Saeid Pourdanesh; Mahdi Behniafar
Abstract
This article is concerned of the problem that weather Tarski’s definition of the ‘logical consequence’ in his seminal article ‘On the Concept of Logical Consequence’ (1936), as his article claims, captures the common concept of logical consequence or not. First of all, for ...
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This article is concerned of the problem that weather Tarski’s definition of the ‘logical consequence’ in his seminal article ‘On the Concept of Logical Consequence’ (1936), as his article claims, captures the common concept of logical consequence or not. First of all, for understanding what defect had prevailing approach of logical consequence (proof- theoretical approach) that led him to attempt to present new definition of concept of logical consequence, I introduce proof-theoretical approach to logical consequence and examine its default and then explain two interpretations of his definition of the common concept of logical consequence. the First interpretation is that the common concept of logical consequence is the concept that all of ordinary and non-professional peoples in philosophy, logic and mathematics use. the Second interpretation is that what Tarski means by the common concept of logical consequence is the concept that for professional peoples in logic and mathematics is ‘common’ and already used in axiomatics. I defend the second interpretation and after descriptive-analytic examination of his suggested definition of this concept and presentation of example of it, I finally conclude that Tarski in his attempting for capture of the common concept of logical consequence has succeeded.
Mahdi Behniafar
Abstract
This paper examines two rival versions (normative-axiomatic and psychologistic) about the nature of deduction and its relation with intuition in Descartes' thought. The ideal of the first version is to reduce the role of the faculty of memory and, sometimes, the role of the faculty of imagination in ...
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This paper examines two rival versions (normative-axiomatic and psychologistic) about the nature of deduction and its relation with intuition in Descartes' thought. The ideal of the first version is to reduce the role of the faculty of memory and, sometimes, the role of the faculty of imagination in long chains of deduction due to their fallibility in Descartes' view. Achieving this ideal also depends on the mental training and practicing to place longer inferential chains in a single Cartesian intuition. This version accepts the independence of a logical consequence, considers deduction to be definable on the basis of definiens such as rules of inference and the basic principles of logic, and does not contradict the axiomatic tree of Cartesian knowledge. But the second version essentially sees deduction as nothing more than an intuitive grasping: a simple mental act that is nothing more than a complex intuition of several intuitive things. Therefore, this version considers deduction to have no logical regulations and considers it indefinable based on definiens such as logical principles and rules, and instead places the grasp of a truth that manifests in a kind of psychological clarity experienced by the knowing subject.These two versions try to seem compatible with cognitive objectivity and offer an innate and inadoptable reading of Cartesian logic; But since the second version contradicts both the more fundamental points of Descartes' thought and the independence of logic, this version cannot lead to the cognitive objectivity and innateness of logic in an acceptable way.
