Brent Meeker wrote:

>Jesse Mazer wrote:
> >>Lennart Nilsson wrote:
> >>
> >>We use mathematics as a meta-language, just like you kan describe what 
> >>said in latin by using italian. That does not make italian
> >>logically/evolutionary prior to latin of course.
> >
> >
> > But in this case we are using mathematics to describe actual events in 
> > real world, specifically the way gene frequencies change over time in
> > response to natural selection. Surely these events were obeying the same
> > mathematical laws even before we could describe them as doing so using
> > whatever specific mathematical symbols we use to represent these laws, 
> > just the same way that "the earth is round" is a statement describing a 
> > that was true before we came up with the words "earth", "round", etc. In
> > other words, it's the specific mathematical symbols we use to represent
> > mathematical truths that are analogous to italian or some other human
> > language, but they represent truths that have been true all along, just 
> > the earth has been round all along even before humans came up with the
> > language to describe it (or don't you believe it makes sense to say 
> >
> > Jesse
>That the Earth is a spheroid (WGS84 ?) is a model and the *model* "obeys" 
>certain mathematical laws
>- because the mathematical laws are just rules of a language we invented 
>for talking about such
>things.  The Earth, understood as some not completely knowable object in 
>reality, doesn't obey
>anything.  Same with gene frequencies.

But to me, "obey" simply means that *if* there had been someone around in 
the past to observe the earth/gene frequencies and compare with the model, 
they would have matched up with it at all times, even times when there 
wasn't actually anyone there to make such a comparison. And really, can we 
make any statements about what external reality is or was "really like" 
without using models? If we want to say that back in the Cretaceous, T. 
Rexes were larger than dragonflies, isn't the concept of "bigger than" just 
as much based on a model of sorts as the concept of "roundness"? Maybe we're 
getting into the territory of Kantian philosophy here, with the question of 
whether we can say anything about reality "in itself" without using various 
a priori mental concepts such as numbers. In any case, it still seems 
incoherent to me to imagine that uncovering the evolutionary history of 
these a priori concepts should somehow undermine our belief in them as 
genuine truths, since we are completely dependent on them in our 
understanding of "evolutionary history" or anything else involving external 


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