Locke on Innateness
Locke has many arguments against the theory that we have innate ideas. The first thing to figure out is just what theory it is that he is arguing against. Generally speaking, he is arguing against the theory that 1) we are in possession of ideas that are prior to experience in the sense that the ideas are in the mind before the mind is furnished with the sorts of ideas we come by in experience and 2) that we come to have possession of ideas in any other way than by the processes that he claims furnish us with ideas - processess that all include experience insofar as they require impressions of either sensation or reflection. In general, you should keep in mind that not all proponents of the theory of innate ideas are as Locke depicts them. Sometimes, he may be setting up a straw man (a depiction of an opponent's position that is misleading and easy to refute).
Below I will sketch some of the reasons Locke has for thinking that the theory of innate ideas is incorrect. I would like you to fill in the details yourself - many times this will involve actually filling in the argument that supports the reason.
Locke's reasons for thinking the theory of innate ideas is incorrect
The theory of ideas is explanitorily idle, i.e., we do not need to invoke it to explain the ideas we have.
The theory of innate ideas hold that all normal persons are in possession of, and regard as true, those ideas that are innate, e.g., everyone agrees that everything is what it is and not another thing. This is what Locke means by 'universal assent'. The theory of innate ideas takes universal assent as an indicator of whether an idea is innate. According to Locke, universal assent is neither a necessary nor sufficient indicator of whether an idea is innate. It is not sufficient because it is in principle possible that a non-innate idea could receive universal assent. It is not necessary because many, if not most, people neither know or assent to the ideas that are often offered as being innate.
If there were innate ideas in the mind, then, given that perceiving (experiencing) just is having an idea in mind, than all persons would at all times, immediatly perceive the purported innate ideas. But they don't.
The innate idea theorist coulld respond here by saying that innate ideas require the use of reason in order for one to experience and assent to them. But the faulty of reason, according to Locke, is the faculty of deducing unknown truths from known truths. Since innate ideas are supposed to be already known, reason can't aid us in discovering them.
Even if reasons did aid us in knowing, for example, that everything is what it is and not another thing, this would not show that this is an innate idea, since reason aids us in knowing all sorts of other ideas that are not innate.
If the use of reason were necessary to uncover innate ideas, then children who come to use reason at an early age would thereby come to be in immediate, certain possession of the innate ideas - but they don't.
Even if some ideas could not be had unless we used the faculty of reason, this would not show that such ideas are innate, because there are a lot of ideas that require deduction that are not innate.
The theory of innate ideas also often takes immediate assent as an indication that an idea is innate. In other words, if, upon hearing someone say, for example, '2+2=4', you immediatly assent, and do not have to go look at the world to see that it is true or do not haveto go through a proof, then, the theory claims, it is because the natural light of reason has revealed to you one of your innate ideas.
That one immediatly knows mathematical truths like 2+2=4, when we hear them does not show that these truths are innate, they merely show that the person understands the meanings of the constituent ideas, like '2' and '='. One comes to know these meanings by forming the constituent ideas through experiencing them, attaching names to them, and abstracting from them to form general ideas.
If all propostions to which one immediatly assents are innate, we're going to have a lot of innate ideas, since we would not only have, for example, the general innate idea that everything is what it is and not another thing, but we would also have an innate idea of every particular instance of the general idea. So, we would also have an innate idea of "A square is not a circle", "Red is not blue", etc. etc.
If we did have an innate idea that a square is not a circle, or red is not blue, then these complex ideas would have to consist in simpler innate ideas, but this would make the idea of redness, for example, innate, which it clearly is not, given that, for example, blind people have no such idea.
If innate ideas were already implicit in our minds, then upon making them explicit, we would have learned nothing. So, for example, upon hearing a geometrical axiom one would not have learned anything new - if it was innate, you already knew it - but clearlym we do learn something new when we learn geometery.
If there were innate ideas, they should be clearest and most obvious in those who are as yet uncorrupted by experience - infants, etc. But they are not.
Some innate idea theorists claim that there are innate moral ideas or truths. For example, one should act towards others only in ways to which you would consent to be treated. But this principle is even less evident than that everything is what it is and not another thing. If they're both innate, they should be equally as evident, but they're not.
If there were innate ideas, they would require no proof - they're the sorts of things to which you are supposed to immediarly assent - but moral principles both require and admit of proof.
Moral ideas and principles are even less likely to admit of universal assent than speculative ideas (like everything is what it is and not another thing). Obviously different people in different cultures practice different moral customs based on different moral principles.
The innate idea theorist could respond by saying that all people assent to the same moral principles, but their actions to do not bear this out. This is implausible because 1) in general, people's ideas are the grounds of thier actions and 2) it would be odd to have all these innate moral principles which have no practical effect in behavior.
If we knew, for example, the golden rule innately, we would never break it. Why would we knowingly violate a moral principle we knew to be true?
Most moral principles are imperatives, not statements. Imperatives direct us to act, while statements make claims. Only statements are the sorts of things that can be either true or false. Imperatives have no truth-value. For example, "Close the door!" is neither true nor false - it does not describe a state of affairs in the world. If moral principles cannot be true, they cannot be innate truths, know to all.
If we had innate ideas, we would know what they were and they would be easily distinguishable from the other ideas we have. But no innate idea theorist has ever given us a definitive, exhaustive list of them. Indeed, many who invoke innate ideas disagree about which ones they are.
Most supposed innate ideas are vacuous - they merely elucidate the meanings of the terms employed in sentences, like "All bachelors are unmarried men." Why would God go through the trouble of giving us all these innate, but vacuous ideas?
If the innate idea theorist responds to the argument that putative innate moral truths are constantly violated by claiming that such violation is the result of education, custom and culture corrupting the mind, they will have given up the claim that such principles receive universal consent.
If ideas like every thing is what it is and not another thing were innate, they would be made up of simple innate ideas - in this case, identity. Such innate ideas would have to be clear and distinct. However, the idea we have of identity is obscure and indistinct (it's ambigious).
Our idea of God can't be innate since there are many who have no such idea. Even if the idea of God were universal, this would not show that it waas innate since we could explain universal assent by appealing to the theory that attrative ideas spread across cultures quickly.