلة «تشخّص» پرداخته و پاسخ‌هایی را ارائه داشته‌اند و ازین رو، سرگذشت این بحث به طور کلّی در سنّت فلسفی اسلام قابل مطالعة جدّی و تدقیقات همه‌جانبه است، امّا در اینجا قصد ما پرداختن به جنبه‌ای از نقش فارابی در تطوّر و تکامل این سیر تاریخی است، تا از این طریق پرتوهایی بر زوایای مغفول و ناشناخته‌تر سنّت عقلانی مسلمانان افکنده شود. یکی از کسانی که این بحث را بسی بیش (...) از پیش محلّ توجّه متفکّران قرار داد، ملّاصدراست که به تبع فلسفة اصالت وجود خویش، مطالب بدیعی را در باب تشخّص ابراز نمود. یکی از نکات اصلی ملّاصدرا این است که مساوقت «تشخّص» و «وجود» را به فارابی نسبت می‌دهد. در نزد اندیشمندان دورة قدیم یا حتّی دوره معاصر، هیچ‌گاه تردیدی یا مطالعه‌ای در باب صحّت این انتساب صورت نگرفته است. این مقاله بر آن است تا انتساب تقریباً به رسمیّت شناخته شده به فارابی را که از سوی ملّاصدرا صورت گرفته است مطمح‌نظر قرار داده و از رهگذر برخی مستندات متنی و تاریخی نشان دهد که این انتساب می‌تواند تا حدّ زیادی محلّ مناقشه باشد، و حتّی اساساً این مطلب که فارابی بحثی ذیل عنوان «تشخّص» داشته است خود بسیار متزلزل به نظر می‌رسد. (shrink)

In the article we consider the relationship of traditional provisions of basic logical concepts and confront them with new and modern approaches to the same concepts. Logic is characterized in different ways when it is associated with syllogistics (referential – semantical model of logic) or with symbolic logic (inferential – syntactical model of logic). This is not only a difference in the logical calculation of (1) concepts, (2) statements, and (3) predicates, but this difference also appears in the treatment of (...) the calculative abilities of logical forms, the ontological-referential status of conceptual content and the inferential-categorical status of logical forms. The basic markers or basic ideas that separate ontologically oriented logic from categorically oriented logic are the (1) concept of truth, the (2) concept of meaning, the (3) concept of identity, and the (4) concept of predication. Here, this differences are explicitly demonstrated by the introduction of differential terminology. From this differential methodology follows a new set of characterizations of logic. (shrink)

The article develops and justifies, on the basis of the epistemological argumentation theory, two central pieces of the theory of evaluative argumentation interpretation: 1. criteria for recognizing argument types and 2. rules for adding reasons to create ideal arguments. Ad 1: The criteria for identifying argument types are a selection of essential elements from the definitions of the respective argument types. Ad 2: After presenting the general principles for adding reasons (benevolence, authenticity, immanence, optimization), heuristics are proposed for finding missing (...) reasons, for deductive arguments, e.g., semantic tableaux are suggested. (shrink)

"However that may be, Aristotelian syllogistic concerned itself exclusively with monadic predicates. Hence it could not begin to investigate multiple quantification. And that is why it never got very far. None the less, the underlying grammar of Aristotle's logic did not in itself..

How to say no less, no more about conditional than what is needed? From a logical analysis of necessary and sufficient conditions (Section 1), we argue that a stronger account of conditional can be obtained in two steps: firstly, by reminding its historical roots inside modal logic and set-theory (Section 2); secondly, by revising the meaning of logical values, thereby getting rid of the paradoxes of material implication whilst showing the bivalent roots of conditional as a speech-act based on affirmations (...) and rejections (Section 3). Finally, the two main inference rules for conditional, viz. Modus Ponens and Modus Tollens, are reassessed through a broader definition of logical consequence that encompasses both a normal relation of truth propagation and a weaker relation of falsity non-propagation from premises to conclusion (Section 3). (shrink)

The dissertation is an investigation into the structure of Aristotle's modal propositions through careful attention to the text of the Prior Analytics. I take account not only of recent attempts to formalize Aristotle's modal syllogistic but also of the discussion that Aristotle himself provides about modal statements. I provide evidence that his modal propositions are to be construed in a de re manner and then go on to investigate the problems raised by a de re analysis, particularly those problems concerned (...) with Aristotle's modal conversion principles. A large part of my project is to show that these can be given a valid de re analysis that sits well with the results Aristotle sketches. Terms in modal syllogistic premises are shown to be restricted in ways that reflect Aristotle's early metaphysics and notions of predication. (shrink)

Natural syllogisms are expressed in terms of classes and properties of the real world. They exploit a categorisation present in semantic memory that provides a class inclusion structure. they are enthymematic and typically occur within a dialogue. Their form is identical to a formal syllogism once the minor premise is made explicit. It is claimed that reasoners routinely execute natural_syllogisms in an effortless manner based on ecthesis, which is primed by the class inclusion structure kept in long term memory.

Aristotle's General Definition of the Syllogism may be taken as consisting of two parts: the Inferential Conditions and the Final Clause. Although this distinction is well known, traditional interpretations neglect the Final Clause and its influence on syllogistic. Instead, the aforementioned tradition focuses on the Inferential Conditions only. We intend to show that this neglect has severe consequences not just on syllogistic but on the whole exegesis of Aristotle's Prior Analytics I. Due to these consequences, our objective is to analyse (...) the General Definition's Final Clause and its consequences on syllogistic. We propose a reading of the Final Clause as an additional criterion for distinguishing some arguments as properly syllogistic ones and as a main theme which connects all parts of the Prior Analytics I into one coherent piece of work. (shrink)

Aristotle's theory of demonstration, developed in the Posterior Analytics, is not restricted to determining the formal requirements for formulating probative arguments that establish properly the results of scientific investigation. To the probative aspect of demonstration it shall be added its primarily explanatory character, orientated by theses of strong ontological and metaphysical content and involving notions like substance, essence and causation. We shall analyze the relation between those two ranges of Aristotle's philosophy of science and investigate how the formal features of (...) demonstration maintain an affinity with the metaphysical background to which scientific activity is conditioned. (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 studies syllogistic argumentation in Sophistical Refutations and Prior Analytics. In the latter he focuses on the formal and syntactic character of arguments and treats the sullogismoi and non-sullogismoi as argument patterns with valid or invalid instances. In the former Aristotle focuses on semantics and rhetoric to study apparent sullogismoi as object language arguments. Interpreters usually take Sophistical Refutations as considerably less mature than Prior Analytics. Our interpretation holds that the two works are more of a piece than previously believed (...) and, indeed, that Aristotle's treatment of fallacious reasoning presupposes the results of the formal theory. (shrink)

While the nature of warrants is unclear in both Toulmin’s Uses of Argument and in textbook pedagogy based on it, the theory of non-monotonic reasoning could clarify and enhance our understanding of warrants.

We give a simple definition of validity for syllogisms involving necessary and assertoric premises which validates all and only the Aristotelian apodeictic syllogisms.

This paper presents two systems of natural deduction for the rejection of non-tautologies of classical propositional logic. The first system is sound and complete with respect to the body of all non-tautologies, the second system is sound and complete with respect to the body of all contradictions. The second system is a subsystem of the first. Starting with Jan Łukasiewicz's work, we describe the historical development of theories of rejection for classical propositional logic. Subsequently, we present the two systems of (...) natural deduction and prove them to be sound and complete. We conclude with a ‘Theorem of Inversion’. (shrink)

In the paper we examine the method of axiomatic rejection used to describe the set of nonvalid formulae of Aristotle's syllogistic. First we show that the condition which the system of syllogistic has to fulfil to be ompletely axiomatised, is identical to the condition for any first order theory to be used as a logic program. Than we study the connection between models used or refutation in a first order theory and rejected axioms for that theory. We show that any (...) formula of syllogistic enriched with classical connectives is decidable using models in the domain with three members. (shrink)

This note considers deductive systems for the operator a of unprovability in some particular propositional normal modal logics. We give thus complete syntactic characterization of these logics in the sense of Lukasiewicz: for every formula  either `  or a  (but not both) is derivable. In particular, purely syntactic decision procedure is provided for the logics under considerations.