A talk on Gail Fine’s paper about false beliefs in the “Theaetetus”
Grimesby Roylott
In the “Theaetetus” Socrates and Theaetetus talk about whether or not it is possible to have a
false belief. Socrates states that according to Theaetetus’ definition of knowledge being true belief one
must be able to define and obtain its opposite, false belief which he maintains is not possible. One
argument that Socrates presents against false beliefs is as follows and which I shall refer to as K:
(1) For any x, either one knows x or one does not know x.
(2) For any x such that one has a belief about x, either one knows x or one does not know x.
(3) It is impossible for one both to know and not to know the same thing.
(4) If one has a false belief that x is y, either
(a) One knows x and y; or
(b) One knows x or y, but not both; or
(c) One knows neither x nor y.
(5) None of (4) (a)-(c) is possible.
(6) Therefore there is no false belief
The first problem is why (4a-c) is not possible. (1-3) follow from logical laws, thus we can
validate (4) by modifying and earlier statement while making sure that not to change the meaning. The
easiest statement to modify is (2) since it the only one that pertains to having beliefs. The simplest
alteration would be changing (2) to:
(2a) For any x such that one has a belief about x, one knows x
This interpretation helps to bring about (4b&c) since if one is totally ignorant of something than one
cannot form beliefs about it. (4a) still presents problem as it is possible to know something and yet still
hold a belief about it which is false. For instance I could know where in the solar system Pluto is located
what it is made of and how large it is and still hold the belief that it is a planet.
Since (2a) fails to bring about (5) we will have to change it to
(2b) for any x such that one has a belief-about x, one is acquainted with x.
In this case should you take acquaintance in the typical sense in which you are acquainted with person it
would not suffice to bring about (4a) for instance if I know president Obama and have met him but I
could still falsely believe that he was born in Iran. However it bring about (4a) should you say that one
has acquaintance only that which they are directly aware of and that further knowledge is not possible.
At this point though (2b) looks more like:
(2c) for any x such that one has a belief about x, one either knows everything about x or is totally
ignorant of x
While this does bring about (5) it is not without problems. (2c) rules out the possibility that someone
might have a base knowledge of a subject and yet still have a belief about that subject. For instance I
have the belief about math that it is hard. According to (2c) since I have a belief about math I know
everything about math which false. Since I don’t know everything about math (2c) states that I am
completely ignorant about math which is also false.
Even with this refutation to his first argument Socrates refutes Theaetetus in other ways.
Theaetetus brings up the idea that most if not all false beliefs are caused by someone confusing
concepts and misplacing objects under the wrong concept, like confusing beauty with ugliness such as in
the following argument as shown in Fine’s paper:
(11) Theaetetus thinks that Socrates is beautiful.
(12) Socrates is ugly.
(13) Therefore Theaetetus thinks that ugly Socrates is beautiful
This concept is referred to as allodoxia. There are a few ways to look at this argument with two of them
being:
(7) Theaetetus thinks that ugliness is beauty
(8) Theaetetus thinks of ugliness that it is beauty
(7) is a case of confusion which would be implausible, since confusing something so as to think it is
actually its opposite would be a lack of a grasp of definition and not a case of confusion. (8) is not saying
that ugliness is beauty but that rather that things with the property of ugliness are beautiful.
Two other ways of proposing allodoxia are:
(9) Theaetetus thinks that the ugly thing is beautiful
(10) Theatetus thinks of the ugly thing that it is beautiful
In (9) Theaetetus directly states that ugly is beautiful which runs into the same problem that (7) does,
being implausible and contradictory. For (10) Theaetetus is saying that he believe that that the thing is
beautiful. This is similar to saying that Theaetetus thinks that the thing is beautiful.
The above example using (11) (12) (13) can be expanded to:
We can schematize Plato's argument like this:
(11) Theaetetus thinks that Socrates is beautiful (10).
(12) Socrates is ugly.
(13) Therefore Theaetetus thinks that ugly Socrates is beautiful.
The move from (1 1) and (12) to (13) can be validated with the aid of the K:
(14) Theaetetus knows Socrates and beauty, since they figure in his
Judgment (2c).
(15) Theaetetus, since he knows Socrates, knows that he is ugly.
(16) Theaetetus thinks (a) Socrates is ugly (15), and (b) Socrates is
beautiful (1 1).
(17) Therefore Theaetetus thinks that ugly Socrates is beautiful (13)
This is refuted using the earlier refutation of (2c), but beyond that a big issue is that the argument is
using the subjective concepts of beauty as though they are objective. In the above argument I shall
target (12). Where did (12) come from, by whose or what standard is Socrates ugly. Since ugliness is
subjective a large group people will rarely unanimously agree to accepting (12) and if they should then
(assuming that Socrates does not have a physical anomaly like a conjoined twin that never physically
developed past being an infant) each individual will judge him based on their own criteria. Due to this
lack of a standard for judging ugliness in those that are not a physical anomaly it is possible and plausible
that though one person finds Socrates to be ugly with one set of criteria another person would be
equally correct in finding him to be beautiful with their own criteria. This can be overcome by replacing
the subjective concepts with something objective. In the above case one could replace beautiful with
female and ugly with male therefore the argument becomes:
(11) Theaetetus thinks that Socrates is female.
(12) Socrates is male.
(13) Therefore Theaetetus thinks that male Socrates is female.
The move from (1 1) and (12) to (13) can be validated with the aid of the K:
(14) Theaetetus knows Socrates and female, since they figure in his
judgment (2c).
(15) Theaetetus, since he knows Socrates, knows that he is male.
(16) Theaetetus thinks (a) Socrates is male (15), and (b) Socrates is
female (1 1).
(17) Therefore Theaetetus thinks that male Socrates is female (13)
In this revised argument the logic chain is still false and yet since male and female is not subject one
cannot argue against it using the idea of differing criteria.