Sextus Empirĭcus in Harpers Dictionary of Classical Antiquities (1898)
A physician who was a contemporary of Galen, and lived in the first half of the third century of the Christian era. Two of his works are extant-Πυρρώνιαι Ὑποπτυπώσεις, dealing with the skeptical learning of Pyrrho (q.v.), in three books; and Πρὸς τοὺς Μαθηματικοὺς Ἀντιρρητικοί, in eleven books, against all positive philosophy. The first six books strive to show the falsity of the sciences of grammar, rhetoric, geometry, arithmetic, astrology, and music; the last five attack logic, physics, and ethics. Edited by Fabricius (Leipzig, 1718). See Haas, Leben des Sextus Emp. (1882); id. Ueber die Schriften des Sextus Emp. (1883); and the monographs by Jourdain (1858) and Pappenheim (1878).
Sextus Empiricus in Wikipedia
Sextus Empiricus (c. 160-210 AD), was a physician and philosopher, and has been variously reported to have lived in Alexandria, Rome, or Athens. His philosophical work is the most complete surviving account of ancient Greek and Roman skepticism.
In his medical work, tradition maintains that he belonged to the "empiric school", as reflected by his name. However, at least twice in his writings, Sextus seems to place himself closer to the "methodic school", as his philosophical views imply.
Sextus Empiricus's three known works are the Outlines of Pyrrhonism (Πυῤῥώνειοι ὑποτύπωσεις or Pyrrhōneioi hypotypōseis, thus commonly abbreviated PH), and two distinct works preserved under the same title, Against the Mathematicians (Adversus Mathematicos), one of which is probably incomplete.
The first six books of Against the Mathematicians are commonly known as Against the Professors, but each book also has a traditional title (Against the Grammarians (book I), Against the Rhetoricians (book II), Against the Geometricians (book III), Against the Arithmeticians (book IV), Against the Astrologers (book V), Against the Musicians (book VI)). It is widely believed, with perhaps the exception of Sextus scholar Richard Bett, that this is Sextus's latest and most mature work.
Books VII-XI of Against the Mathematicians form an incomplete whole; scholars believe that at least one, but possibly as many as five books, are missing from the beginning of the work that was originally entitled Skeptical Treatises (Skeptika Hupomnēmata). The extant books have the traditional titles Against the Logicians (books VII-VIII), Against the Physicists (books IX-X,) and Against the Ethicists (book XI). Against the Mathematicians VII-XI is sometimes distinguished from Against the Mathematicians I-VI by giving it the title Against the Dogmatists (in which case Against the Logicians are called books I-II, Against the Physicists are called books III-IV, and Against the Ethicists is called book V, despite the fact that it is commonly believed that the beginning of the work is missing and it is not known how many books might have preceded the extant books).
Note that none of these titles except Against the Mathematicians and Outlines of Pyrrhonism, are found in the manuscripts.
Sextus Empiricus raised concerns which applied to all types of knowledge. He doubted the validity of induction long before its best known critic David Hume, and raised the regress argument against all forms of reasoning:
Those who claim for themselves to judge the truth are bound to possess a criterion of truth. This criterion, then, either is without a judge's approval or has been approved. But if it is without approval, whence comes it that it is truthworthy? For no matter of dispute is to be trusted without judging. And, if it has been approved, that which approves it, in turn, either has been approved or has not been approved, and so on ad infinitum.
Because of these and other barriers to acquiring true beliefs, Sextus Empiricus advises that we should suspend judgment about virtually all beliefs, that is, we should neither affirm any belief as true nor deny any belief as false. This view is known as Pyrrhonian skepticism, as distinguished from Academic skepticism, as practiced by Carneades, which, according to Sextus, denies knowledge altogether. Sextus did not deny the possibility of knowledge. He criticizes the Academic skeptic's claim that nothing is knowable as being an affirmative belief. Instead, Sextus advocates simply giving up belief: that is, suspending judgment about whether or not anything is knowable. Only by suspending judgment can we attain a state of ataraxia (roughly, 'peace of mind'). Sextus did not think such a general suspension of judgment to be impractical, since we may live without any beliefs, acting by habit.
Sextus allowed that we might affirm claims about our experience (e.g., reports about our feelings or sensations). That is, for some claim X that I feel or perceive, it could be true to say "it seems to me now that X." However, he pointed out that this does not imply any objective knowledge of external reality. Though I might know that the honey I eat at a certain moment tastes sweet to me, this is merely a subjective judgment, and as such may not tell me anything true about the honey itself.
Interpretations of Sextus's philosophy along the above lines have been advocated by scholars such as Myles Burnyeat, Jonathan Barnes, and Benson Mates.
Michael Frede, however, defends a different interpretation, according to which Sextus does allow beliefs, so long as they are not derived by reason, philosophy or speculation; a skeptic may, for example, accept common opinions in the skeptic's society. The important difference between the sceptic and the dogmatist is that the sceptic does not hold his beliefs as a result of rigorous philosophical investigation. In Against the Ethicists, Sextus in fact directly says that "the Skeptic does not conduct his life according to philosophical theory (so far as regards this he is inactive), but as regards the non-philosophical regulation of life he is capable of desiring some things and avoiding others." (XI, 165). Thus, on this interpretation (and as per Sextus' own words), the skeptic may well entertain the belief that God does or does not exist or that virtue is good. But he may not believe that such claims are true on the basis of reasons.
It must also be remembered that by "dogma" Sextus means "assent to something non-evident [ἄδηλος, adēlos]" (PH I, 16). And by "non-evident" he means things which lie beyond appearances (and thus beyond proof or disproof), such as the existence and/or nature of causality, time, motion, or even proof itself. Thus, the skeptic will, for example, believe the proposition that "Dion is in the room" if sense-data and ordinary reasoning led to the emergence of such a belief. On the other hand, if she were to "strongly" assert that Dion was "really" in the room, then she may be met with opposing arguments of equal psychological force against the self-same proposition and experience mental disquietude as a result. Thus, the Pyrrhonian does not assent to the proposition "Dion is in the room" in a dogmatic way as that would purport to describe a non-evident reality which lies beyond the "appearance" [φαινόμενον, phainomenon] of Dion being in the room. The Skeptic simply goes along with the appearance just as "a child is persuaded by...his teacher." (PH I, 229). It is for this reason then that Sextus says the Skeptic lives undogmatically in accordance with appearances and also according to a "fourfold regimine of life" which includes the guidance of nature, compulsion of pathe (feelings), laws and customs, and instruction in arts and crafts. The Skeptic follows this course of life while suspending judgment concerning the ultimate truth of the non-evident matters debated in philosophy and the sciences (PH I, 17). Thus, the Pyrrhonian Skeptic is one who believes possibly many things, but yet does not dogmatize about those beliefs since she finds no ultimate justification for them. Thus, Pyrrhonian achieves ataraxia not by finding certain knowledge, but rather by suspending judgment on whether not finding certain knowledge is an inherently bad thing in the first place (as was assumed previously).
The Ten Modes of Pyrrhonism
Pyrrhonism is more a mental attitude or therapy than a theory. It involves setting things in opposition and owing to the equipollence of the objects and reasons, one suspends judgement. "We oppose either appearances to appearances or objects of thought to objects of thought or alternando." The ten modes induce suspension of judgement and in turn a state of mental suspense followed by ataraxia. If ever one is in a position in which they are unable to refute a theory, Pyrrhonists reply "Just as, before the birth of the founder of the School to which you belong, the theory it holds was not as yet apparent as a sound theory, although it was really in existence, so likewise it is possible that the opposite theory to that which you now propound is already really existent, though not yet apparent to us, so that we ought not as yet to yield assent to this theory which at the moment seems to be valid." These ten modes or tropes were originally listed by Aenesidemus.
1. "The same impressions are not produced by the same objects owing to the differences in animals." 
2. The same impressions are not produced by the same objects owing to the differences among human beings.
3. The same impressions are not produced by the same objects owing to the differences among the senses.
4. Owing to the "circumstances, conditions or dispositions," the same objects appear different. The same temperature, as established by instrument, feels very different after an extended period of cold winter weather than after mild weather in the autumn. Honey tastes sweet to most but bitter to someone with jaundice. Things appear different when drunk as opposed to sober, sick as opposed to well, etc.
5. "Based on positions, distances, and locations; for owing to each of these the same objects appear different." The same tower appears rectangular at close distance and round from far away.
6. "We deduce that since no object strikes us entirely by itself, but along with something else, it may perhaps be possible to say what the mixture compounded out of the external object and the thing perceived with it is like, but we would not be able to say what the external object is like by itself."
7. "Based, as we said, on the quantity and constitution of the underlying objects, meaning generally by "constitution" the manner of composition." So, for example, goat horn appears black when intact and appears white when ground up.
8. "Since all things appear relative, we will suspend judgement about what things exist absolutely and really existent. "Do things which exist "differentially" or "have a distinct existence of their own as opposed to a relative existence" differ from relative things or not? If they do not differ, then they too are relative; but if they differ, then, since everything which differs is relative to something..., things which exist differentially are relative."
9. "Based on constancy or rarity of occurrence." The sun is more amazing than a comet, but because we see the sun daily and the comet rarely, the latter commands our attention.
10. "There is a Tenth Mode, which is mainly concerned with Ethics, being based on rules of conduct, habits, laws, legendary beliefs, and dogmatic conceptions."
Superordinate to these ten modes stand three other modes:
I - that based on the subject who judges (modes 1, 2, 3 & 4).
II - that based on the object judged (modes 7 & 10).
III - that based on both subject who judges and object judged (modes 5, 6, 8 & 9)
Superordinate to these three modes is the mode of relation.
An influential Latin translation of Sextus's "Outlines" was published by Henricus Stephanus in Geneva in 1562, and this was followed by a complete Latin Sextus with Gentian Hervet as translator in 1569. Petrus and Jacobus Chouet published the Greek text for the first time in 1621. Stephanus did not publish it with his Latin translation either in 1562 or in 1569, nor was it published in the reprint of the latter in 1619. Sextus's "Outlines" were widely read in Europe during the 16th, 17th and 18th centuries, and had a profound impact on Michel de Montaigne, David Hume, and G.W.F. Hegel, among many others. Another source for the circulation of Sextus's ideas was Bayle's Dictionary. The legacy of Pyrrhonism is described in Richard Popkin's The History of Skepticism from Erasmus to Descartes and High Road to Pyrrhonism. The transmission of Sextus's manuscripts through antiquity and the Middle Ages is reconstructed by Luciano Floridi's Sextus Empiricus, The Recovery and Transmission of Pyrrhonism. Oxford: Oxford University Press, 2002.