@jeeprs,
jeeprs;97082 wrote:This view is the same as John Stuart Mill's, so it is not without precedent. The problem with that argument is that humans are born with innate ideas and with different levels of ability.
In what sense are we born with ideas? Obviously, there are certain ideas and schema which all humans (or almost all) share because they are related to a biology which we all share and are born with. But that's not the same as being born with the ideas themselves. Maybe we are using 'idea' in different ways. I mean, roughly, something which can be thought: something which one can
have in mind, so to speak. If I have it in mind, if I am imagining/thinking of something, then doesn't it have to consist, directly or indirectly, of sensual impressions? What is a thought which isn't characterized by color, shape, pattern, relation, etc.? It seems to me that any 'thought' which
doesn't consist of those properties/qualities cannot be thought of at all - so it's not a thought.
Quote:Some (e.g. me) have no innate mathematical ability whatever, others have great aptitude.
But mathematical ability, however that might be measured (i.e. if not by thinking mathematical thoughts) is not the same as a mathematical thought, e.g. an understanding of the fundemental principle of calculus.
If I have an innate ability to understanding the fundemental principle of calculus and you do not, I still cannot think of it unless it can be thought of in terms of something familiar - i.e. something experienced.
Quote:I suppose you could argue that this is the result of the 'experience of previous generations' but that is a stretch in my view. Second, as remarked above, Einstein (for one example) was able to make accurate predictions decades before they could be verified by experiment (or experience). On a more general note, mathematic reasoning can and does tell us many things about the nature of reality that we would never otherwise understand, even if they are later verified by experiments.
For my part at least, the claim isn't that ideas must originate from experience directly: e.g. as when I imagine a dog after seeing a dog. There are plenty of ideas that are not borrowed so directly from experience, but that doesn't mean that they arose independently of experience: e.g. a unicorn can be imagined though it was never experienced - but the idea 'unicorn' still consists of various things that were experienced (horse, horn, etc.) recombined in thought. This is Hume's view.
Re your last post,
What does it mean for mathematical thinking to not be based, ultimately, on experience? It means that the concepts, parts, elements, whatever you like to call them, in terms of which mathematical thinking occurs (e.g. numbers, the concept of subtraction, the concept of the permutation, et al) did not originate in experienced reality. Well, does anyone
not live in experienced reality? How would one know about something one didn't experience? So, didn't those concepts have to originate in the mind of some person, who was thinking about things in his experienced reality?