2.2: Justified True Belief
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- 52247
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)SOCRATES: Yes, my boy, and so do I; and my desire is to learn of him, or of anybody who seems to understand these things. And I get on pretty well in general; but there is a little difficulty which I want you and the company to aid me in investigating. Will you answer me a question: 'Is not learning growing wiser about that which you learn?'
THEAETETUS: Of course.
SOCRATES: And by wisdom the wise are wise?
THEAETETUS: Yes.
SOCRATES: And is that different in any way from knowledge?
THEAETETUS: What?
SOCRATES: Wisdom; are not men wise in that which they know?
THEAETETUS: Certainly they are.
SOCRATES: Then wisdom and knowledge are the same?
THEAETETUS: Yes.
SOCRATES: Herein lies the difficulty which I can never solve to my satisfaction--What is knowledge? Can we answer that question? What say you? which of us will speak first? whoever misses shall sit down, as at a game of ball, and shall be donkey, as the boys say; he who lasts out his competitors in the game without missing, shall be our king, and shall have the right of putting to us any questions which he pleases…
***
THEAETETUS: I cannot say, Socrates, that all opinion is knowledge, because there may be a false opinion; but I will venture to assert, that knowledge is true opinion: let this then be my reply; and if this is hereafter disproved, I must try to find another.
SOCRATES: That is the way in which you ought to answer, Theaetetus, and not in your former hesitating strain, for if we are bold we shall gain one of two advantages; either we shall find what we seek, or we shall be less likely to think that we know what we do not know--in either case we shall be richly rewarded. And now, what are you saying?--Are there two sorts of opinion, one true and the other false; and do you define knowledge to be the true?
THEAETETUS: Yes, according to my present view.
SOCRATES: Is it still worth our while to resume the discussion touching opinion?
THEAETETUS: To what are you alluding?
SOCRATES: There is a point which often troubles me, and is a great perplexity to me, both in regard to myself and others. I cannot make out the nature or origin of the mental experience to which I refer.
THEAETETUS: Pray what is it?
SOCRATES: How there can be false opinion--that difficulty still troubles the eye of my mind; and I am uncertain whether I shall leave the question, or begin over again in a new way.
THEAETETUS: Begin again, Socrates,--at least if you think that there is the slightest necessity for doing so. Were not you and Theodorus just now remarking very truly, that in discussions of this kind we may take our own time?
SOCRATES: You are quite right, and perhaps there will be no harm in retracing our steps and beginning again. Better a little which is well done, than a great deal imperfectly.
THEAETETUS: Certainly.
SOCRATES: Well, and what is the difficulty? Do we not speak of false opinion, and say that one man holds a false and another a true opinion, as though there were some natural distinction between them?
THEAETETUS: We certainly say so.
SOCRATES: All things and everything are either known or not known. I leave out of view the intermediate conceptions of learning and forgetting, because they have nothing to do with our present question.
THEAETETUS: There can be no doubt, Socrates, if you exclude these, that there is no other alternative but knowing or not knowing a thing.
SOCRATES: That point being now determined, must we not say that he who has an opinion, must have an opinion about something which he knows or does not know?
THEAETETUS: He must.
SOCRATES: He who knows, cannot but know; and he who does not know, cannot know?
THEAETETUS: Of course.
SOCRATES: What shall we say then? When a man has a false opinion does he think that which he knows to be some other thing which he knows, and knowing both, is he at the same time ignorant of both?
THEAETETUS: That, Socrates, is impossible.
SOCRATES: But perhaps he thinks of something which he does not know as some other thing which he does not know; for example, he knows neither Theaetetus nor Socrates, and yet he fancies that Theaetetus is Socrates, or Socrates Theaetetus?
THEAETETUS: How can he?
SOCRATES: But surely he cannot suppose what he knows to be what he does not know, or what he does not know to be what he knows?
THEAETETUS: That would be monstrous.
SOCRATES: Where, then, is false opinion? For if all things are either known or unknown, there can be no opinion which is not comprehended under this alternative, and so false opinion is excluded.
THEAETETUS: Most true.
SOCRATES: Suppose that we remove the question out of the sphere of knowing or not knowing, into that of being and not-being.
THEAETETUS: What do you mean?
SOCRATES: May we not suspect the simple truth to be that he who thinks about anything, that which is not, will necessarily think what is false, whatever in other respects may be the state of his mind?
THEAETETUS: That, again, is not unlikely, Socrates.
SOCRATES: Then suppose some one to say to us, Theaetetus:--Is it possible for any man to think that which is not, either as a self-existent substance or as a predicate of something else? And suppose that we answer, 'Yes, he can, when he thinks what is not true.'--That will be our answer?
THEAETETUS: Yes.
SOCRATES: But is there any parallel to this?
THEAETETUS: What do you mean?
SOCRATES: Can a man see something and yet see nothing?
THEAETETUS: Impossible.
SOCRATES: But if he sees any one thing, he sees something that exists. Do you suppose that what is one is ever to be found among non-existing things?
THEAETETUS: I do not.
SOCRATES: He then who sees some one thing, sees something which is?
THEAETETUS: Clearly.
SOCRATES: And he who hears anything, hears some one thing, and hears that which is?
THEAETETUS: Yes.
SOCRATES: And he who touches anything, touches something which is one and therefore is?
THEAETETUS: That again is true.
SOCRATES: And does not he who thinks, think some one thing?
THEAETETUS: Certainly.
SOCRATES: And does not he who thinks some one thing, think something which is?
THEAETETUS: I agree.
SOCRATES: Then he who thinks of that which is not, thinks of nothing?
THEAETETUS: Clearly.
SOCRATES: And he who thinks of nothing, does not think at all?
THEAETETUS: Obviously.
SOCRATES: Then no one can think that which is not, either as a self-existent substance or as a predicate of something else?
THEAETETUS: Clearly not.
SOCRATES: Then to think falsely is different from thinking that which is not?
THEAETETUS: It would seem so.
SOCRATES: Then false opinion has no existence in us, either in the sphere of being or of knowledge?
THEAETETUS: Certainly not.
***
SOCRATES: Then, once more, what shall we say that knowledge is?--for we are not going to lose heart as yet.
THEAETETUS: Certainly, I shall not lose heart, if you do not.
SOCRATES: What definition will be most consistent with our former views?
THEAETETUS: I cannot think of any but our old one, Socrates.
SOCRATES: What was it?
THEAETETUS: Knowledge was said by us to be true opinion; and true opinion is surely unerring, and the results which follow from it are all noble and good.
SOCRATES: He who led the way into the river, Theaetetus, said 'The experiment will show;' and perhaps if we go forward in the search, we may stumble upon the thing which we are looking for; but if we stay where we are, nothing will come to light.
THEAETETUS: Very true; let us go forward and try.
SOCRATES: The trail soon comes to an end, for a whole profession is against us.
THEAETETUS: How is that, and what profession do you mean?
SOCRATES: The profession of the great wise ones who are called orators and lawyers; for these persuade men by their art and make them think whatever they like, but they do not teach them. Do you imagine that there are any teachers in the world so clever as to be able to convince others of the truth about acts of robbery or violence, of which they were not eye-witnesses, while a little water is flowing in the clepsydra?
THEAETETUS: Certainly not, they can only persuade them.
SOCRATES: And would you not say that persuading them is making them have an opinion?
THEAETETUS: To be sure.
SOCRATES: When, therefore, judges are justly persuaded about matters which you can know only by seeing them, and not in any other way, and when thus judging of them from report they attain a true opinion about them, they judge without knowledge, and yet are rightly persuaded, if they have judged well.
THEAETETUS: Certainly.
SOCRATES: And yet, O my friend, if true opinion in law courts and knowledge are the same, the perfect judge could not have judged rightly without knowledge; and therefore I must infer that they are not the same.
***
THEAETETUS: That is a distinction, Socrates, which I have heard made by some one else, but I had forgotten it. He said that true opinion, combined with reason, was knowledge, but that the opinion which had no reason was out of the sphere of knowledge; and that things of which there is no rational account are not knowable--such was the singular expression which he used--and that things which have a reason or explanation are knowable. …
SOCRATES: Well, and what is the meaning of the term 'explanation'? I
think that we have a choice of three meanings.
THEAETETUS: What are they?
SOCRATES: In the first place, the meaning may be, manifesting one's thought by the voice with verbs and nouns, imaging an opinion in the stream which flows from the lips, as in a mirror or water. Does not explanation appear to be of this nature?
THEAETETUS: Certainly; he who so manifests his thought, is said to explain himself.
SOCRATES: And every one who is not born deaf or dumb is able sooner or later to manifest what he thinks of anything; and if so, all those who have a right opinion about anything will also have right explanation; nor will right opinion be anywhere found to exist apart from knowledge.
THEAETETUS: True.
SOCRATES: Let us not, therefore, hastily charge him who gave this account of knowledge with uttering an unmeaning word; for perhaps he only intended to say, that when a person was asked what was the nature of anything, he should be able to answer his questioner by giving the elements of the thing.
THEAETETUS: As for example, Socrates...?
SOCRATES: As, for example, when Hesiod says that a wagon is made up of a hundred planks. Now, neither you nor I could describe all of them individually; but if any one asked what is a wagon, we should be content to answer, that a wagon consists of wheels, axle, body, rims, yoke.
THEAETETUS: Certainly.
SOCRATES: And our opponent will probably laugh at us, just as he would if we professed to be grammarians and to give a grammatical account of the name of Theaetetus, and yet could only tell the syllables and not the letters of your name--that would be true opinion, and not knowledge; for knowledge, as has been already remarked, is not attained until, combined with true opinion, there is an enumeration of the elements out of which anything is composed.
THEAETETUS: Yes.
SOCRATES: In the same general way, we might also have true opinion about a wagon; but he who can describe its essence by an enumeration of the hundred planks, adds rational explanation to true opinion, and instead of opinion has art and knowledge of the nature of a wagon, in that he attains to the whole through the elements.
THEAETETUS: And do you not agree in that view, Socrates?
SOCRATES: If you do, my friend; but I want to know first, whether you admit the resolution of all things into their elements to be a rational explanation of them, and the consideration of them in syllables or larger combinations of them to be irrational--is this your view?
THEAETETUS: Precisely.
SOCRATES: Well, and do you conceive that a man has knowledge of any element who at one time affirms and at another time denies that element of something, or thinks that the same thing is composed of different elements at different times?
THEAETETUS: Assuredly not.
SOCRATES: And do you not remember that in your case and in that of others this often occurred in the process of learning to read?
THEAETETUS: You mean that I mistook the letters and misspelt the syllables?
SOCRATES: Yes.
THEAETETUS: To be sure; I perfectly remember, and I am very far from supposing that they who are in this condition have knowledge.
SOCRATES: When a person at the time of learning writes the name of Theaetetus, and thinks that he ought to write and does write Th and e; but, again, meaning to write the name of Theododorus, thinks that he ought to write and does write T and e--can we suppose that he knows the first syllables of your two names?
THEAETETUS: We have already admitted that such a one has not yet attained knowledge.
SOCRATES: And in like manner be may enumerate without knowing them the second and third and fourth syllables of your name?
THEAETETUS: He may.
SOCRATES: And in that case, when he knows the order of the letters and can write them out correctly, he has right opinion?
THEAETETUS: Clearly.
SOCRATES: But although we admit that he has right opinion, he will still be without knowledge?
THEAETETUS: Yes.
SOCRATES: And yet he will have explanation, as well as right opinion, for he knew the order of the letters when he wrote; and this we admit to be explanation.
THEAETETUS: True.
SOCRATES: Then, my friend, there is such a thing as right opinion united with definition or explanation, which does not as yet attain to the exactness of knowledge.
THEAETETUS: It would seem so.
SOCRATES: And what we fancied to be a perfect definition of knowledge is a dream only. But perhaps we had better not say so as yet, for were there not three explanations of knowledge, one of which must, as we said, be adopted by him who maintains knowledge to be true opinion combined with rational explanation? And very likely there may be found some one who will not prefer this but the third.
THEAETETUS: You are quite right; there is still one remaining. The first was the image or expression of the mind in speech; the second, which has just been mentioned, is a way of reaching the whole by an enumeration of the elements. But what is the third definition?
SOCRATES: There is, further, the popular notion of telling the mark or sign of difference which distinguishes the thing in question from all others.
THEAETETUS: Can you give me any example of such a definition?
SOCRATES: As, for example, in the case of the sun, I think that you would be contented with the statement that the sun is the brightest of the heavenly bodies which revolve about the earth.
THEAETETUS: Certainly.
SOCRATES: Understand why:--the reason is, as I was just now saying, that if you get at the difference and distinguishing characteristic of each thing, then, as many persons affirm, you will get at the definition or explanation of it; but while you lay hold only of the common and not of the characteristic notion, you will only have the definition of those things to which this common quality belongs.
THEAETETUS: I understand you, and your account of definition is in my judgment correct.
SOCRATES: But he, who having right opinion about anything, can find outthe difference which distinguishes it from other things will know that of which before he had only an opinion.
THEAETETUS: Yes; that is what we are maintaining.
SOCRATES: Nevertheless, Theaetetus, on a nearer view, I find myself quite disappointed; the picture, which at a distance was not so bad, has now become altogether unintelligible.
THEAETETUS: What do you mean?
SOCRATES: I will endeavour to explain: I will suppose myself to have true opinion of you, and if to this I add your definition, then I have knowledge, but if not, opinion only.
THEAETETUS: Yes.
SOCRATES: The definition was assumed to be the interpretation of your difference.
THEAETETUS: True.
SOCRATES: But when I had only opinion, I had no conception of your distinguishing characteristics.
THEAETETUS: I suppose not.
SOCRATES: Then I must have conceived of some general or common nature which no more belonged to you than to another.
THEAETETUS: True.
SOCRATES: Tell me, now--How in that case could I have formed a judgment of you any more than of any one else? Suppose that I imagine Theaetetus to be a man who has nose, eyes, and mouth, and every other member complete; how would that enable me to distinguish Theaetetus from Theodorus, or from some outer barbarian?
THEAETETUS: How could it?
SOCRATES: Or if I had further conceived of you, not only as having nose and eyes, but as having a snub nose and prominent eyes, should I have any more notion of you than of myself and others who resemble me?
THEAETETUS: Certainly not.
SOCRATES: Surely I can have no conception of Theaetetus until your snub-nosedness has left an impression on my mind different from the snub-nosedness of all others whom I have ever seen, and until your other peculiarities have a like distinctness; and so when I meet you to-morrow the right opinion will be re-called?
THEAETETUS: Most true.
SOCRATES: Then right opinion implies the perception of differences?
THEAETETUS: Clearly.
SOCRATES: What, then, shall we say of adding reason or explanation to right opinion? If the meaning is, that we should form an opinion of the way in which something differs from another thing, the proposal is ridiculous.
THEAETETUS: How so?
SOCRATES: We are supposed to acquire a right opinion of the differences which distinguish one thing from another when we have already a right opinion of them, and so we go round and round:--the revolution of the scytal, or pestle, or any other rotatory machine, in the same circles, is as nothing compared with such a requirement; and we may be truly described as the blind directing the blind; for to add those things which we already have, in order that we may learn what we already think, is like a soul utterly benighted.
THEAETETUS: Tell me; what were you going to say just now, when you asked the question?
SOCRATES: If, my boy, the argument, in speaking of adding the definition, had used the word to 'know,' and not merely 'have an opinion' of the difference, this which is the most promising of all the definitions of knowledge would have come to a pretty end, for to know is surely to acquire knowledge.
THEAETETUS: True.
SOCRATES: And so, when the question is asked, What is knowledge? This fair argument will answer 'Right opinion with knowledge,'--knowledge, that is, of difference, for this, as the said argument maintains, is adding the definition.
THEAETETUS: That seems to be true.
SOCRATES: But how utterly foolish, when we are asking what is knowledge, that the reply should only be, right opinion with knowledge of difference or of anything! And so, Theaetetus, knowledge is neither sensation nor true opinion, nor yet definition and explanation accompanying and added to true opinion?
THEAETETUS: I suppose not.
SOCRATES: And are you still in labour and travail, my dear friend, or have you brought all that you have to say about knowledge to the birth?
THEAETETUS: I am sure, Socrates, that you have elicited from me a good deal more than ever was in me.
SOCRATES: And does not my art show that you have brought forth wind, and that the offspring of your brain are not worth bringing up?
THEAETETUS: Very true.
SOCRATES: But if, Theaetetus, you should ever conceive afresh, you will be all the better for the present investigation, and if not, you will be soberer and humbler and gentler to other men, and will be too modest to fancy that you know what you do not know. These are the limits of my art; I can no further go, nor do I know aught of the things which great and famous men know or have known in this or former ages. The office of a midwife I, like my mother, have received from God; she delivered women, I deliver men; but they must be young and noble and fair. And now I have to go to the porch of the King Archon, where I am to meet Meletus and his indictment. To-morrow morning, Theodorus, I shall hope to see you again at this place.