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Science Forum Index » Logic Forum » primitive recursive: obsolete?...
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| Nam D. Nguyen... |
 Posted: Wed May 28, 2008 12:08 am |
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MoeBlee wrote:
Quote: On May 25, 9:27 pm, "Nam D. Nguyen" <namducngu... at (no spam) shaw.ca> wrote:
MoeBlee wrote:
On May 17, 9:10 am, "Nam D. Nguyen" <namducngu... at (no spam) shaw.ca> wrote:
Then re-read what he wrote which is quoted above, the one that has
"Solely on basis of ... repeatedly applying the "add one"-operation ...".
If that doesn't sound like Presburger artihmetic to you then that's
your own reading, not mine!
No, Presburger arithmetic has the two axioms for addition:
x+0=x
x+(Sy)=S(x+y).
As far as "add one" is concerned Sn = n + 1, so how does that *refute*
my saying that his *informal* statement sound like Presburger arithmetic?
You argued that if he's going to go to Presburger arithmetic then why
not go on to multiplication too. I just pointed out that he didn't
specify Presburger arithmetic.
You got to learn how to listen to what people said: that's *not* what I
argued, not with Aatu and not with you! (Where is your proof of that?)
In addition, you have a habit of avoiding a simple question on its own merit!
By many accounts, Presburger arithmetic is basically Q or PA without
multiplication. So if one *only hears* "add", "+", etc..., there's
nothing wrong for one to say that it *sounds* like Presburger arithmetic.
If you want to refute that, do so *with some technical facts*. If you
can't do it, admit so. But you can't avoid answering it then talk about
something else entirely: you didn't know what I argued and that Aatu didn't
mention about multiplication is more relevant, in this context of my
questioning him, than that he "didn't specify Presburger arithmetic"!
Until you concentrate and listen on what people state or ask, without too many
pre-notions or prejudices, it'd be extremely difficult to have any argument
with you. Seriously. |
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