Jesse Mazer wrote:
>>Lennart Nilsson wrote:
>>We use mathematics as a meta-language, just like you kan describe what is
>>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 the 
> 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, in 
> just the same way that "the earth is round" is a statement describing a fact 
> 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 like 
> 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 that?)
> 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.  Gene frequencies are part of the map 
(theory of natural 
selection) not the territory.  It's easy to fall into confusing the map and 
territory because we 
have only maps to refer to and describe the territory.  Positivists recognized 
this and decided we 
should stop assuming that there is any territory - but this doesn't work 
because a map is only a map 
if it's a map *of* something.

Brent Meeker

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