Jon Johanning wrote:
>
> On Jan 1, 2005, at 3:56 PM, Carrol Cox wrote:
>
> > The universe was here before people existed. But it didn't operate
> > according to mathematical laws, it just operated, period. Laws (unlike
> > Plato's Forms), however, exist only in human brains; they represent our
> > collective effort (never complete, never exact) to understand that
> > operating of the universe. No human brains, no laws, mathematical or
> > otherwise. It has been a long time since I read the _Anti-Duhring_, but
> > as I understood it at the time, Engels held to this position: i.e., he
> > held that the belief in the non-mental existence of laws led to
> > idealism. The universe is extra-mental; laws are mental.
>
> OK, let's try it this way. For a long time before human beings existed,
> the moon orbited the earth, and the earth and the other planets orbited
> the sun in basically the same way they do now -- right? Since Newton,
> we have been able to describe this behavior mathematically using his
> law of gravitation: the force by which two masses attract each other is
> proportional to the product of their masses divided by the square of
> the distance between them -- right? So even before human beings
> existed, *these masses behaved according to Newton's Law.* (I would put
> these words in caps and double-underscore them, but I want to send a
> plain-text e-mail, and all-caps isn't polite.) That law was *not*
> invented by Newton or any other human beings -- right?
I'm not sure there is as much difference between my description and yours as you think there is. The _law_ is an explanation of the motion of the planets -- and, moreover, the planets did not need Newton's permission to go about their business. What I'm after is the mode of existence of those "laws" -- I'm not in the least denying either the pre-human existence of the planets (in fact, with Lenin, I would want to insist strongly on that) or the accuracy of Newton's "law" in describing and explaining that motion. But where does Newton's law exist? What is its mode of existence? Where is it physically located? (And remember, "it" is the law, not the planets which "obey" it.)
(I did not use, I have never used, the phrase "social construction." In fact quite a few years ago, on either this list or its predecessor, the Spoons marxism list, I argued vigorously that we should avoid the phrase, because while it _seems_ to be used as more or less a synonym for "historical," in fact it is a wedge to suggest that whatever is "socially constructed" is constructed _in discourse_, is merely a verbal construct. It would be correct to say that white supremacy is a social construct, but also misleading, in ways that you fear saying laws are "mental constructs" will be misleading. I don't happen to fear the latter; in fact I fear the idealistic implications of denying that laws are mental constructs.)
>
> I think the following quote puts my view better than I could:
>
> "The realisation that most scientific observations are
> context-dependent has led some philosophers to argue that science is a
> social construct which has nothing to do with reality and is solely a
> matter of human convention.
It is a social construct, but it _also_ has EVERYTHING to do with reality. "Social construct" is _not_ the same as merely "human convention." Human conventions themselves need to be explained, and the explanation of many of them is -- surprise, surprise -- that through human social practice it has been found (for example) that the results of grasping a live wire while grounded are disastrous. _Descriptions_ or _laws_ exist only in thought & language, but the reality which those descriptions refer to exists independently of being known. But a description cannot exist independently of the mind which offers it or the minds which accept it.
> Now, the question you raise is whether the "mathematician's circle"
> exists in an "extra-mental reality." This is a very big topic in the
> philosophy of mathematics [clip] to this day,
> and still controversial. [clip]
>
> However, as Godel showed (see [clip]
>
> In short, I think people who want to get involved in this discussion
> need to do a little homework first.
Not really. That would end up with only specialists in very tiny fields talking to each other. (I happen to have read quite a bit -- some years ago -- on this mathematical controversy, but every time I go back to Godel I have to start from scratch again; I don't know enough math for the demonstrations to stick in my mind though I can follow while reading them.) And the debate over the mode of existence of laws, as distinct from the extra-mental reality they describe, can be carried on in some detail without knowing the details of any particular "law" or theorem.
That is, you really don't have to be a mathematician (even as much of a mathematician as I am, which isn't much of one) to engage in the argument over the "mathematician's circle." That isn't a controversy that can be decided _within_ mathematics. If it belongs to any speciality, it would be history rather than the mathematical sciences.
Carrol