Berkeley and the Primary Qualities: Idealization vs. Abstraction

In the First of the Three Dialogues, Berkeley’s Hylas, responding to Philonous’s question whether extension and motion are separable from secondary qualities, says:

What! Is it not an easy matter, to consider extension and motion by themselves, . . . Pray how do the mathematicians treat of them?

After some introductory comments I propose to contrast Philonous’s (Berkeley’s) answer to this question, with an alternative, arguing for the following. (1) A distinction, Berkeley would accept should be made between abstraction as Berkeley conceives it in The Introduction to the Principles of Human Knowledge and idealization, exemplified by Galileo’s ignoring friction in formulating the law of free-fall. (2) Idealizations, being neither sensible objects nor Platonic forms, illustrate the way mathematically inclined natural philosophers of the time would treat some sensible objects. (3) Therefore one puzzle Berkeley raises, whether extension can exist without color or tactile qualities, disappears. (4) So too can the resemblance puzzle be easily avoided, that is how ideas (taken here to be sensible objects) can resemble what’s in principle insensible. Lastly I suggest this way of developing Hylas’s above remark is consistent with, though not requiring, Berkeley’s idealist metaphysics.