Both wrestle with the concept that everything we ordinarily view as “reality” could be in fact a highly convincing illusion.
“Kant’s Compromise” is a name for the fact that the philosopher Immanuel Kant is generally viewed as creating a middle ground between the warring philosophical outlooks of (Continental) Rationalism, as epitomized by French philosopher René Descartes, and (British) Empiricism, as epitomized by Scottish philosopher David Hume. The former emphasized the mind, and the use of reason and other mental faculties as the primary way of relating to the world. The latter focused instead on sensory experience and direct evidence. Kant’s Compromise, stated roughly, is that both (sensory evidence and reason/judgment) are necessary.
I have the unpleasant intuition that someone may be trying to get me to complete their philosophy homework or essay question here. Nonetheless, applying the principle of charity and assuming this query is legitimate, I’ll try to give at least a brief answer:
In general, Descartes’ project is to doubt everything he possibly can, including whether the world exists as we perceive it, or is simply an illusion or deliberately deceiving simulation (as in the movie “The Matrix”). At the end of his process of extreme doubt, all he can be sure of is his famous dictum: “I think, therefore I am”. In other words, he knows he is thinking, because otherwise, he couldn’t even be doubting the things he doubts, and since something must exist in order to think, he knows that he must exist in some form, even if that form is not what he thinks it is. In other words, Descartes might be a space alien, or a creature of pure energy, or a disembodied spirit, or a mathematical abstraction, but he must be something, and that something must be able to think, since he can verify the fact of his thinking by immediate experience.
To put a quick gloss on the situation, this convinces Descartes that what he is in his most essential form is a creature that thinks, since all the material facts about himself could be other than they are without changing the central core of his identity as a thought-capable entity.
Hope that helps you with your test– oops! I mean with your sense of deep philosophical bewilderment. 🙂