Re: An instance of Russell's paradox?
- From: Barb Knox <see@xxxxxxxxx>
- Date: Thu, 01 Sep 2005 14:29:40 +1200
In article <1125495160.749010.133720@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"A.T." <andrzej-tomaszewski@xxxxx> wrote:
>Ms Knox wrote:
>
>[snip]
>
>> >Ms Knox, may I also ask you to kindly make some remarks regarding the
>> >other two questions I posted, namely, the question suggesting the
>> >infinite generalization of the arity of every predicate (I got this
>> >idea from Quine, but I lost trace of the actual source),
>>
>> Sorry, that's something I'm neither knowledgeable about nor interested
>> in. Do you recall what benefit(s) there might be in making this
>> extension?
>
>I expected that would be uniformity. But, well, I am not a
>professional, hence my confused queries.
>
>> ISTM that giving up finite expressions would be giving up a
>> lot.
>
>Your argument truly does sound most rational. But the uniformity case
>seems rational too. I just wish I recalled the passage from Quine where
>he makes a mention of it. As far as I remember, he put quite a lot of
>stress on this.
>
>> >as well as the
>> >question pertaining to the actual difference between an atom and a
>> >predicate in philosopher(socrates) transformed into [philosopher,
>> >socrates], where the predicate is(?) really the first atom of the
>> >analogous list form of a proposition (the problem is, I really see no
>> >difference whatsoever).
>>
>> Firstly, there is a difference. In Prolog, the [a b c] representation
>> of lists is actually syntactic sugar for the binary (and nullary) term
>> ".":
>> .(a, .(b, .(c, .())))
>>
>> Similarly, in Lisp the (a b c) representation of lists is sugar for
>> (a . (b . (c . NIL))))
>
>Yes.
>
>> Secondly, in Prolog the =.. predicate converts between an arbitrary term
>> such as philosopher(socrates) and the prefix list representation of it.
>
>Yes.
>
>> These are *not* interchangeable.
>
>No, they are not.
>
>> Internally to a Prolog implementation
>> terms may indeed be represented as some sort of list, but that is wholly
>> different from the *external* representation of Prolog "[...]" lists
>> using '.' terms.
>
>I am aware of these facts. Thank you very much, Ms Knox.
>
>Please, kindly let me rephrase my question. Listed below are the three
>alternative Prolog notations for the same term: the dot (internal)
>notation, the list notation, and the operator notation.
But as I said, they are *not* the same term. The first and second are,
but the third is not a list term. Note that if every term were equal to
its list-representation term then you would immediately have infinite
terms:
[a] = .(a, .()) = [., a, [.]] = .(., .(a, .(., .()), .()))
= [., [., a, [., ., [.]] [.]] [.]] = etc. etc.
>In the context
>of the operator notation we would call "a" - a predicate, and in the
>other two contexts - an atom (or, better, the first atom on the list).
>My question is, since these are merely different ways of representing
>the same algebraic structure, are predicates really atoms (I mean, is
>it nothing but a terminological convention to call "a" [an atom] in the
>context of the list and dot notation, whereas [a predicate] in the
>context of the operator notation)?
>
>.(a, .(b, .(c, .())))
>[a b c]
>a(b, c)
>
>Thank you very much for your time (and I am sorry if I have confused
>something again).
>Tom
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