Sep 20 - In my lecture last Thursday, I may not have given sufficient emphasis to an important point about instantiation, namely that instantiation only works (is only valid) when the premise is an explicitly universal one, that is, applies to everything. In the first argument from MENO, the premise is explicitly universal: All knowledge is teachable, or equivalently: Everything is such that if it is knowledge then it is teachable, or again equivalently: For every x, if x is knowledge then x is teachable. So the form of this argument is: (Prem) For every x, if P(x) then R(x); (Concl) For some particular x, say a, if P(a) then R(a). The form of this argument can also be expressed by abbreviating the premise and conclusion even further: (Prem) For every x, Q (x); (Concl) Q (a). (Here 'Q(x)' abbreviates 'If P(x) then R(x)'.)

The important point, which I may not have made clear, is that 'For every x' or some other expression indicating universality (such as 'all x's' or 'every x') must be explicitly stated in order for instantiation to be valid. To go from 'Some knowledge is teachable' to 'If virtue is knowledge then virtue is teachable' would be illegitimate, because if only some knowledge is teachable, virtue could be knowledge that is not teachable, and in that case a true premise would lead to a false conclusion.

I have modified the transparency about instantiation to make this point more forcefully. Please check the new version of Transparency No.2 for Lecture 5 on the course web site.

Sep 21 - Also in my lecture Thursday, I distinguished several different kinds of knowledge, and said that Plato restricts his claim that learning something (coming to know it) is a matter of recollecting to one kind of knowledge only, namely a priori knowledge. There was no mention of this point in the outline for that lecture. So I have also modified the outline of that lecture on the web site. Please check the new version of Outline for Lecture 4 there as well.