[FOM] vagueness in mathematics?
SCOTT RANDAL TIDWELL
srtidwell at ucla.edu
Mon Feb 20 17:00:47 EST 2017
Timothy Chow wrote:
This is not a flaw in WIS. It is merely an observation that WIS is a kind
> of reductio ad absurdum argument. Assume towards a contradiction that it
> makes sense to talk about rules, so that we are free to use rules in our
> discussion. Then conclude that rules don't make sense, QED.
It's worth noting that this is not how Wittgenstein took these examples. He
took them as a reductio of a certain view about the nature of rules. That
is, the view that I am only following a rule if the formulas, pictures and
examples available to me determine all possible applications of the rule.
(These formulas, pictures and examples are the materials the example
proposes are used to teach and correct the martian or incorrigible pupil.)
The example seems to show that the materials available do not, in and of
themselves, determine every application of the rule. Yet, Wittgenstein,
claims, we do in fact follow rules. Therefore, this conception of rules is
not correct.
I'm not sure what positive account of rules Wittgenstein has in mind. He
does seem to think that it is a contingent fact about human beings that we
do not often make the kind of mistake we are imagining the martian or
incorrigible pupil making. If we did make those mistakes regularly,
following rules would lose its utility.
Best,
Scott Tidwell
On Mon, Feb 20, 2017 at 8:39 AM, <fom-request at cs.nyu.edu> wrote:
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> Today's Topics:
>
> 1. Re: vagueness in mathematics? (Timothy Y. Chow)
> 2. Re: vagueness in mathematics? (Joe Shipman)
> 3. ThEdu'17: Call for Extended Abstracts & Demonstrations
> (Achim D. Brucker)
> 4. Re: Kurt G?del: Maxims and Philosophical Remarks, Volume X
> (Mark van Atten)
> 5. PLS 11 Second Call for Papers (Alexandra Soskova)
> 6. 3rd FILOMENA Workshop - CFP (Sanderson Molick)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Fri, 17 Feb 2017 21:36:30 -0500 (EST)
> From: "Timothy Y. Chow" <tchow at alum.mit.edu>
> To: fom at cs.nyu.edu
> Subject: Re: [FOM] vagueness in mathematics?
> Message-ID: <alpine.LFD.2.20.1702172122550.11310 at LAURENT.MIT.EDU>
> Content-Type: text/plain; charset=US-ASCII; format=flowed
>
> Harvey Friedman wrote:
>
> > The above formulation of WIS, which is about as good very brief
> > formulation that I am familiar with, is itself a (dogmatic) claim that
> > if we follow a given rule then we get a given result.
> [...]
> > So WIS seems to me to be compelling us to think in a way that is
> > essentially the same as the way that WIS is criticizing.
>
> This is not a flaw in WIS. It is merely an observation that WIS is a kind
> of reductio ad absurdum argument. Assume towards a contradiction that it
> makes sense to talk about rules, so that we are free to use rules in our
> discussion. Then conclude that rules don't make sense, QED.
>
> Henning Basold wrote:
> > In this latter view, the sequences that can be expressed depend of
> > course of what processes we allow (c.f. lawless vs. lawlike vs.
> > computable). But surely, there are systems that allow us to specify a
> > process that represents a sequence precisely and without any ambiguity
> > (Stream Coalgebras; Stream Differential Equations by Jan Rutten;
> > Corecursion Schemes ? la Hagino, Mendler, and others; Copattern Calculus
> > by Abel et al.; etc.).
>
> The point of the skeptical argument is precisely to challenge the "surely"
> here. The skeptical argument can be applied to even the simplest possible
> rule, e.g., the constant sequence 1,1,1,1,1,1,1,1,... Suppose I tell the
> Martian that the rule is that this sequence is the constant sequence, with
> every member of the sequence being exactly the same as all the others.
> The Martian nods and, when asked to produce more terms of the sequence to
> confirm understanding, generates 1's obediently for a while and then,
> inexplicably to us, puts down a 0. When challenged, the Martian looks
> surprised and befuddled. Didn't we say that all the terms of the sequence
> are identical? Well, then, that rule obviously implies that there should
> be a 0 at that point in the sequence. Why are we putting something at
> that point in the sequence that is not identical to all the others? The
> discussion then moves towards what words such as "identical" and "all"
> mean. But if we didn't have any luck agreeing on the constant sequence
> then the prospects are dim for agreeing on what these words mean. In the
> Martian's mind, the Earthling "identical" means something like, "identical
> up to the 251st term and then you have to introduce an exception" (cf.
> Goodman's grue paradox).
>
> Tim
>
>
> ------------------------------
>
> Message: 2
> Date: Fri, 17 Feb 2017 21:18:33 -0500
> From: Joe Shipman <joeshipman at aol.com>
> To: tchow at alum.mit.edu, Foundations of Mathematics <fom at cs.nyu.edu>
> Subject: Re: [FOM] vagueness in mathematics?
> Message-ID: <177615A1-A0F2-4A6C-996A-19E1FC1C26E0 at aol.com>
> Content-Type: text/plain; charset=us-ascii
>
> Surely we can agree that a primitive recursive function corresponds to a
> rule, that there is no vagueness about what should count as a primitive
> recursive function, and that the vast majority of rules mathematicians give
> can be represented as primitive recursive functions?
>
> Vagueness is not thereby banished, but it doesn't seem like a central
> problem.
>
> -- JS
>
> Sent from my iPhone
>
> > On Feb 17, 2017, at 5:00 PM, Timothy Y. Chow <tchow at alum.mit.edu> wrote:
> >
> >> On Fri, 17 Feb 2017, Charlie wrote:
> >> Consider Kripke's own example of "quus":
> >>
> >> x ? y = x + y, if x, y < 57
> >> = 5 otherwise.
> >
> > I think it is best if I avoid getting into a debate as to whether Chow's
> version of Kripke's version of Wittgenstein is more authentic than Silver's
> version of Kripke's version of Wittgenstein. Let me just say that I see a
> difference between ChowKripkenstein and SilverKripkenstein and I think that
> ChowKripkenstein is a much deeper skeptical argument about vagueness than
> SilverKripkenstein (or least than ChowSilverKripkenstein).
> >
> > Tim
> > _______________________________________________
> > FOM mailing list
> > FOM at cs.nyu.edu
> > http://www.cs.nyu.edu/mailman/listinfo/fom
>
>
>
> ------------------------------
>
> Message: 3
> Date: Sat, 18 Feb 2017 22:57:07 +0000
> From: "Achim D. Brucker" <brucker at spamfence.net>
> To: fom at cs.nyu.edu
> Subject: [FOM] ThEdu'17: Call for Extended Abstracts & Demonstrations
> Message-ID: <20170218225707.wqeuodac7bsgr5mu at fujikawa.home.brucker.ch>
> Content-Type: text/plain; charset=utf-8
>
> (Apologies for duplicates)
>
>
> Call for Extended Abstracts & Demonstrations
> ThEdu'17
> Theorem proving components for Educational software
> http://www.uc.pt/en/congressos/thedu/thedu17
> at
> CADE 26
> International Conference on Automated Deduction
> 6-11 August 2017
> Gothenburg, Sweden
> http://www.cade-26.info/
>
>
> ThEdu'17 Scope
>
> Computer Theorem Proving is becoming a paradigm as well as a technological
> base for a new generation of educational software in science, technology,
> engineering and mathematics. The workshop brings together experts in
> automated deduction with experts in education in order to further clarify
> the shape of the new software generation and to discuss existing systems.
> Topics of interest include:
>
> * methods of automated deduction applied to checking students' input;
> * methods of automated deduction applied to prove post-conditions for
> particular problem solutions;
> * combinations of deduction and computation enabling systems to propose
> next steps;
> * automated provers specific for dynamic geometry systems;
> * proof and proving in mathematics education.
>
> Important Dates
>
> Extended Abstracts: 18 June 2017
> Author Notification: 2 July 2017
> Final Version: 16 July 2017
> Workshop Day: 6 August 2017
>
> Submission
>
> Interested researchers are invited to submit extended abstracts and system
> descriptions. Both kinds of submissions should be approximately 5 pages in
> length and present original unpublished work not submitted elsewhere.
>
> Submission is in PDF format via easychair,
> https://easychair.org/conferences/?conf=thedu17
> formatted according to
> http://www.easychair.org/publications/easychair.zip
>
> The extended abstracts and system descriptions will be made available
> online. At least one author is expected to presents his/her submission at
> ThEdu'17.
> Joint publication in companion with other CADE26 events is under
> consideration (as a volume in the EPiC Series in Computing).
>
> Program Committee
>
> Francisco Botana, University of Vigo at Pontevedra, Spain
> Achim D. Brucker, University of Sheffield, United Kingdom
> Filip Maric, University of Belgrade, Serbia
> Walther Neuper, Graz University of Technology, Austria (co-chair)
> Pavel Pech , University of South Bohemia, Czech Republic
> Pedro Quaresma, University of Coimbra, Portugal (co-chair)
> Vanda Santos, CISUC, Portugal
> Wolfgang Schreiner, Johannes Kepler University, Austria
> Burkhart Wolff, University Paris-Sud, France
>
> --
> Dr. Achim D. Brucker | Software Assurance & Security | University of
> Sheffield
> https://www.brucker.ch | https://logicalhacking.com/blog
> @adbrucker | @logicalhacking
>
>
> ------------------------------
>
> Message: 4
> Date: Sun, 19 Feb 2017 10:37:53 +0100
> From: Mark van Atten <vanattenmark at gmail.com>
> To: fom at cs.nyu.edu
> Subject: Re: [FOM] Kurt G?del: Maxims and Philosophical Remarks,
> Volume X
> Message-ID:
> <CALAsyW1v7txaH=B3DOm8FXfw8VAon+i1bJgjdchA7Uhe6M0X4Q at mail.
> gmail.com>
> Content-Type: text/plain; charset=UTF-8
>
> Dear Bill,
>
> > Did IAS give any reason for not allowing an English translation?
>
> Thanks for asking -- when asking our project leader, Gabriella Crocco,
> for the details, it turned out that there had been a serious
> misunderstanding on my part. The IAS did not withold permission for an
> English translation by us, because, as I have now learned, it had
> never been asked. I apologise to the IAS and to FOM for my mistake.
>
> > Another question would be, could some other group undertake an English
> translation of your German addition.
>
> Of course, provided they obtain permission from the IAS (who owns the
> copyright to the original shorthand notebook) and from the editors of
> this transcription (who own the copyright to it). Prof. Crocco
> informed me that the latter will be granted to any interested party
> who asks; she can be contacted at gabriella DOT crocco AT wanadoo DOT
> fr
>
> The French journal Philosophia Scientiae is now planning to ask both
> permissions and have an English translation prepared, for publication
> in a special bi-lingual issue later this year.
>
> > BTW, congratulation on getting the German edition out!
>
> Many thanks!
>
> Best wishes,
> Mark.
>
>
> ------------------------------
>
> Message: 5
> Date: Sun, 19 Feb 2017 21:40:04 +0200 (EET)
> From: Alexandra Soskova <asoskova at fmi.uni-sofia.bg>
> To: fom at cs.nyu.edu
> Subject: [FOM] PLS 11 Second Call for Papers
> Message-ID:
> <1923879520.577277.1487533204771.JavaMail.zimbra at fmi.uni-sofia.bg>
> Content-Type: text/plain; charset=utf-8
>
> ======================================================================
> PLS11: THE ELEVENTH PANHELLENIC LOGIC SYMPOSIUM
> July 12-16, 2017, Delphi, Greece
> The National and Kapodistrian University of Athens and
> the National Technical University of Athens.
> The University of Cyprus will help in the organization.
> http://pls11.cs.ntua.gr/
> ======================================================================
> IMPORTANT DATES
> Deadline for submission: Wednesday, April 12, 2017
> Notification: Friday, May 12, 2017
> Final copy due: Friday, June 2, 2017
> ======================================================================
> INVITED TALKS
> - Zo? Chatzidakis, ENS, Paris
> - Hannes Leitgeb, LMU, Munich
> - Yiannis Moschovakis, UCLA
> - Andrea Sorbi, Siena University
> - Wolfgang Thomas, RWTH, Aachen
> - Timothy Williamson, Oxford University
> ======================================================================
> TUTORIALS
> - Valentina Harisanov, George Washington University,
> "Computable Model Theory"
> - Ya'acov Peterzil, University of Haifa, "O-minimality"
> - Anand Pillay, Notre Dame, "Model theory"
> ======================================================================
> SPECIAL SESSIONS:
> Computability Theory (Organizer: Alexandra Soskova)
> - Damir Dzhafarov, University of Connecticut
> - Ekaterina Fokina, Vienna University of Technology
> - Andy Lewis-Pye, London School of Economics
> - Joseph Miller, University of Wisconsin, Madison
> - Antonio Montalban, UC Berkeley
> - Paul Shafer, University of Gent
> Model Theory (Organizers: Pantelis Eleftheriou, Rizos Sklinos)
> - Artem Chernikov, UCLA
> - Amador Martin-Pizarro, Lyon 1
> - Sergei Starchenko, University of Notre Dame, TBC
> - Frank Wagner, Lyon 1
> ======================================================================
> SECOND CALL FOR PAPERS
> The Scientific Committee cordially invites all researchers in the
> area of the conference to submit their papers until April 12, 2017
> (in PDF-format, in English, at most 6 pages) for presentation at
> PLS11 to htps://www.easychair.org/conferences/?conf=pls11.
> Papers should be prepared using the EasyChair class style
> from http://www.easychair.org/publications/?page=1594225690).
> All submitted papers will be reviewed by the Scientific Committee
> of the symposium, who will make final decisions on acceptance.
> During the symposium, each accepted paper will be presented
> (a twenty minutes talk) by one of its authors, with five extra
> minutes for questions.
> If possible, each submitted paper should be classified in one of
> the following areas:
> - Ancient Logic
> - Computability Theory
> - History and Philosophy of Logic
> - Logic in Computer Science
> - Model Theory
> - Nonclassical and Modal Logics
> - Proof Theory
> - Set Theory
> ======================================================================
> POSTER SESSION
> Graduate students and young researchers are invited to submit a short
> abstract on work in progress. Authors of accepted abstracts will have
> an opportunity to present their results in poster form in a special
> poster session. Interested students and young researchers should
> submit abstracts of no more than one page in PDF form by June 2, 2017,
> by sending them by e-mail to: pls11 at softlab.ntua.gr
> ======================================================================
> GRANTS
> ASL Student Travel Grants:
> PLS11 is sponsored by the Association for Symbolic Logic. All student
> members of the ASL can apply for travel funding. To be considered for
> a Travel Award, please (1) send a letter of application, and (2) ask
> your thesis supervisor to send a brief recommendation letter. The
> application letter should be brief (preferably one page) and should
> include: (1) your name; (2) your home institution; (3) your thesis
> supervisor's name; (4) a one-paragraph description of your studies and
> work in logic, and a paragraph explaining why it is important to
> attend the meeting; (5) your estimate of the travel expenses you will
> incur; (6) (for citizens or residents of the USA) citizenship or visa
> status; and (7) (voluntary) indication of your gender and minority
> status. Women and members of minority groups are strongly encouraged
> to apply. Applications should be sent to asl at vassar.edu before April
> 12, 2017.
> EMS grants for Young Researchers:
> Thanks to the generous support from European Mathematical Society,
> PLS11 is glad to be able to offer free registration for Masters and
> PhD students in Logic and young early career researchers for
> participating at PLS 11. In order to apply for grants please send a CV
> to pls11 at softlab.ntua.gr until April 12, 2017.
> Preference will be given to researchers who submitted a paper.
> ==================================================================
> SCIENTIFIC COMMITTEE
> - Costas Dimitracopoulos, National and Kapodistrian University of Athens
> - Pantelis Eleftheriou, University of Konstanz
> - Vassilis Gregoriades, Universit? di Torino, Italy
> - Antonis Kakas, University of Cyprus
> - Lefteris Kirousis, National and Kapodistrian University of Athens
> - Nikolaos Papaspyrou, National Technical University of Athens
> - Athanasios Pheidas, University of Crete
> - George Tourlakis, York University, Canada
> - Rizos Sklinos, Universit? Lyon 1
> - Alexandra Soskova, Sofia University, Chair
> - Stathis Zachos, National Technical University of Athens
> ORGANIZING COMMITTEE
> - Antonis Kakas, University of Cyprus, Chair
> - Nikolaos Papaspyrou, National Technical University of Athens
> - Panos Rondogiannis, National and Kapodistrian University of Athens
> - Petros Stefaneas, National Technical University of Athens
> - Yannis Stephanou, National and Kapodistrian University of Athens
> ======================================================================
> SYMPOSIUM WEBPAGE: http://pls11.cs.ntua.gr/
> E-MAIL: pls11 at softlab.ntua.gr
> CONTACTS:
> - Alexandra Soskova <asoskova at fmi.uni-sofia.bg>
> Chair of the Scientific Committee
> - Antonis Kakas <antonis at ucy.ac.cy>
> Chair of the Organizing Committee
>
>
> ------------------------------
>
> Message: 6
> Date: Sun, 19 Feb 2017 22:13:22 -0300
> From: Sanderson Molick <smolicks at gmail.com>
> To: fom at cs.nyu.edu
> Subject: [FOM] 3rd FILOMENA Workshop - CFP
> Message-ID:
> <CAGDuLV==D6tdC3Vm9WubFNUCnoYjpm-3+Gu8asjS75=KrMyNkA at mail.gmail.
> com>
> Content-Type: text/plain; charset="utf-8"
>
> Call for papers:
> 3rd Workshop on Philosophy, Logic and Analytical Metaphysics
> http://filomenaworkshop.weebly.com/current-edition.html
> Aug 21-23, 2017
> Natal/RN, Brazil
> ?
> ? The third edition of the FILOMENA Workshop (FIlosofia, LOgica e
> MEtaf?sica aNAl?tica), promoted by the Group for Logic and Formal
> Philosophy from the UFRN, has the purpose of gathering logicians working at
> the intersection of Logic and Metaphysics, through the application of
> formal methods in Philosophy. Logic, a branch of Philosophy on its own, has
> outgrown its original purposes and found connections with other areas of
> Philosophy, such as Philosophy of Language, Philosophy of Mathematics,
> Philosophy of Science and Philosophy of Mind. Logic has proved to be a
> powerful tool for analyzing different philosophical theories, as well as
> their foundations and implications; moreover, the birth and development of
> non-classical logics has expanded its domain of application much beyond the
> dreams of its progenitors.
>
> Topics of interest for our workshop include, but are not limited to:
> Modal metaphysics
> Reference and descriptions
> Philosophical topics in non-classical logics
> Truth-values
> Logical consequence
> Logical pluralism
> Meta-ontology?
>
> The workshop will allow 30 minutes for each contributed talk, divided into
> 20 minutes for exposition followed by 10 minutes of discussion. The
> abstracts may be written in English or Portuguese. Abstracts should have at
> most 500 words and should include relevant information about the author
> (name, e-mail address, and scientific affiliation). Please submit an
> editable file (such as .doc, .odt, .tex) along with a .pdf file of your
> abstract. A model of the abstract in .tex is is available at
> https://goo.gl/vGzrvb.
>
> This year it is also possible to submit a proposal for a tutorial (two
> sessions of 2 hours each). The proposal must indicate the content that will
> be presented, along with relevant bibliography. The proposal may be written
> in English or Portuguese, should have at most 1000 words and include
> relevant information about the author (name, e-mail address, and scientific
> affiliation). Please submit an editable file (such as .doc, .odt, .tex)
> along with a .pdf file.
>
> Submissions must be sent to the email filomenaworkshop at gmail.com by* April
> 07*, and the authors will be notified of acceptance or rejection by* May
> 15*
> .
>
> Invited Speakers:
> Tuomas Tahko (University of Helsinki)
> Jonas Arenhart (Federal University of Santa Catarina)
> Giorgio Venturi (State University of Campinas)
>
> After the event, participants will have the chance to submit full papers
> for the proceedings of the event, which will be published online in a
> blind-reviewed book by the upcoming publisher of PPGFil, the graduate
> program of Philosophy from UFRN.
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