PHL200Y1 Lecture Notes - Lecture 5: Greek Mathematics, Platonic Realism, General Idea
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October 19, 2015 Plato’s Phaedo Part 2
The Argument from Recollection – 2nd Argument
• The general idea of the recollection argument is that recollection is a psychological phenomenon for
which one fundamental requirement is that you would have to have previously experienced what you
are going to recollect.
• You cannot recollect something you did not originally experience.
• The strategy of this argument is to show that this principle is applicable to cognitive activities we
unquestionably engage in.
• The application of the principle is, you could not have done this, unless you already had experience of
that which you are cognizing. If we have this knowledge, but we did not learn it here, then we must
have acquired this knowledge prior to incarnation.
o If this is the case, then we must have existed prior to our embodiment, because we are
recollecting an experience that we have already had. This is the basic structure of the
o A couple of premises for the recollection argument are problematic. To say that we could
not have done what we did without having previously experience a platonic form sounds
Question#1: Why does Plato think this?
• We could not have experience it unless it was a case of recollecting that in virtue of which we have
o The particular case in this example is two things being equal. Now, the text does not specific
whether it is numeral equality, or equality as we know.
o The point of the argument is not that we could not tell that two things are equal unless we
had experience a form of equality prior to our embodiment.
! If this were to be the argument, it would be obvious that one would retort, “I
learned about [mathematical concept of] equality in JK.” At some point, you
! This being the case, the argument does not even get started, because it is not the
case that in order to judge two things are equal, you would have to recollect
having an experience of equality prior to embodiment.
! Maybe you have to recollect what equality is, but you certainly could have
acquired this concept in school. There is something in the recollection
argument, which is tricky.
! The problem arises in the argument when Socrates [keep in mind he is talking
to other philosophers] is asking them to acknowledge not just that they know
that two things are equal, but, that they know that they are equal and yet they
are deficiently equal – they leave something out.
Question#2: What in the world are two things were equal will leave out with respect to equality? What are
you talking about Socrates?
• It is important to understand the idiom of Ancient Greek mathematics.
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October 19, 2015 Plato’s Phaedo Part 2
• In Ancient Greek Mathematics, they think of equality as A having the property of being equal to B,
and B having a property of being equal to A, and these two propositions are mutually entangling, but
that equality is a property that one thing has in a relation to another, entailing that the other thing has
the same property in relation to it.
• This does not change the concept of equality, but it would be easier to think about equality as a
property of, for example, one-meter stick having in relation to another meter stick.
Question#2a: Why the meter stick that is a meter long is leaving out something with respect to equality?
• What it does not mean is that the stick is not equal to the other stick.
• Your first thought would be to think that when Plato says it is leaving something out deficiently in
certain respect that means it is not exactly equal.
o If you were really careful with measurements, then you might have said that the two
things we thought were equal are not really equal after all. This is not what he is talking
• When Plato suggests that there is a form of equality over above the equal things, he is suggesting
that this is the form of these equal things, if they were deficient with respect to equality, what
would be generated would not be a form of equality, but a form of sort of equality – or almost
o A form is that which many things in common, in virtue of which they are called by the
same name. If two things are equal, there is a form of equality, and there equality if it is
deficient, does not consist in them being unequal.
Question #3: What does the deficiency consist in?
• When asked this question, you might think, and this is a sophisticated thought, “they are deficient
because it is not real equality, it is a kind of illusory equality.”
• Plato thinks that equal stick and stones are not really equal but sort of like fake equality – like
counterfeit money, it is not real money. This is a bit closer to the truth but not right.
• When Socrates talks about the deficient reality of sensible (in general sensible that has properties),
he does not mean that they do not have the property, even though they are deficient with respect to
the paradigms (paradeigma) that the forms are.
• In page 69b5, Socrates contrasts illusory virtue with true virtue.
• When Socrates says illusory, he means something, which is an image of the real, but not really
o For example, A Belgium painter drew a hyper realistic picture of a pipe, a very detailed and
accurate drawing of a pipe, and at the bottom of the painting it wrote, “This is a pipe [in French]”.
On the one hand, you would say the drawing is a drawing of a pipe. On the other hand, you would
have to admit that it is not a pipe – you cannot smoke the drawing. That is analogies to what Plato
is talking about when he talks about illusory virtue vs. true virtue. Illusory virtue is not virtue; it
isn’t not virtue
• Illusory virtue is not the real thing; it is diminished in reality. If you recall, the dianomo (?) of the
ascent in the symposium – the higher mysteries, the philosophy who sees the form of beauty will
produce true virtue, and if you recall, What true virtue is in the Symposium is exactly what true
virtue is in the Phaedo. Though there he does not call the contrasting virtue illusory virtue.
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