The independence of Quine's axioms *200 and *201

1941 ◽  
Vol 6 (3) ◽  
pp. 96-97
Author(s):  
Barkley Rosser
Keyword(s):  
New York ◽  
Mathematical Logic ◽  
The Other ◽  
Single Object ◽  
Technical Details ◽  
Truth Value ◽  
Image Position

We refer to the axioms in Quine's book, Mathematical logic, New York, 1940.To prove the independence of *200, give xϵ α the truth value F in all cases and give (x)ϕ the same truth value as ϕ. Then clearly all formulas derivable from the other axioms besides *200 have the value T, whereas from *200 one can derive (∃x)(∃α)(xϵ α) which has the value F. This method of proving independence amounts to taking for a model a universe consisting of the single object Λ.For *201 we prove a contingent independence. That is, we prove that if Quine's system is consistent, then *201 is independent. The line of argument is the following. Suppose *201 can be derived from the other axioms. Let us replace xϵ α by throughout all the axioms. Then what *201 becomes can be derived from what the other axioms become. However what *201 becomes will lead to a contradiction in Quine's system whereas the rules which the other axioms become are valid in Quine's system.We now get down to technical details. Let us refer to the replacement of xϵ α by throughout an expression as an r replacement. Denote the result of performing an r replacement on ϕ by ϕr. Let Wα denoteThenNote that if x and y are variables, then by D10,

scholarly journals REPRESENTING CONJUNCTIVE DEDUCTIONS BY DISJUNCTIVE DEDUCTIONS

2016 ◽  
Vol 10 (1) ◽  
pp. 145-157
Author(s):  
KOSTA DOŠEN ◽  
ZORAN PETRIĆ
Keyword(s):  
Point Of View ◽  
The Other ◽  
Theoretical Point ◽  
Single Object ◽  
Finite Products ◽  
Image Position ◽  
Propositional Letter

AbstractA skeleton of the category with finite coproducts${\cal D}$ freely generated by a single object has a subcategory isomorphic to a skeleton of the category with finite products ${\cal C}$ freely generated by a countable set of objects. As a consequence, we obtain that ${\cal D}$ has a subcategory equivalent with ${\cal C}$. From a proof-theoretical point of view, this means that up to some identifications of formulae the deductions of pure conjunctive logic with a countable set of propositional letters can be represented by deductions in pure disjunctive logic with just one propositional letter. By taking opposite categories, one can replace coproduct by product, i.e., disjunction by conjunction, and the other way round, to obtain the dual results.

The combinatory foundations of mathematical logic

1942 ◽  
Vol 7 (2) ◽  
pp. 49-64 ◽  
Author(s):  
Haskell B. Curry
Keyword(s):  
New York ◽  
Mathematical Logic ◽  
Formal System ◽  
The Other ◽  
Foundations Of Mathematics ◽  
Primary Motivation ◽  
Other Hand ◽  
Points Of View ◽  
The One ◽  
Deductive Power

In investigations of the foundations of mathematics we can distinguish two separate tendencies. On the one hand, one may seek to define his subject with greatest possible explicitness: to obtain a formulation which satisfies the most exacting demands for precision, and which is at the same time free from paradoxes and adequate for the purpose. On the other hand, besides the problem of formulation, there is that of simplification; one can seek to find systems based upon processes of greater and greater primitiveness. The reduction of a piece of mathematics to a formal system, and still further to a completely formalized system (as explained, for example, in my New York address a year ago), is a step toward the first of these objectives. But it is evident that one can formalize in various ways, and that some of these ways constitute a more profound analysis than others. Although from some points of view one way of formalization is as good as any other, yet a certain interest attaches to the problem of simplification, as is shown by the attention which some of the greatest mathematicians have devoted to it.The researches about which I am reporting today are directed toward the second of these objectives. In fact we are concerned with constructing systems of an extremely rudimentary character, which analyze processes ordinarily taken for granted. This is properly part of the business of mathematical logic. Of course there are those, even among logicians, who doubt the utility of this sort of thing—who profess to have no interest in improvements which do not lead to increases in deductive power or what not. However that may be, this second objective certainly has some interest in its own right; and it is this interest which has formed the primary motivation for these researches.

Review: Islam and politics in Iranian Kurdistan at a time of revolution: the life of Ahmad Moftizadeh

2017 ◽  
Vol 5 (1) ◽  
pp. 80-87
Author(s):  
Martin Van Bruinessen
Keyword(s):  
New York ◽  
Middle East ◽  
Political Order ◽  
The Other ◽  
Islam And Politics ◽  
Cultural Rights ◽  
Revolutionary Regime

Ali Ezzatyar, The Last Mufti of Iranian Kurdistan: Ethnic and Religious Implications in the Greater Middle East. New York: Palgrave Macmillan, 2016. xv + 246 pp., (ISBN 978-1-137-56525-9 hardback).For a brief period in 1979, when the Kurds had begun confronting Iran’s new Islamic revolutionary regime and were voicing demands for autonomy and cultural rights, Ahmad Moftizadeh was one of the most powerful men in Iranian Kurdistan. He was the only Kurdish leader who shared the new regime’s conviction that a just social and political order could be established on the basis of Islamic principles. The other Kurdish movements were firmly secular, even though many of their supporters were personally pious Muslims.

From the New York Herald to the Italian screen

2017 ◽  
Vol 3 (2) ◽  
pp. 175-193 ◽  
Author(s):  
Katherine Frances Nagels
Keyword(s):  
New York ◽  
The Other ◽  
Comic Strip ◽  
Women In The Workplace

The popular 1907–9 American newspaper comic strip character Fluffy Ruffles was an iconic embodiment of contemporary American femininity between the eras of the Gibson Girl and the later flapper and “it” girl. This article discusses Fluffy Ruffles as a popular phenomenon and incarnation of anxieties about women in the workplace, and how she underwent a metamorphosis in the European press, as preexisting ideas of American youth, wealth, and liberty were grafted onto her character. A decade after her debut in the newspapers, two films—Augusto Genina's partially extant Miss Cyclone (La signorina Ciclone,1916), and Alfredo Robert's lost Miss Fluffy Ruffles (1918)—brought her to the Italian screen. This article looks at how the character was interpreted by Suzanne Armelle and Fernanda Negri Pouget, respectively, drawing on advertisements and the other performances of Negri Pouget to reconstruct the latter. The article is illustrated with drawings and collages based on the author's research.

Producers' Response to Changes in Prices and Marketing Policies: A Case Study of Sugarcane and Paddy in Eastern U.P. by S. C. Gupta and A. Majid. New York: Asia Publishing House, 1965.

1968 ◽  
Vol 8 (2) ◽  
pp. 308-309
Author(s):  
Mohammad Irshad Khan
Keyword(s):  
New York ◽  
Time Series ◽  
Time Series Data ◽  
Publishing House ◽  
Economic Incentives ◽  
The Other ◽  
Series Data ◽  
Poor Countries ◽  
Northern India

It is alleged that the agricultural output in poor countries responds very little to movements in prices and costs because of subsistence-oriented produc¬tion and self-produced inputs. The work of Gupta and Majid is concerned with the empirical verification of the responsiveness of farmers to prices and marketing policies in a backward region. The authors' analysis of the respon¬siveness of farmers to economic incentives is based on two sets of data (concern¬ing sugarcane, cash crop, and paddy, subsistence crop) collected from the district of Deoria in Eastern U.P. (Utter Pradesh) a chronically foodgrain deficit region in northern India. In one set, they have aggregate time-series data at district level and, in the other, they have obtained data from a survey of five villages selected from 170 villages around Padrauna town in Deoria.

Alive Still

2019 ◽  
Author(s):  
Cathy Curtis
Keyword(s):  
New York ◽  
Modern Art ◽  
Severe Form ◽  
The Other ◽  
Left Hand ◽  
Right Hand ◽  
The 1950S ◽  
Village Voice

In 1942, at age twenty, after a vision-impaired and rebellious childhood in Richmond, Virginia, Nell Blaine decamped for New York. Operations had corrected her eyesight, and she was newly aware of modern art, so different from the literal style of her youthful drawings. In Manhattan, she met rising young artists and poets. Her life was hectic, with raucous parties in her loft, lovers of both sexes, and freelance design jobs, including a stint at the Village Voice. Initially drawn to the rigorous formalism of Piet Mondrian, she received critical praise for her jazzy abstractions. During the 1950s, she began to paint interiors and landscapes. By 1959, when the Whitney Museum purchased one of her paintings, her career was firmly established. That year, she contracted a severe form of polio on a trip to Greece; suddenly, she was a paraplegic. Undaunted, she taught herself to paint in oil with her left hand, reserving her right hand for watercolors. In her postpolio work, she achieved a freer style, expressive of the joy she found in flowers and landscapes. Living half the year in Gloucester, Massachusetts, and the other half in New York, she took special delight in painting the views from her windows and from her country garden. Critics found her new style irresistible, and she had a loyal circle of collectors; still, she struggled to earn enough money to pay the aides who made her life possible. At her side for her final twenty-nine years was her lover, painter Carolyn Harris.

The Turn of the Screw and Other Stories

2008 ◽  
Author(s):  
Henry James
Keyword(s):  
New York ◽  
The Other ◽  
Victorian Culture ◽  
Ghost Story ◽  
Country House ◽  
Small Children ◽  
New York Edition

A young, inexperienced governess is charged with the care of Miles and Flora, two small children abandoned by their uncle at his grand country house. She sees the figure of an unknown man on the tower and his face at the window. It is Peter Quint, the master's dissolute valet, and he has come for little Miles. But Peter Quint is dead. Like the other tales collected here – ‘Sir Edmund Orme’, ‘Owen Wingrave’, and ‘The Friends of the Friends’ – ‘The Turn of the Screw’ is to all immediate appearances a ghost story. But are the appearances what they seem? Is what appears to the governess a ghost or a hallucination? Who else sees what she sees? The reader may wonder whether the children are victims of corruption from beyond the grave, or victims of the governess's ‘infernal imagination’, which torments but also entrals her? ‘The Turn of the Screw’ is probably the most famous, certainly the most eerily equivocal, of all ghostly tales. Is it a subtle, self-conscious exploration of the haunted house of Victorian culture, filled with echoes of sexual and social unease? Or is it simply, ‘the most hopelessly evil story that we have ever read’? The texts are those of the New York Edition, with a new Introduction and Notes.

Low Vision Services in an Agency: Structure and Philosophy

1975 ◽  
Vol 69 (6) ◽  
pp. 241-248
Author(s):  
Eleanor E. Faye ◽  
Clare M. Hood
Keyword(s):  
New York ◽  
Low Vision ◽  
Medical Director ◽  
The Other ◽  
Special Services ◽  
Full Discussion ◽  
Loan System ◽  
Training Services ◽  
And Training

The development and present structure of the comprehensive Low Vision Service of the New York Association for the Blind are used as the basis for a full discussion of the operation of such a clinical service, including its positive and negative features. The clinic is administered by a medical director and by an administrator who coordinates the work of a staff consisting of ophthalmologists, optometrists, low vision assistants, volunteers, registrar, and receptionist. A separate Optical Aids Service stocks low vision aids which it sells by prescription to clinics, doctors, and patients within and without the agency. Referrals for special services are made to the other departments of the agency. Also described are the low vision examination itself, follow-up and training services, and the aid loan system.

scholarly journals An Application of Hankel Transforms in Axially Symmetric Potential Flow

1956 ◽  
Vol 9 (3) ◽  
pp. 128-131
Author(s):  
A. G. Mackie
Keyword(s):  
New York ◽  
Incompressible Fluid ◽  
Circular Hole ◽  
Potential Flow ◽  
Fourier Transforms ◽  
The Other ◽  
Axially Symmetric ◽  
Symmetric Potential ◽  
Physical Interest ◽  
Hankel Transforms

In his book on Hydrodynamics, Lamb obtained a solution for the potential flow of an incompressible fluid through a circular hole in a plane wall. More recently Sneddon (Fourier Transforms, New York, 1951) obtained Lamb's solution by an elegant application of Hankel transforms.Since the streamlines in this solution are symmetric about the wall, it is not of particular physical interest. In this note, Sneddon's method is used to give a solution in which the fluid is infinite in extent on one side of the aperture but issues as a jet of finite diameter on the other side.

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