Mathematical 'objects' c/o TPM

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"Fine's position is called 'procedural postulationism'. When we postulate, when we do a certain sort of reflection on mathematical objects, our acts in a sense bring those objects into existence. But what's going on is not quite like author imagining a character. It's more like intellectually bumping into something, where the bumping and the something result in a new grip on mathematical objects. But he suggests that the objects, once we have them, in a  sense have always been there. I ask him how he makes sense of the idea." p.23.

"The right picture isn't one in which we just create the objects the way you might create a statue, bring into existence something that didn't exist before. What you're doing when you postulate is extending the domain of quantification, you're extending the objects about which you're talking. It's not that you're bringing them into existence. You're targeting the domain of quantification, a domain of discourse which hadn't been previously targeted. These objects are themselves mathematical objects that don't exist in time, in fact, if they exist they necessarily exist. So it's not that they previously didn't exist, it's just that you now managed to target a new domain of eternal, necessary existence." p.23.

"Logical and philosophical investigations into parts and wholes have been dominated by a certain tradition that goes under the name 'mereology'. ... I hold the view according to which there are many different ways in which parts can form wholes, and many of those ways are not mere sums. I think it's unfortunate for philosophy that philosophers focus so much on mereology as traditionally conceived."

"But how can a thing be more than the sum of its parts? Where does the more come from? Fine explains, 'If you take a tower of blocks that a child might make, that's composed of the blocks, but it's not a mere sum of the blocks. The blocks have to be in a certain order, one has to be on top of the other. I'm inclined to think of that tower as the blocks in a certain arrangement. So when you think of it in that way it's not a mere sum of the blocks. If you want to actually understand mereological structure as it's presented to us, it's very rare that we're going to be talking about mere sums. We're going to be talking about objects structured in a certain way to constitute a whole.'" p.25.

Garvey, J., with Fine, K. The silence of the lambdas, The Philosopher's Magazine, 4th Quarter 2011. 55: pp.19-27

https://as.nyu.edu/faculty/kit-fine.html