Surlethe wrote:This seems a trivial proposition, with an answer satisfying only to a mathematician*. ...
It looks to be more of a case of "if there are natural laws at all, then they do not need a special/nontrivial explanation." Or at least, an attempt to argue that. The rest is just to leave open the possibility that some things happen that are not under any natural law (I'm not sure what that would actually mean, but let's call them "miracles".)
Simon_Jester wrote:I think it's more subtle than that: logical impossibility is the only thing that has enough force to make a question incoherent, as opposed to merely pointless- a question that need not have an answer is likely to be pointless.
You're really hung up on that word. It's not as if the argument hinges on it. The whole of my original post is that there is nothing else to look for:
Kuroneko wrote:What would it mean to give a cause to the existence of an aggregate, other than accounting for each of its parts and for how those parts acquired their particular configuration? In other words, if everything in a system has a cause, and the overall arrangement also has cause, then the existence of the whole thing seems to be properly accounted for.
I called this 'incoherent' just in the sense that asking to complete an already completed process doesn't really make sense. You can substitute whatever descriptor you feel best.
Simon_Jester wrote:That raises a question: how do we say we live in a world where no one will ever steal the Pope's hat? Under the regularity conception, you have to be able to predict confidently that no one ever will before you can say that there is a natural law barring anyone from doing so. The regularity conception doesn't free scientific theories from the need to have predictive power.
Right, but that's also beside the point.
Simon_Jester wrote:If I could predict that no one will ever steal the Pope's hat from some other observed regularity of nature, or if numerous, repeated attempts to steal the hat failed when I had every reason to expect them to succeed... then yes, at some point I would have to say that it was physically impossible to steal the Pope's hat, that some sort of bizarre interference was preventing anyone from doing so.
And that's quite fine as well. What's important here is what how do you interpret this law after you conclude this. If you're a proper regularity theorist, you would sweep the metaphysical issues aside, and you would just say that it's a law because of that's how things happen. What
explains it being a law is the regularity itself, because all there is to being a law is accurately reporting a regularity.
Now, either the law reciprocates by explaining the regularity in some manner, or there is no explanation whatsoever for it (or else it would itself be a law). Thus, for this conception of natural law, the situation is either closed or there's no answer to be found at all--either way, there is no further work to do beyond trying to find out the natural laws themselves.
Simon_Jester wrote:Since you appear to use a different interpretation, what would you do if you did find yourself in a universe where the Pope's hat was by all appearances unstealable? What if the Pope was willing to cooperate in all sorts of elaborate attempts to steal his hat, by any means imaginable, allowing you to do controlled experiments in hat-theft that persistently failed... .
I would also conclude that it is a matter of physical law that the hat is unstealable. But that's not the point. Let me try to illustrate the difference with a further hypothetical: in addition to all you state above, that I am also completely omniscient about what happened or will ever happen to that hat *, and thus I can establish as a complete fact that it has never been nor ever will be stolen. Under the regularity conception of natural law, it is then completely and unambiguously correct to say that it is a law that the hat is unstealable. I wouldn't just know this law with good certainty or beyond a reasonable doubt or whatever--I would be completely correct about my conclusion in the maximal, absolute sense.
Under the alternative, I could still be wrong about my conclusion even in the case of being omniscient about its history, for it could be just an accident (albeit perhaps very unlikely, depending on how thorough I am in testing the issue) that all attempts at such failed. But this only makes sense if there is something to 'lawhood' that carries some metaphysical force.
* If the future history of this troubles you despite this being a hypothetical, just assume I somehow convince the Pope to destroy the hat, or whatever.
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Simon_Jester wrote:Fair enough; what's the fundamental dimensionless quantity behind Boltzmann's constant? How would we describe, in dimensionless terms, a universe in which all other measures were identical but the mean particle kinetic energy corresponding to a given temperature was 1.001 times larger?
If you're interested in the Boltzmann constant in particular, that part's easy. What is k? A bookkeeping device designed to keep temperature and energy from having the same units. Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac statistics--all dependent on kT. Thermodynamics--just rescales entropy from measuring the number of available microstates directly. One can quite literally do all of physics, model any phenomenon, without ever once encountering the Boltzmann constant, and all one needs to do is measure temperature in units of energy, which is actually
more fundamental, because then the unit of temperature is amount of energy needed to change entropy (which is then dimensionless and measures microstates directly) by one unit.
Simon_Jester wrote:We could, of course, redefine the Kelvin scale so that 1 newkelvin = 1.001 oldkelvins and restore the original numerical values for everything, but is there a nontrivial way to express what has "changed" instead of merely doing that?
Yes, but it's not unique. Given that k is a peculiarity of our definition of the Kelvin scale, what might it mean for it to be different? If it means anything physical at all, it's that the behavior of water is different, because that's how the Kelvin scale is defined. Any number of dimensionless quantities could make that change--fine structure constant (which is a dimensionless measure of electron charge), gravitational coupling constant (which is a dimensionless measure of electron mass), electron-to-proton mass ratio (which introduces some corrections to the energy levels of atoms), and probably some more I'm failing to think up.
As I said before, I don't think it's important to the debate, though.