On Social Statement Spaces

On Social Statement Spaces In this fundamental draft we shall introduce the concept of social propositional spaces as a general notion of social science and in particular language, logic and methodology. This should help us bridge an old gap between extension and cognition, or said in more specific words, between space as conceived in mathematics or physics and space as is brought in by social location, by the meaning of predicates, their explanation and logic. 1 We shall not rely on the idea of factor analysis where some “main components” are fit into the data. Because the notion of euclidean normalization and orthogonality, in this context, is a bit artificial. We first show how combinatorial manifolds of statements can be represented in finite vector spaces over the Galois field F 2. This space which we denote as logic statement space can be spanned by generators of alternating codes. In this way the old concepts of truth tables and interaction attributes can be linked to informatics and in particular code theory and geometry. Extending the logic statement space onto a real vector space by mapping units of the finite rings onto units of the real rings we obtain logistic statement spaces. It turns out that vectors in logistic statement spaces represent cross-tables of logits connected with logistic regression analysis. As a completion of the theory we show that the logit is the first derivative of entropy with respect to probability. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

On Social Statement Spaces

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2005 by Springer
Subject
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1007/s11135-004-5007-9
Publisher site
See Article on Publisher Site

Abstract

In this fundamental draft we shall introduce the concept of social propositional spaces as a general notion of social science and in particular language, logic and methodology. This should help us bridge an old gap between extension and cognition, or said in more specific words, between space as conceived in mathematics or physics and space as is brought in by social location, by the meaning of predicates, their explanation and logic. 1 We shall not rely on the idea of factor analysis where some “main components” are fit into the data. Because the notion of euclidean normalization and orthogonality, in this context, is a bit artificial. We first show how combinatorial manifolds of statements can be represented in finite vector spaces over the Galois field F 2. This space which we denote as logic statement space can be spanned by generators of alternating codes. In this way the old concepts of truth tables and interaction attributes can be linked to informatics and in particular code theory and geometry. Extending the logic statement space onto a real vector space by mapping units of the finite rings onto units of the real rings we obtain logistic statement spaces. It turns out that vectors in logistic statement spaces represent cross-tables of logits connected with logistic regression analysis. As a completion of the theory we show that the logit is the first derivative of entropy with respect to probability.

Journal

Quality & QuantitySpringer Journals

Published: Oct 19, 2004

References

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