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.
Some (e.g. me) have no innate mathematical ability whatever, others have great aptitude.
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.
[Kant said that] it is the representation that makes the object possible rather than the object that makes the representation possible. This introduced the human mind as an active originator of experience rather than just a passive recipient of perception. Something like this now seems obvious: the mind could not be a tabula rasa, a "blank tablet," any more than a bathtub full of silicon chips could be a digital computer. Perceptual input must be processed, i.e. recognized, or it would just be noise -- "less even than a dream" or "nothing to us," as Kant alternatively puts it.
All very good questions. Obviously, the question of what constitutes 'an idea' is a difficult one to articulate exactly. One answer is that this debate is really a recapitulation of Kant's reaction to the John Locke's proposal that we are born a 'blank slate', a tabula rasa. Really the whole thrust of Kant's thinking was to show that there are certain innate ideas - which he referred to as intuitions - upon which our very cognition depends.
This way of thinking is still current via the streams of 'constructivism' and of course to the allied European sport of deconstructionism.
Of course, we do have ideas based on our experience also. If i have never seen a giraffe I will have a hard time forming a picture of one in my mind. But in practical terms, the way we make connections between elements of experience, or the conclusions we come to based on our experiences, obviously cannot just be a factor of what we have experienced. Otherwise everybody in the same environment could be expected to be more or less the same. A number of people will see a giraffe, but a Matisse will paint it and in so doing reveal some aspect of giraffe-hood which nobody had ever noticed before. And the rest of the kids who went to school with Albert Einstein did not make predictions that could not be experimentally verified until decades later, yet presumably their experience was similar.
I would like to have some Grand Theory that explained all of this, but I am not proposing one. All I am saying is that the mind, intellect, whatever you want to call it, has considerable powers which are not derived from experience. Logically speaking, if your mathematical abilities were derived solely from experience, then how could an Einstein make predictions about things that had never, and may never, be experienced? Sure you can say we 'abstract' elements from experience and then project them but there is nothing in experience that corresponds with many of the logical conclusions of mathematical operations.
The Platonist view, very broadly (and idiosyncratically) speaking, is that the intellect mirrors the deeper structure of reality. Mathematics is only one example of the way that 'the soul's innate knowledge' is able to comprehend things that are not at all apparent to sensory experience. And it is mathematical physics that is holding out against the primitive empiricist insistence on the sole reality of the sensory realm. The findings of mathematical physics in regards to sub-atomic physics have undermined the naive empiricist view of the nature of reality as something which is utterly 'there'.
As I said, I don't have a grand theory which explains all this. Just beware that this 'it all comes from experience' argument is highly suspect. If you look at the Wikipedia entry on 'philosophy of maths' you will realise that the idea of number itself - which you would think is really obvious, a dead simple thing to explain - is actually highly controversial. There are huge disagreements about what 'number' is (other than the obvious fact of 'something that signifies quantity'). Of course some empiricist will come along and say 'no its not, it is all perfectly simple'. Well I am afraid it is not. They only they say that because they hate anything mysterious.:bigsmile:
If I have learned anything from philosophy, it is that things are considerably more mysterious than most people are willing to contemplate.
I think I have to go along with Kant on this, you come into the world preconfigured to view the world in certain ways, space, time, causality, reason, etc.
Without this preconditioned perceptual apparatus, experience would not be much help. Lots of life forms have exposure to the same empirical experience, it is the preconfigured wiring that helps us interpret it.
Bearing all of that in mind, it can still be argued that 'empiricism' has an ideological agenda, which is basically to keep your gaze wholly fixed on the realm of ordinary experience in a secular world. It is part of the whole rejection of metaphysics and the idea of the sacred from ordinary life.
Yes, fixed on what is evidence. To say that it is rejecting something else which is there is to beg the question.
Ah, but what is evident? If you only consider what is available to the senses and to material analysis, you cannot form a coherent understanding of the nature of experience. You have to look at the nature of experience itself, which is obviously not an 'empirical' operation, because experience itself is not an objective reality.
The question hinges on what is "real", what "exists" , what is "evidence" and what is "experience". I simply do not understand the drive to deny "the undeniable reality of experience". As Whitehead noted "those scientists who wish to explain away their own experience, make an interesting subject for study".
Science and "objective" evidence, as great a tool as it is for understanding the material aspects of the world offers only a partial and incomplete picture of "total reality" as experienced. In order to form a complete worldview (which must incorporate values and aesthetics) it is necessary to engage in rational speculation (philosophy or religion).
Rationalism vs Empiricism
Why pick one over the other? Both reason and perception are useful methods of acquiring knowledge. As Thomas Reid said, both came out of the same shop, and one has no reason to doubt the usefulness of one compared to the other.
What justifies belief is the tricky issue.
Particularly whether "pure reason" can do the job alone.
And nor can pure empiricism ala Locke, Berkeley, Hume
Hence why I mentioned the issue of justification for one's belief
No empiricist (I believe) has thought that claims to know can be justified by sense-perception alone.
Even Hume believes that reason plays some role.
But is that consistent with empiricism, that is, all knowledge derives from sense experience?
So the question of empiricism or rationalism is null. You need both to justify belief, which is what I originally stated.
Contingent on the basic sense impressions we obtain (his foundationalism). So we cannot reason beyond our sense impressions. Obviously this poses significant difficulties in a number of areas, especially justifying our belief in an external world.