For parents who are philosophers and/or cognitive scientists, children are a constant source of wonderment. Also, the temptation of drawing tenuous one-shot inductions on child cognition on the basis of conversations with one's children is very high (although, if properly cultivated, as in Piaget's case, it can lead to some genuine insights). So what I write here should be taken too seriously, but here goes.
Today I was talking to my daughter about the existence of numbers. She is currently seven, and has been for some years intrigued by numbers and their properties. She was demonstrating her abilities for calculating big numbers today by saying things like "one billion plus two billion is three billion". So I challenged her and asked: "can you be sure about that?" "Yes, of course, she replied, it's just one plus two and a bunch of zeroes". "But nobody has counted it", I countered. "It doesn't matter", she said, "because in maths the numbers always add up, no matter what people do". So, intrigued, I asked, "Do you think then that even if there were no people, 2 + 2 would still be 4"? "Of course", she replied. "And very long ago", I continued, "When two dinosaurs met two dinosaurs, was the result 4 dinosaurs?" (she knows that humans and dinosaurs did not coexist). "Of course", she said: "numbers exist, it doesn't matter what humans think about them". (The example of the dinosaurs comes, I think from a book by Sal Restivo, but I can't find the reference anymore).
Perhaps children are intuitive mathematical platonists? This is not as far-fetched as it may sound at first. After all, developmental psychologists argue that children are also intuitive essentialists (see e.g., work by Susan Gelman) and entertain something akin to Aristotelian teleology, as studies by Deb Kelemen point out. If that's the case, Platonism might be more intuitive than other positions on the ontology of mathematical objects, such as fictionalism.
Recent Comments