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 (ntuples
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)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontologforum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontologforum/
Unsubscribe: mailto:ontologforumleave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgibin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontologforum@xxxxxxxxxxxxxxxx (06)
