### 1.1 Problematic Platonism

Rational metaphysics is

 1. a priori - no sense experience or experiment needed,
 2. necessary - could not have been otherwise,
 3. about abstract objects.

Mathematics ticks all these. :)

> the knowledge is concerned with objects that
> are not located in space or time, and that don't participate in
> causal relationships. Such objects are said to be *abstract*."

This is different from the definition: abstract object is what is the result of abstraction, i.e. removing unnecessary details.


### 1.5 The integration challenge

> the challenge is to integrate
> the metaphysics of mathematics (namely, what mathematics is about)
> with its epistemology (namely, how we form our mathematical beliefs)

### 2.4 How do we grasp mathematical objects?

> to abstract is to "extract" from a class of
> things a feature that these things have in common when they are
> equivalent in some respect.