HDTenEightyP/NetNews huggingface dataset:
From: rar@csl.sri.com (Bob Riemenschneider)
Newsgroups: sci.logic
Subject: Re: A only if B
Date: 16 Oct 92 14:02:05
Organization: Computer Science Lab, SRI International, Menlo Park, CA.
NNTP-Posting-Host: birch.csl.sri.com
In-reply-to: rkaivola@mits.mdata.fi's message of Mon, 12 Oct 1992 15:07:14 GMT

In article <rkaivola.718902434@mits> rkaivola@mits.mdata.fi (Risto Kaivola) writes:

     Exactly how should one formalize the English notion of 'only if'
   in the language of the propositional calculus?
     That is, given the sentence
   "Tom will visit us only if we invite him.",
   is the correct formalization

   A = "Tom will visit us."

   B = "We invite him."

   A  -->  B

Yes.

Think about it this way: When is "Tom will visit us only if we invite
him" false?  It's certainly false if Tom visits without being invited,
i.e., if A is true and B is false.  If the sentence is true, any of the
other cases -- Tom is invited and visits, Tom is invited but doesn't
visit, and Tom is not invited and doesn't visit -- is possible.  Well,
those are precisely the truth conditions for A -> B.  So if you're going
to treat "Tom will visit us only if we invite him" as a truth-functional
compound of "Tom will visit us" and "We invite him", it's simply a
conditional.  (Of course some, including myself, would argue that
attempting to treat this as a truth-functional compound is not good
enough for some purposes.  For example,

    Tom will visit us only if we invite him.

might be thought of as indicating a general disinclination of Tom to
visit uninvited, making this something like a universal generalization
of a conditional rather than a conditional.  But this is beside the
point, which is that "only if" corresponds to -> in the same way that
"if" corresponds to <-.)

                                                        -- rar
From: ard@cs.bham.ac.uk (Antoni Diller)
Newsgroups: sci.logic
Subject: Re: A only if B
Date: 12 Oct 92 17:25:56 GMT
Organization: School of Computer Science, University of Birmingham, UK

In article <rkaivola.718902434@mits> rkaivola@mits.mdata.fi (Risto Kaivola) writes:
>
>  The following is no doubt a little trivial for the participants of this
>group, but I hope someone is willing to help me, nevertheless.
>  Exactly how should one formalize the English notion of 'only if'
>in the language of the propositional calculus?
>  That is, given the sentence
>"Tom will visit us only if we invite him.",
>is the correct formalization
>
>A = "Tom will visit us."
>
>B = "We invite him."
>
>A  -->  B
>
>
>Or, should this perhaps be B --> A (not in my opinion), or A <--> B
>(this last alternative is more likely to be correct than B --> A, in my
>opinion)?
>
>This isn't homework.
>
>--
>Risto Kaivola
>(Internet address:   rkaivola@mits.mdata.fi)

I'd go for:

(B --> A) & (-B --> -A)


Antoni Diller
From: burt@aupair.cs.athabascau.ca (Burt Voorhees)
Newsgroups: sci.logic
Subject: Re: A only if B
Date: 13 Oct 92 04:25:33 GMT

A-->B = if A then B
A<-->B = A if and only if B
A<--B = A only if B = if B then A  This is read: A is true only if B is
true since a true statement cannot imply a falsehood.
From: loader@vax.oxford.ac.uk
Newsgroups: sci.logic
Subject: Kreisel Lacombe Shoenfield and HEO
Date: 8 Oct 92 14:15:56 GMT
Organization: Oxford University VAX 6620

The Kreisel-Lacombe-Shoenfield theorem states that any partial recursive
function f that gives a well defined functional on recursive functions ( ie
if {a} and {b} are total and equal then f(a)=f(b) ) is recursively continuous
( i.e. If {a} is total then there is recursive n(a) such that f(a)=f(b)
whenever {b} is total with {a}(x)={b}(x), x=0 ... n(a) )

(For a proof see eg 'Foundations of Constructive Math.', M Beeson, 1985)

It is not hard to see that the conclusion is equivalent to saying that there
is a recursive functional F with F({a})=f(a) whenever {a} is total.

Thus in terms of the model HEO, the KLS theorem states that:

   Any equivalence class of (N -> N) -> N is                         (*)
   given by a recusive functional of this type.

Question: What happens to (*) at other finite types?

For types of rank 1, this is the trivial statement that a recursive functional
with no function parameters is a recursive function.

For types of rank 2, the question can be reduced to (*).

What happens at higher types???

R Loader, Oxford
Newsgroups: sci.logic
From: baljeual@uther.calvin.edu (Alan Baljeu)
Subject: Re: A only if B
Organization: Calvin College
Date: Mon, 12 Oct 1992 21:27:03 GMT

rkaivola@mits.mdata.fi (Risto Kaivola) writes:

>A = "Tom will visit us."

>B = "We invite him."

You want "A only if B"

Think: if not B?       then not A
so !B -> !A

Think: if A?			  if not B then not A, so we must assert B is true.
A -> B

Both of these are equivalent.
Newsgroups: sci.logic
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: A set cannot contain itself as a member
Keywords: recursion
Organization: Computer Science Department,  Stanford University.
Date: Thu, 8 Oct 1992 03:35:42 GMT

In article <Oct05.201328.96457@yuma.ACNS.ColoState.EDU> sa114984@longs.lance.colostate.edu (Steven Arnold) writes:
>
>	I am not an expert in set theory or the predicate
>calculus, but I was leafing through a book on the subject and the
>following informal "proof" occured to me.  Could any of you experts out
>there tell me if this contains a major flaw -- and if so, what it
>is?  Thanks.
>
>	The proposition to be proven is: A set can never contain
>itself as a member.

One more point about this "proof":

If in your proof you replace "set" by "list", and write X = [g,X] in
place of X = {g,X} to denote a list instead of a set, then you will
have proved that such lists cannot exist.  This contradicts what
happens in Lisp.  Lisp lists are necessarily finite, but may contain
cycles.  Peter Aczel's treatment of AFA does in careful detail for sets
what Lisp long ago did for lists, albeit without the mandatory
agonizing over whether this would blow the universe's fuse.

-- 
=================================================== In short, I am floundering
Vaughan Pratt   pratt@cs.Stanford.EDU  415-494-2545 around and don't take what
=================================================== I say seriously.
Newsgroups: sci.logic,sci.math,comp.theory,sci.philosophy,sci.philosophy.meta,comp.ai.philosophy
From: rz@mips.complang.tuwien.ac.at (Richard Zach)
Subject: CfP: Computational Logic and Proof Theory
Followup-To: poster
Reply-To: kgs@csdec1.tuwien.ac.at
Organization: Technische Universit"at Wien
Date: Thu, 15 Oct 1992 16:11:35 GMT


            3rd Kurt Goedel Colloquium KGC'93

           Computational Logic and Proof Theory

       August 24--27, 1993      Brno, Czech Republic

                    First Announcement
                            and
                     CALL FOR PAPERS


The Kurt Goedel Society will hold its 3rd Kurt Goedel Colloquium
from Tuesday, August 24, to Friday, August 27, 1993 in Brno,
Czech Republic, the town where Kurt Goedel was born.

KGC'93 is the third in a series of biannual colloquia on logic,
theoretical computer science and philosophy of mathematics.
The first two colloquia took place in Salzburg (1989) and in
Kirchberg am Wechsel (1991).

The scientific program will consist of invited lectures and short
contributions, which will be selected from the submitted papers. All
contributions will be refereed for a Proceedings volume.

Scope:  The colloquium is intended for logicians and computer
scientists interested in the proof-theoretic and algorithmic
aspects of logic. Topics include, but are not limited to:
proof theory, automated theorem proving, unification theory,
complexity theory, logics of programs, non-standard logics for
theoretical computer science and AI, recursion theory,
logic programming, lambda-calculus.

Paper Submission:  Authors are kindly requested to submit 3 copies
of a full draft paper (in English) not exceeding 12 pages not later
January 31, 1993, to the program committee chairman

Alexander Leitsch, Technische Universitaet Wien,
Institut fuer Computersprachen E185.2,
Resselgasse 3/1, A-1040 Vienna, Austria/Europe.

Authors from locations where access to reproduction facilities is
severely limited may submit one copy only.

Notification:  Authors will be notified of acceptance or rejection
of their submissions by March 31, 1993. The final camera-ready
version of the paper must be received by May 31, 1993.


Program Committee                  Organizing Committee

K. Ambos-Spies, Heidelberg         E. Fuchs, Brno
M. Baaz, Vienna                    K. Hoerwein, Vienna
W. Bibel, Darmstadt                E. Koehler (chair), Vienna
N. Brunner, Vienna                 P. Materna, Bratislava
G. Gottlob, Vienna                 H.-D. Schwabl, Vienna
Y. Gurevich, Ann Arbor             J. Starek, Brno
H. Kleine Buening, Paderborn       R. Zach, Vienna
J. Krajicek, Prague                J. Zlatuska, Brno
A. Leitsch (chair), Vienna
P. Materna, Bratislava
D. Mundici, Milan
P. Pudlak, Prague
D. Scott, Linz


Correspondence and Paper Submission

KGC'93
Technische Universitaet Wien
Institut fuer Computersprachen E185.2
Resselgasse 3/1
A-1040 Vienna, Austria

Phone:   +43 (1) 58801-4088
Fax:     +43 (1) 504 15 89
email:   kgs@csdec2.tuwien.ac.at
From: burt@aupair.cs.athabascau.ca (Burt Voorhees)
Newsgroups: sci.logic
Subject: Re: A only if B
Date: 13 Oct 92 17:45:17 GMT
 <burt.718993396@aupair.cs.athabascau.ca>

>>A-->B = if A then B
>>A<-->B = A if and only if B
>>A<--B = A only if B = if B then A  This is read: A is true only if B is
>>true since a true statement cannot imply a falsehood.

>  Appologies, this is clearly wrong. :(  That's what I get for posting
>late at night and thinking about things like necessary and sufficient.
>Guess that puts me one up on Dogwood (Much Ado About Nothing) as he only
>wanted to be written down an ass.  :):):)
>  Let's try again:  How about A only if B = (B-->A)&(-B-->-a)

  Nope, this is just if and only if

>bv

  Okay, let's go for the hat trick here.
1.  Tim will come to dinner if we invite him
2.  Tim will come to dinner if and only if we invite him
3.  Tim will come to dinner only if we invite him.

A = Tim will come to dinner; B = We invite him
so we have
1.  B-->A that is, tim will come if invited
2.  B<-->A  tim will come if invited, and if tim comes he was invited
3'.  B<--A  if tim comes he was invited
  Claim is that 3' = 3
  Tim will come only if we invite him means that if tim comes he was
invited.  Or, contrapositive, if he is not invited, he will not come:
i.e., -B-->-A  But this is equivalent to --a-->--B; i.e., A-->B
  The Phoenix rises
confusion of logical and causal thinking.

bv
Newsgroups: sci.logic,sci.cognitive,comp.ai.neural-nets
From: amnell@klaava.Helsinki.FI (Marko Amnell)
Newsgroups: sci.logic
Subject: John Etchemendy
Date: 7 Oct 92 06:58:15 GMT
Organization: University of Helsinki

Somebody mentioned Etchemendy and Barwise's _The Liar_.  I'm having
trouble with my newsreader, so I couldn't follow-up that article.
This is a very good book, I'm told.  Similar results with ill-founded
sets are obtained in Patrick Grim's new book _The Incomplete Universe_.

On an unrelated note, I have in front of me a new book by Etchemendy,
_The Concept of Logical Consequence_.  This looks like a brilliant
book.  Etchemendy is arguing that both the syntactic and the orthodox
Tarskian semantic characterizations of the entailment relation fail
to capture what we truly mean by the concept of logical consequence.
The first part of this is hardly controversial, but the second is
novel.  I haven't read more than the first chapter yet, but this looks
like essential reading for all students of logic.  An original
first-rate treatise in the philosophy of logic is a rare thing indeed,
but here we have one. (Harvard U.P. 1990)

-- 
Marko Amnell
amnell@klaava.helsinki.fi
Graduate Student in Philosophy
Newsgroups: sci.logic
From: adam@symcom.math.uiuc.edu (Adam H. Lewenberg)
Subject: Half volume of JSL up for grabs
Organization: Math Dept., University of Illinois at Urbana/Champaign
Distribution: usa
Date: Fri, 9 Oct 1992 14:22:18 GMT

I have issues 3 and 4 of volume 54 (1989) of the Journal of Symbolic
Logic that I want to get rid of. If anyone wants these they can have
them (if they pay the mailing costs).   Adam Lewenberg
                                        adam@math.uiuc.edu
-- 
University of Illinois at Champaign-Urbana, Dept. Of Mathematics
INTERNET: adam@math.uiuc.edu   or    a-lewenberg@uiuc.edu

Newsgroups: sci.logic
From: mrh7507@tamsun.tamu.edu (Michael Hand)
Subject: Re: The Mathematical Universe
Organization: Texas A&M University, College Station
Date: Fri, 9 Oct 1992 21:28:43 GMT

Randall Holmes and Chris Menzel write:

Holmes> I also maintain that the physical world is a "mathematical object".

Menzel> I take it you don't think the physical world is *literally* a 
      > mathematical object, if only for the fact that, as you yourself 
      > hint, any number of other mathematical objects would have served 
      > just as well.

Holmes> Indeed many other objects would have served as well (do in
      > fact serve as well?); our position makes it impossible to discover
      > which one has in fact served :-)

Recall Benacerraf on a similar skepticism + absurd ontological 
identification (namely, identifying numbers with certain sets 
instead of certain others, much as Holmes identifies the world
with a certain mathematical object instead of another that would
serve as well); the application to Holmes's view is obvious.
I also recommend that anyone interested in attacking Benacerraf
on this issue read his paper instead of reacting just to these
suggestive quotes.

  If the numbers constitute one particular set of sets, and not another, 
  then there must be arguments to indicate which...

  In awaiting enlightment on the true identity of 3 we are not awaiting a 
  proof of some deep theorem.  Having gotten as far as we have without 
  settling the identity of 3, we can go no further.  We do not know what a 
  proof of that *could* look like.  The notion of "correct account" is 
  breaking loose from its moorings if we admit of the possible existence 
  of unjustifiable but correct answers to questions such as this...

  ...[T]here is little to conclude except that any feature of an account
  that identifies 3 with a set is a superfluous one -- and that therefore
  3, and its fellow numbers, could not be sets at all.

  [from "What Numbers Could Not Be"]
-- 
_______________________________________________________________________
-----------------------------------------------------------------------
Michael Hand                     phone (409)845-5660, fax (409)845-0458
Dept of Philosophy, Texas A&M Univ, College Station TX 77843-4237 U.S.A.
Newsgroups: sci.logic
From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: The Mathematical Universe
Organization: Boise State University
Date: Tue, 13 Oct 1992 19:19:30 GMT

In article <1992Oct9.203658.25387@tamsun.tamu.edu> e343mh@tamuts.tamu.edu (Michael Hand) writes:
>Randall Holmes and Chris Menzel write:
>
>Holmes> I also maintain that the physical world is a "mathematical object".
>
>Menzel> I take it you don't think the physical world is *literally* a 
>      > mathematical object, if only for the fact that, as you yourself 
>      > hint, any number of other mathematical objects would have served 
>      > just as well.
>
>Holmes> Indeed many other objects would have served as well (do in
>      > fact serve as well?); our position makes it impossible to discover
>      > which one has in fact served :-)
>
>Recall Benacerraf on a similar skepticism + absurd ontological 
>identification (namely, identifying numbers with certain sets 
>instead of certain others, much as Holmes identifies the world
>with a certain mathematical object instead of another that would
>serve as well); the application to Holmes's view is obvious.

But this approach applies to anything being itself rather than
something else.

>I also recommend that anyone interested in attacking Benacerraf
>on this issue read his paper instead of reacting just to these
>suggestive quotes.
>
>  If the numbers constitute one particular set of sets, and not another, 
>  then there must be arguments to indicate which...
>
>  In awaiting enlightment on the true identity of 3 we are not awaiting a 
>  proof of some deep theorem.  Having gotten as far as we have without 
>  settling the identity of 3, we can go no further.  We do not know what a 
>  proof of that *could* look like.  The notion of "correct account" is 
>  breaking loose from its moorings if we admit of the possible existence 
>  of unjustifiable but correct answers to questions such as this...
>
>  ...[T]here is little to conclude except that any feature of an account
>  that identifies 3 with a set is a superfluous one -- and that therefore
>  3, and its fellow numbers, could not be sets at all.
>
>  [from "What Numbers Could Not Be"]
>_______________________________________________________________________
>-----------------------------------------------------------------------
>Michael Hand                     phone (409)845-5660, fax (409)845-0458
>Dept of Philosophy, Texas A&M Univ, College Station TX 77843-4237 U.S.A.
  
Au contraire, it is obvious which set the cardinal number 3 is.  It is
the set of all sets with three elements (this _can_ be defined in a
non-circular manner, by the way).  The technical problem is that this
set is not a first-class citizen in the usual set theory ZFC.  It is
in the set theory NFU of Quine and Jensen, however.

But there are some other objects closely related to 3, too.












-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu
Newsgroups: sci.logic,sci.math,comp.theory,sci.philosophy,sci.philosophy.meta,comp.ai.philosophy
From: sasghm@theseus.unx.sas.com (Gary Merrill)
Newsgroups: sci.logic
Subject: Re: The Mathematical Universe
Keywords: inconsistent multiplicities
Date: 7 Oct 92 14:06:36 GMT
Organization: SAS Institute Inc.
Originator: sasghm@theseus.unx.sas.com


In article <1992Oct6.202938.20909@ccu.umanitoba.ca>, sbloch@silver.cs.umanitoba.ca (Stephen Bloch) writes:
|> holmes@opal.idbsu.edu (Randall Holmes) writes:
|> >|> No, my view is that there is only one universe, and this includes all
|> >|> of the "possible worlds", _all_ of which are actual.  I am a possible
|> 
|> and sasghm@theseus.unx.sas.com (Gary Merrill) replies:
|> >But certainly there *is* a distinguished world (which we normally refer
|> >to as the "actual" one).  You may say that *all* of the possible worlds
|> >are actual (or real, or whatever), but if you wish to retain a distinction
|> >between what *is* and what *might be*, then *some* distinction must be
|> >made.  No?  If not, I don't see how to distinguish between fact and fiction.
|> 
|> Imagine I live in a suburban neighborhood containing lots of nearly
|> indistinguishable houses (in fact, to avoid being able to say "the house
|> at the northwest corner," let's suppose this suburb extends infinitely
|> in at least one dimension.  God, how depressing!)  I can still refer to
|> "the house," and everyone who hears me will understand that I mean
|> "the one I'm in."  If somebody else, living in a different house, says
|> "the house", she means the one's SHE's in.  The statement "A cat lives
|> in the house" may be fact in one and fiction in another.
|> 
|> This entire "neighborhood" of possible physical worlds is a subset of
|> The Logical Universe (comprising "things that could be").

Yes, but what you have provided here is just a general account of how
indexicals are handled in our language (and in formal languages).
It is still the case that among the indices there often is a *special*
one:  I, now, here, the actual world, ...

If all you are interested in is theorems concerning statements with
indexicals in them, there *may* indeed be no reason to single out
a special one.  Even if there is, the content of these theorems may
be of *logical* interest only in that they have no empirical content.
For example, I recall a system of David Kaplan's in which
"I am here now" is a theorem.  But there is *still* an important
distinction not captured by the set of theorems.  *I* am
typing *this*, and *you* are not -- though you *might* be.

As a logician, I can say "There is nothing special about the actual
world.  It's just one of the possible ones."  But as a *scientist*
or as an epistemologist, there certainly *is* something special.
And this usually is captured by saying that the actual world is
*real* and the other possible worlds are not.
-- 
Gary H. Merrill  [Principal Systems Developer, C Compiler Development]
SAS Institute Inc. / SAS Campus Dr. / Cary, NC  27513 / (919) 677-8000
sasghm@theseus.unx.sas.com ... !mcnc!sas!sasghm
Newsgroups: sci.logic
From: Brian F G Bidulock <bbidulo1%agt@cs.ualberta.ca>
Subject: Re: A only if B
X-Xxdate: Thu, 15 Oct 92 23:50:23 GMT
Organization: AGT Limited Research & Development
X-Useragent: Nuntius v1.1.1d9
Date: Thu, 15 Oct 92 22:43:29 GMT

In article <rkaivola.718902434@mits> Risto Kaivola,
rkaivola@mits.mdata.fi writes:
>"Tom will visit us only if we invite him.",
>is the correct formalization
>
>A = "Tom will visit us."
>
>B = "We invite him."
>
>A  -->  B

How about:
~A --> ~B
or
"If we don't invite Tom, he will not visit us."  == "Tom will visit us
only if we invite him."
Newsgroups: sci.logic
From: sasghm@theseus.unx.sas.com (Gary Merrill)
Subject: Re: A only if B
Originator: sasghm@theseus.unx.sas.com
Date: Tue, 13 Oct 1992 12:58:51 GMT
Organization: SAS Institute Inc.


In article <burt.718950333@aupair.cs.athabascau.ca>, burt@aupair.cs.athabascau.ca (Burt Voorhees) writes:

|> A<--B = A only if B = if B then A  This is read: A is true only if B is
|> true since a true statement cannot imply a falsehood.

I don't know what to make of this, except ...

	1.	A <-- B

	   certainly is non-standard notation, so I guess you can
	   impose on it whatever semantics you like.

	2.  If the claim is that

		A only if B

	    and

		if B then A

are equivalent (in the truth-functional, or any other, sense), then
a serious mistake is being made.
-- 
Gary H. Merrill  [Principal Systems Developer, C Compiler Development]
SAS Institute Inc. / SAS Campus Dr. / Cary, NC  27513 / (919) 677-8000
sasghm@theseus.unx.sas.com ... !mcnc!sas!sasghm
Newsgroups: sci.logic