Numbers, Language, and the Human Mind

Numbers, Language, and the Human Mind

Numbers, Language, and the Human Mind

Numbers, Language, and the Human Mind

Synopsis

What constitutes our concept of numbers and makes it possible for us to work with them the way we do? Which mental faculties contribute to our grasp? What qualities do we share with other species, and which ones are specific to us? This book addresses these questions to reveal that language plays a crucial role in the development of systematic number concepts. It analyzes the relationship between numerical thinking and the human language faculty, providing psychological, linguistic, and philosophical perspectives on numbers, their evolution, and development in children.

Excerpt

Numbers play a central role in our lives. Numbers and number expressions arise early both in human history and in the individual development of children. Numerical notations existed long before the invention of script, and archaeological evidence suggests that at least 30,000 years ago our ancestors used notches as primitive representations for collections of things. Newborns in their first week of life can already distinguish two from three objects, and children start using number words and engage in counting games as early as two years of age. in our everyday life we use numbers in a wide range of different contexts; we employ them not only for counting, but also for telling the time, on price tags, for football scores, to rank runners in a marathon, for bus lines, as telephone numbers, in lotteries, and so on. and in one way or the other, numbers play a role in the spiritual contexts of most cultures. They are employed in fortune-telling, and in many cultures certain numbers, say 13, are associated with bad luck, or certain kinds of number assignments fall under taboo restrictions, for instance, it might be considered imprudent to count people or to count your own children.

What makes numbers such a fascinating topic? I think the fascination that numbers have for us arises from their great significance as reasoning devices, as powerful and highly flexible mental tools. Here is a passage by the nineteenth- to twentieth-century mathematician Richard Dedekind that emphasises the role that this concept of numbers plays in our thinking:

Of all the devices the human mind has created to make its life — that is, the task of reasoning — easier, there is none that has such a great effect and is so indivisibly connected to its innermost nature, as the concept of number …Every thinking human, even if he does not feel it clearly, is a numerical being.

What is it that makes us 'numerical beings'? What does our concept of number encompass? One aspect that initially comes to mind is cardinality, the property that we ask for in 'How many?' We assess this property in

Richard Dedekind, in Ewald (1996: vol. 2, p. i), emphasis in the original (my translation, H. W.).

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