This argument should be held tentatively but I think it should spark some interest. What is intuition? Typically, philosophers hold that an intuitive belief is one held by perception independently of any process. Natural empiricists, naturally (pun intended), cannot hold to this type of knowledge (also called a priori) since the only knowledge considered to be valid is that gained from observation of the natural world. However, it seems we can hold beliefs independently of any reasoning process or perception that are actually true. If this is the case, intuitive belief is justified. One such argument would look like this:
1. If we can hold justified true beliefs independently of any process or perception, then we have intuitive knowledge.
2. We can hold justified true beliefs independently of any process or perception.
3. Therefore, we have intuitive knowledge.
The second premise isn’t a good one, since the first premise is just a definition of intuitive knowledge. In short, there’s not a really good reason for accepting (2) unless we already accept it or create an entirely new argument for accepting it. Perhaps a different argument would be helpful here.
4. The laws of logic are justified upon their examination (application of empiricism).
5. Inference is an application of the laws of logic.
6. Inference must be used upon application of empiricism.
7. If (4-6), the laws of logic must be justifiably known.
8. If (4-7), the justification is known logically prior to empiricism.
9. If (4-8), then (2) is true.
10. If (2) is true, then (3) is true, and hence we have intuitive knowledge.
As already discussed (1) is true by definition. (4) is also definitional under an intuition-less empiricism (or even an empiricism which includes some intuition, for that matter). (5) may be controversial for the empiricist, but it really should not be. Anytime a conclusion is drawn, even tentatively, about anything in empiricism, a rational inference is made. Otherwise we would not even be sure the law of gravity was a law! We would marvel at how it drops over and over, but we would never make the inference that if we would release the object the next time that it would drop, much less come up with the law of gravity! Of course, I have mixed the justification for (6) in along with (5) since they are so closely related. If you accept one you accept the other.
(7) is just analytically true and simply says we justifiably know the laws of logic to be true on either method, which makes it a certainty that these laws are justifiably known. (8) may also seem at first blush to be controversial, but it is logically required. Since empiricism requires the laws of logic in order to make inference, and since (5) tells us laws of logic can be empirically verified, it follows necessarily that such laws are known prior to their empirical, or a fortiori, discovery.
(9) may be objected to on the basis that having knowledge prior to its empirical justification or drawing of inference from observation of the world is not intuitive knowledge. But in that case they’ll have to deny (1). A denial of the first premise as a material conditional necessitates the objector believes holding justified, true beliefs independently of any process or perception is not intuitive knowledge. In that case, the objector owes us an account of what intuitive knowledge is! If (9) is true, then (2) and (10) are, and in that case we do have intuitive knowledge after all!
What does it matter? First, intuition is vitally important to understanding some metaphysical truths. For instance, how did mankind know moral obligations, if they are indeed objective, before the Bible (or for atheists or non-Christians, how did we know these obligations without such?)? It seems such knowledge is just built in. It’s why we just know stealing is wrong. While fellow Christians will point to the Bible for moral prescriptions, I think we would all agree that we Christians, even without the Bible, would likely view murder as wrong in all circumstances. Second, these metaphysical truths help form a basis for accepting certain premises in theistic argument. Now, one can object to the argument for intuition above, but only by denying one of the premises. I think intuitive knowledge is justified and we indeed cannot live without it. Please let me know what you think below!
 To be thorough and robust, it should be noted that “perception” really means “perception external to intuition itself,” lest anyone think the very definition is self-refuting.
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