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By Heike Wiese

What constitutes our inspiration of numbers and allows us to paintings with them the best way we do? Which psychological colleges give a contribution to our take hold of? What features can we percentage with different species, and which of them are particular to us? This ebook addresses those inquiries to show that language performs a vital position within the improvement of systematic quantity ideas. It analyzes the connection among numerical pondering and the human language school, delivering mental, linguistic, and philosophical views on numbers, their evolution, and improvement in little ones.

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Extra resources for Numbers, language, and the human mind

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The numerical statement is meaningful if the number sequence from 1 to n has the same cardinality as the set s, that is, if there is a one-to-onemapping between the numbers from 1 to n and the elements of s. Number assignments including measure units (direct and indirect measurement) can be defined as a special case of cardinal number assignments. The crucial property of numbers is their sequential order within a progression: starting with 1, each element of the number sequence N has a fixed position within N, and therefore terminates a unique initial sequence of N.

Accordingly, any number assignment where the order of the numbers reflects the order of our empirical objects would be a meaningful ordinal assignment. However, conventionally we use the sequence of natural Numbers and objects 37 8 3 7 Figure 16 Nominal number assignment (labelling of football players) numbers starting with 1 as our numerical relational structure, and this is what I will assume for the following discussion. n o m i n a l n u m b e r a s s i g n m e n ts : ‘ bu s # 3’ , ‘f o ot b a l l p l aye r # 3 ’ In nominal number assignments we use numbers as labels for empirical objects.

These requirements make sure that our empirical relational structure is a sequence. Again, like the number line, this sequence has to be a progression; it must have an initial element that will receive the 1 in our number assignment. In our runner example, this element was Charles. Obviously, it would not do to define him as the ‘first’ runner, because that would be kind of circular (‘The first runner is the one that gets the number 1’). Instead, we can identify him with respect to our ordering relation, ‘faster than’: Charles is the fastest runner in our race; in other words, there is no runner who is faster than Charles.

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