Explain and analyze Berkeley’s arguments for the rejection of abstract ideas in the introduction to the Principles. What motivates this rejection and what role does it play in his rejection of materialism?

Abstract general ideas are arrived at through irresponsible use of language. Designating a word as a ‘sign’ for an assortment of similar objects, particular ideas of those objects, allegedly taxonomizes all particulars circumscribed by [the sign] as an abstract general idea. That is to say, all the particulars have a likeness in which they all partake.

Yet, each particular cannot be entirely abstracted from, and thus the idea that the word signifies might refer to a strong resemblance of particulars, viz. a general idea, but conceiving certain qualities as inseparable from any particular idea is always ineluctable.

Insofar as knowledge is about universal notions, the notions are general but not abstracted away from in the manner premised by Locke. This universal notion bears a relation to all the particulars it signifies insofar as they are sufficiently represented [by it].

Names or notions such as 'man’, 'horse’, 'car’, are not abstract general ideas, for one always bears a particular idea in mind when reflecting on the universality. Thus the reflection on an idea is always of a particular idea, with particular qualities. You cannot, for instance, have a notion of 'man’ with no nose in particular, no hair in particular, no body in particular, for then the idea is no longer of 'man’ but of something else, an inconceivable blur.

It is imperative, however, that the particular notion of 'man’ one reflects upon is, qua notion, accurately representative of 'man’ in the universality of the signification for [the signification] to hold. So the word 'man’ signifies the universality of all men you encounter in time and space, which partake in [it].

A definition does not signify a determinate abstraction from all its signified particulars. It is, on the contrary, an umbrella sign for all the varying particulars annexed by close notional relations. Hence names do not signify an exact, determinate idea. Rather, they operate as variables or place holders that grant access to the understanding for taxonomizing particulars. Names signify an indeterminate set of particulars.

In other words, names signify collections of ideas, particular ideas that designate an object. A book, for instance, has certain qualities we associate with the notion of 'book’, but to abstract from all these particular ideas would be to divest the object of its notion; for 'book' is the compendium of all these particular ideas (which impress themselves onto our senses).

It thus follows that ideas exist insofar as a mind exists to perceive them. For the qualities of red, salty, rough, loud, do not exist but in the mind–as perceptions or ideas of objects; and abstracting them from the object would leave an inconceivable “extended” object of no particular notion, which as was aforesaid, is nonsensical. It cannot be, then, that 'matter’ as is commonly understood exists. For it relies on an abstract general idea, in other words, on a contradictory notion of something that exists with no differentiating ideas and no qualities in particular.