Embedding: Multi-purpose Device for Understanding Mathematics and its Development, or Empty Generalization?

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Abstract

“Embedding” as a technical concept comes from linguistics, more precisely
from grammar. The present paper investigates whether it can be applied
fruitfully to certain questions that have been investigated by historians (and
sometimes philosophers) of mathematics:
1. The construction of numeral systems, in particular place-value and quasi
place-value systems.
2. The development of algebraic symbolisms.
3. The discussion whether “scientific revolutions” ever take place in
mathematics, or new conceptualizations always include what preceded
them.
A final section investigates the relation between spatial and linguistic
embedding and concludes that the spatio-linguistic notion of embedding can
be meaningfully applied to the former two discussions, whereas the apparent
embedding of older within new theories is rather an ideological mirage.
Original languageEnglish
JournalGanita Bharati
Volume38
Issue number1
Pages (from-to)1-29
ISSN0970-0307
Publication statusPublished - 2016

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