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A Negation-free Proof of Cantor's Theorem

N. Raja
2005 Notre Dame Journal of Formal Logic  
One of the proofs we present is inspired by Yablo's non-self-referential Liar's paradox, and it seems to bear a dual relationship to yet another proof.  ...  We present various proofs of Cantor's theorem in set theory: namely that the cardinality of the power set of a set X exceeds the cardinality of X, and in particular the continuum is uncountable.  ...  Acknowledgments Thanks to Kosta Dosen, Zoran Petric, Jouku Väänänen and Noson Yanofsky for critically reading and commenting on preliminary versions of this paper.  ... 
doi:10.1305/ndjfl/1117755152 fatcat:winspil5qfbpreskxt7imzowd4

Page 562 of The Philosophical Review Vol. 61, Issue 4 [page]

1952 The Philosophical Review  
application of the notion of a class in.the Paradox.  ...  THE PHILOSOPHICAL REVIEW take note of the mistake of condemning reflexiveness as meaningless on the ground that the Paradoxes reduce reflexiveness to an absurdity. They do not.  ... 

Page 213 of The Review of Metaphysics Vol. 6, Issue 22 [page]

1952 The Review of Metaphysics  
For is it not significant that in all the vast literature on Russell's paradox or the paradox of the “impredicable” no one to our knowledge has ever undertaken to explain why or on what grounds the class  ...  Instead, the procedure is invariably one of simply invoking the law of excluded middle — the class of non-self-membered classes must be either self-membered or not; or the concept of the “‘‘impredicable  ... 

Logic of paradoxes in classical set theories [article]

Boris Čulina
2021 arXiv   pre-print
We show how the known paradoxical classes follow from the productivity principle and how the principle gives us a uniform way to generate new paradoxical classes.  ...  The principle behaves as a logical regulator of any theory we formulate to explain and describe sets. It provides tools to identify paradoxical classes inside the theory.  ...  The class of not -n -cyclic sets, the class N I of sets which are not isomorphic to one of its elements, and the class of grounded sets are all classes on which identity is productive.  ... 
arXiv:2105.14121v1 fatcat:alqvx7cafvhurjlkptksihuzqy

Elizabeth Cady Stanton's 1854 "Address to the Legislature of New York" and the Paradox of Social Reform Rhetoric

Ryan Skinnell
2010 Rhetoric Review  
s 1854 'Address to the Legislature of New York' and the Paradox of Social Reform Rhetoric [P]ut identification and division ambiguously together, so that you cannot know for certain just where one ends  ...  and speaker in America for more than half of the 19 th Century, and her legacy as a "preeminent advocate of women's legal and political rights" (Gordon xvii) and the "[Woman] movement's philosopher and  ...  shared Cady Stanton and the Paradox of Social Reform 19 some common ground with the men from whom they sought institutional recognition of their demands.  ... 
doi:10.1080/07350191003613419 fatcat:fztuw36upvf2lp6fiouatvnnzm

School of Mechanic Arts at the Alabama Polytechnic Institute

1888 Science  
One of these classes of persons seeks to induce belief in improbable things, on the ground that most now accepted truth has once been held to be improbable.  ...  One of these classes of persons seeks to induce belief in improbable things, on the ground that most now accepted truth has once been held to be improbable.  ... 
fatcat:oiljr6scprgt3lzcz3ziivqhfm

Page 153 of Journal of Political Economy Vol. 55, Issue 2 [page]

1947 Journal of Political Economy  
NOTES ON THE HISTORY OF THE GIFFEN PARADOX crease rather than decrease the consump- tion in this country,’’* and Edgeworth ex- pressed disbelief on grounds of “a priori un- verified probability”—which  ...  In this case, for instance, it suggests a paradox. And I submit that there is no paradox at all. Take a parallel case.  ... 

Two Fuzzy Logic Programming Paradoxes Imply Continuum Hypothesis="False" & Axiom of Choice="False" Imply ZFC is Inconsistent [article]

Rafee Ebrahim Kamouna
2009 arXiv   pre-print
The first paradox is due to two distinct (contradictory) truth values for every ground atom of FLP, one is syntactical, the other is semantical.  ...  Two different paradoxes of the fuzzy logic programming system of [29] are presented.  ...  The set B L of all ground atomic formulas over L is called the Herbrand base of L.  ... 
arXiv:0807.2543v4 fatcat:ahqvb563tzakxeoataptoffftm

The Paradox of Online Education: Images, Perceptions, and Interests

Ali Kamali, Ladan Kianmehr
2015 US-China Education Review. A  
habits; their experiences and expectations; and the effects that the e-environment has on the decision to enroll in online classes.  ...  Two additive scales-Structural Motives Scale and Experiential Factors Scale-measure the imagery and the reasons for the student preference for a learning environment-i.e., online, ground, or hybrid courses  ...  ., online, ground, or hybrid classes) and the actual enrollment.  ... 
doi:10.17265/2161-623x/2015.09a.002 fatcat:hbujszhahbeuxphnz2s3wo4kfi

A MATHEMATICAL PARADOX

Philip E. B. Jourdain
1910 The Monist  
We stand uninjured on the same ground as before in spite of all the desperate assaults from the strong hand of Russell, who has utterly failed to disground us. Yoshio Mirami. Ohara, Kazusa, Japan.  ...  In my opinion what is paradoxical to the ordinary mind in this is: We have two classes of an infinity of members each (ar ranged in some order) ; now ask a person if there is a highest in the first class  ... 
fatcat:kisb74cievfkhhoroxzsol75j4

A Mathematical Paradox

Philip E. B. Jourdain, Sherwood J. B. Sugden
1910 The Monist  
We stand uninjured on the same ground as before in spite of all the desperate assaults from the strong hand of Russell, who has utterly failed to disground us. YOSHIO MIKAMI. OHARA, KAZUSA, JAPAN.  ...  In my opinion what is paradoxical to the ordinary mind in this is: We have two classes of an infinity of members each (arranged in some order) ; now ask a person if there is a highest in the first class  ... 
doi:10.5840/monist191020135 fatcat:aatrbmzmpfbz5h2w5rbk3535xm

Page 91 of Mathematical Reviews Vol. 15, Issue 2 [page]

1954 Mathematical Reviews  
Paradox of the class of all grounded classes. J. Symbolic Logic 18, 114 (1953).  ...  Two similar paradoxes are described which concern the class of all non-circular classes, and the class of all not n-circular classes.  ... 

Dynamics of mechanical systems with two sliding contacts: new facets of Painlevé's paradox

Péter L. Várkonyi
2016 Archive of applied mechanics (1991)  
mode in each class.  ...  Many types of solution inconsistency and the indeterminacy are identified and new phenomena related to Painlev\'e"s non-existence and non-uniqueness paradoxes are discovered.  ...  In class 254, all 4 regular contact modes are consistent but only 1 of them is stable.  ... 
doi:10.1007/s00419-016-1165-1 fatcat:64vdlpcgabbhjizjygztgodogu

Page 211 of The American Mathematical Monthly Vol. 53, Issue 4 [page]

1946 The American Mathematical Monthly  
On the ground of all his experience Gédel makes a strong plea for the realistic standpoint where classes are conceived as real objects, namely as “pluralities of things,” or as structures consisting of  ...  In addition to Russell’s own work concerning the solution of the paradoxes, two other possible directions are mentioned in which, as Russell himself had pointed out, a “criterion for the existence of classes  ... 

WITTGENSTEIN'S TRACTATUS 3.333 AND RUSSELL'S PARADOX

U Sutrop
2009 Trames  
I investigate and compare the different forms of this formula in Wittgenstein's manuscripts and in the different editions of the 'Tractatus'.  ...  This solution is disregarded both by the Russellians and most Wittgensteinians. In this paper I try to read the above formula and translate it into a class membership language (CML).  ...  I am very grateful to the fellows of the Wittgensteinarkivet for their kind help. I thank also the Wittgenstein Trustees for the kind permission to quote some Wittgenstein's manuscripts.  ... 
doi:10.3176/tr.2009.2.06 fatcat:kq3rdmftenfe5bkatic7kc734i
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