I have been doing a course on edx.org entitled The Conscious Mind - A Philosophical Road Trip. It's a gentle beginner's guide to phenomenology, and I am a gentle beginner to philosophy in general (and also a beginner on this site!). As part of the course we are given a short extract from Sartre's "The Imaginary" to read.
In the extract Sartre seems to be saying that objects of imagination cannot be learned, that everything there is to know about them is known already in an instant, whereas objects of perception can be learned, there is always more to see about them.
For example, he says: "In a word, the object of perception constantly overflows consciousness; the object of an image is never anything more than the consciousness one has of it; it is defined by that consciousness: one can never learn from an image what one does not know already."
I was wondering, how does this apply to mathematical things, such as triangles, for example? I can imagine a triangle, but there are I suppose many things I do not know about it, that seem to be true, that I can verify by interacting with the "real world", by talking to people, using a calculator etc. Perhaps I imagine a right-angled triangle, perhaps I don't know much about those, but then learn that the square of the longest side is equal to the sum of the squares of the other two sides. The triangle seems to be something imaginary, but there is a lot about it that I don't know, but can find out, can learn, and this seems to contradict my understanding of what Sartre is saying.
Any help on this would be appreciated - where am I going wrong here? Or does Sartre go on to explain this elsewhere?