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Cognition of the many and mathematical knowledge

The CEU Campus
Monday, April 18, 2016, 5:30 pm – 7:00 pm

In this talk, I will present a conception of natural numbers and clarify a source of knowledge of mathematics, in particular arithmetic.  In my view, natural numbers are properties of a special kind.  They are what I call plural properties, properties that in some sense pertain to the many as such.  The number two, for example, is the numerical property of being two, and this is a property instantiated by any two things albeit not by any one of them.  And we have empirical, and even perceptual, access to some of the numerical properties identified as natural numbers (e.g., being two or being three), just as we have empirical access to some colors or shapes.  We can see that the eggs in front of us are two, that the chairs over there are three, etc.  I will argue that this view of numbers, and of our cognitive access to them, yields a suitable response to the challenge to explain how we can have mathematical knowledge that dates back to Plato and has recently been forcefully presented by Paul Benacerraf.