@kennethamy,
kennethamy wrote:
talk72000 wrote:
There will always be a little prejudice as you will think in relation to your viewpoint and interests. What you are interested in is what you are making an effort to know more about.
Why can I nor think about whether 13x10=130 without prejudice?
Isn't the worry at play here that if we are to know anything about how things really are, we need a perspective on reality that is not influenced by our concepts or the particular features and limits of that viewpoint (I think this worry is misplaced, but here it is). We want to get at the things that are really out there, and leave behind those features of experience that are dependent on our point of view; for example, colours are often taken to be artefacts of our own subjective perspective on reality. So the idea is that we want a view from outside our beliefs and concepts. As Nagel puts it, a view from nowhere; or as McDowell puts it, a sideways on perspective; or to gloss it in terms of the Davidsonian dualism between scheme and content, we want to get at the bare content of reality, and leave the scheme behind.
The problem with this hankering, of course, is that what we hanker for is unintelligible. A view from nowhere is a contradiction, we are confronted by reality from the standpoint of engagement; the head on view rather than the sideways on view, and it is difficult to see how it could be any other way. One way of resolving this has been to hanker after view point that isn't just a mere point of view, but is instead something like a transparent viewpoint that does reveal the fabric of the world to us.
Modern science plays this role in our culture. At least, it plays the role of something that is working its way towards transparency. The idea being that the scientific method is gradually revelatory of how things actually are, and at the ideal point that the 20th century pragmatists envisaged, 'the end of inquiry', it will give us the transparent view that we hanker for.
However, the problem here is that the original problem simply raises its head again at this level. What reason have we got to suppose that the scientific method provides a transparent viewpoint? The choice we make as to our method of inquiry will inevitably be determined by how we believe the world to be. That is to say, the way I believe the world to be will determine how I go about acquiring knowledge of it. One's beliefs about which sorts of transactions with the world yield knowledge are not prior to one's beliefs about what the world is like. I don't go to the oracle, because I don't think the world is constituted such that the oracle's prophecies yield knowledge. The point is that the question, "Does this reasoning deserve our allegiance?" can only intelligibly be asked from a point of engagement, from which the answer will generally be yes.
I don't see any reason why the thought shouldn't generalise to mathematics.