Hume distinguishes between two kinds of skepticism: antecedent and consequent skepticism, both of which come in an extreme and a moderate form. He identifies the extreme form of skepticism with the universal doubt of ##Descartes##, which calls into question all former opinions and even the testimony of the senses. No claim is acceptable to the Cartesian skeptic unless is can be deduced from some indubitable first principle. Hume suggests that, first, there is no first principle that is so self-evident as to be beyond doubt, and second, even if there were such a first principle, we couldn't advance beyond it, having not yet rescued from doubt our ability to reason deductively.
Though this extreme antecedent skepticism is unworkable, Hume commends it in a more moderate form. It consists simply in forming unprejudiced opinions, progressing by small steps from sound first principles, and examining one's conclusions frequently and carefully.
The skepticism of the Enquiry has been instead a kind of consequent skepticism, that questions our habitual conclusions and judgments by doubting the grounds on which they are secured. Hume considers in particular the testimony of the senses, which suggests to us the existence of a world external to and independent of our senses. We are led by a powerful instinct to suppose that what our senses report to us is an accurate representation of this external world. However, not only do our perceptions change as we move about in the world, but there are cases of dreams or madness where our senses deceive us entirely. We can only justify our belief in an external world through experience, but experience cannot take us beyond the very perceptions that we are calling into doubt. Thus, Hume concludes, our belief in an external world is not rationally justified.
In its extreme form, consequent skepticism can lead us to complete inaction. While philosophers tend to draw a distinction between secondary qualities, such as color, sound, or texture, and primary qualities, such as extension and solidity, our understanding of both is dependent upon experience: we cannot conceive of an extended body that has no color or shape. If we doubt the testimony of our senses, we have no understanding of matter. Similarly, mathematical reasoning can lead us to counter-intuitive conclusions about space and time, presenting them to us as infinitely divisible. Consequent skepticism also leads us to doubt causal reasoning, since no conclusions that outstrip the observation of constant conjunction are rationally justified.
Such skepticism, however, dries up when we ask to what use we can put it. We cannot help but reason causally, and to refuse to do so on the basis of skeptical reasoning would lead us to desist from acting or judging altogether. Our natural instincts cannot help but reinstate what skeptical reasoning tries to dismantle.
While this extreme form of consequent skepticism is clearly unlivable, Hume again finds it useful in a more moderate form. Dogmatic and hasty reasoning may be mitigated by a constant recognition that reasoning can go astray and judgments should never be absolute. Reasoning about relations of ideas can only teach us mathematical truths, and cannot lead us to more general metaphysical principles. Reasoning about matters of fact is supported only by experience, and so we cannot provide logical proofs of the existence or non-existence of any entity. The closing line of the Enquiry urges us to ask of any book: "Does it contain any abstract reasoning concerning quantity of number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: For it can contain nothing but sophistry and illusion."