Plato and innatism

What is the first issue with the slave boy arg

It's not clear that the slave boy leant how to double the area of the square. He says at the end of Socrates' questioning: 'By Zeus, Socrates, I do not know.' Socrates says at the end of the dialogue, 'not only does he not know the answer; he doesn't even think he knows.'

What is the second issue with the slave boy arg

Secondly, the doubling of the square could simply be an instance of reasoning in action. It might be a case of acquired conceptual a priori knowledge. There can be a priori analytic truths - truths which are true by definition - which no one claims are innate, for example, 'all bachelors are unmarried men'. We acquire this knowledge as we acquire language, but its proof is independent of experience.
Also, it seems that Socrates' questioning is leading. He uses closed questions which he feeds back on to the Slave boy. In this way, the boy can work out what the right answer ought to have been and so learn.

What is the arg from universals?

R1: The senses can only reveal particular instances (usually imperfect examples).
R2: The mind can grasp perfect universal concepts (or knowledge) (usually through a process of reasoning).
IC: These concepts cannot be derived from the senses.
C: These concepts must be contained within us to begin with (they are innate).

What is the first issue that could be raised against the arg from universals?

this is acquired a priori analytic knowledge and perhaps people learn universals through questioning in life.

What is the second problem for the arg from universals?

when Plato extends his point about general concepts beyond maths and geometry, to include such general terms as beauty and justice, he finds it hard to specify what the universal and perfect Forms of justice and beauty are.

What is the third problem?

empirically minded philsophers will argue that we develop perfect and universal ideas of things by experiencing imperfect instances and then abstracting the imperfections, mentally.

How will Plato respond to the third issue?

Plato will insist that we could not arrive at such universal and perfect knowledge of, say, the circle, by the process of abstraction. Normally, if you see only a number of instances of imperfect things, it is not possible to arrive at a perfect definition which will apply in all cases.

What are the qualities of the forms?

self-predicating- They give to themselves their quality (predicate). While a set square is triangular because its triangularity is an instance of the Form of the triangle, i.e. it receives its predicate from outside itself, this is not true of the Forms. The Form of triangle, is triangular due to itself.

Perfect- The Form of a triangle does not just participate in triangularity to a greater or lesser extent, it is it, perfectly, i.e. it exactly fulfils the necessary and sufficient conditions for a triangle.

permanent- unaltering in their perfection. Material things can change becoming better or worse instances of a Form. But the Forms themselves are timeless and unchanging archetypes.

Simple- A Form, is nothing more than what it is a Form of. The Form of the triangle is triangular.