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[ontolog-forum] Mathematical objects

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Tue, 24 Apr 2007 23:12:30 -0500
Message-id: <DECB8C01-DAEC-4ED3-A9AC-33BB9699E724@xxxxxxxx>
> ...In the absence of human beings, and even if you have human  
> beings but there is no mathematics in their culture, mathematics  
> simply don't exist.  "Ah," you may say, "but 1 and 1 are still 2!"   
> No.    (01)

"I don't think so" might be a bit more appropriate here.  I mean,  
that there were no arithmetical truths before there were human beings  
is a *really* controversial view -- not that controversial views are  
necessarily a bad thing.  But the claim is exceptionally difficult to  
defend.  A flat "No" sort of suggests that your view is obvious.   
Which it isn't.    (02)

> There is no class of all single things, and no class of all pairs,  
> in a world without a person to imagine the classes and to recognize  
> their instances.    (03)

So if I'm the first to imagine a class and recognize its instances,  
how is it that just by doing that the class exists?  And in what  
manner does it exist?  Seems to me your only answer could that it is  
in my head.  After all, how else could it be that I bring this class  
into existence?  So given that it is in my head, does it cease to  
exist when I'm asleep or reading a good novel?  And if I tell you  
about this class I've brought into being, isn't the class in your  
head necessarily different from the one in my head?  And how is it  
that I imagine the class of, say, blades of grass on the White House  
lawn, since I'm not acquainted with any of its instances?    (04)

I don't actually want to discuss these questions.  I raise them only  
to illustrate that your view has to face a lot of really hard  
questions.  It is also far from obvious what relevance such a view  
has for ontological engineering.    (05)

Chris Menzel    (06)

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