bluuebunny/crossref_metadata_2025 huggingface dataset:
The Soviet Central Committee: An Elite Analysis
Authors: Gehlen Michael P. , McBride Michael
Published: May 2006

This paper is a study of the backgrounds of the members of the Central Committee of the Communist Party of the Soviet Union. The purpose of its first part is to present and interpret certain quantitative material concerning the background characteristics of the members of the Central Committee. The conclusion elaborates premises regarding the function of co-optation in the higher Party organs and suggests possible relationships of this function to the education and career experiences of the Central Committee membership as discussed in the first part. To pursue an ideal study of this type, we recognize that extensive interviews and depth exploration of the sociological histories of the members would be desirable. In the case of the Soviet political elite such a course is obviously not possible at the present time. Nevertheless, sufficient data exist to make a modest beginning toward what we hope will help to lay a foundation for more extensive analysis of elites in the Soviet system in the future.

Two basic assumptions underlie our interest in the backgrounds of the Soviet political elite. First, and more important for this paper, is the premise that persons are co-opted into the Central Committee primarily, though not exclusively, as a result of the group associations they have made during the courses of their careers. These associations are largely career associations, and most of the members become part of the elite of important functional groups before they become members of the Party elite. Educational backgrounds, age, Party status, role associations, occupation, and other factors all converge to influence the development of the careers of the members.
Political Participation and Government Responsiveness: The Behavior of California Superior Courts
Authors: Kuklinski James H. , Stanga John E.
Published: May 2006

Students of democratic politics have long been concerned with the role of political participation in linking government and the people it serves. Whereas participation is generally defined in terms of voting, this article defines participation as the communication of citizen preferences to public officeholders. We show that aggregate sentencing decisions of California superior courts changed to reflect more closely prevailing public opinion after a large percentage of the populace expressed their preferences on a marijuana issue. The fact that members of California superior courts are seemingly immune from any effective electoral sanction serves both to underline the importance of this form of participation to a responsive system of government and to caution against conceiving of the participation-responsiveness relationship only in terms of punitive electoral devices.
Dissolving International Politics: Reflections on the Nation-State
Authors: Hanrieder Wolfram F.
Published: May 2006

The diminishing salience of territorial issues, the restraints imposed by the nuclear balance, the shift away from the primacy of military-strategic elements of power to the primacy of economic elements, the day-to-day realities of economic interdependence, and changes in the nature of the nation-state have produced a new international order which resembles in important ways the domestic political systems prevalent in the industrialized noncommunist part of the world. This leads to the “domestication” of international politics. At the same time competitive nationalism, the vitality of the nation-state, differing perceptions of the proper role of government in the economy, and other considerations allow not much more than a tenuous coordination of foreign policies even among similar nation-states, making it unlikely that the European Economic Community and the Atlantic alliance will proceed beyond existing structures toward tighter integration.
Analyzing Diffusion and Contagion Effects: The Urban Disorders of the 1960s
Authors: Midlarsky Manus I.
Published: May 2006

This study concerns the analysis of diffusion and contagion processes using a lognormal model of overdispersion phenomena. The urban disorders of the past decade are examined and two processes are found to exist in the 1966–67 period. One is a classic diffusion effect in which disorders are precipitated by events which are independent of each other, but lead to outcomes such as numbers of arrests which are proportional to previous disorders. The second process is a contagious one in which disturbances occur as a consequence of smaller cities imitating the behavior of large ones experiencing a disorder. It was found that the explanatory power of the interaction effect between police and black city residents tended to increase as city size increased. Concomitantly, the effects of environmental variables tended to decrease in explanatory power as city size decreased.
Aggregate Economic Variables and Votes for Congress: A Rejoinder
Authors: Arcelus Francisco , Meltzer Allan H.
Published: May 2006

Our interest in the effect of aggregate economic variables on election results began in 1970 following a conversation with an administration official that we have reported elsewhere. We doubted both the implicit theory of voting behavior and the ability of the administration to achieve rates of inflation and unemployment even close to the ranges mentioned. We take this opportunity to note that the unemployment rate was higher and the inflation rate substantially higher than the adviser's estimate, but President Nixon was reelected.

At the time, the principal econometric evidence of the effects of aggregate economic variables was a study by Kramer. Kramer found evidence of an effect of real income, but despite (or perhaps because of) the flaws in his procedure, he found no evidence of an effect of inflation or unemployment. Furthermore, then and now, most of the reported evidence pertains to congressional not presidential elections and to votes for congressmen, not seats in the Congress.
The Permanent Court of International Justice, the International Court of Justice, the League of Nations, and the United Nations: A Comparative Empirical Survey
Authors: Coplin William D. , Rochester J. Martin
Published: May 2006

After a brief discussion of the existing literature and a description of the data set, the paper compares the role of four international institutions in two-party disputes in terms of (1) participant behavior and characteristics, (2) relationships between participants, and (3) characteristics of the disputes and institutional responses. The major purpose of the comparison is to assess various middle-range theoretical ideas that have been suggested by scholars and to determine whether the differences on the variables are a function of structural (PCIJ and ICJ versus League and UN) or historical (PCIJ and League versus ICJ and UN) variations. A final section of the paper presents a scheme for further research on the role of international institutions in the international bargaining process.
Soviet Elections Revisited: Voter Abstention in Noncompetitive Voting
Authors: Karklins Rasma
Published: May 2006

This analysis of voters and nonvoters in a large sample of recent emigrants from the Soviet Union shows that nonvoting is correlated with high interest in politics, a critical political outlook, and dissident modes of behavior. Thus, voter abstention in noncompetitive balloting can be hypothesized to constitute a significant political act rather than passivity. Single-party states use single-candidate elections for a variety of purposes, one of these being the psychological reinforcement of unity between regime and subjects. In this context, the only choice left to the dissenting citizen is not to vote at all. In the contemporary Soviet Union, nonvoting is regionally focused on Moscow and Leningrad, and is associated with post-Stalinist generational change. The covert nature of vote evasion and its informal tolerance provide a new perspective on the character of the Soviet system and its political culture.
The Structuring Principle: Political Socialization and Belief Systems
Authors: Searing Donald D. , Schwartz Joel J. , Lind Alden E.
Published: May 2006

This paper assesses the theoretical significance of data on childhood political learning. Two socialization models are involved. Each confers relevance on childhood learning by linking it with political outcomes. The first is an allocative politics model, which seeks a linkage with policy outputs. The other is a system persistence model, looking toward the stability and continued existence of political systems. Each model incorporates the following assumptions: (a) the primacy principle: childhood learning is relatively enduring throughout life; (b) the structuring principle: basic orientations acquired during childhood structure the later learning of specific issue beliefs.

It is this structuring principle which we examined and tested in the present paper. The data show no or little association between childhood orientations and the later learning of specific beliefs about the most important political issues of the day. Our evidence suggests a need to carefully reexamine the basic assumptions and directions of current political socialization research.
The Committee Function: An Influence Equation
Authors: Casstevens Thomas W.
Published: May 2006

In legislative systems a bill is commonly considered and reported by an appropriate committee before it is considered on the floor of the house. Since motions on the floor frequently relate to such bills, it is often apposite to refer to a motion's relevant committee. This article presents a mathematical model of the relationship between the relevant committee's divisions on the floor and a motion's probability of passing. Let x be the proportion of the relevant committee voting yea on the floor, z be the proportion of the relevant committee voting nay on the floor, and y be the proportion of the relevant committee neither voting yea nor voting nay on the floor, then a motion's probability of passing is (x2 + y2)/(x2 + y2 + z2). The fit between theory and observation is quite good: six hundred eleven roll calls from the 90th and 91st Congresses have been analyzed; 0.628 of the motions actually passed; and 0.613 of the motions were expected to pass.
Crude Communism and Revolution
Authors: Resnick David
Published: May 2006

The paper is an examination of the relationship between Marx's theory of communism and his theory of revolution in the early writings. Avineri's claim that the Paris Manuscripts contain a two stage theory of future society is critically evaluated. It is argued that by crude communism Marx meant an incorrect theory of communism and not a description of the next stage of society. Confusion results from taking Marx's discussion of two stages in the Critique of the Gotha Program and reading the more sophisticated analysis of the later works back into the early writings. A discussion of the relationship between revolutionary theory and practice as formulated in the early writing is offered in order to substantiate the claim that Marx never thought that socialist society had to pass through the stage of crude communism.
A Reassessment of Conventional Wisdom About the Informed Public: National Political Information in Ghana
Authors: Hayward Fred M.
Published: May 2006

This study examines the extent, impact and implications of political information in Ghana using survey data. A major interest is to identify and examine variables which influence level of information and to look at the consequences for the political process of different levels of political information. I examine conventional wisdom concerning the ignorance of the masses about national politics and call into question some common assumptions. Many of the differences usually assumed between developed and underdeveloped nations are found either not to exist or to be smaller than hypothesized. The data suggest that in some areas of national political information the masses in non-modernized societies are more politically aware than their counterparts in modernized societies. It is also suggested that there is no necessary link between education (literacy) and political information and that there are a number of functional equivalents to formal education. In the last section of the study several propositions about the informed citizenry are discussed.
Prediction Analysis in Political Research
Authors: Hildebrand David K. , Laing James D. , Rosenthal Howard
Published: May 2006

Procedures for empirical tests of political theory should be designed to evaluate the success of the specific prediction being tested. This paper introduces; (1) a formal language, termed “prediction logic,” for stating an important class of predictions, including predictions that imply there will be relatively few cases in certain cells of a cross-classification; (2) a population measure, (“del”), that indicates the degree of success achieved by a statement in the language; (3) partial measures for the multivariate case; (4) bivariate statistical inference methods when the data arise from a sample rather than a population, both for an a priori prediction statement and for a statement selected post hoc. A number of well-known measures of “association” are measures for specific prediction logic statements. Research applications are indicated through the use of contingency tables appearing in APSR articles by Eulau and Eyestone, Goldberg, Muller, Riker and Zavoina, Rosenthal, Sawyer and MacRae, Sickles, Wolfinger and Field, and Wolfinger and Heifetz.
The Divisive Primary Revisited: Party Activists in Iowa
Authors: Johnson Donald Bruce , Gibson James R.
Published: May 2006

This study was conducted to test the frequently made assertion that primary elections are divisive among party activists who participate in primary and subsequent general election campaigns. Analysis of data collected from 209 campaign workers personally identified by five candidates in two vigorously contested races for Congress in Iowa's First District indicated that the activists were an elite group on whom the primary had a divisive impact that was particularly notable among those who supported candidates who lost the primary. The alienation felt by many respondents who worked for losers in both parties adversely affected their general party support, voting, and the willingness to perform the many conventional activities necessary to a general election campaign, but it did not appear to have a substantial influence on the general election. Generally, those who defected were less experienced and less strongly identified with their parties than those who remained active. Moreover, most of the antagonism may be limited to the single general election; eighty per cent of all participants in the study expected to be as active or more active in future campaigns.
Political Parties and the Porkbarrel: Party Conflict and Cooperation in House Public Works Committee Decision Making
Authors: Murphy James T.
Published: May 2006

This study of the House Public Works committee examines the relationship between membership goals and the degree of party conflict, identifies conditions of party conflict and cooperation, and links party conflict and cooperation to policies adopted by the House.

Party conflict is the Public Works committee's most striking behavioral characteristic. This party conflict stems from (a) the issues processed by the committee and (b) the partisan program orientations of committee members. Beyond these initial sources of party conflict on Public Works, there is a norm of partisanship adopted by each of the parties on the committee in order to achieve an extra measure of party cohesion. Public Works committee party conflict is, to be sure, often modified by shared interests cutting across party lines. Committee party cooperation stems, however, not from widespread shared interests but, instead, from a fundamental distrust between the parties respecting the allocation of federal largesse. To preclude porkbarreling, Congress has adopted fixed allocation formulas for distributing the boodle on programs likely to involve a majority in each party, thereby constraining the parties on the committee to cooperate on such proposals.

Whether Public Works is united or divided when reporting legislation, the House of Representatives will typically adopt its proposals. This success of the Public Works committee is attributable to a mixture of anticipation and influence.
Individual and Contextual Variables in British Voting Behavior: An Exploratory Note
Authors: Tate C. Neal
Published: May 2006

This note reports the results of an initial exploration into the significance of the social environments (“contexts”) in which people live in the shaping of their individual political behavior. Many scholars have argued that social scientists should pay more serious attention to contextual variables when they go about constructing social theories. But there have been few systematic efforts to demonstrate empirically the overall importance of contextual variables as predictors of individual behaviors, especially relative to the importance of personal (“individual”) predictors. Here the relative potency of two sets of predictors—one individual and one contextual—is investigated for a sample of British voters by means of a well-known multivariate search strategy, “tree analysis.” The results suggest that contextual variables have little to add to explanations of voting behavior based on individual variables—at least for these data.
Rationality, Morality, and Impossibility Theorems
Authors: Frohock Fred M.
Published: May 2006

The impossibility theorem developed by Kenneth Arrow has implications for both rationality and morality in political thought. Transitivity in a collective ordering can be assured only with a decisive set, but this outcome is acknowledged as morally undesirable. The alternatives exhibited by the theorem thus seem to require a choice between rationality and morality. But exit routes can be cut out of this dilemma with the idea of a conditional ordering, one where warranting factors attach to a ranking of alternatives. Conditional orderings form two senses of collective rationality. One is represented by compound directives, which avoid the rational problems of the theorem by warranting local orderings. The second is moral fusion, which requires a reasoned dominance in collective outcomes. These two forms of conditional rationality put into relief the restricted scope of the composition rules and individualism of Arrow's theorem, and suggest alternative relationships of individual and social whole.
Prisoners' Financial Dilemmas: A Consociational Future for Lebanon?
Authors: Moore Clement Henry
Published: May 2006

Lebanon's banking system is viewed as an “international regime” that held the country together in the face of all pervasive warfare. The system illustrates the underlying logic of such regimes, in that the banks' credit policies operationalized the rational choice model of an iterated prisoner's dilemma game. And just as international regimes are supposed to reflect the interests of state actors, analysis of the banks' balance sheets and income statements reveals changes in capital structure that reflect changes in Lebanon's political balance. While sustaining elite cohesion, the banks serviced political clienteles and might, if a political settlement were reached, support the restructuring of a consociational system more in line with Lebanon's demographic balance. If, on the other hand, no settlement is reached, the poor country's suicide may highlight certain aspects of international reality that seem recalcitrant to the theory of international regimes.
Changes in the Vote Margins for Congressional Candidates: A Specification of Historical Trends
Authors: Garand James C. , Gross Donald A.
Published: May 2006

Recent research on House elections has focused on the decline in congressional competition since the mid-1960s. However, this body of research suffers from three major problems: 1) an imprecise specification of the nature of change in the degree of congressional competition, 2) its exclusive reliance on a limited time frame, which calls into question the generalizability and adequacy of its explanations, and 3) its overemphasis on incumbency-oriented explanations. Using a Multiple Interrupted Time Series (MITS) analysis of trends in aggregate electoral data from 1824 to 1980, we find that current low levels of congressional competition are not historically unique, but instead constitute a continuation of a long-term trend established in the mid-1890s. In addition, and in contrast to the general thrust described in the literature, there appears to be a post-1965 trend toward greater competition, although the absolute level of competition is lower after the mid-1960s. Finally, a disaggregation of electoral results by incumbency status suggests a growth in the incumbency advantage since the mid-1890s, but that lower post-1965 levels of congressional competition are the result of a winners' and not an incumbency, advantage. Such findings cast doubt on the adequacy of explanations that focus on post-1965, incumbency-oriented factors.
In Search of the Center of European Party Systems
Authors: Daalder Hans
Published: May 2006

Duverger's famous dictum that “the center does not exist in politics” is the starting point of an inquiry into the possible meanings of the concept of a center, and of center parties, in European party systems. This article consists of six sections; the first five sections deal with the center as a pivot in voting, the center in traditional left-right distributions, the notion of a center in multidimensional party spaces, the center in terms of mechanics, applying rather different metaphors of scales-in-balance and of centripetal versus centrifugal forces, and the center analyzed in terms of social cleavages. Following this search for conceptual meaning, in which the writings of Duverger and Sartori receive particular attention, the record of European party systems is examined to see whether the presence or absence of center parties in party systems can contribute to a realistic classification of European party systems.
Ruling: Guardians and Philosopher-Kings
Authors: Steinberger Peter J.
Published: May 2006

According to some accounts, Plato views ruling as a philosophical activity; according to others, he understands it to be a craft. Given the apparent discrepancy between philosophical and technical endeavor, it seems that the two interpretations cannot both be correct. The issue is explored in light of the relationship between guardians and philosopher-kings as it manifests itself in the basic structure of the Republic and also with respect to questions of education, character, and deceit.
Organizational Maintenance and the Retention Decision in Groups
Authors: Rothenberg Lawrence S.
Published: May 2006

Understanding why members leave or remain in groups has received little attention despite its fundamental importance for organizational maintenance. In this analysis, a theory of experiential search is proposed and applied to Common Cause. Group participation is conceptualized as a process by which imperfectly informed decision makers learn about the organizations they join. This framework makes quitting understandable and provides a link between the initial membership choice and follow-up decisions.
Age and Turnout in New Electorates and Peasant Societies
Authors: Niemi Richard G. , Barkan Joel D.
Published: May 2006

In established electorates in developed countries, voting turnout has a familiar curvilinear relationship with age. In new electorates, however, lack of experience and supposed resistance to new behavior among middle-aged voters suggest that turnout might be greater among the young. In peasant societies, the start-up costs that reduce turnout among young adults might not apply because of immobility of the population and resulting familiarity with local politics. Data from an early election in rural Kenya and from rural Turkey show that the familiar relationship holds even in these circumstances. The results suggest that increased electoral experience and resistance to newly available behavior do little to shape turnout. Mobility of the young, even in peasant populations, and psychological factors associated with aging are more powerful elements.
Reading Nietzsche and Foucault: A Hermeneutics of Suspicion?
Authors: Johnson J. Scott , Thiele Leslie Paul
Published: May 2006

To what extent and in what respects does the political thought of Michel Foucault reflect the influence of Friedrich Nietzsche's ideas? In the September 1990 issue of thisReview, Leslie Paul Thiele firmly asserted Nietzschean roots for Foucault's thought. In thisControversy, Thiele's claims are disputed by J. Scott Johnson. Johnson argues that Foucault's theory is rooted as much in Marx as in Nietzsche and that Foucault himself refuted Thiele's interpretation. In his response, Thiele takes issue with Johnson's critique.
Parliament and Political Support in Canada
Authors: Clarke Harold D. , Kornberg Allan , Stewart Marianne C.
Published: May 2006

Legislatures are widely recognized as institutional embodiments of the concept of representation in contemporary liberal democracies, but how support for legislatures and evaluations of their members's activities influence support for national political regimes and communities is imperfectly understood. This article investigates the question with the use of data from a 1979 national survey of the Canadian public. Analyses of a model of support demonstrate that feelings about parliament and assessments of MPs' performance have significant effects on levels of support for the national political community and regime. Other important variables include cost-benefit evaluations of the personal impact of governmental activity, more general evaluations of governmental performance, and subcultural variations in political socialization.
Presidential Coattails in Senate Elections
Authors: Campbell James E. , Sumners Joe A.
Published: May 2006

Despite the diminished importance of partisanship, greater split-ticket voting, and a growth in Senate campaign spending, a party's presidential vote in the states remains positively related to its Senate vote in recent elections. We investigate to what extent presidential coattails are responsible for this association. State election returns for Senate and presidential contests are examined in presidential election years from 1972 to 1988. The analysis indicates that (1) presidential coattails exert a modest but significant influence on the Senate vote, probably affecting the election outcomes in twelve cases, and (2) partisanship remains a significant linkage between presidential and Senate elections.
James Madison on Religion and Politics: Rhetoric and Reality
Authors: Lindsay Thomas
Published: May 2006

The recentOregon v.Smithdecision's shifting of the burden in free exercise cases from legislatures to minority religious claims has brought fierce opposition, most conspicuously from leading nonpreferentialist Richard J. Neuhaus, who sees in it the foundation of majority tyranny. AgainstSmith, Neuhaus employs Madison's “Memorial and Remonstrance Against Religious Assessments,” which is universally read to argue that the superiority of religion to politics proscribes majoritarian hegemony over religious practices. I contend that the Memorial's appeals are better understood as rhetoric than as reflecting Madison's true view. I find Madison hostile not only to religious establishments but also to religion itself. This hostility was the basis of his rejection of the nonpreferentialists' utility-based argument for government support of religion. In this light, I uncover a curious historical irony: the nonpreferentialist Neuhaus seeks today to protect religion from hostility by adhering to a position that was originally animated, in key respects, by hostility both to religion and to its nonpreferential support.
Politics and the Contemplative Life
Authors: de Grazia Sebastian
Published: May 2006

If there is practice without theory, perhaps there is theory without practice. We have fairly fixed notions of practice without theory—action without reflection, hand-to-mouth existence, meeting problems as they arise, disdain of plans or strategy, and so on. Of theory without practice there seems but one common idea—theory that because of abstraction or irrelevance cannot be applied. Plato told us the story of Thales of Miletus who, gazing at the stars, fell into a well. A little maid laughed to see such sport. Her laughter still rings in our ears, reminding us to practice navigating the earth rather than contemplate the stars.

Theory without practice, then, seems to be theory that cannot be applied. Applied to what? Applied to problems. Which problems? Problems that arise among men or in the community. Who there defines a problem? Not to get bogged down at the start, let us say merely that some men do or that some part of the community does.

We can also conceive of a theory not being applied because it seems farfetched or too costly or immoral, or because the moment for its need is not yet at hand. These are not the main objections, even though they all have a bearing in one way or another on the ideas we are about to discuss. The main objections are usually the ones already mentioned—theory irrelevant or too abstract. Abstractness, for our purposes, can be dismissed. It means either that the theory cannot be understood—a matter of communication, we assume—or that steps are lacking to bring the theory down to the applied level. We are really back to the question of application. Either a theory has relevance but for one reason or another cannot be put into practice, or it has no relevance at all and that is the end of that.
Constitutional Law in 1958–1959: II
Authors: Fellman David
Published: May 2006

Censorship of Motion Pictures. A recent amendment to the New York statute dealing with the licensing of motion pictures defines as “immoral” a picture “the dominant purpose or effect of which is erotic or pornographic; or which portrays acts of sexual immorality, perversity, or lewdness, or which expressly or impliedly presents such acts as desirable, acceptable or proper patterns of behavior.” The Education Department denied a license to the distributor of “Lady Chatterley's Lover” on the finding that three scenes were “immoral.” On appeal, the Regents of the University of New York upheld the denial of the license on the broader ground that “the whole theme of this motion picture is immoral under said law, for that theme is the presentation of adultery as a desirable, acceptable and proper pattern of behavior.” In affirming the denial, the Court of Appeals unanimously and explicitly rejected any notion that the film was obscene, but found rather that the picture as a whole “alluringly portrays adultery as proper behavior,” and that the only part of the statute applicable here was that which bars films which portray “acts of sexual immorality … as desirable.” Though there was no agreement on a single opinion, the Justices were unanimous in reversing the Court of Appeals. In behalf of a bare majority, Justice Stewart argued that since the state construction took the case outside the scope of such concepts as “obscenity” or “pornography,” and did not even suggest that the film would incite to illegal action, the state has in effect prohibited the exhibition of a motion picture because it advocates an idea, that under certain circumstances adultery may be proper behavior. This runs contrary to the basic guarantee of the First Amendment, which is the “freedom to advocate ideas,” and thus the state has quite simply “struck at the very heart of constitutionally protected liberty.” For the state misconceives what the Constitution protects. “Its guarantee,” wrote Justice Stewart, “is not confined to the expression of ideas that are conventional or shared by a majority. It protects advocacy of the opinion that adultery may sometimes be proper, no less than advocacy of socialism or the single tax. And in the realm of ideas it protects expression which is eloquent no less than that which is unconvincing.” Free speech, he went on to argue, cannot be denied where advocacy falls short of incitement, and where there is nothing to indicate that the advocacy will be acted on immediately.
Family Matters: Aristotle's Appreciation of Women and the Plural Structure of Society
Authors: Dobbs Darrell
Published: May 2006

Aristotle is no misogynist, but the way this charge is answered can skew the understanding of his political theory as a whole. Those who dismiss the charge of misogyny on grounds that Aristotle covertly advocates women's participation in civic affairs tend to obscure the leading thesis of thePolitics, namely, that polis and household differ in kind, not merely in number. I argue that Aristotle condones the exclusion of women from civic affairs because this practice conforms to the natural complementarity of the sexes and because it fortifies the naturally pluralistic structure of society. By securing these underpinnings, Aristotle frames a constitution that best supports women and men in their pursuit of human excellence.
Arithmetical definability of field elements
Authors: Robinson Raphael M.
Published: May 2006

If F is a field, and α is an element of F, we say that α is arithmetically definable in F if there is a formula containing one free variable and any number of bound variables, involving only the concepts of elementary logic and the operations of addition and multiplication, which is satisfied by α and by no other element of F. The range of the bound variables is understood to be F. Without changing the sense of the above definition, we can allow in our formulas symbols for specific integers, or even (if F has characteristic zero) symbols for specific rational numbers, since these are arithmetically definable.

As an example, consider the field F = R(2¼), obtained by adjoining the positive fourth root of 2 to the field R of rationals. Notice that 2¼ is not defined arithmetically by the formula x2 = 2, since this equation has two roots in F.

However, 2¼ may be defined arithmetically by the equivalence

where we have used the logical symbols ↔ (if and only if), ∨ (there exists), and ∧ (and). For the equation y4 = 2 is satisfied by no elements of F except y = ±2¼, and in both cases y2 = 2¼. On the other hand, 2¼ is not arithmetically definable in F, since there is an automorphism of F which takes 2¼ into −2¼, so that every arithmetical condition satisfied by 2¼ is also satisfied by −2¼.

In any field F, a necessary condition for the arithmetical definability of an element α is that α should be fixed for all automorphisms of F. That this condition is not always sufficient is shown by considering the field of real numbers. Here there is no automorphism but the identity, but there can of course be but a denumerable infinity of arithmetically definable real numbers. Tarski has shown that only the algebraic numbers are arithmetically definable.
Recursive Unsolvability of a problem of Thue
Authors: Post Emil L.
Published: May 2006

Alonzo Church suggested to the writer that a certain problem of Thue [6] might be proved unsolvable by the methods of [5]. We proceed to prove the problem recursively unsolvable, that is, unsolvable in the sense of Church [1], but by a method meeting the special needs of the problem.

Thue's (general) problem is the following. Given a finite set of symbols α1, α2, …, αμ, we consider arbitrary strings (Zeichenreihen) on those symbols, that is, rows of symbols each of which is in the given set. Null strings are included.
An extension of computational logic
Authors: Rose Alan
Published: May 2006

There has recently been developed a system of computational logic to which was given an interpretation in terms of the 2-valued propositional calculus. The object of the present paper is to give the corresponding theory for 3-valued logic. We use the same notation as Levin, except that instead of using the numeral “2” as a constant, we use “3”.
Completeness of the propositional calculus
Authors: Quine W. V.
Published: May 2006

The completeness of the prepositional calculus was first proved by Post. His somewhat condensed proof has been succeeded by more detailed presentations of substantially the same argument, and also by several proofs of radically different forms. The present paper contains still another proof, offered because of its relative simplicity. In part this proof follows a plan which was sketched by Wajsberg for another purpose, viz. for proving the completeness of the sub-calculus involving only the material conditional.

For the present proof a systematization of the propositional calculus will be used which is due to Tarski, Bernays, and Wajsberg. It involves the material conditional “⊃” and the falsehood “F” as primitive; thus the formulae are recursively describable as comprising “F”, the variables “p”, “q”, “r”, …, and all results of putting formulae for “p” and “q” in “(p⊃q)”. The denial “˜p” is definable as “(p⊃F)”, and all other truth functions are then definable in familiar fashion. (Conversely, in a system admitting “˜” instead of “F” as primitive, “F” might be explained as an abbreviation of “˜(P⊃P)”.) The postulates are four:

(1) ((p⊃q)⊃((q⊃r)⊃ (p⊃ r)))

(2) (((p⊃(q⊃p)⊃p)

(3) (p⊃(q⊃p))

(4) (F⊃p).
The Burali-Forti paradox
Authors: Rosser Barkley
Published: May 2006

In the system presented by Quine in his book Mathematical logic, one can derive the Burali-Forti Paradox. It is the purpose of this paper to present the details of this derivation. For the derivation, only familiarity with Quine's book is assumed.

The present derivation is based on the derivations given by Hobson and by Whitehead and Russell.

In both these sources, the primary interest is the theory of ordinals, and the Burali-Forti Paradox is of interest only as something to be avoided. In the present paper the primary interest is the Burali-Forti Paradox, so that much of the theory of ordinals is absent from this paper and only those details remain which are relevant to the derivation of the paradox.
Ein Verfahren der mathematischen Logik
Authors: Pepis Józef
Published: May 2006

Zu jedem Zählausdruck A in der allgemeinen pränexen Normalform

kann man bekanntlich einen, in bezug auf die Erfüllbarkeit, gleichwertigen Zählausdruck B in der spezielleren Normalform (Skolemsche Nonnalfonn)

konstruieren, indem man auf A mehrmals (n–1 Mal) das sogenannte Skolemsche Verfahren anwendet. Dieses Verfahren hat nämlich die Eigenschaft, daß es auf einen Zählausdruck in der pränexen Normalform n-ten Grades (n > 1) angewandt zu einem gleichwertigen Zählausdruck in der pränexen Normalform (n–1)-ten Grades führt, wobei unter “Grad eines Zählausdrucks in der pränexen Normalform, die ein mit einem Allzeichen beginnendes und mit einem Seinszeichen endendes Präfix hat” die Anzahl der durch Seinszeichen voneinander getrennten Komplexe von Allzeichen dieses Präfixes zu verstehen ist. Da nun A—wie aus (1) ersichtlich ist—ein Zählausdruck n-ten Grades ist, so kommt man nach (n–1)-maliger Anwendung des Skolemschen Verfahrens tatsächlich zu einem gleichwertigen Zählausdruck ersten Grades, also zu einem gleichwertigen Zählausdruck der Form (2).
Contextual definitions in nonextensional languages
Authors: Bergmann Gustav
Published: May 2006

The purpose of this note is to contribute to the discussion of nonextensional languages that is now in progress. A formal language, L, that contains, besides the lower functional calculus, predicates and predicate variables of higher type will here be called nonextensional if the sentence
Representations of calculi
Authors: Fitch Frederic B.
Published: May 2006

A previous paper proposed a finitary system of logic which was surmised to be basic in the sense that every finitary system of logic could be defined within it. In the present paper this anticipated result, or rather its syntactical counterpart, is definitely established as Theorem VI. The calculus K is a formalization of the basic logic. Its main features were described in the previous paper, acquaintance with which is presupposed here. Attention is called to the fact that from now on the class Y of atomic U-expressions will be assumed to be finite instead of infinite. This is a relatively minor change and does not affect the previously established results. The account of the nature of calculi, as given in the other paper, is to be made more precise by stating that a calculus is any class of expressions having as a Gödel representation a recursively enumerable class of integers. A system of logic is regarded as being finitary if it is capable of formalization by means of an appropriate calculus.
Note on a problem of L. Henkin
Authors: Robinson Abraham
Published: May 2006

A statement X in the lower predicate calculus is said to be persistent with respect to the set of statements K ([2], [3]), if whenever X holds in a model M of K then X holds also in all extensions of M which are models of K. If X is persistent with respect to the empty set, then it may be said to be absolutely persistent.

A statement X is called existential, if it is in prenex normal form and does not contain any universal quantifiers. This includes the possibility that X does not contain any quantifiers at all.

Let E be the class of all existential statements. Then it is not difficult to see that E is quasi-disjunctive. That is to say, given statements Y1, Y2 in E, there exists a statement Y in E such that

is provable.

L. Henkin [1] has raised the question how to characterise the statements X which are persistent with respect to a given set K (e.g. a set of axioms for a field or a group) by a syntactical condition. He has shown that, in order that a statement X be absolutely persistent, it is necessary and sufficient that there exist a statement Y ϵ E such that

is provable.
Reduction to a symmetric predicate
Authors: Cobham Alan
Published: May 2006

It has been shown by Quine that an interpreted theory Θ, formulated in the notation of quantification theory, is translatable into a theory Θ′ in which the only primitive predicate is a dyadic F. In establishing this result Quine takes for the universe of Θ′ a set which comprehends the universe of Θ and has the property that if x and y are members then so is {x, y}. For this fragmentary set theory the distinctness of x from {x, y} and {{x}} is assumed. It will be shown here that, if a pair of somewhat more stringent restrictions are assumed for the set theory, then there is a symmetric dyadic predicate G definable within Θ′, i.e., in terms of F alone, in terms of which F is in turn definable. It follows from this extended result that the theory Θ is translatable into a theory in which the only primitive predicate is symmetric and dyadic.
An extended procedure in quantificational logic
Authors: Stanley Robert
Published: May 2006

The aim of this paper is to present a decision procedure which seems to be as easy to use as other available procedures in quantification theory, but which is considerably stronger than the others, providing a mechanical test for a sub-species of polyadic validity which is very much broader than monadic validity. Of course, a test for polyadic validity in general is out of the question, but the present test's limits, short of polyadic validity, are not known. That is, of all the polyadically valid schemata which have been tested, ncne has failed to yield decisions under this method. The material thus examined includes schemata corresponding to the cases of all absolute metatheorems in ML's Chapters II and III, and five polyadic samples from MeL. The handiness of this test is illustrated by sample applications in § 3 below.
Paradox of the class of all grounded classes
Authors: Yuting Shen
Published: May 2006

A class A for which there is an infinite progression of classes A1, A2, … (not necessarily all distinct) such that

is said to be groundless. A class which is not groundless is said to be grounded. Let K be the class of all grounded classes.

Let us assume that K is a groundless class. Then there is an infinite progression of classes A1, A2, … such that

Since A1 ϵ K, A1 is a grounded class; since

A1 is also a groundless class. But this is impossible.

Therefore K is a grounded class. Hence K ϵ K, and we have

Therefore K is also a groundless class.

This paradox forms a sort of triplet with the paradox of the class of all non-circular classes and the paradox of the class of all classes which are not n-circular (n a given natural number). The last of the three includes as a special case the paradox of the class of all classes which are not members of themselves (n = 1).

More exactly, a class A1 is circular if there exists some positive integer n and classes A2, A3, …, An such that

For any given positive integer n, a class A1 is n-circular if there are classes A2, …, An, such that

Quite obviously, by arguments similar to the above, we get a paradox of the class of all non-circular classes and a paradox of the class of all classes which are not n-circular, for each positive integer n.
A note on the Entscheidungsproblem
Authors: Church Alonzo
Published: May 2006

In a recent paper the author has proposed a definition of the commonly used term “effectively calculable” and has shown on the basis of this definition that the general case of the Entscheidungsproblem is unsolvable in any system of symbolic logic which is adequate to a certain portion of arithmetic and is ω-consistent. The purpose of the present note is to outline an extension of this result to the engere Funktionenkalkul of Hilbert and Ackermann.

In the author's cited paper it is pointed out that there can be associated recursively with every well-formed formula a recursive enumeration of the formulas into which it is convertible. This means the existence of a recursively defined function a of two positive integers such that, if y is the Gödel representation of a well-formed formula Y then a(x, y) is the Gödel representation of the xth formula in the enumeration of the formulas into which Y is convertible.

Consider the system L of symbolic logic which arises from the engere Funktionenkalkül by adding to it: as additional undefined symbols, a symbol 1 for the number 1 (regarded as an individual), a symbol = for the propositional function = (equality of individuals), a symbol s for the arithmetic function x+1, a symbol a for the arithmetic function a described in the preceding paragraph, and symbols b1, b2, …, bk for the auxiliary arithmetic functions which are employed in the recursive definition of a; and as additional axioms, the recursion equations for the functions a, b1, b2, …, bk (expressed with free individual variables, the class of individuals being taken as identical with the class of positive integers), and two axioms of equality, x = x, and x = y →[F(x)→F(y)].
Finite models for inequations
Authors: Gladstone M. D.
Published: May 2006

By inequation is meant an expression of the form,

where a, b are terms taken from any first-order formal language. An inequation is consistent iff it cannot be brought to the form,

by substitution.
Subformula theorems for N-sequents
Authors: Leblanc Hugues
Published: May 2006

With all seven of ‘∼’, ‘⊃’, ‘&’, ‘ν’, ‘≡’, ‘∀’, and ‘∃’ understood to serve as primitive signs, let an expression of the sort

A1, A2, … , An → B1, B2, … , Bm,

where A1, A2, …, Aη (η≥ 0), B1, B2, …, and Bm (m > 0 if n = 0, otherwise m ≥ 0) are wffs of the first-order quantificational calculus (QC), count as an L-sequent of QC; let an L-sequent of QC of the sort

A1, A2, … , An → B

count as an N-sequent of QC;2 and let an L-sequent S of QC count as a Gentzen L-sequent of QC if no individual variable of QC occurs both bound and free in S.
On the Craig-Lyndon interpolation theorem
Authors: Oberschelp Arnold
Published: May 2006

In his paper [3] Henkin proved for a first order language with identity symbol but without operation symbols the following version of the Craig-Lyndon interpolation theorem:

Theorem 1. If Γ╞Δ then there is a formula θ such that Γ ├Δand

(i) any relation symbol with a positive (negative) occurrence in θ has a positive (negative) occurrence in some formula of Γ.