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Re: [ontolog-forum] web-syllogism-and-worldview

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Fri, 17 Apr 2009 12:50:53 -0500
Message-id: <A7AAA562-F012-4DB3-8BC5-09BBBB0180F4@xxxxxxxx>
On Apr 16, 2009, at 6:32 PM, Bart Gajderowicz wrote:
> Here's the way I see the argument whether syllogisms, recursive or  
> not, are valid, and why we can continue using programming languages  
> based on the principles of turing machines.
> As with any proper recursive function, we need a stop condition. We  
> of course can't use a turing machine to figure this out, as it will  
> not stop if the program does not terminate.  That's a theoretical  
> issue.    (01)

I am not understanding some of your terminology here.  As standardly  
(and pretty much universally) defined in logic, syllogisms are  
arguments with two premises and a conclusion satisfying a certain  
general form in which the notion of recursion plays no role whatever  
(understandably, since the notion of a syllogism is largely unchanged  
since it was first introduced by Aristotle).  Could you say what you  
mean by a recursive syllogism and perhaps give an example?    (02)

Second, what do you mean by a "proper recursive function"?  A  
recursive function is simply a mathematical function from (n-tuples  
of) natural numbers to natural numbers.  (Through the magic of  
encoding, of course, we can extend the notion to functions on, e.g.,  
real numbers, strings, database records, etc.)  A "stop condition" (if  
I'm understanding you) is a programming construct that has nothing to  
do with functions per se.  Of course, it is possible to *characterize*  
the class of recursive functions in terms of programming languages --  
a recursive function is any function (from N^m into N) calculated by a  
program in a language meeting certain conditions.  But even then I am  
confused by your comment that "any proper recursive function" --  
understood to mean any proper *program* that calculates a recursive  
function -- needs a "stop condition".  For this appears to mean that,  
for any recursive function, a program that calculates that function  
has to terminate when executed.  And that, of course, is false.    (03)

Perhaps you could clarify.    (04)

Chris Menzel    (05)

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