The first is perception (αἴσθησις). Our perceptions are "true" (ἀληθῆ), at least to us, a kind of private knowledge. But they may be dreams or illusions. (160D)

The second is true (ἀληθῆ) opinion or belief (δόξαν). Socrates asserts that Protagoras' relativistic argument that "man is the measure of all things," means "what is true is what is true for me." But "myriad" others may properly judge your opinion false (ψευδῆ).(170D)

The third is true belief that had some reasons (λόγος) or justification (συλλογισμῶ), a rational explanation for the belief. True (or right) opinion accompanied by reason is knowledge. (δόξαν ἀληθῆ μετὰ λόγου ἐπιστήμην εἶναι) (202C)

This third possibility that knowledge is "justified true belief" has come down to modern times as the three-part "traditional" theory of knowledge.

Although Socrates' "negative" dialectic never established any certain knowledge, Plato believed that Socrates' method of inquiry (ἔλεγχος) was the way to achieve knowledge.

Nevertheless, the Theaetetus ends with Socrates' utter rejection of perception, true belief, or true belief combined with reasons or explanations as justification. Socrates says:

And it is utterly silly, when we are looking for a definition of knowledge, to say that it is right opinion with knowledge, whether of difference or of anything else whatsoever. So neither perception, Theaetetus, nor true opinion, nor reason or explanation combined with true opinion could be knowledge (epistéme). (Harold Fowler translation)

καὶ παντάπασί γε εὔηθες, ζητούντων ἡμῶν ἐπιστήμην, δόξαν φάναι ὀρθὴν εἶναι μετ᾽ ἐπιστήμης εἴτε διαφορότητος εἴτε ὁτουοῦν. οὔτε ἄρα αἴσθησις, ὦ Θεαίτητε, οὔτε δόξα ἀληθὴς οὔτε μετ᾽ ἀληθοῦς δόξης λόγος προσγιγνόμενος ἐπιστήμη ἂν εἴη.

Plato's Theaetetus, (210A-B)

Aristotle revised his master Plato's theory of Forms and Ideas. Although he too sought the fundamental essences of things and ideas (their Being - τὸ ὄν), for Aristotle all things were a combination of form (εἴδος) and matter (ὑλῆ), and understanding how real physical things change (their Becoming) was as important as knowing their essences (their Being).

In his Metaphysics, Aristotle dealt with the problem of knowledge (epistemology) and with the question of Being (ontology of both physical and abstract things). The opening line of Book I of the Metaphysics is "All men desire knowledge (to know) by nature." (πάντες ἄνθρωποι τοῦ εἰδέναι ὀρέγονται φύσει.)

Aristotle sharpened the use of language (dialectic) and logic as our means of knowing to a level still in use today. He analyzed subject-predicate sentences and puzzled over the relationship between being or essence and the copula "is." He elucidated the simplest rules of logic - needed for the reasoning (συλλόγος) behind justification of knowledge - the Law of Identity (A is A), the Law of Non-Contradiction, and the Law of the Excluded Middle. And he developed the rules for logical inference, identifying many types of syllogism (Socrates had identified the simplest syllogism - S is M, M is P, therefore S is P).

But Aristotle went beyond reason and Platonic dialectic. He added the need for demonstration (ἀποδειξις) to discover the cause (ἀιτια) and explanation of a phenomenon. This was the beginning of empirical knowledge, the observations and experiments that form the basis of modern science, as opposed to the kind of personal and subjective knowledge available directly to our perception, intuition, or reflective introspection.

Aristotle identified four basic causes (material, formal, efficient, and final) and said that chance might be a fifth cause. Not everything happens of causal necessity, but some things as chance will have it.

He distinguished certain a priori knowledge, for example logic and mathematics, which was true by necessity, from the merely probable and contingent a posteriori knowledge of ethics and politics. He denied that the truth of a proposition about the future entailed the necessity of a future event (as claimed by Diodorus Cronus with his actualism).

For Aristotle, there were different methods of inquiry and different kinds of knowledge depending on the subject matter, for example knowledge of the things themselves in the external world (ontology and metaphysics) that we would call today the physical sciences, and knowledge about people (ethics and politics) that today we would call the social sciences. We might add psychology, especially the subjective and reflective knowledge of self by introspection. And although he wanted to be more empirical than Plato, he held onto some necessary truths or first principles that were self-evident. He also recognized "theses" (θέσισ) and "axioms" (ἄξιος).

And Aristotle distinguished many kinds of logical argument. When the premises are true and certain (he does not explain how this can be the case except for those that are self-evident "first principles" - ἀρχὴ or πρῶτων), and the deductive syllogism is correct so that the conclusions follow, Aristotle calls this a demonstration, the truth of it is apodeictic (ἀπόδειξις), a logical proof. The resulting knowledge is demonstrative knowledge (ἀποδεικτικὲω ἐπιστήμην).

Aristotle realized that not all reasons given to justify beliefs could themselves have reasons without an infinite regress or circular argument, so he proposed that some reasons could be "self-evident" axioms, worth believing on their own merits or because they are popular opinion.

Returning to Plato here, Aristotle says that all parts of this demonstration - premises, deductions, and conclusions - are necessary. When the premises are popular opinion, their truth merely probable, the argument is dialectical. When the premises are false, the argument is sophistical, and can prove anything. Much of modern epistemology feels somewhat sophistical.

Plato's Academy itself came to adopt skepticism under Arcesilaus in the third century. Arcesilaus doubted that the senses could discover truths about the physical world. Skeptics, especially Carneades, who followed Arcesilaus as leader of the Academy, denied the claims of their opponent Stoics as mere dogmatism.

Philo of Larissa, the last leader of Academic Skepticism in Athens, escaped the Mithradatic wars and went in 88 BCE to Rome where he mentored Marcus Tullius Cicero. Cicero gave us perhaps the best ancient comparison of the Stoic, Epicurean, and Skeptical schools of philosophy in his dialogue De Natura Deorum (On the Nature of the Gods).

Aenesidemus, the first-century leader of Academic skepticism in Alexandria, qualified the obvious self-referential error in the skeptical claim that nothing could be known. He encouraged a return to Pyrrho's suspension (εποχή) of any judgment. Aenesidemus identified ten tropes or modes of knowing by perception through different senses, which he showed can be mutually inconsistent. Epistemological justification of any absolute objective knowledge is therefore impossible.

According to Sextus Empiricus (Outlines of Pyrrhonism, 1.164-77), these ten tropes were reduced by Agrippa to five

• Disagreement among the philosophers
• An infinite regress of justification
• Relativity - all concepts are meaningful only in some context
• Hypotheses cannot be self-evident
• Circular reasoning

That nothing can be apprehended through itself (immediate knowledge) or through another thing (mediate knowledge) is shown by the controversies among the philosophers. And the infinite regress of reasons is caused by the lack of a criterion for truth (κριτεριόν τῆσ ἀληθείας). These two problems are still very much with us today,

An infinite regress arises when we ask what are the justifications for the reasons themselves.

If the reasons count as knowledge, they must themselves be justified with reasons for the reasons, etc., ad infinitum.

Chrysippus saw logic as the core of a divine reason that rules the universe. The Laws of Nature are synonymous with the Laws of God, since Stoics identified God with Nature. In his time, Chrysippus' logic was considered superior to Aristotle's.

Descartes shifted the emphasis of knowledge from the external world to his internal thoughts, and began an effort to find indubitable truths as foundations for all knowledge. Descartes' introspective "quest for certainty" changed the focus of problem of knowledge to what 20th-century philosophy would come to call "foundationalism and "internalism"."

Even if Descartes could have arrived at subjective knowledge that he personally could not doubt, such knowledge would be inaccessible to others. And others would be properly skeptical of his egocentric knowledge claims.

Gottfried Leibniz argued that certainty could be had for necessary truths that were "true in all possible worlds." Leibniz' Principle of Sufficient Reason was a claim that knowledge of the physical future was implicit in the fact that every event has a sufficient cause. This is despite Aristotle, who knew that future events might or might not happen.

David Hume, skeptical that anything could be proved true by induction, declared causality to be simply a matter of repeated conjunctions of apparent cause and effect. With his empirical colleagues, Locke and Berkeley, he denied any knowledge of the "things themselves" behind our perceptions. We have only sense impressions of Locke's "secondary qualities."

Hume, following Leibniz, admitted as knowledge only two things, analytical mathematical logical reasoning, and empirical facts. This is essentially the analytic-synthetic knowledge distinction.

If we take into our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Consign it then to the flames: For it can contain nothing but sophistry and illusion.

Despite his skepticism about causality, Hume's "naturalism" convinced him of the practical truth of strict causal determinism.

"What can I know?" asked Immanuel Kant. Faced with the skepticism of Hume which put into doubt all phenomenal knowledge gained by perception alone, he postulated a noumenal world accessible to the mind by introspection. There the "things themselves" exist along with God, human freedom, and immortality. But since they are outside the phenomenal world - the physical world governed by strict causal deterministic laws of motion - Kant's claim to knowledge was as weak as Hume's skeptical claim was strong.

Kant accepted Hume's (and Aritotle's) distinction between abstract analytic a priori knowledge and experimental or empirical synthetic a posteriori knowledge. But he claimed that the human mind imposed certain categories of understanding on the world, leading to some necessary empirical truths, or what he called synthetic a priori knowledge. Among these are that space must necessarily be Euclidean, that "7 + 5 = 12" is mathematically necessary, and that the deterministic laws of Newton must be strictly true.

Although all these "truths" have been found empirically to be false, modern developmental psychology finds that some ideas are indeed "built-in" to the mind, as Kant held. Infants are born able to recognize continuity, contiguity, causality, and form. These conceptual abilities are immediately available. They do not need a set of prior experiences from which to abstract. Thus Locke's tabula rasa dictum that everything that is known comes first through the senses is wrong.

The 19th-century hermeneuticists Schleirmacher and Dilthey argued for some knowledge accessible in non-scientific ways. They claimed that cultural knowledge can only be appreciated and understood by someone immersed in the culture.

Charles Sanders Peirce defined knowledge - truths about the real world - as that knowledge that would eventually be agreed upon "intersubjectively" by a community of inquirers who follow an open scientific method of hypothesis, deduction, and experimental testing of predictions by means of observations.

As to Descartes' search for indubitable certain knowledge, Peirce agreed that any knowledge can be doubted. But, explaining Descartes' error, Peirce says first that everything can not be doubted at the same time. And second, that nothing is ever certain because the method of science always leaves open the possibility for improvements in our knowledge. His pragmatic "truth" is something that is only asymptotically approached over time by the open community of inquirers.

Peirce's "pragmatic" philosophy identified truth with beliefs that informed action and had valuable consequences. This led to John Dewey's idea of truth as "warranted assertability," with the warrants to be found in the empirical consequences.

Bertrand Russell declared that science is the only source of knowledge, "What science cannot discover, mankind cannot know." This came to be called "scientism."

Logical empiricists, following Russell's student and colleague Ludwig Wittgenstein, could never agree on the method of justification. The Vienna Circle philosophers, Rudolf Carnap and Moritz Schlick, never could get general agreement on the "verification" of a proposition about the world.

A. J. Ayer, who sat in on some Vienna Circle meetings, put their ideas forward in his Language, Truth, and Logic. He said (again following Hume and Aristotle) that two kinds of propositions are meaningful - analytic sentences (tautologies and definitions of language terms) or statements that can be empirically verified.

Karl Popper denied that "verification" could ever lead to certain knowledge, but argued that a negative experimental result could "falsify" a proposition.

In the early 1950's, Willard van Orman Quine challenged the ancient analytic-synthetic distinction, arguing that in the end the "truth" of analytic statements, the proofs of mathematical theorems, and the use of logic, also depend on some empirical verification.

The key idea of Quine's empiricism is to deny the existence of any a priori knowledge of the world (or of words - statements, propositions), whether analytic or synthetic. As Peirce had said, nothing is logically and necessarily true of the physical world. Logical truths like the Principles of Non-Contradiction and Bivalence (Excluded Middle) might be true in all possible worlds, but they tell us nothing about our physical world, unless they are applicable and empirically verified.

The conditions postulated in Gettier-type examples are extraordinarily unlikely to occur, but the mere possibility demonstrates the difficulty of making logical arguments about contingent real world situations. The most sophisticated linguistic analysis is problematic as a source of "truth" or justification.

There is a technical similarity between Gettier cases and Frankfurt-type examples of an agent who apparently acts "freely" but a counterfactual demon insures that there is only one possibility for action. In 1969 Harry Frankfurt developed logical counterexamples to the traditional idea that alternative possibilities are a prerequisite for free agency..

Gettier cases artificially construct a "true" situation which is not true for the apparent reasons. Frankfurt cases artificially construct a "free" action in which the agent actually is not free to choose the apparent alternative possibilities.

Gettier and Frankfurt cases have spawned a vast philosophical literature in the past few decades. But they have produced little advance in understanding either knowledge or freedom. They are little more than clever sophisticated examples of analytic language philosophy.

Skepticism alone should have indicated that logical proofs of knowledge, or logical analyses of any justification scheme for knowledge, were bound to fail.

Gettier and Frankfurt cases are applied skepticism or sophistry that cast doubt on the likely validity of common sense justifications and knowledge by developing extremely unlikely if not implausible cases.

They depreciate the value of the central project of epistemology, which is to help us to know (if only in a virtuous circle) when our arguments for knowledge are as strong as we can make them.

Until Descartes's turn inward, theories of knowledge all assumed that justification included the relation of beliefs to objects and events in the world.

Descarte's "internalist" turn continued well into the twentieth century, with most epistemologists endorsing his "foundationalist" theory of knowledge. They included C.I. Lewis (1946), Roderick Chisholm, John Pollock (1986), Richard Foley (1987), Paul Moser (1989), William P. Alston (1989), and Robert Audi (1993).

But several philosophers moved toward an "external" view of epistemology.

As early as the 1920's, Frank Ramsey had proposed the idea of reliability, which depends on some kind of external causal process. He said that a belief was knowledge if it was (i) true, (ii) certain, (iii) obtained by a reliable process.

In 1967, Alvin Goldman amplified the Ramsey view, endorsing both a "causalist" theory of knowledge and what he called "reliabilism."He claimed that justification for a belief is to be found in the natural cause of the belief.

In 1971, Fred Dretske offered what he called "Conclusive Reasons" as a form of justification. They included evidence, grounds, and reasons.

In 1973, David Armstrong called for a return to what he called "externalism," defined as "a certain relation holding between the believer and the world."

For example, one can not only believe, but know, that the room is hot because the excessive heat one feels is the cause of one's belief.

Armstrong further divided externalist theories into "causal" (like Goldman) and "reliability" (like Dretske and Ramsey) theories.

There are other externalist theories, including naturalism, evidentialism, and evolutionary epistemology.

The Vienna Circle espoused a verification theory of meaning but did not take it seriously enough. If we recognize with Peirce that the meaning of a sentence turns purely on what would count as evidence for its truth, and if we recognize with Duhem that theoretical sentences have their evidence not as single sentences but only as larger blocks of theory, then the indeterminacy of translation of theoretical sentences is the natural conclusion.

Philosophers have rightly despaired of translating everything into observational and logico-mathematical terms. They have despaired of this even when they have not recognized, as the reason for this irreducibility, that the statements largely do not have their private bundles of empirical consequences. And some philosophers have seen in this irreducibility the bankruptcy of epistemology. Carnap and the other logical positivists of the Vienna Circle had already pressed the term "metaphysics" into pejorative use, as connoting meaninglessness; and the term "epistemology" was next. Wittgenstein and his followers, mainly at Oxford, found a residual philosophical vocation in therapy: curing philosophers of the delusion that there were epistemological problems.

Epistemology, or something like it, simply falls into place as a chapter of psychology and hence of natural science. It studies a natural phenomenon, viz., a physical human subject...

The old epistemology aspired to contain, in a sense, natural science; it would construct it somehow from sense data. Epistemology in its new setting, conversely, is contained in natural science, as a chapter of psychology. But the old containment remains valid too, in its way... There is thus reciprocal containment, though containment in different senses: epistemology in natural science and natural science in epistemology.

(Ontological Relativity and Other Essays 1969, pp.80-3)

Although Quine's reciprocal containment suggested that epistemology might still play a foundational role in scientific understanding, his work appeared to many to reduce epistemology to psychology. Quine seemed to deny the normative role of traditional epistemology, which hoped to justify all knowledge, including scientific knowledge.