phiwum
Penultimate Amazing
- Joined
- Aug 25, 2010
- Messages
- 13,590
I'm still not sure exactly why do you think it makes premise 2 the same. Just like with physics, a rock still falls in the same time even if a human isn't around to calculate it, a mathematical theorem is true or false regardless of whether a human is around to calculate it.
The most trivial example is statistics. If a die has a 1/6 chance of landing on a particular side, it will still have the same chance even if it just fell of a shelf in an eathquake, with no human around.
Or if you want maths theorems, Bayes still applies whether there are humans around to calculate those odds or not. The probability for a bird to be a penguin if it's got a black back is still the same, regardless of whether a human calculates it or not.
The theorem of choice? Sure. It just refers to cartesian products in a nutshell, and you can find cartesian products involved in describing for example joint systems. But guess what? The possible state or phase combinations of such a system are still the same, regardless of whether there's any human around to do the maths or not.
None of that requires a judgment in the same way that morality does.
First, let me say that I'm not committed to the claim that mathematics is fundamentally dependent on human opinion. I'm also not saying that mathematics is dependent on human opinion if morality is. I agree that there are fundamental differences between the two.
I was trying to show that Ian's argument works just as well if we substitute certain mathematical concepts for morality, but the conclusion would be absurd in that case. Hence, his argument doesn't seem to work.
Since then, Ian has said I misrepresented his conclusion, and I confess I am still unsure what conclusion he had in mind, so let's leave the argument as a whole out of the question and just focus on whether or not the second premise works with mathematical concepts substituted for morality. The second premise was:
No other known living things, have ever expressed any such notion [as morality].
Clearly, no other known living things have expressed any such notion as categorical limits, the axiom of choice or the continuum hypothesis[1]. That is all the premise says. It doesn't say anything about whether nature is somehow consistent with certain claims about these concepts (which I chose because there's no apparent physical analogues, by the way, but that is really beside the point).
So, the second premise as stated is, I think, obviously true when we substitute mathematical concepts for morality.
[1] Or Bayes' theorem, but for dull, technical reasons that we needn't get into at present, I'd prefer to focus on these concepts. We can talk about why I don't think Bayes' theorem is a good choice for this point, but in any case, I'm only committed to the claim that certain mathematical concepts work for this argument, and that's enough.