Defining Knowledge


This time I am going to concern myself with the problem of defining knowledge. As this takes more pains than I initially expected, I must postpone my suggestion of a strategy against (radical) scepticism (of knowledge) to future articles.
I begin with a summary of Plato’s dialogue ΘΕΑΙΤΗΤΟΣ (Theatetos) (1). Immanuel Kant (2) and A. J. Ayer (3), then, will lead me to contemporary epistemology. (I shall deal with Edmund L. Gettier’s paper ‘Is Justified True Belief Knolwedge?’, which at first I planned to include in this article, in a separate article to come.)

1. Plato’s Theatetos

In his ΘΕΑΙΤΗΤΟΣ (Theatetos), Plato puts three suggestions for a definition of knowledge on trial. The first one is, as allegedly held by Protagoras and Heraclitus, that knowledge reduce to perception (ἐπιστήμη),1 and as a consequence to (mere) opinion,2 with the result that knowledge turns out relative to a respective point of view. In other words, there is no objective but only subjective knowledge. This follows from the equation of ‘appearance’ (φαντασία) with ‘perception’ (αἴσθησις),3 and ‘perception’ with ‘knowledge’.
Plato, speaking through the imaginative figure of his teacher, Socrates, gives a reductio ad absurdum in virtue of a large amount of examples in order to refute the definition of knowledge as perception. The most convincing one, in my view, is that if knowledge were reducable to perception, and thus to (mere) opinion, even madmen would be right in considering themselves gods, or the dreaming in conceiving of themselves as having wings and flying in their dreams, and no one could, whatever they may seem to them, (correctly) say that they (the madmen and the dreaming) be wrong.4
Another important objection to the position of Protagoras and Heraclitus is the threat of self-contradiction by the necessarily following (global) relativism. For if what is true, and thereby knowledge, be only what appears to be true to each respective viewpoint, why should we admit that Protagoras and Heraclitus are right in their view if it seems wrong to us?5 We are, as it happens, confronted with a classical dilemma. Either Protagoras’s and Heraclitus’s position is right, whereby it would be wrong because it would be absolutely right, and thus there would be an absolute truth, so that consequently not only what appears to each person as true would be true but also (at least) one opinion objectively; or Protagoras and Heraclitus are wrong in holding that only what appear to each person as true be true, that is to say, wrong anyway. Formally, the argument looks like this (where ‘P’ stands for ‘premise’, and ‘C’ stands for ‘conclusion’):

P1 p → ~p
P2 ~p → ~p
C ~p

At best, Protagoras and Heraclitus, or whoever adhere to their position, would be argumentatively isolated, that is, they could not convince anyone of their opinion. Personally, I hold the stronger view, that is, that (global) relativism, which is the result of Protagoras’s and Heraclitus’s position, is wrong, since it contradicts itself – as becomes apparent from the formal version of the dilemma argument given above. If it be logically true that if p, then p, it necessarily is a contradiction that if p, then ~p [p → p: → ~ .p → ~p]. In short, the first premise violates the law of excluded contradiction.

After discussing many other examples, Plato (as the imaginative Socrates) eventually rejects the hypothesis of knowledge being reducable to perception. The second tentative definition is that knowledge be true opinion (ἀληθὴς δόξα).6 It is follwed by a long scrutiny with regard to what false opinion be, including the question whether it be possible in principle. This is not the place to pursue the details of this enterprise, however. Suffice it, therefore, to state the outcome: The only manners wherein one can have a false opinion (τὰ ψευδῆ δοξάσαι) are (i) to both remember someone or something S and S′, and have a perception of both, but at the same time mistake S for S′ and vice versa; and (ii) to both remember someone or something S and S′, and have a perception of either S or S′ (but not both), while not having a perception of the other, and mistake the one one has a perception of for the other one has no perception of.7 To put it a bit differently, if one both remembers and perceives a and b, but mistakes a for b, and b for a, one’s opinion is false. Likewise, if one both remembers a and b, and perceives a but mistakes a for b, or perceives b but mistakes b for a, one’s opionion is false.
If, for all that, one can be persuaded to hold some opinion or other, as orators (ῥήτωροι) and advocates (δικαvικόι) do, such that ‘persuade’ means ‘bring it about that some opinion be held in a certain manner’, true opinion cannot be the same as knowledge.8

The final tentative definition of knowledge Plato suggests is that knowledge be true opinion with an explanation.9 The ensuing passages, if those up to now have not yet done so, prove Plato to be one of the most ingenious men in the history of philosophy, and I am not sure whether I fully understand his investigation as concerns the term ‘explanation’. What he seems to say is the following. The first option is that an explanation be a portrait of thoughts by the voice. Socrates rejects this interpretation for the reason that everybody is able to do this unless they be blind or deaf. There would not be any difference between holding an opinion and giving expression to it by means of one’s voice, that is, uttering it verbally.10
The second, then, is that albeit one hold a true opinion, having in mind all the elements, which latter counts as an explanation (a whole consists of its parts, thus, knowing all the parts explains the whole), one may, all the same, be wrong, and thus not hold knowledge.11 In the text, Socrates, in order to provide a concrete instance, asks Theatetos to envisage someone writing ‘Theatetos’, thereby being of the opinion he need to write ‘Th’ and ‘e’, and actually does so; whereas when he want to write ‘Theodoros’, he be of the opinion that he need to write ‘T’ and ‘e’, and actually does so. Asked then whether he (the writing person) can be said to know (ἑπίστασθαι) the first syllable of both names respectively, Theatetos responds in the negative.12,13
The third and final analysis Plato contemplates is that an explanation be telling a thing asked for from everything else. This reading, though, he refutes as well as follows. If he (speaking through Socrates) have a true opinion of Theatetos, the definition of knowledge as ‘true opinion with an explanation’ would bar his true opinion from qualifying as knowledge unless he be able to say how Theatetos differ from everyone else. The objection now runs that if this were true, he (Socrates) could not have an opinion rather of Theatetos than of anyone else. On the other hand, if he know to what extend Theatetos differ from anyone else, then it would be useless to demand that he also have an opinion regarding how Theatetos differ from anyone else, for it would be already entailed by his true opinion.14
Thus, the dialogue ends with no viable solution to the problem of what knowledge be.

2. Immanuel Kant

More than 2000 years later, in 1781, Immanuel Kant writes in his Kritik der reinen Vernunft (Critique of Pure Reason), ‘Endlich heißt das sowohl subjektiv als objektiv zureichende Fürwahrhalten das W i s s e n.’15 (‘Lastly, when the holding of a thing to be true is sufficient both subjectively and objectively, it is knowledge.’)16 Stated in modern jargon, Kant holds knowledge to be justified true belief – subjectively sufficient is the holding of something (a proposition) to be true if one believes it; objectively sufficient is it if one has evidence for it which does not depend upon one’s holding it to be true in order that it be true. This will be an important point in my next article.

3. A. J. Ayer

In 1956, A. J. Ayer added two further conditions in the chapter ‘Knowing as Having the Right to be Sure’ of his Book The Problem of Knowledge:

If we are not to be bound by ordinary usage, it is still open to us to make it a rule that only what is certain can be known. That is, we could decide, at least for the purposes of philosophical discourse, not to use the word ‘know’ except with the implication that what was known was necessarily true, or, perhaps, certain in some other way. The consequence would be that we could still speak of knowing the truth of a priori statements, such as those describing the content of one’s own present experience, that were certain in themselves, they too might be included; but most of what we now correctly claim to know would not be knowable, in this allegedly strict sense. […]17

Some pages later, he goes on:

I conclude then that the necessary and sufficient conditions for knowing that something is the case are first that what one is said to know be true, secondly that one be sure of it, and thirdly that one should have the right to be sure. This right may be earned in various ways; but even if one could give a complete description of them it would be a mistake to try to built it into the definition of knowledge, just as it would be a mistake to try to incorporate our actual standards of goodness into a definition of good. And this being so, it turns out that the questions which philosophers raise about the possibility of knowledge are not all to be settled by discovering what knowledge is. […] 18

In order to see why Ayer thinks that being sure as well as the right to be sure need to be added to our conception of knowledge, imagine the following situation. Sarah, a woman of 25 years of age, under normal circumstances (she has normal sight, normal hearing, is not drugged or traumatized, and so forth) witnesses on a sunny day with no rain, no clouds, and no obstacles to her visual field something crossing her visual field. Her friend, Mary-Ann, joins her immediately after this occurrence, and Sarah tells Mary-Ann that she believes that she has witnessed a wasp crossing her visual field. As it happens, it was a wasp which crossed her visual field. So far so good. Sarah believes that p [= ‘a wasp crossed my visual field’], p is true, and Sarah ist justified in believing that p in virtue of her perceptual evidence, that is, she has the right to be sure. Unfortunately, Sarah then adds: ‘I believe a wasp crossed my visual field, but I am not sure.’ If stating that one be not sure implies entertaining the counterfactual thought that one may falsely believe that p, then one’s justified true belief would not count as knowledge. Therefore, although Sarah’s belief is justified and true, including the right to be sure, it does not qualify as knowledge.

1. Platon: Theätet. Griechisch-deutsch. Kommentar von Alexander Becker; Frankfurt am Main: Suhrkamp Verlag; Erste Auflage 2007, 151e [All following citations and references are from/to this edition (Theätet, for short). The pagination follows the Greek edition by Henricus Stephanus from 1578.]
2. In today’s philosophical vocabulary, the term ‘belief’ has prevailed over the term ‘opinion’, yet this is negligible for the present enterprise.
3. Theätet, 152c.
4. Op. cit., 158b.
5. Op. cit., 161d-e.
6. Op. cit., 187b.
7. Op. cit., 193b-c.
8. Op. cit., 201a-c.
9. Op. cit., 201d.
10. Op. cit., 206d-e.
11. Op. cit., 208a-b.
12. Op. cit., 207e-208a.
13. Op. cit., 208a: ‘Ἀλλ’ ἄρτι ὡμολογήσαμεν τὸν οὕτως ἔχοντα μήπω εἰδέναι.’
14. Op. cit., 208c-209e.
15. Kant,Immanuel: Kritik der reinen Vernunft; Hamburg: Felix Meiner Verlag 1998, A 822/B 850. [The pagination follows the two original (German) editions from 1781 (A) and 1787 (B).]
16. Kant, Immanuel: Critique of Pure Reason; translated by Norman Kemp Smith; New York: Palgrave Mcmillan 1929; second edition published 1933, A 822/B 850. [The pagination follows the two original (German) editions from 1781 (A) and 1787 (B).]
17. Ayer, A. J.: ‘Knowing as Having the Right to be Sure’ in The Problem of Knowledge; London: Macmillan 1956; reprinted in Bernecker, Sven and Dretske, Fred: Knowledge. Readings in Contemporary Epistomology; Oxford: Oxford University Press 2000, reprinted 2005, pp. 7-8.
18. Op. cit., pp. 10-11.


One thought on “Defining Knowledge

  1. Pingback: Defining Knowledge | Ich bin das Wort ist ich | Ancient Origins of Science |

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