Category: Mathematics

  • Uninstantiatables in Aristotelian Mathematics

    Any successful Aristotelian foundations of mathematics needs to account for mathematical objects that are uninstantiated and even uninstantiatable. Examples include (1) positive whole (or “natural”) numbers larger than the number of objects in reality, (2) negative numbers, and (3) infinities. Uninstantiated natural numbers As the Aristotelian sees things, we abstract quantity and structure from reality, →

  • Analogy at the foundations of mathematics

    Consider the Benacerraf identification problem in philosophy of maths: there are multiple different ways of “defining” natural numbers in terms of sets, so there is no way of determining which definition is the “correct” one. This is not just a problem about natural numbers but they’re a useful notion to introduce the problem with. In fact, →

  • True mathematical propositions

    Platonists believe that abstract objects such as numbers, colours, sets, ideas and so on are actually existing things (often referred to as the “Platonic realm”). So, if you’re a Platonist and a mathematician, you can take the axioms of maths as descriptions of the kind of objects, found in the Platonic realm, that you want →