>> Hmm, OK. That seems simple enough. I guess the problem is that all 
>> that relational calculus stuff is abstracted to the point where it's 
>> just moving symbols around and it's difficult to determine how this is 
>> related to reality.
> 
> Um, yes. Indeed, that's precisely exactly why you would use formal 
> relational calculus stuff: it's just moving symbols around with no 
> relation to reality. That's why you can program computers to do it - 
> that's all computers can do.
> 
> That's true of most all formal math, tho: everything related to algebra 
> or calculus is ultimately moving symbols around with no relation to 
> reality.

The trick is to be able to associate all this abstraction with reality 
in your mind, so that you can use it to do Useful Stuff. ;-)

>>> There are, of course, standard rules of deduction, like
>>>   "for all X, pred(X)"
>>> is the same as
>>>   "not for some X, not pred(X)"
>>> and so on.
>>
>> But, notably, if X being true implies Y being true, then X being false 
>> does not necessarily imply Y being false.
> 
> Um, yes? :-) Was that supposed to be a relevant comment?

Apparently large numbers of people aren't aware of this particular fact.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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