Crysknife wrote:
Then if nothing is provable outside of math then you shouldn't believe anything or conversely, you should believe whatever you want? Is that what you are saying? So science is a religion because nothing is provable?
You can believe whatever you want to believe, but it may come at the expense of logical consistancy. The theories in science cannot be proved, but that does not mean we cannot accept them, or that they are all equivalently valid. Even if we had a deductive system it would require empirical reasoning, and that is the best we are going to get. This puts science on a less firm foundation than maths.
If evolution isn't provable then by all means explain to me where you came from. There are facts in this reality that can only come about by strong inductive reasoning. Simple logic does not create knowledge.
Evolution isn't provable, not in the sense that 1 + 1 =2 is provable. Just because I claim it's not provable doesn't mean I need to have a replacement theory for where I come from!
Many things in math I have to take on faith. I will never prove a difficult geometric theorem, but I must trust the people working on it to prove it in a "clean" fashion. Thus I trust scientists to find evidence and use the scientific method to find facts about our reality. Here is the kicker.......if all humans were to die and another race of sentient beings were to evolve, they would have mathematics exactly like we do, but they would also have the theory of evolution EXACTLY as we do. But who knows what other various "religions" they might create that look nothing like ours.
I think that's a really good point, but I suspect that religions built by other sentient beings would have quite alot in common with ours - a narrative on 'where we came from', a set of conventions or principles on how to act, ideas about what a perfect society/state/land would be, etc.
About the other thing......math works to define our reality as we see it. But can you ever have a perfect circle? Does anything reduce down to one of anything? I am a human, but I am billions of cells. Would an atom in my body see me as one human from its perspective? A being in the quantum world might disagree that 1 + 1 always equals 1.
I know 1 + 1 = 2, but the "1" is a subjective choice.
EDIT: meant to say inductive rather than deductive...I changed it.
How would being in a quantum world change the nature of mathematics? Doesn't physics claim we do live in a quantum world? I don't think anybody in physics disputes the claim 1 + 1 = 2.
A perfect circle is a mathematical object, not a physical one. We've known about perfect circles ever since the concept was discovered.
However, physics currently assumes that space is continuous and 3-dimensional. A perfect circle exists in 3-dimensional spaces over the real numbers.
This gives me a chance to make my viewpoint more explicit:
Usually scientists are very realistic about scientific theories, for example in Newtonian mechanics, we don't say that this thing we call space is
like the Euclidean space in the theory, we say it
is such a space. So the Newtonian physics in particular has a narrative about how to interpret the math. We call things particles, or rigid bodies (etc) and that they have certain properties we have defined such as energy and momentum, and that the trajectories of these particles are described by certain dynamical laws. We take this interpretation to be a true description of reality.
However quantum mechanics subsumes Newtonian mechanics, yet provides a very different physical picture. The process of taking a theory, a tool for prediction, and attaching a physical picture to it is, it seems to me, a very slippery activity. There are some scientists (Hawking, last time I heard) who believe that science isn't telling us anything about reality, but is just a useful tool for prediction.
So do perfect circles exist physically? Physics seems to make this claim, yet people don't seem to believe that to be true.
(Thanks for being so patient with me, by the way.
)
Sadcyn doesn't even know if swans exist!
I am unfamiliar with any scientific (or otherwise
) theory of swans.
... sorry. 
