Empiricist Arguments

The mind is a 'tabula rasa' (blank slate) from birth. This means that we are born without any innate ideas. Locke described innate ideas as concepts or propositions the mind is aware of from birth. Any innate ideas must be known by everyone, including children and idiots. There is no truth that every person including children and idiots assents to from birth, so no ideas are innate.

Criticism
No major philosopher has tried to defend innate knowledge using Locke's definition of innate. Nativists define innate ideas as ideas the content of which cannot be derived from sense experience. Innate knowledge is known at birth but requires stimulation from the environment in order for it to be accessed by the mind.

Hume believed that there were only two types of knowledge: relations of ideas and matters of fact.

Relations of Ideas: Analytic statements known a priori

Matters of Fact: Synthetic statements known a posteriori

Ideas that seem to relate to nothing in our sense experience (e.g. unicorns) are nothing more than the combining and altering of things we have already experienced. All complex ideas (such as the unicorn), no matter how abstract,  can be broken down in to simple ideas (white, horse, horn), and these simple ideas are copies of sense impressions.

Concepts such as substance and self that cannot be broken down in to simple ideas simply do not exist. We have them confused with other concepts. For example, what we consider to be substance is actually similarity. For something to have substance it must be the same throughout all of space and time, yet we cannot experience anything throughout all of space and time. Instead, we keep seeing what looks like the same object and assume it has substance. For all we know it is not the same object, all we can ever be certain of is that it is similar to the object we previously saw. 

Criticism

To simply dismiss concepts such as substance and self is not a very convincing argument. This would make most of our common sense faulty, making empiricism too challenging to accept.