Completion, reduction and analysis: three proof-theoretic processes in aristotle’s<i>prior analytics</i>

Boger, George

doi:10.1080/01445349808837311

Cited by 14 publications

(12 citation statements)

References 17 publications

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“…There is no doubt that detailed information on and descriptions of Aristotelian logic are to be found in several good works. Only some of them are clearly, for example, Boger (1998Boger ( , 2001Boger ( , 2004, Burnett (2004), Gasser (1991), , Miller (1938), Parsons (2008), Smith (1991), or Woods and Irvine (2004), but my arguments in this section will be based mainly (although not exclusively) on that of Parsons (2008). Having said that, a first important point about Aristotelian logic is that, as it is also well known, the syllogisms consist of three sentences: two premises and a conclusion.…”

Section: Aristotelian Logic and Its Valid Categorical Syllogismsmentioning

confidence: 99%

Does Aristotelian logic describe human reasoning? Valid syllogisms and canonical models

López‐Astorga

2016

KJHSS

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In the case of quantified propositions, the mental models theory distinguishes between canonical and noncanonical models. While people identify the canonical models in an immediate, rapid, and easy way, the noncanonical models cannot be detected without reflection and cognitive effort. In this paper, I try to show that all of the valid syllogisms in Aristotelian logic can be considered to be correct by resorting only to the canonical models of their sentences. In this way, I argue that this means that Aristotelian logic can be a useful criterion to explain, describe, and even predict people’s conclusions from quantified assertions.

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Section: Aristotelian Logic and Its Valid Categorical Syllogismsmentioning

confidence: 99%

Does Aristotelian logic describe human reasoning? Valid syllogisms and canonical models

López‐Astorga

2016

KJHSS

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“…Let us mention the project of the Semantic Web, where formal ontologies belong to the main building blocks of a gigantic world-wide information system. This projected system even outstrips the futuristic plans of Leibniz and his characteristica universalis 1 .…”

Section: Introductionmentioning

confidence: 92%

“…In order to fully specify the basic level of Aristotelian logic, we rst dene the syntax of the well formed formulas of his logic: Denition 1.1. (well formed formulas) (1) We are given an innite set T of (nonlogical) constants t 1 , t 2 , t 3 , ....which play the role of categorical terms (e.g. 'man', animal', 'living being', ...).…”

Section: Aristotelian Term Logic: Deductionmentioning

confidence: 99%

“…In the following, we will deal solely with the syntax of the syllogistic logic of Aristotle 3 . To be more specic: We will explore the inner structure of the set of Aristotelian syllogisms a 1 An introduction into the modern theory of formal ontology and some of its relations to ancient logic is Sowa [18]. -The Semantic Web is a project of the W3C (World Wide Web Consortium).…”

Section: Introductionmentioning

confidence: 99%

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Aristotelian Syntax from a Computational–Combinatorial Point of View

Glashoff¹

2005

Journal of Logic and Computation

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This paper translates Aristotelian logic into the sphere of computational-combinatorical research methods. The task is accomplished by formalising Aristotle's logical system in terms of rule-based reduction relations on a suitable basic set, which allow us to apply standard concepts of the theory of such structures (Newman lemma) to the ancient logical system. In this way we are able to reproduce Aristotle's method of deriving syllogisms within a precisely dened formal environment, and we can analyse the structure of the set of syllogistic rules by means of a computer program. Thus we show that Aristotle's syllogistic logic is a formal system of its own, which can be modelled independently of predicate logic and set theory. Our research is very much in the spirit of Smiley's and Corcoran's modelling of Aristotelian logic as a deductional system, and we aim to staying close to Aristotle's own termlogical concepts.

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“…Without such criteria, the idea that the gap between conceptual and technical accounts of validity can be bridged is put under pressure. 3 The paper proceeds as follows. We start in Section 2 with a discussion of Aristotle's goals and results in the Prior Analytics and of Corcoran's interpretation of Aristotle's enterprise.…”

Section: Introductionmentioning

confidence: 99%

Validity, the Squeezing Argument and Alternative Semantic Systems: the Case of Aristotelian Syllogistic

Andrade-Lotero

Novaes

2010

J Philos Logic

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We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran's deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the goal is to offer a general discussion of the relations between informal notions-in this case, an informal notion of deductive validity-and logical apparatuses such as deductive systems and (model-theoretic or other) semantic systems that aim at offering technical, formal accounts of informal notions. Specifically, we will be interested in Kreisel's famous 'squeezing argument'; we shall ask ourselves what a plurality of semantic systems (understood as classes of mathematical structures) may entail for the cogency of specific applications of the squeezing argument. More generally, the analysis brings to the fore the need for criteria of adequacy for semantic systems based on mathematical structures. Without such criteria, the idea that the gap between informal and technical accounts of validity can be bridged is put under pressure.

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Completion, reduction and analysis: three proof-theoretic processes in aristotle’sprior analytics

Cited by 14 publications

References 17 publications

Does Aristotelian logic describe human reasoning? Valid syllogisms and canonical models

Does Aristotelian logic describe human reasoning? Valid syllogisms and canonical models

Aristotelian Syntax from a Computational–Combinatorial Point of View

Validity, the Squeezing Argument and Alternative Semantic Systems: the Case of Aristotelian Syllogistic

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