SVIBOR - Project code: 6-01-262

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Project code: 6-01-262


APRIORISM IN MATHEMATICS AND LOGIC


Main researcher: JAKIĆ, MIRKO (79162)


Assistants
Type of research: basic
Duration from: 06/30/91. to 06/30/96.
Papers on project (total): 9
Institution name: Filozofski fakultet, Zadar (70)
Department/Institute: Department of Philosophy
Address: K. P. Krešimira IV, 2
City: 23000 - Zadar, Croatia
Communication
Phone: 385 (0)57 437-447
Summary: Statement is quite an important issue in philosophy. One aspect of the analysis of statement can't be neglected:in sensu divisio vs in sensu compositio, or de re vs de dicto, or analyticity vs synthetics, or apriorism vs aposteriority. In the history of the philosophy similar research has already been practised in Middle Ages and it strongly influenced the thought of Leibnitz refferning to his distinction of the truth of mind and the truth of the fact. Kant's philosophy makes the core of the analysis of statemsnts in general.In contemporary analytical philosophy this field of research makes the part of the apriorism dealing with mathematics and logic. Concerning the mathematics we aim to make the following research:Aprioristic approach to the statement relevant in mathematics - problem of the growth of information in the process of deduction, what kind of information comes out, if it exists? Referential meaning of the statement which appears in mathematics - investigation of arguments. A notion of truth valid in mathematics - whether a realism in mathematics has its cognitive basis and what kind of basis is supposed to be? According to the logic of apriorism we can express the following goals: Apriority of the deductive analysis of the intensional context. Logic and epistemology - what serves as basis? What is role of some singular and general terms in the philosophical logic - what is the role of presupposition?

Keywords: entailment (deduction), apriorism, truth, reference, sense, presupposition, knowledge, information, processing, artificial intelligence, propositional attitude, rationalism;

Research goals: It is our aim to analyse two dominant approaches to apriorism: mathematics-logical and semantic-cognitive. Some basic thesis ought to be analysed: a priori and a posteriori reasoning, esentialism and epistemic context, epistemology as theory of belief changes - basis for logic, pesupposition as a problem of the logic analysis, apriorism vs platonism in mathematics, natural language vs artificial intelligence, cognitive processing vs epistemology. We expect to reach such results which will support the credibility of the mathematics-logical approach with its specific definition of the notions such as truth and apriorism. It is our intention to prove the possibilities of the aprioristic mathematic knowlwdge reached through the organs of senses, too. We support standard logical aproach taking into consideration the research which has alredy been present in the epistemology as theory of belief changes.

COOPERATION - INSTITUTIONS


  1. Name of institution: Faculteit der Wiskunde en Informatica, European Association for Logic, Language and Information (FoLLI)
    Type of institution: State administration
    City: 1018 TV - Amsterdam, Holland
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Last update: 10/22/95
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