The Logical Syntax of a Numeral. A Study in Cognitive Science, Part I

• Authors: Wojciech Krysztofiak

Title variants

PL

Logiczna składnia liczebnika. Studium kognitywistyczne. Część I

EN

The Logical Syntax of a Numeral. A Study in Cognitive Science, Part I

• Languages of publication: PL

Abstracts

PL

In the paper there are presented main assumptions underlying the construction of theoretic models of mental processes of numeral reference in mathematical practice which comprises such abilities as counting, solving story-tasks, estimating cardinalities and comparing magnitudes. Numerals are understood as any expressions which enable mind to refer to numbers, cardinalities and magnitudes. The main research question formulated in the article sounds: What cognitive processes do there occur in the mind during execution of various numeral acts of reference? In the first section there is presented the Jumblese quasi-paradox of the surface syntactic structures of numerals. The solution of this quasi-paradox is based on the assumption that numerals possess hidden deep structures alongside their surface structures. The second section comprises syntactic analyses of deep structures of numerals. They are understood as grammatical structures of mental representations of numerals, encoded in mind. The main conclusion of this section is a contention according to which deep structures of numerals are encoded in mind with the help of special functors reflecting the property called positionality of digital record. The third chapter is an analysis of numerals and their deep structures on the ground of categorial grammar. This section results in the construction of the categorial model of deep structures of numerals with help of Ajdukiewicz’s indices of syntactic categories. In the last part there are specified basic mental mechanisms of processing representations of numerals with respect to their deep structures. Results of the paper are intended as an intuitive basis for formal theory of numerals’ syntax. They will be presented in the next paper.

• Publisher: University of Warsaw, Institute of Philosophy
• Journal: Filozofia Nauki
• Year: 2012
• Volume: 20
• Issue: 1
• Pages: 59-91

Dates

published

2012-03-01

Contributors

author

Wojciech Krysztofiak