HDTenEightyP/NetNews huggingface dataset:
From: holmes@garnet.idbsu.edu (Randall Holmes)
Subject: Re: Russell's Paradox
Organization: Boise State University
Date: Thu, 12 Nov 1992 17:05:57 GMT

In article <1992Nov11.175842.123427@Cookie.secapl.com> frank@Cookie.secapl.com (Frank Adams) writes:
>In article <1992Nov10.001234.18488@guinness.idbsu.edu> holmes@garnet.idbsu.edu (Randall Holmes) writes:
>>In article <1992Nov09.172532.43648@Cookie.secapl.com> frank@Cookie.secapl.com (Frank Adams) writes:
>>>All right; but what would you put in it's place?  I'm not willing to call
>>>something "set theory" unless it has *some* recognizable form of the axiom
>>>of comprehension.  Can you formalize your ideas?
>>
>>ii.  NFU:
>
>Yes, Randall, I know that's what *you* would put in its place.  If you can
>show that NF[U]'s comprehension rule is free from the kind of objection David
>is making, I will grant that you have given a good reason for taking NFU
>seriously.  It isn't enough to show that a few examples work, however.

I agree with your remarks absolutely.  The case for NFU does not rest
on a few examples.  There is an equiconsistency proof with set
theories of the usual type.  Rosser developed the foundations of
mathematics in _Logic for Mathematicians_ in a way which can be
adapted to NFU (he used NF itself).  Finally, there is a philosophical
argument of sorts (due to myself (unfortunately for my attempt to
cloak it with Authority!)) indicating why unstratified formulae should
not be understood to define legitimate properties of sets.

NFU is impredicative, which may cause Gudeman to object to it.  If
impredicativity is rejected, mathematics is weakened considerably.
The predicative fragment NFI of NF is consistent (with full
extensionality!) but weaker than Peano arithmetic.  (When I say NFU, I
mean NFU + at least the Axiom of Infinity; NFU by itself is also
weaker than arithmetic, as is the theory of types without infinity).
But it allows a much wider range of definitions of sets than the usual
set theory (for example, most natural categories are sets in NFU).


-- 
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
From: frank@Cookie.secapl.com (Frank Adams)
Subject: Re: Russell's Paradox
Date: Wed, 11 Nov 1992 17:58:42 GMT
Organization: Security APL, Inc.

In article <1992Nov10.001234.18488@guinness.idbsu.edu> holmes@garnet.idbsu.edu (Randall Holmes) writes:
>In article <1992Nov09.172532.43648@Cookie.secapl.com> frank@Cookie.secapl.com (Frank Adams) writes:
>>All right; but what would you put in it's place?  I'm not willing to call
>>something "set theory" unless it has *some* recognizable form of the axiom
>>of comprehension.  Can you formalize your ideas?
>
>ii.  NFU:

Yes, Randall, I know that's what *you* would put in its place.  If you can
show that NF[U]'s comprehension rule is free from the kind of objection David
is making, I will grant that you have given a good reason for taking NFU
seriously.  It isn't enough to show that a few examples work, however.
Newsgroups: sci.logic
From: holmes@garnet.idbsu.edu (Randall Holmes)
Subject: Re: Russell's Paradox
Organization: Boise State University
Date: Fri, 13 Nov 1992 16:59:51 GMT

In article <11040@uqcspe.cs.uq.oz.au> brendan@cs.uq.oz.au writes:
>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.

Naive set theory uses first order logic, which precludes this.  This
is a way of trying to avoid the paradoxes; it is not particularly
satisfactory.  Saving logic is more important that saving the Russell
class.


>
>--
>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."


-- 
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
Xref: sparky sci.logic:1931 alt.uu.future:256
From: higa@lclark.edu (Keith Higa)
Newsgroups: sci.logic,alt.uu.future
Subject: Re: Are all crows black? => Logic as an essential subject?
Date: 5 Nov 92 18:25:13 GMT
Organization: Lewis & Clark College, Portland OR

In article <1992Nov4.170813.27890@CSD-NewsHost.Stanford.EDU> 
pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>I have very mixed feelings about this.  Freshman math at Gunn High
>(where my 14 year old goes) started out this year with a couple of
>weeks of propositional logic before getting into geometry etc.  My
>intuitive feeling was that she got much less useful math out of the
>logic than out of the geometry.  On the other hand logic is fundamental
>to thought, and even if humans don't reason propositionally it is good
>to at least be aware of a logical system that they could plausibly
>reason in, albeit clumsily.

My logic professor brought up the story of Bertrand Russell.  I think
(correct me if I'm wrong), that he and a co-author set out to prove that
all math was based on logic, and it took them two volumes to logically
prove that 1+1=2.


-- 
Keith K. Higa                         Lewis & Clark College    
higa@lclark.edu                       Portland, OR, USA
In a hierarchy each member tends to rise to his/her level of incompetence.
                                 --The Peter Principle
Xref: sparky sci.logic:1988 sci.classics:974
From: maj@waikato.ac.nz
Newsgroups: sci.logic,sci.classics
Subject: Ad hominum
Date: 11 Nov 92 17:36:12 +1300
Organization: University of Waikato, Hamilton, New Zealand

Gary Merrill in sci.classics :


Brian, you're being really dense here.  The point is not what kinds
of insight one acquires by being a woman, a slave, or a serf, but
rather what *position* one may gain by being a "feminist philosopher",
a "slave philospher",  or a "serf philosopher".



Gary Merrill in sci.logic  :


Ah yes.  The ultimate academic bugaboo:  funding.  Everything (even your
taxonomy of cognitive disciplines) must be a slave to funding.


-- 
Murray A. Jorgensen [ maj@waikato.ac.nz ]    University of Waikato
Department of Mathematics and Statistics     Hamilton, New Zealand      
__________________________________________________________________
'Tis the song of the Jubjub! the proof is complete,
if only I've stated it thrice.'
From: torkel@sics.se (Torkel Franzen)
Newsgroups: sci.logic
Subject: Re: Impredicativity - was: Russell's Paradox
Date: 5 Nov 92 14:37:25 GMT
Organization: Swedish Institute of Computer Science, Kista

In article <TORKEL.92Nov5103134@isis.sics.se> torkel@sics.se (Torkel Franzen)
 writes:

   >the range of a function f defined on the natural numbers, where
   >f(n)={n,f(n+1)} for all n.

  Not the range, of course, but f(1).
Xref: sparky sci.logic:1960 comp.ai.philosophy:6693 comp.robotics:2280 comp.databases.theory:596 comp.theory:2370
From: arodgers@dcs.qmw.ac.uk (Angus H Rodgers)
Newsgroups: sci.logic,comp.ai.philosophy,comp.robotics,comp.databases.theory,comp.theory
Subject: Re: Human Computers....
Date: 8 Nov 92 20:25:38 GMT
Organization: Computer Science Dept, QMW, University of London

In <Qez6sI200iVgI2bYwP@andrew.cmu.edu>
Mark Alan Lang <Elistan+@CMU.EDU> writes:

>Excerpts from netnews.comp.robotics: 7-Nov-92 Human Computers.... by
>Eskinder Sahle@csgrad.cs pl.na nasa slab. 
>> Hello all:

>	Hi there!
>  
>> I need some help....  I'm looking for examples in fiction literature
>> of super sophisticated communicative computers a la HAL. That is,
>> computers that talk and communicate like humans.  I'm not so much 
>> interested in those instances where it's a robot that cannot be
>> distinguished from a human being as in computers sounding human without
>> being almost totally human-like....  .
>>  
>> Thanks in advance.
>> Ahmed 

"Michaelmas", by Algis Budrys? (Not quite sure of this reference.)
--
Angus H. Rodgers  (PhD student), | arodgers@dcs.qmw.ac.uk  
Dept. of Computer Science, Queen | [ +44 | 0 ] 71 975 5241   
Mary & Westfield College,  Mile  | "But what is contact? No two points
End Rd., London E1 4NS, England  | are in contact." -- A.N. Whitehead.
Xref: sparky sci.logic:1991 sci.classics:979
From: sasghm@theseus.unx.sas.com (Gary Merrill)
Newsgroups: sci.logic,sci.classics
Subject: Re: Ad hominum
Date: 11 Nov 92 13:44:55 GMT
Organization: SAS Institute Inc.
Originator: sasghm@theseus.unx.sas.com


In article <1992Nov11.173613.12104@waikato.ac.nz>, maj@waikato.ac.nz writes:
|> Gary Merrill in sci.classics :
|> 
|> 
|> Brian, you're being really dense here.  The point is not what kinds
|> of insight one acquires by being a woman, a slave, or a serf, but
|> rather what *position* one may gain by being a "feminist philosopher",
|> a "slave philospher",  or a "serf philosopher".
|> 
|> 
|> 
|> Gary Merrill in sci.logic  :
|> 
|> 
|> Ah yes.  The ultimate academic bugaboo:  funding.  Everything (even your
|> taxonomy of cognitive disciplines) must be a slave to funding.
|> 
|> 
|> -- 
|> Murray A. Jorgensen [ maj@waikato.ac.nz ]    University of Waikato
|> Department of Mathematics and Statistics     Hamilton, New Zealand      
|> __________________________________________________________________
|> 'Tis the song of the Jubjub! the proof is complete,
|> if only I've stated it thrice.'

No, not exactly.  While these remarks *might* be attacked as being
certain types of fallacies of relevance, the fallacy in question
are *not* ad hominem.  I refer you to Carney & Scheer, _Logic and
Argument_ for the details (or any decent book on rhetoric).

Moreover, since these were *not* offered as *arguments*, it is
somewhat inaccurate to characterize them thus.  Think of them as
armchair (though based on some experience with these matters)
sociological observations concerning *why* certain things are of
intense interest to academics at certain times.  I not, at least,
that you do not impugn the *truth* of these remarks.

-- 
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: posegga@margaux.ira.uka.de (Joachim Posegga)
Subject: Looking for references on IF-THEN-ELSE connectives
Organization: Karlsruhe University, Dept of Comp Science, FRG
Distribution: sci
Date: Fri, 13 Nov 1992 11:25:38 GMT


I am looking for references on ternary IF-THEN-ELSE connectives in
logic. Church, for instance, treats expressions of the form [A,B,C],
meaning "(B -> A) & (~B -> C)", in his book "Introduction to
mathematical logic".

Does anyone know of other papers/books on this? I am aware of Bauer &
Wirsing (1991), Orlowska (1967 and 1969), and Shannon (1938).

I am not looking for references on BDDs, which are closely related to
this, but on publications written from a logical point of view. The
reason I am asking is that I am writing a paper on BDDs and intend to
give a brief description of the (historical) background. So, references
to early publications are appreciated as well.

As this is probably not of general interest, please respond by email.

Thanks in advance

	Joachim.
Newsgroups: sci.logic
From: holmes@garnet.idbsu.edu (Randall Holmes)
Subject: Re: Russell's Paradox
Organization: Boise State University
Date: Tue, 10 Nov 1992 00:12:34 GMT

In article <1992Nov09.172532.43648@Cookie.secapl.com> frank@Cookie.secapl.com (Frank Adams) writes:
>In article <25916@optima.cs.arizona.edu> gudeman@cs.arizona.edu (David Gudeman) writes:
>>No, I am not complaining about elementhood being a proposition, I am
>>complaining about a syntactic circularity begin treated as though it
>>had semantic significance.  Neither am I concerned about the
>>unrestricted range of the quantification.  As the set {x : x = x}
>>clearly shows, there is no inconsistency inherent in either
>>self-membership or impredicativity.  I claim that {x : x = x} is a
>>perfectly reasonable set and that the mere fact that ZF proves the
>>opposite is enough to show that ZF is not an adequate axiomatization
>>of set theory.
>
>All right; but what would you put in it's place?  I'm not willing to call
>something "set theory" unless it has *some* recognizable form of the axiom
>of comprehension.  Can you formalize your ideas?

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?

ii.  NFU:

	Axiom 1.  Objects with elements that have the same elements
	are equal.  (this allows multiple objects with no elements).

	Axiom 2.  Stratified comprehension (any instance of
comprehension which would make sense in the simple theory of types
under some assignment of types to its variables holds -- further
details available on request).

	Axiom 3.  The universe is infinite.

	Axiom 4.  The universe can be well-ordered (choice).

	This is a set theory with the same consistency strength as
Russell's theory of types; it is untyped (a set definition makes sense
if it would make sense in the theory of types, but objects in this
theory are not typed).  {x|x=x}, the universe, exists (the definition
would make sense in TT); {x|~x E x}, the Russell class does not exist
(the definition would not make sense in TT -- if the first x had type
n, the second would have type n+1).

	This theory is known to be consistent (R. B. Jensen, On the
consistency of a slight (?) variation of Quine's New Foundations,
Synthese, vol. 19), and adequate for most mathematical purposes.  It
-- 
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
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 00:47:25 GMT

In article <1992Nov4.134534.17092@husc3.harvard.edu> zeleny@husc10.harvard.edu (Michael Zeleny) writes:
>
>Taylor:
>>>The slick form of AF, that every nonempty set has a member disjoint from it,
>
>Pratt:
>>Where is this form given?  
>
>Most everywhere [...]
>
>>Pratt:                And why doesn't it rule out Omega = {Omega}?
>>(Just asking, I'm not expert on this stuff.)
>
>Neither am I, but that will not prevent me from being charitable
>enough to let you answer your own question.

Why, do you turn in all your Usenet posts along with your tax return?

Actually it's just me being dense (and Bill being nonstandard).  I took
Bill's AF to mean AntiFoundation when he meant Axiom of Foundation
(whence he *meant* to rule out Omega={Omega}).  I should have figured
that out sooner (broken enough eggs in the past two days to start an
omelette parlor).

>[...] e.g. in Drake (_Set Theory_), whose pithy comments on
>the Axiom of Replacement (a.k.a. the `F' in `ZFC') will go a long way
>toward disabusing you of your wacky revisionist notions.

Thank god.  I've been posting wacky messages for weeks and no one seems
to have noticed till now.  How do you do it?

But let's get our facts straight on what I'm proposing to revise.  I
haven't lifted a finger against Replacement, in fact I need it to make
money with it by 2012 (come on, Replacement, come on, be strong for
me!).

>Some _philosophical_ reservations concerning Replacement can be made
>from a generic Limitation of Size standpoint, -- right now I do not
>have the references, but they are likely to be found in Maddy's JSL
>expository articles on the ZFC axioms.  However, from the more refined
>standpoint of the cumulative hierarchy, Drake more or less has the
>last word.

Again, I'm not in the market to be talked out of Replacement, or talk
anyone out of it.  Foundation on the other hand seems as pointless as
the cumulative hierarchy: each needs the other and neither seems to be
much use to the rest of mathematics.  Now who can you point me at with
a convincing pitch for Foundation?

>Always looking for
>logico-philosophical esoterica, Italian motorcycle parts, Swiss
>firearms, or XVIIIth century French smut.

Oh.  Guess that answers my second last question.  :-)
-- 
Vaughan Pratt				There's no truth in logic, son.
From: gudeman@cs.arizona.edu (David Gudeman)
Newsgroups: sci.logic
Subject: Re: Russell's Paradox
Date: 5 Nov 92 20:22:02 GMT
Organization: U of Arizona CS Dept, Tucson

In article  <1992Nov04.233228.16942@Cookie.secapl.com> Frank Adams writes:
]In article <24780@optima.cs.arizona.edu> gudeman@cs.arizona.edu (David Gudeman) writes:
]>This (or so I claim) is the single, simple, obvious cause of Russel's
]>paradox.  In particular, R = {x : x not elem x} is a definition of
]>type (2) that contains an implicit reference to R because x quantifies
]>over a set that contains R.  (Or you could show the recursion in the
]>definition of elem as I did before)...
]
]It appears to me that you are complaining not about elementhood being a
]proposition, but about the unrestricted range of the quantification in the
]axiom of comprehension.  Note that your complaint about the implicit
]reference to R is just as applicable to R = {x : x = x}, which gives the
]universal set without using elementhood.

No, I am not complaining about elementhood being a proposition, I am
complaining about a syntactic circularity begin treated as though it
had semantic significance.  Neither am I concerned about the
unrestricted range of the quantification.  As the set {x : x = x}
clearly shows, there is no inconsistency inherent in either
self-membership or impredicativity.  I claim that {x : x = x} is a
perfectly reasonable set and that the mere fact that ZF proves the
opposite is enough to show that ZF is not an adequate axiomatization
of set theory.
-- 
					David Gudeman
gudeman@cs.arizona.edu
Newsgroups: sci.logic
From: casley@Tarski.Stanford.EDU (Ross Casley)
Subject: Re: Are all crows black? => Logic as an essential subject?
Organization: Computer Science Department, Stanford University.
Date: Sun, 8 Nov 1992 07:21:49 GMT

In article <1992Nov5.182513.25397@lclark.edu> higa@lclark.edu (Keith Higa) writes:
>My logic professor brought up the story of Bertrand Russell.  I think
>(correct me if I'm wrong), that he and a co-author set out to prove that
>all math was based on logic, and it took them two volumes to logically
>prove that 1+1=2.
>

The other author is Whitehead.  The work is "Principia Mathematica".  Russell
and Whitehead argue against the position, advanced by Immanuel Kant, that
mathematical truths are neither empirical (to be established by observation)
nor "analytic" (to be established by reasoning about the meanings of words).
They do this by showing that mathematical truths are analytic after all.
They manage to develop a good deal of the basics of mathematical logic
along the way.

It does take a lot of work to get to a position where a statement that is
clearly mathematical is clearly analytic too.  But that doesn't seem to 
have any bearing on whether it is worthwhile to learn elementary logic
in high school.

-Ross

PS  Who drew the cartoon with a customer saying to a waiter "Yes,
the addition seems correct, but I am concerned that the axioms of arithmetic
may be inconsistent thus rendering the computation invalid?"

Xref: sparky sci.logic:1916 comp.ai:4161 comp.theory:2338
From: torkel@sics.se (Torkel Franzen)
Newsgroups: sci.logic
Subject: Re: Impredicativity - was: Russell's Paradox
Date: 5 Nov 92 20:05:09 GMT
	<1992Nov5.170354.29866@guinness.idbsu.edu>
Organization: Swedish Institute of Computer Science, Kista

In article <1992Nov5.170354.29866@guinness.idbsu.edu> holmes@garnet.idbsu.edu
 (Randall Holmes) writes:

   >Neither A nor B can be shown to represent a unique object in ZFC-.

  Of course not! The question I was commenting on was whether it
is provable in ZF without foundation that if there is a function f
defined on the natural numbers satisfying f(n)={n,f(n+1)}, then there
is a set x such that x={1,x}, and my answer was that in all likelihood
this is not so.
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 17:00:56 GMT

In article <TORKEL.92Nov5100828@isis.sics.se> torkel@sics.se (Torkel Franzen) writes:
>What I am interested in is whether or not you can explain what
>you are talking about, as has been done with the "standard" theory of
>non-well-founded sets (in that case by giving a model of the theory in ordinary
>mathematics).

My interpretation of the intertranslatability of ZF with FA or AFA is
that any argument such as mine in favor of one or the other can only
find support outside ZF, e.g. in psychology or esthetics.  I find an
AFA world very appealing, but clearly it's not for everyone.  I claim
no more.
-- 
Vaughan Pratt				There's no truth in logic, son.
Newsgroups: sci.logic
From: sasghm@theseus.unx.sas.com (Gary Merrill)
Subject: Re: Natural Kinds (was re: Are all crows black?)
Originator: sasghm@theseus.unx.sas.com
Date: Tue, 10 Nov 1992 14:40:24 GMT
Organization: SAS Institute Inc.


In article <burt.721346028@aupair.cs.athabascau.ca>, burt@aupair.cs.athabascau.ca (Burt Voorhees) writes:
|> 
|> 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

That's Fred Suppe (no 's':  That's Pat Suppes).  The book is _The
Structure of Scientific Theories_.  It is a good book in terms of
explicating a number of positions (very thick as well).  By the
way, it's 'Hempel'.  A good (though aging) treatment of the D/N
model is to be found in Nagel's _The Structure of Science_.  One
should also look at Clark Glymour's _Theory and Evidence_.


-- 
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