[FOM] 510: More Undefinable Elements 2
adriano paolo shaul gershom palma
palmaadriano at gmail.com
Mon Dec 3 01:49:12 EST 2012
dear dr. Forster, is there a way to see the analysis?
in there a published or on line text?
thank you
On Sun, Dec 2, 2012 at 1:39 PM, T.Forster at dpmms.cam.ac.uk <
T.Forster at dpmms.cam.ac.uk> wrote:
> Harvey, Do you know Wilfrid Hodges' model-theoretic analysis of Aquinas'
> theory of the Trinity? All three members of the Trinity realise the same
> 1-type, but they realise distinct 2-types. There is a binary relation of
> `procedes from'. I don't think he ever published it, but it might be worth
> chasing up in the present context. It might further soften the hearts of
> the Templeton people towards logic!
>
>
> On Dec 1 2012, Harvey Friedman wrote:
>
> >THIS RESEARCH WAS PARTIALLY SUPPORTED BY THE JOHN TEMPLETON FOUNDATION
> >
> >*****************************************
> >
> >THIS POSTING IS A CONTINUATION OF
> >http://www.cs.nyu.edu/pipermail/fom/2012-November/016806.html
> >http://www.cs.nyu.edu/pipermail/fom/2012-November/016809.html
> >
> >*****************************************
> >
> >The Trinity - see
> >http://www.cs.nyu.edu/pipermail/fom/2012-November/016809.html -
> >suggests the following.
> >
> >A STRUCTURE WITH EXACTLY THREE UNDEFINABLE ELEMENTS x,y,z, EACH
> >DEFINABLE FROM EACH OTHER, WHERE NO NONEMPTY SUBSET OF {x,y,z} IS
> >DEFINABLE.
> >
> >More generally,
> >
> >A STRUCTURE WITH EXACTLY n UNDEFINABLE ELEMENTS x_1,...,x_n, EACH
> >DEFINABLE FROM EACH OTHER, WHERE NO NONEMPTY SUBSET OF {x_1,...,x_n}
> >IS DEFINABLE.
> >
> > Here definability of elements and finite sets always means without
> > parameters.
> >
> >This can be done by adaptation of the arguments in
> >http://www.math.osu.edu/~friedman.8/manuscripts.html #74. As in there,
> >we can get the structure to be a graph, and handle "there exists
> >infinitely" and quantitative quantifiers.
> >
> >*****************************************
> >
> >I use http://www.math.ohio-state.edu/~friedman/ for downloadable
> >manuscripts. This is the 509th in a series of self contained numbered
> >postings to FOM covering a wide range of topics in f.o.m. The list of
> >previous numbered postings #1-449 can be found
> >in the FOM archives at
> >http://www.cs.nyu.edu/pipermail/fom/2010-December/015186.html
> >
> >450: Maximal Sets and Large Cardinals II 12/6/10 12:48PM
> >451: Rational Graphs and Large Cardinals I 12/18/10 10:56PM
> >452: Rational Graphs and Large Cardinals II 1/9/11 1:36AM
> >453: Rational Graphs and Large Cardinals III 1/20/11 2:33AM
> >454: Three Milestones in Incompleteness 2/7/11 12:05AM
> >455: The Quantifier "most" 2/22/11 4:47PM
> >456: The Quantifiers "majority/minority" 2/23/11 9:51AM
> >457: Maximal Cliques and Large Cardinals 5/3/11 3:40AM
> >458: Sequential Constructions for Large Cardinals 5/5/11 10:37AM
> >459: Greedy CLique Constructions in the Integers 5/8/11 1:18PM
> >460: Greedy Clique Constructions Simplified 5/8/11 7:39PM
> >461: Reflections on Vienna Meeting 5/12/11 10:41AM
> >462: Improvements/Pi01 Independence 5/14/11 11:53AM
> >463: Pi01 independence/comprehensive 5/21/11 11:31PM
> >464: Order Invariant Split Theorem 5/30/11 11:43AM
> >465: Patterns in Order Invariant Graphs 6/4/11 5:51PM
> >466: RETURN TO 463/Dominators 6/13/11 12:15AM
> >467: Comment on Minimal Dominators 6/14/11 11:58AM
> >468: Maximal Cliques/Incompleteness 7/26/11 4:11PM
> >469: Invariant Maximality/Incompleteness 11/13/11 11:47AM
> >470: Invariant Maximal Square Theorem 11/17/11 6:58PM
> >471: Shift Invariant Maximal Squares/Incompleteness 11/23/11 11:37PM
> >472. Shift Invariant Maximal Squares/Incompleteness 11/29/11 9:15PM
> >473: Invariant Maximal Powers/Incompleteness 1 12/7/11 5:13AMs
> >474: Invariant Maximal Squares 01/12/12 9:46AM
> >475: Invariant Functions and Incompleteness 1/16/12 5:57PM
> >476: Maximality, CHoice, and Incompleteness 1/23/12 11:52AM
> >477: TYPO 1/23/12 4:36PM
> >478: Maximality, Choice, and Incompleteness 2/2/12 5:45AM
> >479: Explicitly Pi01 Incompleteness 2/12/12 9:16AM
> >480: Order Equivalence and Incompleteness
> >481: Complementation and Incompleteness 2/15/12 8:40AM
> >482: Maximality, Choice, and Incompleteness 2 2/19/12 7:43AM
> >483: Invariance in Q[0,n]^k 2/19/12 7:34AM
> >484: Finite Choice and Incompleteness 2/20/12 6:37AM__
> >485: Large Large Cardinals 2/26/12 5:55AM
> >486: Naturalness Issues 3/14/12 2:07PM
> >487: Invariant Maximality/Naturalness 3/21/12 1:43AM
> >488: Invariant Maximality Program 3/24/12 12:28AM
> >489: Invariant Maximality Programs 3/24/12 2:31PM
> >490: Invariant Maximality Program 2 3/24/12 3:19PM
> >491: Formal Simplicity 3/25/12 11:50PM
> >492: Invariant Maximality/conjectures 3/31/12 7:31PM
> >493: Invariant Maximality/conjectures 2 3/31/12 7:32PM
> >494: Inv Max Templates/Z+up, upper Z+ equiv 4/5/12 4:17PM
> >495: Invariant Finite Choice 4/5/12 4:18PM
> >496: Invariant Finite Choice/restatement 4/8/12 2:18AM
> >497: Invariant Maximality Restated 5/2/12 2:49AM
> >498: Embedded Maximal Cliques 1 9/18/12 12:43AM
> >499. Embedded Maximal Cliques 2 9/19/12 2:50AM
> >500: Embedded Maximal Cliques 3 9/20/12 10:15PM
> >501: Embedded Maximal Cliques 4 9/23/12 2:16AM
> >502: Embedded Maximal Cliques 5 9/26/12 1:21AM
> >503: Proper Classes of Graphs 10/13/12 12:17PM
> >504. Embedded Maximal Cliques 6 10/14/12 12:49PM
> >505: Function Transfer Theory 10/21/12 2:15AM
> >506: Finite Embedded Weakly Maximal Cliques 10/23/12 12:53AM
> >507: Finite Embedded Dominators 11/6/12 6:40AM
> >508: Unique Undefinable Elements 11/27/12 3:30PM
> >509: More Undefinable Elements 11/27/12 10:03PM
> >
> >Harvey Friedman
> >_______________________________________________
> >FOM mailing list
> >FOM at cs.nyu.edu
> >http://www.cs.nyu.edu/mailman/listinfo/fom
> >
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
>
--
palma, KZN
*יד* וַיַּעַן עָמוֹס, וַיֹּאמֶר אֶל-אֲמַצְיָה, לֹא-נָבִיא אָנֹכִי, וְלֹא
בֶן-נָבִיא אָנֹכִי: כִּי-בוֹקֵר אָנֹכִי, וּבוֹלֵס שִׁקְמִים.
palma
University of KwaZulu-Natal
Howard College Campus, philosophy department
Durban 4041 South Africa
Tel off: [+27] 03 12 60 15 91 Fax [+27] 03 12 60 30 31
admn Y. Hordyk : [+27] 03 12 60 22 92
mobile 07 62 36 23 91 from abroad +[27] 76 23 62 391
EMAIL: palma at ukzn.ac.za
palma's office 280 (3rd flr of Mtb)
from 2o13\o1 p212 on cognition p308 on rigidity p102 intrPHIL
- check venues&schedule at administrator office TBA
*only when in Europe*:
inst. J. Nicod
29 rue d'Ulm
f-75005 paris france
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*The common base of all the Semitic creeds, winners or losers, was the*
*ever present idea of world-worthlessness. Their profound reaction from*
*matter led them to preach bareness, renunciation, poverty; and the*
*atmosphere of this invention stifled the minds of the desert*
*pitilessly. A first knowledge of their sense of the purity of*
*rarefaction was given me in early years, when we had ridden far out*
*over the rolling plains of North Syria to a ruin of the Roman period*
*which the Arabs believed was made by a prince of the border as a*
*desert-palace for his queen. The clay of its building was said to have*
*been kneaded for greater richness, not with water, but with the*
*precious essential oils of flowers. My guides, sniffing the air like*
*dogs, led me from crumbling room to room, saying, 'This is jessamine,*
*this violet, this rose'.*
*
*
*But at last Dahoum drew me: 'Come and smell the very sweetest scent of*
*all', and we went into the main lodging, to the gaping window sockets*
*of its eastern face, and there drank with open mouths of the*
*effortless, empty, eddyless wind of the desert, throbbing past. That*
*slow breath had been born somewhere beyond the distant Euphrates and*
*had dragged its way across many days and nights of dead grass, to its*
*first obstacle, the man-made walls of our broken palace. About them it*
*seemed to fret and linger, murmuring in baby-speech. 'This,' they told*
*me, 'is the best: it has no taste.*
*Thomas Edward Lawrence, the seven pillars of wisdom, ch.3*
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