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Termin liczba jako nazwa i jako funktor. Arytmetyka liczb naturalnych z liczbą-funktorem jako terminem pierwotnym

100%
Wojciechowski E.
Kwartalnik Filozoficzny
|
2020
|
vol. 48
|
issue 3
137-154
EN
The distinction between number as a name and number as a functor alludes to the important Zahl-Anzahl distinction emphasised by Gottlob Frege. We start from Peano's expression of the axiomatics of natural numbers in the framework of Leśniewski's elementary ontology (OE). Next, we proceed to the enrichment of elementary ontology with Frege's predication scheme (OEsub) and propose such formulation of this axiomatics in which the primitive term natural number (N) is replaced by the term number-functor (A). The nominal constants natural number (N) and zero (0) as well as the functor of the successor (S) are defined here.
2

Hylemorphism within a new formal framework

86%
Wojciechowski E.
Kwartalnik Filozoficzny
|
2020
|
vol. 48
|
issue 4
213-227
EN
In Aristotle's philosophy the term form has multiple meanings. The object of the present analysis is the notion of form in its static meaning. The term form in this meaning appears in two syntactically different propositional phrases: (1) x is a form of a, where a is a proper name or a common name and (2) x is a form of y, where is a form is a relative expression. A conversion of x is a form of y is y is a matter of x. The term matter from the equivalent of phrase (2) is treated here as logically primal and characterised axiomatically (B1-B4). These axioms are an interpretation of Frege's predication scheme (with specific axioms A1-A4). Our base system is elementary ontology. The term form which appears in phrase (1) is a functor in the substantial meaning. The theory of hylemorphism (HM) proposed here can be extended to include the postulate of singularity or non-singularity of the substantial form. The functor of form (F) in the abstract sense is introduced by definition. The expression xεFa is a formal equivalent of phrase (1). The special cases of form in this sense, which are defined, are individual form and species form.
3
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ONTOLOGIA ELEMENTARNA I KLASYCZNY RACHUNEK RELACJI

72%
Wojciechowski E.
Roczniki Filozoficzne
|
2013
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vol. 61
|
issue 2
27-38
EN
The notion of relation is one of the most important concepts present in our language. This study propose some extension of elementary ontology (OE) for relational variables and defining in his framework the concepts of the classical calculus of relations. Such enriched elementary ontology (OER) is a better tool for the analysis of natural language. It is shown that syllogistic with the negative terms enriched by so called oblique syllogisms (SNU with the axioms C1–C5) is a fragment of OER system (Theorem 1). The OER system is enriched next with individual variables (a,b,c) and by assuming the individual term referentiality (axiom A2) we obtain OER* system. The Proof that the classical calculus of relations (KRR) is a part of the system OER* (Theorem 2) is given.
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