Jesse Mazer wrote:
> 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 
>>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. 

That's your second-order model, i.e. a model in which you embed the earth/gene 
model - I take their 
past validity to simply be part of the (first-order) model.

>And really, can we 
> make any statements about what external reality is or was "really like" 
> without using models? 

No, we can't.  That's why positivists tried to get rid of the notion that 
models were models *of* 
anything.  But the essence of a model is that does assume an underlying 
something, or in other words 
it presumes to be able to predict beyond just the data on which it was based.  
It's more than 
curve-fitting or cataloging.

>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, 

Are you talking about the "truths" of mathematics - which I regard as just 
rules of consistency for 
talking about things, i.e. constructing models that are not internally 
inconsistent.  Or are you 
talking about the Kantian concepts like "round" and "prime", which I regard as 
existing only in our 
models and are neither true nor false.

>since we are completely dependent on them in our 
> understanding of "evolutionary history" or anything else involving external 
> reality.

But we're not completely dependent on them.  Some of them are essentially 
hardwired into us by our 
evolution, but we can go beyond them.  For example our intuitive understanding 
of probabilities is 
very poor - but we can go beyond it by forcing ourselves to be consistent 
(mathematical) in 
discussing probabilities.  I think the difficulty in interpreting quantum 
mechanics arises because 
"intepretation" essentially means giving Newtonian picture of what happens and 
we feel that we can't 
really understand a picture unless it is Newtonian - even though we have a 
perfectly consistent 
model that isn't.

Brent Meeker

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