What is the highest good? To be a bit more precise, what is the highest good attainable by us though our own (individual or collective) efforts? One perennially attractive, if unambitious, answer is that of the Pyrrhonian skeptics: our highest good lies in ataraxia. The term connotes tranquillity, peace of mind, freedom from disturbance, unperturbedness. Other Hellenistic schools also identified the summum bonum with ataraxia, but let us confine ourselves to skepticism as represented by Sextus Empiricus.
The Pyrrhonian skeptic, then, seeks ataraxia as the summum bonum. This freedom from disturbance is supposed to be achieved by an epoché (ἐποχή) or suspension of doxastic commitments of a certain sort. One is supposed to achieve the happiness of tranquillity by suspending one's belief on a certain range of issues, those issues that typically cause contention, enmity, and bloodshed. Among these will be found philosophical, theological, and political issues. My elite readers can easily supply their own examples.
The suspension of belief is supposed to ensue when it is seen that reason is impotent to decide the disputed questions, when it is seen that for every argument for some dogma, there is an equally good counterargument for its negation. So what the skeptical therapist does is run through the arguments on both sides of an issue with an eye to showing how they cancel out: one is left with no reason to prefer one side over the other.
Having thus attained insight into reason's impotence to decide the disputed questions, the 'patient' abandons his contentious and argumentative comportment, suspends belief, and 'chills out' into a state of ataraxia.
But there is a serious problem here. Among the beliefs that inspire dispute and contention and militate against mental tranquillity are the beliefs that are part and parcel of any philosophical therapy. Practioners argue over the right therapy and they compete for patients — and often the arguing and the competing are less than edifying. In particular, the skeptic is committed — is he not? — to the belief that no contradiction is true. For the suspension of belief is supposed to be consequent upon insight into the (putative) fact that there are equally good arguments for both a thesis T and its negation ~T, for all contention-inspiring values of 'T.' But the existence of these equally good arguments shows the impotence of reason only if it is assumed that no contradiction is true. If some contradictions are true, then the fact that there are equally good arguments for a thesis and its negation has no tendency to show that reasoning is not a route to truth.
Of course, our skeptic will not assert the Law of Non-Contradiction — he is too wily for that — but he is committed to its truth. So here is one 'dogmatic' proposition belief in which he cannot suspend. His skeptical procedure presupposes a doxastic commitment to LNC. His whole practice rests on it. His skepticism cannot be thoroughgoing. He cannot free himself from a central dogmatic commitment.
He may refrain from avowing it; he may even slip into self-deception about his commitment to it. But the commitmemt remains, if not occurrently then dispositionally, and is betrayed by his actions.
There is no living without beliefs, and this includes beliefs that range beyond the sensory and immediate. Believe we must, and inquire we must. Skepticism is a failed attempt at evading these, our responsibilities. We cannot live belieflessly. I have shown this with respect to our belief in LNC. It can be shown with respect to other beliefs as well.