On Apr 17, 2009, at 2:36 PM, Christopher Menzel wrote:
>> CM > I am not understanding some of your terminology here. As
>>> (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
>> Sorry Chris, I should have referenced the following threads better:
>> AW >> The problem with the "syllogisms will never work" argument
>>>> is that, if you allow them to be recursive, they have Turing
>>>> machine power. That means that they can compute anything that
>>>> can be computed.
>> JFS > Every major programming language (e.g., FORTRAN, COBOL, LISP,
>>> ALGOL, PL/I, C, C++, C#, Ada, Java, Python, Ruby, PHP, etc.)
>>> has the following two properties:
>>> 1. They have the power of a Turing machine.
>>> 2. It's undecidable whether an arbitrary program written in
>>> any of those languages will terminate.
>> My response was to the argument that if we allow syllogisms to be
>> recursive, they will become useless. JFS's point, I believe, was
>> this since programming language constructs are based on turing
>> machines, which are recursive, there's no issue here.
> If I can restate: Your claim was that if, in a logical framework
> capable of expressing syllogisms, syllogisms are allowed to be
> recursive, then the resulting framework will be useless because it
> will have the expressive power of a (universal) Turing machine.
> John's response is that all programming languages have that power and
> are, obviously, useful. John's response therefore seems to be a
> counterexample to your claim. (01)
After re-reading Adrian's response and looking at yours again
*carefully*, I see that I was not reading what you were saying
correctly. I thought you were responding to John's argument, not
Adrian's. Apologies, my mistake. I think my other two comments still
apply, however. (03)
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