HDTenEightyP/NetNews huggingface dataset:
Newsgroups: sci.logic
Subject: Re: Impredicativity - was: Russell's Paradox.
From: zeleny@husc10.harvard.edu (Michael Zeleny)
Date: 5 Nov 92 12:19:21 EST
 <1992Nov3.162547.25630@guinness.idbsu.edu> <1992Nov3.201225.9524@CSD-NewsHost.Stanford.EDU>
Organization: The Phallogocentric Cabal

In article <1992Nov3.201225.9524@CSD-NewsHost.Stanford.EDU> 
pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:

>In article <1992Nov3.162547.25630@guinness.idbsu.edu>
>holmes@garnet.idbsu.edu (Randall Holmes) writes:

>>In article <1992Nov3.041515.27732@CSD-NewsHost.Stanford.EDU>
>>pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:

VP:
>>>The iterative hierarchy is consistent with Z but not with ZF.
>>>Replacement (F) says in effect that any construction you can iterate
>>>yields a set.  Hence if the universe is an iterative hierarchy it is a
>>>set.

RH:
>>Same remark as before (this is ludicrous) + the obvious remark that
>>set-theorists will be awfully surprised by this pronouncement, since
>>they use the iterative hierarchy all the time (iterated power sets of
>>the empty set indexed by the ordinals, taking unions at limit
>>ordinals, which exhaust the universe in ZF -- the iterative hierarchy
>>is not only consistent with ZF, it is established by a THEOREM of ZF!)

VP:
>What exactly do you mean by "ZF can establish the iterative
>hierarchy"?  Do you mean that it can establish the *existence* of the
>hierarchy?  Why wouldn't that be equivalent to asserting the
>consistency of ZF within itself?

ZF proves that every set has a rank.

VP:
>Or do you mean that in ZF one can prove that every set can be built up
>iteratively?  Assuming the Foundation Axiom I have no quarrel with the
>latter, but then you just have a statement about individual sets being
>built up iteratively, not about their collectively forming a
>hierarchy.

Obviously, you cannot refer to the totality of sets in ZF.  Try
thinking charitably, -- it will aid your comprehension.

VP:
>I'm probably just being my usual dense self, but I just can't figure
>out how to talk about the hierarchy itself within ZF.  What is the
>trick?  And what is a more precise wording of the theorem you refer to
>above?

You can talk about the hierarchy, -- without referring to it as a
completed totality, -- by axiomatizing the notion of rank.  See Dana
Scott's paper "Axiomatizing Set Theory" in the 1974-5 AMS colloquium,
and Michael Potter's elementary book _Set Theory_, based on Scott's
axiomatization.

>-- 
>Vaughan Pratt			Ain't no truth in logic, son.

cordially,
mikhail zeleny@husc.harvard.edu
" -- I shall speak bluntly, because life is short."
From: mjb@dws014.unr.edu (Mike Brown)
Newsgroups: sci.logic
Subject: Programs for simple logic proofs:  where are they?
Date: 12 Nov 92 05:30:28 GMT
Reply-To: mjb@dws020.unr.edu (Mike Brown)
Followup-To: sci.logic
Organization: University of Nevada, Reno  Department of Computer Science

I am looking for programs that will do proofs like:
			Prove: Q            \
	1 P then Q	Premis               > The problem
	2 P		Premis              /
	3 Q             1, 2, Modus Ponens  >  The program's proof

(The proofs do get more involved)

I have looked around, but can't find a program for this.
(I tried archie searches for many keywords and didn't find a program)

Is there a program out there that will do these proofs?

Thanks
--
Mike Brown, mjb@cs.unr.edu    "I am the scratch monkey"
Xref: sparky sci.logic:1970 sci.philosophy.meta:2432
From: martinc@grover.cs.unc.edu (Charles R. Martin)
Newsgroups: sci.logic,sci.philosophy.meta
Subject: Re: Natural Kinds (was re: Are all crows black?)
Date: 9 Nov 92 14:52:18 GMT
	<1992Nov4.163618.17991@dcs.qmw.ac.uk>
	<1992Nov4.200546.2196@CSD-NewsHost.Stanford.EDU>
	<Bx8yvo.6ty@unx.sas.com> <1992Nov8.210316.5922@dcs.qmw.ac.uk>
	<BxGAvC.7Lo@unx.sas.com>
Followup-To: sci.logic
Organization: UNC Department of Computer Science
In-reply-to: sasghm@theseus.unx.sas.com's message of 9 Nov 92 13:30:47 GMT

In article <BxGAvC.7Lo@unx.sas.com> sasghm@theseus.unx.sas.com (Gary Merrill) writes:
   I don't have a problem with this.  But notice that it makes
   CS a subdiscipline of mathematics -- and it still lacks significant
   distinguishing features of the genuine sciences.  

It still appears that the problem is with you stating or implying too
strong a constraint on what the "genuine" sciences are.

   It also suggests that there is (or ought to be) a distinction between
   CS and software engineering along the lines of the distinction
   between (say) applied (or even pure) mathematics and civil
   engineering.  But this does not seem to be the case.  And it isn't
   obvious that it should be.

Any of these distinctions are somewhat arbitrary.  I once had a
conversation with my ex-wife's uncle, trying to explain to him what
software engineering was.  He was a chemical engineer for Dow for about
five hundred years, so I started out by saying that SE was to computer
science as chemical engineering was to chemistry.  This opened the
proverbial can of worms.

Sci.logic isn't the place for the controversy, but just as in chemical
engineering vs. chemistry, there are techniques and methods that apply
to software engineering that are *used* in computer science, and
(naturally) methods and techniques from computer science that must be
used by software engineers.

As to whether they *should* be separate: of course not.  All software
engineers know that computer science is a subdiscipline of software
engineering. 
--
		Charles R. Martin/(Charlie)/martinc@cs.unc.edu
     Dept. of Computer Science/CB #3175 UNC-CH/Chapel Hill, NC 27599-3175
	    3611 University Dr #13M/Durham, NC 27707/(919) 419 1754
     "Oh God, please help me be civil in tongue, pure in thought, and able
      to resist the temptation to laugh uncontrollably.  Amen." -- Rob T
Newsgroups: sci.logic,alt.uu.future
From: esz001@cck.coventry.ac.uk (Will Overington)
Subject: Re: Are all crows black? => Logic as an essential subject?
Organization: Coventry University
Date: Mon, 9 Nov 1992 10:23:47 GMT

It was me that asked whether logic should be a compulsary subject.

For many years I have done a little Boolean algebra, but only this
summer have I even learned of syllogisms, and am indeed amazed that
I could be a graduate without not having learned of syllogisms and
their rules as part of general education.

Can I ask please, is syllogisms and the like what sci.logic is about,
or am I missing something fundamental.

Please post replies, as I am sure that there may be other people in
the same position.
From: gavan@elc.mth.uct.ac.za (Gavan Tredoux)
Newsgroups: sci.logic
Subject: Re: Types of type theory
Date: 12 Nov 92 14:46:54 GMT
Article-I.D.: ucthpx.1992Nov12.144654.7493
Organization: University of Cape Town
X-Newsreader: Tin 1.1 PL4

dzik@access.digex.com (Joseph Dzikiewicz) writes:
: I have come across two uses of the term "type theory" in logic that seem
: to be referring to different things.
: 
: In one, Type Theory seems to relate to the rules for higher-order-logics
: (ie, second order logic and up).  This is discussed in Peter Andrews'
: book "An Introduction to Logic and Type Theory: To Truth through Proof."
: I have also seen it referred to as "Church's Type Theory."
: 
: In the other, types are sets of formulas in first order logic.  This
: is discussed in some detail in Chang and Keisler's book "Model Theory."
: 
: Am I correct in thinking that these are two different things with the same
: name, or are they the same thing presented differently by two
: different groups of authors?

Type theory *is* higher-order logic, where the types are used to
avoid the paradoxes. One version -- the one Andrews explains --
is Church's Simple Theory of Types. There are others -- the Ramified
Theory of types (Ramsey) and the original, Russell's type theory.

The Simple Theory of Types is just Predicate Calculus 
enriched with typed lambda calculus. 

Types themselves can be thought of as sets, with a little care, 
depending on how you want to give the *semantics*. Chang and Kreisler
deal with models, Andrews with the logic. 

But, ahem, types pitch up all over the place: they just prevent certain
things (eg. applying a function to the wrong arguments) from happening.
Eg. types of variables in computer languages.

Gavan Tredoux
UCT
Xref: sparky sci.logic:1983 sci.philosophy.meta:2469
From: jg@cl.cam.ac.uk (Jim Grundy)
Subject: Help finding Lukasiewicz papers?
Reply-To: jg@cl.cam.ac.uk
Organization: Cambridge Hardware Verification Group
Date: Thu, 12 Nov 1992 15:36:33 GMT

Hi

Does some kind person have English translations of these papers that they
could send me copies of?

                            '      '
Jan Lukasiewicz. O logice trojwartosciowej. Ruch filozoficzny, 5:170-171, 1920.

and
                             .    '
Jan Lukasiewicz. O pojecie mozliwosci. Ruch filozoficzny, 5:169-170, 1920.
                       `
Thanks in advance

Jim

-- 
===============================================================================
Jim Grundy               
University of Cambridge | Phone: +44 223 334760            | This space has
Computer Laboratory     | Fax:   +44 223 334678            | been intentionally
New Museums Site        | Telex: CAMSPLG 81240             | left blank for
Pembroke Street         | email: jg@cl.cam.ac.uk           | formatting
Cambridge  CB2 3QG      |                                  | purposes.
UNITED KINGDOM          |                                  |
===============================================================================
Newsgroups: sci.logic
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Are all crows black?
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Fri, 6 Nov 92 02:23:05 GMT

In article <1992Nov4.184630.3575@hubcap.clemson.edu> steve@hubcap.clemson.edu ("Steve" Stevenson) writes:

>Isn't this the "grue" problem? The "grue" problem came about (if I remember
>correctly) because all emeralds were green and believed by reputable scientists
>that they could only be green. Then they found blue ones...

Are you joking here?  Anyway, in case anyone hasn't heard about the grue
paradox, this isn't it!  
Newsgroups: sci.logic
From: lombardo@ghost.dsi.unimi.it (franco lombardo)
Subject: Functions for n-valued logic
Keywords: n-valued logic
Organization: Computer Science Dep. - Milan University
Date: Thu, 12 Nov 1992 14:57:35 GMT

Hi!
I have this problem:
i have a function f:{0,1/2,1}^3--->{0,1/2,1}^3 completely described
by a table and i  want to express it using the operators of
a three-valued Lukasiewicz logic: and, or, not and
Lukasiewicz implication.
Would you like to help me?
                           Franco Lombardo.
			   lombardo@ghost.dsi.unimi.it
Newsgroups: sci.logic,alt.uu.future
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Are all crows black? => Logic as an essential subject?
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Wed, 11 Nov 92 22:59:53 GMT

In article <BxGFw2.AJv@cck.coventry.ac.uk> esz001@cck.coventry.ac.uk (Will Overington) writes:

>Can I ask please, is syllogisms and the like what sci.logic is about,
>or am I missing something fundamental.

Syllogisms are what logicians were up to in the Middle Ages, and there's
a lot of interesting stuff that has happened since.  (Actually logicians
were already doing lots of other stuff in the Middle Ages.)  In the late
1800's a study of the "foundations of mathematics" and logic began which
led to a lot of spectacular results in this century, such as Goedel's
theorems.  For a tour of logic you could do worse than to take a peek at
the entries about logic in the Encyclopedia of Philosophy.  And you can
read sci.logic to see what sorts of things people argue about.
From: brendan@cs.uq.oz.au (Brendan Mahony)
Newsgroups: sci.logic
Subject: Re: Russell's Paradox
Date: 13 Nov 92 05:35:21 GMT
Reply-To: brendan@cs.uq.oz.au

In <1992Nov10.001234.18488@guinness.idbsu.edu> holmes@garnet.idbsu.edu (Randall Holmes) writes:

>i.  Russell's paradox does have _semantic_ consequences.  Whatever
>membership is, there is no set of all sets that are not members of
>themselves.  Certainly the mechanics of applying the paradox are
>syntactical -- so what?

I don't see that the Russell paradox of itself requires the
non-existence of this object (RP).
The most I could deduce from it is that the predicate

	RP is a member of RP

has no truth value. I.e. the function 'is a member of' is not total.

--
When soldiers form lines or hollow squares, you call it reason.
When wild geese in flight take the form of a letter V, you say instinct.
When the homogeneous atoms of a mineral arrange themselves into shapes
mathematically perfect you have nothing to say. You have not even invented a name to conceal your heroic unreason."
Newsgroups: sci.logic
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Impredicativity - was: Russell's Paradox
Organization: Computer Science Department,  Stanford University.
Date: Thu, 5 Nov 1992 04:40:52 GMT

In article <Bx81Ho.9HL@cantua.canterbury.ac.nz> wft@math.canterbury.ac.nz (Bill Taylor) writes:
>Randall Holmes - a question.  You say that it is a *theorem* of ZF that
>
>   "for any set x, for some ordinal a, x E V(a)" .
>
>[where V(a) is defined by  V(0) = {}
>                           V(a+1) = P{V{a}}
>                           V(L) = U{a < L}[V(a)] (L a limit ordinal). ]
>
>Is this really true ? Surely not. The collection of V's is a model for ZF, yes.
>But the above isn't a theorem, is it? 
>I expect it *is* a theorem of ZF+AxFndtn.

I'm sure that's what Randall meant.  You can't rank sets without FA.
If you weaken FA to AFA you have counterexamples to the above like
Omega = {Omega}, to which the above definition cannot assign any
ordinal in a way that satisfies these equations.  (Consider the least
ordinal a for which Omega E V{a}.  Clearly a is not 0.  Since Omega has
only one element a cannot be a limit ordinal.  So a is a successor
ordinal, call it b+1.  But then Omega is a subset of V{b}, whence
Omega's only element, Omega, is an element of V{b} and hence of rank
less than a, contradiction.)

Conversely, once you have FA you can prove the above theorem by
assigning a rank to each set by the following informally described
procedure.  To rank set x, assign ranks to its elements.  This
recursive procedure is well-defined because there are no infinite
descending membership chains.  Now take the rank of x to be the least
ordinal strictly greater than the rank of any element of x.  This rank
will be 0 when x is empty, a successor ordinal when x contains an
element of rank maximal among its siblings, and otherwise a limit
ordinal.

This informal procedure can be made rigorous as follows.  The form of
FA that I find most useful for these purposes is the Axiom Schema of
Restriction, namely one axiom for every ZF formula phi(x) with one free
variable x.  The axiom says that either phi holds of no set, or there
exists a set y for which phi holds of y but of none of its members.

So now take phi(x) to be "for every ordinal a, x is not in V(a)".  If
phi holds of no set we are done.  Otherwise by restriction there is a
set y for which phi(y) holds but for all members z of y, phi(z) is
false.  If y is empty this contradicts the first equation defining V.
If y is nonempty then all its members have ranks.  If there is a
maximum rank b of those members then y is a subset of V(b), hence an
element of V(b+1) by the second equation.  If there is no maximum rank
then let b be the union of these ranks, necessarily a limit ordinal.
Then y is an element of V(b) by the third equation, and we are done.
(And hence of course phi holds of no sets.)
-- 
Vaughan Pratt				There's no truth in logic, son.
Xref: sparky sci.logic:1977 sci.philosophy.meta:2455
From: burt@aupair.cs.athabascau.ca (Burt Voorhees)
Newsgroups: sci.logic,sci.philosophy.meta
Subject: Re: Natural Kinds (was re: Are all crows black?)
Date: 9 Nov 92 21:53:48 GMT
Article-I.D.: aupair.burt.721346028
Followup-To: sci.logic

[references for philosophy of science other than Popper, Feyerbend, Kuhn,
and Lakatos]:

An excellent book is Forsight and Understanding by Stephen Toulmin - in
some ways it anticipates Kuhn, but in my view gives a better interpretation.

Also, check out Giere for one of the "cognitive/constructive" approaches;
Salmon and Hemphill for covering law ideas; and a book edited by
Fredrick Suppes (can't recall title at the moment) which goes over
a number of different views.
burt voorhees
From: ard@cs.bham.ac.uk (Antoni Diller)
Newsgroups: sci.logic
Subject: Re: Are all crows black?
Date: 5 Nov 92 16:05:19 GMT
Organization: School of Computer Science, University of Birmingham, UK

In article <1992Nov4.184630.3575@hubcap.clemson.edu> steve@hubcap.clemson.edu ("Steve" Stevenson) writes:
>skumar@eagle.wesleyan.edu writes:
>
>>Please correct me if I am wrong but I think that if I found a creature which
>>was like a crow in all respects but it was white in color, I would call it an
>>albino crow or something. I would not call it just "a crow". Does this not mean
>>that we accept "all crows are black" by definition so we need not prove it?
>
>Isn't this the "grue" problem? The "grue" problem came about (if I remember
>correctly) because all emeralds were green and believed by reputable scientists
>that they could only be green. Then they found blue ones...
>
>-- 
>===============================================================================
>Steve (really "D. E.") Stevenson           steve@hubcap.clemson.edu
>Department of Computer Science,            (803)656-5880.mabell
>Clemson University, Clemson, SC 29634-1906

`Grue' was an invented word by Nelson Goodman; something is grue if it is
green before 1 January 2000 and blue thereafter; therefore every confirmation
of the sentence `all Xs are green' is also a confirmation of the
sentence `all Xs are grue' (before 2000).
Xref: sparky sci.logic:1975 sci.philosophy.meta:2443
From: sasghm@theseus.unx.sas.com (Gary Merrill)
Newsgroups: sci.logic,sci.philosophy.meta
Subject: Re: Natural Kinds (was re: Are all crows black?)
Date: 9 Nov 92 18:09:33 GMT
Article-I.D.: unx.BxGnrx.wr
Organization: SAS Institute Inc.
Originator: sasghm@theseus.unx.sas.com


In article <1992Nov9.172610.27502@samba.oit.unc.edu>, Robert.Vienneau@launchpad.unc.edu (Robert Vienneau) writes:

|> Gary, your response disappoints me. I'd seriously like reading
|> suggestions. Who would you suggest is of comparable status? (By limiting
|> yourself to the last 20 years, you provide yourself with a problem even
|> more than I do by limiting myself to the 20th century. It's extremely
|> hard to say whose work will age well, or even if current arguments will
|> not seem pointless and too narrowly focused in another 100 years.)

I mentioned the past 20 years because the people *you* mentioned were
writing largely in this period.  I'm not sure what you mean by "comparable
status", but I get the impression that you are familiar neither with
the positivists (and their successors) whom these guys are arguing
against nor with more recent developments since these guys stopped
publishing.  Even if you like the "flavor" of Kuhn and Lakatos, I'm
surprised that you don't even mention Larry Laudan -- which indicates
to me that your exploration of this area is even more severely dated
than my own participation.  Finding a reading list should be pretty
easy:  Go to Davis Library.  Hang a right to the current journals.
Look at such journals as:

		_Philosophy of Science_
		_British Journal for the Philosophy of Science_
		_Erkenntnis_  (Davis may not have this)
		_Synthese_  (May not have this either, but it *has*
				to be on campus somewhere)

Look at the bibliographies of the phil. of science papers in these.
Or get a recent book by van Fraassen and look at the bibliography.
He's usually pretty complete.

|> Your response also makes me wonder if you know what you are talking
|> about. How can you characterize the four I listed as being of a single
|> school? Granted they were all aware of each other's work and reacted

I ain't gonna fight this battle *again* here.  See the section entitled
"History and the Metaphilosophy of Science" in _PSA 1980_ (ed. by
Peter Asquith & Ron Giere):

	"Toward a Historical Meta-Method for Assessing Normative
	 Methodologies:  Rationability, Serendipity, and
	 the Robinson Crusoe Fallacy" by Stephen J. Wykstra

	"Moderate Historicism and the Empirical Sense of
	 'Good Science'" by G. H. Merrill

	"History and the Norms of Science" by James Robert Brown

I would bet that UNC has this (though I have detected odd gaps in
their phil of science collection -- e.g., they don't seem to have
van Fraassen's recent books, or did not the last time I looked).
After you look at these, *then* you can wonder if I know what I
am talking about.

-- 
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: torkel@sics.se (Torkel Franzen)
Subject: Re: Russell's Paradox
Organization: Swedish Institute of Computer Science, Kista
Date: Thu, 5 Nov 1992 09:45:54 GMT

In article <1992Nov04.233228.16942@Cookie.secapl.com> frank@Cookie.secapl.com
 (Frank Adams) writes:

   >Proper classes arose because it is hard to talk about sets in general
   >without them.  I think it is safe to say that most mathematicians are a bit
   >uncomfortable dealing with proper classes, but their use is at least
   >demonstrably consistent (at least if the underlying set theory is
   >consistent).

  Adding to a set theory T predicative class existence axioms (i.e. axioms
asserting the existence of classes definable by a formula containing
no quantifiers over classes) yields a conservative extension of T, and
the classes in such a case can be regarded as just a convenient way of
referring to formulas. Adding impredicative class existence axioms
yields an essentially stronger theory.
Xref: sparky sci.logic:1986 sci.philosophy.meta:2487 sci.math:14730 sci.physics:18634
From: mrh7507@tamsun.tamu.edu (Michael Hand)
Newsgroups: sci.logic,sci.philosophy.meta,sci.math,sci.physics
Subject: Re: What is Computer Science (was: Natural Kinds)
Date: 10 Nov 92 20:07:23 GMT
Article-I.D.: tamsun.1992Nov10.200723.15798
Organization: Texas A&M University, College Station

Kaushik Banerjee writes:

  >Computer Science is something one can find gainful employment
  >in; mathematics is something one can not find gainful
  >employment in.

Yes, let's not forget that the only good reason for a student
to attend a university is to make possible future gainful
employment, and the university's *raison d'etre* is to
prepare students for same.
B-o} Michael
-- 
_______________________________________________________________________
-----------------------------------------------------------------------
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,sci.philosophy.meta