From Plato's Theaetetus to the replication crisis — a brief survey of the theory of knowledge: its objects, its sources, and the limits of what we may justifiably claim to know.
The dominant working definition of propositional knowledge — knowledge that p — held from antiquity through the mid-twentieth century. To know a proposition is to satisfy three jointly necessary, jointly sufficient conditions.1
1 Plato, Theaetetus 201c-d. Socrates entertains "true judgment with an account" and finds each proposed account wanting.
The first sustained Western treatise on the question what is knowledge? Socrates and the young geometer Theaetetus together test, and reject, three definitions of epistēmē.2
The dialogue establishes the agenda for two and a half millennia: knowledge is not mere information, not mere correctness; something further — justification, account, ground — is required.
"True opinion accompanied by reason is knowledge, but that which is unaccompanied is outside the sphere of knowledge." Theaetetus 202c
2 The contrast epistēmē / doxa structures Books V–VII of the Republic as well.
Descartes inaugurates modern epistemology by inverting the question: rather than ask what we know, ask what we cannot doubt. The method of doubt rejects every belief admitting the slightest uncertainty — senses, mathematics, the external world — until something irrefutable remains.3
Even an omnipotent deceiver cannot deceive me into thinking I exist if I do not. The act of doubting presupposes a doubter. Hence: cogito, ergo sum.
From the cogito Descartes attempts to reconstruct knowledge of God, the external world, and mathematics — an architectonic of foundationalism: certainty resting on indubitable first beliefs.
3 Descartes, Meditations on First Philosophy (Paris, 1641), trans. Cottingham 1986.
For Locke and Hume, the mind is a tabula rasa: all ideas trace, ultimately, to sensory impressions. Knowledge is the patient construction of experience.4 But Hume then exposes a wound at the heart of the empiricist programme.
No deductive argument warrants induction (the future could differ). No inductive argument warrants it without circularity (we'd be assuming what we wish to prove). The bedrock of empirical science thus has no purely rational foundation — only custom and habit.
Distinguishes simple from complex ideas, primary from secondary qualities. Knowledge is the perception of agreement among ideas.
Splits all reasoning into relations of ideas (analytic, certain) and matters of fact (synthetic, contingent). Causation is not observed but inferred — constant conjunction, not necessity.
4 Locke (1690); Berkeley, Principles (1710); Hume, Treatise of Human Nature (1739–40), Bk I.
Against the empiricists, Spinoza and Leibniz hold that reason alone can deliver substantive truths about reality. Mathematics is the paradigm: necessary, universal, gained without observation.5
The Ethics proceeds more geometrico — in the manner of geometry — deriving the structure of substance, mind, and ethics from definitions and axioms. The highest knowledge is scientia intuitiva: direct intellectual grasp of essences.
Distinguishes truths of reason (necessary, knowable through analysis) from truths of fact (contingent, requiring the principle of sufficient reason). Innate ideas are dispositions, "veined" in the marble of the mind.
5 Spinoza, Ethica (1677); Leibniz, Monadologie (1714); Descartes belongs to this lineage as well.
Roused by Hume from his "dogmatic slumber," Kant proposes a Copernican revolution: rather than ask how the mind conforms to objects, ask how objects conform to the mind. Experience is structured by the knower.6
E.g. the propositions of arithmetic and geometry; the principle that every event has a cause. Such judgements are possible because space, time, and the categories of the understanding (substance, causality, unity, …) are forms imposed by the mind on all possible experience.
We know things only as they appear to us (phenomena), structured by our cognitive forms. The thing-in-itself (noumenon) is forever beyond reach.
Kant reconciles empiricism and rationalism: experience supplies content, the mind supplies form. Modern philosophy of science, mathematics, and cognition all begin here.
6 Kant, Prolegomena (1783) is the readable companion volume.
In a three-page paper, Edmund Gettier exhibits cases in which a person has a justified true belief that nonetheless seems not to count as knowledge. JTB is therefore not sufficient.7
Smith is justified in believing Jones will get the job, and Jones has ten coins in his pocket. He validly infers: the man who will get the job has ten coins in his pocket. As it happens, Smith gets the job — and Smith, by coincidence, has ten coins in his pocket. Smith's belief is justified, and true. But did Smith know?
7 Decades of "post-Gettier" analyses (no-false-lemmas, sensitivity, safety) attempt a fourth condition. None has won universal assent.
One influential post-Gettier response abandons the inward demand for justification as the agent sees it, and asks instead about the process that produced the belief.8
A reliable process is one that tends, across a range of relevant counterfactual conditions, to yield true beliefs. Vision in good light is reliable; wishful thinking, guessing, paranoia are not.
8 Externalist alternatives: Nozick's tracking account; Sosa's virtue epistemology; Williamson's knowledge first.
The modern descendant of Descartes' demon. A brain, suspended in nutrient fluid, receives electrochemical inputs from a supercomputer that perfectly simulate ordinary experience. From the inside, you cannot tell the difference. So — how do you know you are not such a brain?9
Responses include contextualism (Lewis, DeRose), contrastivism, semantic externalism (Putnam), and Moorean common-sense rejection of premise 2.
9 The argument generalises Descartes' demon and anticipates the Matrix-style scenarios of contemporary philosophy of mind.
Most of what any one person knows — the date of the French Revolution, the structure of DNA, the existence of Antarctica — was learned from testimony, not direct observation. Knowledge is irreducibly social.10
Is testimonial belief justified by default (anti-reductionism, Reid) or only when independently corroborated (reductionism, Hume)?
The novice/expert problem: how does the layperson rationally identify whom to trust, when by hypothesis she lacks the expertise to evaluate the claims?
Condorcet's jury theorem. If voters are independent and better than chance, majority verdicts approach certainty as n → ∞ — provided independence holds.
10 Miranda Fricker, Epistemic Injustice (Oxford, 2007), distinguishes testimonial from hermeneutical injustice.
Twenty-first century epistemology has turned increasingly formal and empirical. Belief is modelled in degrees, updated by evidence; the actual practices of science are scrutinised for the systematic errors they incubate.11
Beliefs are credences in [0, 1]. Rational agents update by conditionalisation: posterior ∝ likelihood × prior. Epistemic humility = a prior that is not pinned to 1 or 0.
The Open Science Collaboration's 2015 effort replicated only 36% of 100 high-profile psychology results. Subsequent failures in cancer biology, economics, and social priming followed. A live case study in fallible collective knowledge production.
"It ain't what you don't know that gets you into trouble. It's what you know for sure that just ain't so." attrib. Mark Twain
11 Open Science Collaboration, "Estimating the reproducibility of psychological science," Science 349.6251 (2015): 943.
End of plate XIII · Finis.