Beyond Wittgenstein's remarks on the foundation of mathematics: explication of Piaget's suggestion of a biological foundation (Q1343402)

What is a number that we may know it and knowing it, number? The author briefly discusses Wittgenstein's Use Theory of number [see e.g., Remarks on the foundations of mathematics, Basil Blackwell, Oxford, 1964] as a point of entry into an inquiry on a physico-biological theory of number broadly outlined earlier by J. Piaget. Then he examines the properties of a neural network model for explication of simple addition within a biological context. Note that C. S. Peirce already used a burn-in theory to account for any animal habit (e.g., action, response or use) in biological species and developed a deep pragmatic theory of meaning in an ordinal framework well appreciated by W. McCulloch, among many others [see, e.g., the reviewer's report, Philosophical comments on the philosophies of Charles Sanders Peirce and Ludwig Wittgenstein, EERL, University of Illinois, Urbana, Illinois (1961; Zbl 0121.252)]. Finally, the author interprets 27 deep logico-philosophical questions posed by Wittgenstein within the author's reference frame of the biological model and concludes that numbers are particular because of their utter simplicity. However, in the reviewer's opinion, unresolvable perplexities still arise since small numbers have far too many jobs to do (uses)!