> Take Plato, for example: He and his also-famous mentor believed knowledge was a form of recollection from past lives, an idea illustrated with an unconvincing geometry lesson in Phaedo (EDIT: It’s Meno).
I find the line of thought in "Meno" extremly impressiv. Let me try to reformulate it in modern terms.
The literary form of a dialogue emphasizes that the thoughts of the participants should not be considered as doctrines, but the whole as an investigation of a problem domain.
The dialogue starts with a distinction between empirical knowledge ("The way to Larisa") and mathematical knowledge. Empirical knowledge is something that I cannot know from introspection. In contrast, the nature of mathematical knowledge comes from inside the mind. This is demonstrated by an uneducated, but smart child (a slave boy). The child is guided to discover a mathematical insight by questions alone. At first the boy does not know the right answer to an initial question. Then Socartes starts again with a simple question the boy is able to answer. Then a sequence of other questions follows each building on the previous answers. Socrates only questions, the boy only answers. Finally the boy arrives at the correct answer of the initial question whose answer he did not know at the start.
This scene should demonstrate the essence of mathematical proof. First we do not know the answer of a mathematical problem. Step-by-step we clarify our understanding, until we arrive at an answer. At this stage we know whether the particular mathematical statement is true or false. We expanded our understanding by only just thinking. In one way it is new knowledge (we now know something we did not, when we looked for a proof), in another way the knowledge was always there, just hidden in our mind.
At this point Socrates hits a limit where he runs out of questions to invistigate this further. This is when he starts to tell a story (the greek word for story is "myth"). Such stories are just tools to further investigate a problem when purely theoretical thoughts come to an end. In the dialogue it is also accompanied by a lot of joking, and "let me speculate" and "don't take it too serious" sort of remarks. So he reminds his fellows about some old stories (that he adapts and decorates a little to match the problem) about reincarnation where one looses the memory of one's past life but has occasionally some sort of flashbacks. This is more or less the whole point of the story: Perhaps we should think of mathematical knowledge as analogous to memory, but in a in a transcendent way.
Our modern doctrins are not very much off: Our ability of mathematical thinking is something that is inherent to us, more specifically to our brains. The blueprint (a sort of memory?) for our brains are in our genes. This way we are a sort of reincarnation of our parents, but in a state were we have to undergo all the mathematical training again.
What Plato lacks is a theory of evolutionary epistemology. But this is a really new development.
I find the line of thought in "Meno" extremly impressiv. Let me try to reformulate it in modern terms.
The literary form of a dialogue emphasizes that the thoughts of the participants should not be considered as doctrines, but the whole as an investigation of a problem domain.
The dialogue starts with a distinction between empirical knowledge ("The way to Larisa") and mathematical knowledge. Empirical knowledge is something that I cannot know from introspection. In contrast, the nature of mathematical knowledge comes from inside the mind. This is demonstrated by an uneducated, but smart child (a slave boy). The child is guided to discover a mathematical insight by questions alone. At first the boy does not know the right answer to an initial question. Then Socartes starts again with a simple question the boy is able to answer. Then a sequence of other questions follows each building on the previous answers. Socrates only questions, the boy only answers. Finally the boy arrives at the correct answer of the initial question whose answer he did not know at the start.
This scene should demonstrate the essence of mathematical proof. First we do not know the answer of a mathematical problem. Step-by-step we clarify our understanding, until we arrive at an answer. At this stage we know whether the particular mathematical statement is true or false. We expanded our understanding by only just thinking. In one way it is new knowledge (we now know something we did not, when we looked for a proof), in another way the knowledge was always there, just hidden in our mind.
At this point Socrates hits a limit where he runs out of questions to invistigate this further. This is when he starts to tell a story (the greek word for story is "myth"). Such stories are just tools to further investigate a problem when purely theoretical thoughts come to an end. In the dialogue it is also accompanied by a lot of joking, and "let me speculate" and "don't take it too serious" sort of remarks. So he reminds his fellows about some old stories (that he adapts and decorates a little to match the problem) about reincarnation where one looses the memory of one's past life but has occasionally some sort of flashbacks. This is more or less the whole point of the story: Perhaps we should think of mathematical knowledge as analogous to memory, but in a in a transcendent way.
Our modern doctrins are not very much off: Our ability of mathematical thinking is something that is inherent to us, more specifically to our brains. The blueprint (a sort of memory?) for our brains are in our genes. This way we are a sort of reincarnation of our parents, but in a state were we have to undergo all the mathematical training again.
What Plato lacks is a theory of evolutionary epistemology. But this is a really new development.