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Traditional epistemology has been concerned with "justification". According to the classical tripartite model of knowledge, some proposition p is knowledge if and only if
- some agent X believes p,
- p is true, and 3) X is justified in believing in p and
- the third justificatory condition is to be given in non-epistemic terms such as "is deducible from" or "is indubitable." Still, the condition is essentially normative, which makes knowledge itself essentially normative.
Since the time of Descartes, who 1) sought to establish the criteria by which true beliefs could be acquired, and 2) sought to determine those beliefs we are in fact justified in believing, the primary epistemological project has been the elucidation of the justificatory condition in the classic tripartite conception of knowledge (i.e. Justified True Belief).
Naturalized epistemology had its beginnings in the twentieth century with W. V. Quine. Quine's proposal, which is commonly called "Replacement Naturalism," is to excise every trace of normativity from the epistemological body. Quine wanted to merge epistemology with empirical psychology such that every epistemological statement would be replaced by a psychological statement.
"Meta-epistemology" means — Overview over 'Theories of Knowledge' 
"Epistemology" is the Study-or-Theory of Knowledge ("ToK"): — What is knowledge? How is-or-should it be acquired, tested, stored, revised, updated, and retrieved? — etc.
"Meta-" here means "the overview study of...", applied to some "lower-level" study.‡ E.g. metaphilosophy means the "philosophy of philosophy" or effectively "a scrutiny of the assumptions of philosophy itself, (rather than studying whatever else philosophy might normally be looking at)". If that can be done "at arms-length", then so much the better; but that may not always be possible — see the paradox below.
Such overviews are well placed to identify inaccurate traditional assumptions, or hitherto-overlooked scope for generalization. Thus (i) whereas epistemology has usually been seen as a branch of philosophy, the discussion below also takes examples from biology which seem equivalent in relevant ways. Also (ii), insofar as philosophy is involved, there may be a case for extending it beyond its traditional domain of word-based definitions.
‡ [footnote]: Similar overviewing can be expressed by other terms, such as "critique" (in certain contexts) — so that Kant's book-title "Critique of Pure Reason" (1781/1787) effectively means "An overview study of the Nature and Properties of Pure Reason". [Incidentally: At first sight, Kant's own word "transcendental" seems to be another such "overview" case, but that is somewhat misleading. In fact it might be more helpful to think of it as expressing an "underview"! — some pre-existing axiomatic property or "category" (like space or time) which is so basic and "intuitive" that it (supposedly) does not need to be questioned before applying it universally. Piaget eventually challenged that view, as is obvious from his book-titles which contain words like "space" and "time".]
The Scope of Meta-Epistemology, including a Paradox 
Epistemology studies how person-or-system P gains knowledge about a "Subject"-system S — and that is comparatively straightforward as long as these two entities are different (P≠S) — i.e. as long as P is not studying its own internal workings (reflexively).
Normal non-reflexive cases 
Epistemology is the study of knowledge and knowledge-acquisition; and such activity can take many forms. Within philosophy at least, it is usually assumed that the epistemological system (to be studied meta-epistemologically) is the mind/brain of an adult, or a society of such adults — and that such processes will all be conscious. However all such assumptions (and others) are at least open to challenge — see below.
The Paradox of Self-Study 
However it may be seen as possible-and-desirable for the art of epistemology to be applied sometimes to itself (now acting in a "meta-" role) — and if it then gains new insights on how to ensure validity in its subject matter (S), it follows that those insights may be call for a revision of its own procedures (in its P role), thus calling into question the exercise just performed!
This may be seen as a variant of the infinite regress problem, raised within the epistemology discussion; — or compared to a brain-surgeon operating on his/her own brain. In any case, we may see this problem regarding the methodology of Karl Popper, at least in its initial form (1934), in which his methodological (meta-epistemological) rules were essentially laid down by his fiat — rules which dictated how scientific investigation (epistemology) was to be performed in a fiat-free environment.
Ambiguity: Epistemology as one unified whole, or what? 
One might argue that this is depends on an arbitrary choice of whether-and-where to draw boundaries; but there seems to be a better case for accepting the term "epistemology" in two somewhat different senses:
"Epistemology" as one of several knowledge-mechanism possibilities 
E.g. the mind/brain is one, and the immune system is another (see below) — so we should perhaps count these as "two different epistemologies".
"Epistemology" as a general topic-title 
The term is here seen as collectively covering all such possible cases and systems involved in assembling-or-storing knowledge in all its forms. (Such a distinction is not particularly unusual, so it need not be troublesome if we are clear about it. (Otherwise we had better talk of "sub-epistemologies" versus "the epistemology discipline", or suchlike).
The reflexive status of Meta-epistemology 
It purports to handle knowledge concerning each-and-every sub-epistemology, and that seems to mean: (i) that at some stage it must self-study reflexively as discussed above, with the danger of an infinite regress problem; and (ii) by the same token it must be part of its own subject matter, the "epistemology discipline".
Different Schools of Epistemology for Meta-study 
Broadly these are of two types: Mainstream philosophy, and Biology-based theories which nevertheless have a background compatible with philosophy. (Here we may exclude those "pure-science" investigations which may have impeccable empirical credentials but lack a coherent concept of the likely overall epistemological processes under study).
Orthodox Mainstream Philosophy 
This is in the tradition of Whitehead & Russell (1910–1913), and both the early and late incarnations of Wittgenstein's ideas — described by Piaget as "logisticiens", (1949 Introduction).
Practical testing of "coherence" within that tradition 
Professor Paul Thagard (and his philosophy-department team at Waterloo University Canada) developed a computer-based means for assessing the coherence of various scientific theories post hoc; (1992). This offers a practical extension to the mainstream approach.
Biologists investigate other (non adult-human) Knowledge-systems 
To tradition-minded philosophers, this may represent an extension of the concept of what "knowledge" is, and hence what can be classed as an epistemological system. Knowledge can be expressed in language-words. However a horse (or bee!) that knows how to go home, or knows that such-and-such is good food, is clearly not thinking via language as we know it — and yet such knowledge is clearly a vital "map", and without it the horse-or-bee has poor survival prospects.
Nor is it essential for the horse-or-bee (or even the adult human) to be consciously aware of the knowledge it possesses. Our bodies know how to breathe and digest without our awareness — and, as Freud pointed out in the late 1800s, much of our actual thinking goes on at a subconscious level.
Jean Piaget (1896-1980) 
He and his colleagues developed a new approach to epistemology. In particular they showed that Kant was wrong in assuming that concepts of space and time were basic, and instead offered a hypothetical set of subconscious procedures involving basic elements of (presumably encoded) action called "schèmes", by which the space-and-time concepts could be built up through experience with the real world. Such processes were carried out unconsciously, and moreover similar processes could then build upon these results yielding successive stages of development. From this, the ultimate result could be our well-known but mysterious ability to think abstractly. (Note the combination of philosophical concepts with biological principles, notably the Darwinian concept of trial and error to select amongst the arbitrarily-produced "schemes").
W. R. Ashby (1903–1972) 
Ross Ashby (a psychiatrist, "MD", and mathematician) published Design for a Brain (1952–1960), proposing formal mechanisms for an advanced mental hierarchy which seems to be compatible with Piaget's "stages" concept. Each level in the hierarchy was envisaged as a homeostat whose parameters could be adjusted by the next-higher level as a correction whenever it judged (by whatever unconscious formula) that the lower level was not performing satisfactorily.
Nomenclature for Ashby's hierarchical layers. If one says that the base-level is "L", then the next level is a "meta-level: ML", and the one above that is a "meta-meta-level: MML", and so on. Alternatively (Traill, 1978) it may be more convenient to label these "M0L, M1L, M2L, ...", respectively. It is next convenient to tentatively define M0L as corresponding to Piaget's basic "Sensori-motor" stage (of the new-born infant), and then half-expect that the higher levels will also tend to correspond to Piaget's other named stages, at least in some circumstances.
Four Different Natural Epistemologies, and their common features 
The immunologist Niels Jerne (1911–1994) seems to have been the first to explicitly comment on the formal similarity between different "learning" situations — where "learning" is used in a broad sense to include (i) Unconscious natural processes, (such as the immune system learning which proteins etc. are intruders which it should attack), as well as (ii) Learning in the conventional sense. There was arguably some overlap in the cases suggested by Jerne himself, but Popper (1975) and Traill (1999) independently selected the same short list of four significant cases, as follows below. (Also see the references cited by these two authors).
The noteworthy point is that the most basic strategy in all these cases is to depend on Trial and Error — to have a large repertoire of "candidate solutions" which have to compete (yes, in a Darwinian way) — and not by some process of "writing it all down" like a movie-camera or tape-recorder (the Lamarckian strategy).
[Of course tape recorders do get invented and used within our complex society, but they have to be designed by an "outsider" from one of the other domains. They are not sufficiently robust to organize-and-maintain themselves, whereas the four cases below are capable of doing just that.]
This task of creating knowledge (knowledge in the broad sense, and perhaps implicit in structure), and doing so ultimately out of nothing-reliable, looks like an impossible task. Hence Traill argued that there is not likely to be more-than-one solution-strategy to this general epistemology problem; so all four domains are likely to be using the same single formal strategy, even if their material embodiments and time-scales are vastly different. (Traill 1999; 2008 Table S)
(1) A time-scale of days/weeks; (2) Basic stringlike coding (protein which then forms itself into 3D patterns); (3) Huge repertoire of patterns which will only be replicated if needed; (4) Pseudo-Darwinian selection — most codes never used; but of course some are, and these represent the new knowledge.
Society-as-such (as distinct from its members) 
(1) A time-scale of weeks/centuries; (2) Basic stringlike coding (spoken and written language, mostly); (3) Huge repertoire of ideas offered by its members; (4) Pseudo-Darwinian selection — most ideas never adopted long-term; but of course a few are, and these represent the new knowledge. [This gives some scope for transcending Darwinian dice-throwing — by allowing "interference" from individuals. However such interference is not always welcomed by society-as-such!]
Mind/Brain (especially at birth) 
(1) A time-scale of seconds/days; (2) Basic stringlike coding?? (maybe, but that's debatable, see next paragraph); (3) Large repertoire of spontaneous actions-or-Piagetian-"schemes" (and perhaps some encoding for these?); (4) Pseudo-Darwinian selection — most spontaneous micro-actions yield no satisfaction; but of course some do give pleasing results, and these are accepted as new knowledge — at least for the time being.
Because of the supposed formal equivalence here, and for various other reasons, it has been argued that the basic memory-encoding (for logical thought at least) must have some sort of stringlike material basis; and by elimination this must probably be ncRNA. (Traill 1976, 1978, 2008). Current thought attributes ncRNA with the role of biochemical "regulation", though that need not be its only role. But in any case, the whole mind/brain could be seen as just a glorified "regulation" device. (Traill, 2006, abstract).
We would expect the adult brain to have some extra properties. This takes us into the Theory of cognitive development, with Piaget's "stages" and the probably-equivalent control-levels of Ross Ashby. From our present viewpoint, these extra "levels" may be seen as semi-foreign domains "interfering" in the lower infantile domains (like humans interfering in genetics). That makes it possible to achieve purposeful design and indeed pseudo-Lamarckian effects such as tape-recording and the construction of tape-recorders.
References & Further reading 
- Ashby, William Ross; (1952/1960) Design for a Brain. Chapman & Hall: London. [ISBN 0-412-20090-2]
- Beer, Anthony Stafford (1972/1981) Brain of the Firm. Wiley: NY & London.
- Beth, E.W. and Piaget, Jean (1966) Mathematical Epistemology and Psychology. D.Reidel: Dordrecht.
- Furth, H.J. (1969) Piaget and knowledge. Prentice-Hall: NJ.
- Gruber, H.E. and J.J.Vonèche (eds) (1977) The Essential Piaget. Routledge & Kegan Paul: London.
- Hebb, Donald Olding (1949/1964) The organization of behaviour. Wiley: NY & London.
- Kant, Immanuel (1781 "A" / 1787 "B" / 1993 / 2007) Critique of pure reason. Palgrave Macmillan: Boston; [N. Kemp Smith translation, ISBN 978-0-230-01338-4].
- Nitsch, F.A. (1796/1977) A View of Professor Kant's Principles of Man, World and the Deity. Yale University facsimile.
- Piaget, Jean (1923/1926) Language and Thought of the Child. Routledge & Kegan Paul: London.
- Piaget, Jean (1949/1950) Traité de logique, Armand Collin: Paris. — Republished (1972) as Essai de Logique Operatoire, Dunod.
- Piaget, Jean (1952) "La logistique axiomatique ou 'pure', la logistique operatoire ou psychologique, et les réalités auxelles elles correspondent". Methodos, 4(13), 72-85.
- Piaget, Jean (1967/1971) Biology and Knowledge. Chicago University Press.
- Popper, Karl (1934/1959/1972) Logik der Forschung / The Logic of Scientific Discovery. Hutchinson: London.
- Popper, Karl (1975/1994) "The rationality of scientific revolutions"; (i) in Rom Harré (ed.) (1975) Problems of Scientific Revolution. Scientific Progress and Obstacles to Progress in the Sciences, The Herbert Spencer Lectures 1973, Clarendon Press, Oxford. — Also in (ii) M.A.Notturno (ed.)(1994) The Myth of the Framework: In defence of science and rationality; Routledge, London; [ISBN 0-415-11320-2]; pp. 1–32.
- Thagard, Paul (1992) Conceptual Revolutions. Princeton University Press [ISBN 0-691-02390-1] — Or try his actual "ECHO" software, now accessible online: 
- Traill, R.R. (1978) Thesis [on Piaget and Ashby etc.]. Cybernetics Department, Brunel University.  — plus collection of related papers (1976/2007) 
- Traill, R.R. (1999) "Four Learning-system Types (Epistemologies): with a Common Basic Strategy" — Chapter 4, within Mind and Micromechanism. Ondwelle, Melbourne.  — [ISBN 0-9577737-0-6]
- Traill, R.R. (2006 / 2008) Thinking by molecule, synapse, or both? — From Piaget's schema, to the selecting/editing of ncRNA Ondwelle, Melbourne.  — ["Table S" is in the 2008 Supplement, p. 31.] — also available in French / aussi en français: 
- Whitehead, A.N. and B.Russell (1910–1913) Principia Mathematica. Cambridge University Press.