bluuebunny/crossref_metadata_2025 huggingface dataset:
Personality and Conformity: The Learning of Political Attitudes
Authors: Di Palma Giuseppe , McClosky Herbert
Published: May 2006

Why do some men embrace society's values while others reject them? Is conformity a general trait, more uniformly manifested by some people than by others? What social or psychological forces lie behind the tendency to conform or deviate?

Although these questions obviously have significance for the conduct of political life, they have received far less attention from political scientists than from scholars in other disciplines such as psychology and sociology. In view of current challenges to the legitimacy of existing political institutions, the mounting debate over the acceptable limits of protest, and the growing disdain for democratic decision-processes shown by some segments of the population, the need for political scientists to understand the nature and sources of conformity and deviation has become, if anything, more urgent. We hope, in the present paper, to explore the psychological—and to some extent the social and political—meaning of conformity and deviation as reflected in citizen responses to political beliefs. To that end we shall review briefly the present state of psychological theory and research on conformity behavior; suggest, in light of our own research findings, some ways in which current psychological explanations might be modified and extended to account for conformity and deviation within the mass public; and furnish data that might help to explain why individuals who have different personality characteristics and who occupy different roles in the society are likely to accept or reject political norms.
Political Parties, Interest Representation and Economic Development in Poland
Authors: Wiatr Jerzy J.
Published: May 2006

Discussing the character of the Polish party system elsewhere, I have suggested a label of “hegemonic party system” for it, as well as for some other party systems based on similar principles. The hegemonic party systems stand mid-way between the mono-party systems and the dominant party systems as defined by Maurice Duverger. In an earlier paper written jointly with Rajni Kothari we have suggested the following typology of party systems:

1. Alternative party systems, where two or more political parties compete for political power with realistic chances of success;

2. Consensus party systems, where multi-partism does exist but one political party commands in a lasting way the loyalties of a predominant majority of the citizens and permanently runs the government;

3. Hegemonic party systems, where all the existing parties form a lasting coalition within which one of them is accepted as the leading force of the coalition;

4. Mono-party systems;

5. Suspended party systems, where political parties exist but are prevented from regulating political life by other forces (for instance, by the military);

6. Non-party systems, where the government is ideologically hostile toward the political parties as such and does not permit them to function.

Quite obviously, this typology does not exclude mixed types of party systems. On the contrary, the very fact that in political life nothing is absolutely permanent leads to the emergence of transitory types of party systems.
Residential Location and Electoral Cohesion: The Pattern of Urban Political Conflict
Authors: Almy Timothy A.
Published: May 2006

This study examines the assertions of urban scholars that the spatial arrangement of urban populations is important in determining the amount of conflict displayed within American cities. The article analyzes the spatial distribution of class groups within 18 cities and the degree of voting solidarity and conflict displayed within segregated and integrated sections of each community. Data were gathered from precinct voting returns for several local referenda in each city to test the following hypotheses: (1) The residential distribution of social-class groups will significantly influence the degree of electoral cohesion these groups display; (2) The spatial distribution of class groups will significantly influence the amount of electoral disagreement between class groups. The study found that communities that displayed segregated class groups had a high degree of class electoral solidarity. Within cities that manifested spatially integrated class groups, however, the electoral cohesion of each class was low. A social-class group located in an area of a city possessing wide class dissimilarity was not likely to vote in agreement with other groups of the same class located elsewhere in the city. The findings of this article suggest that location may be one of the sources of urban political conflicts.
Maximin Justice and an Alternative Principle of General Advantage
Authors: Rae Douglas
Published: May 2006

John Rawls's theory of justice tries to resolve the question of fair allocation: When, if ever, may some members of society claim rightful privilege over their fellows? Rawls's answer is maximin justice: inequalities are just if, by permitting them, society treats best those whom she treats worst. Rawls attempts to show that this rule binds us all under the terms of a social contract. The present paper tries to show that Rawls's theory will not stand scrutiny. The social contract, as he gives it, disfranchises all but a single social stratum: Why are others bound by it? The maximin principle, allegedly agreed to under this social contract, requires that we judge allocations by ignoring all but one of society's many strata. This leads in turn to arbitrary judgments including ones which at once increase inequality and decrease the total shared by society. An alternative argument is offered, beginning with a social contract requiring agreement on all inequalities among agents for a series of hypothetical social strata. This device is meant to bind all strata, and leads to a principle of general advantage: Inequalities are just if but only if they serve the advantage of some strata and the disadvantage of none. This seemingly paradoxical rule has a clear interpretation and avoids the main difficulties attributed to maximin justice. Like maximin, however, the new doctrine would evidently require a radical redistribution of income in a society like our own.
Justifying Justice: Problems of Psychology, Measurement, and Politics in Rawls
Authors: Barber Benjamin R.
Published: May 2006

The intention of this essay is to raise certain questions aboutA Theory of Justicein Rawls's own terms—accepting his premises but examining his reasoning by his own stated criteria. I believe that such an examination will show that the abstract justificatory appeal to an “original position” is unsatisfactory in certain vital psychological and philosophical ways; that the Rawlsian analysis raises problems of comparison and measurement not adequately disposed of by the doctrine of justice as fairness and its corollary strategy of “maximin”; and that the appeal to congruence on which the latter part of Rawls's argument depends is founded on an inadequate political and historical sociology—which in turn creates further problems for the argument from the original position. In sum, I wish to show that while Rawls has lit his candle at both ends, he has got neither end to burn.
Policy Motivation and Party Differences in a Dynamic Spatial Model of Party Competition
Authors: Chappell Henry W. , Keech William R.
Published: May 2006

We present a model of party competition that produces more realistic patterns of results than those often emphasized in the literature. Reversing Downs (1957), we assume that parties win elections in order to formulate policies, rather than formulate policies in order to win elections. Voters are modeled first as having perfect information about candidate positions, and then under conditions of uncertainty. In simulation experiments we show that policy motivation and voter uncertainty can bring about persistent and predictable party differences in sequential majority rule elections. As the degree of voter certainty decreases, parties diverge towards their optima, whereas increases in voter certainty draw parties towards cycles in which party positions vary, but predictable issue stances are maintained on the average.
Reassessing Parental Socialization: Indicator Unreliability Versus Generational Transfer
Authors: Dalton Russell J.
Published: May 2006

This article challenges recent socialization research which concludes that the family's influence is primarily limited to the generational transfer of partisan values. We first present a new conceptual approach for studying parent-child agreement. Then, we apply a multiple indicator methodology (LISREL) to operationalize this approach. Reanalysis of the Jennings and Niemi socialization survey finds quite substantial levels of family agreement in areas besides partisanship. These results argue for greater attention to the significance of family socialization, and to the persistence of political beliefs across generations.
Modeling War and Peace
Authors: Hussein Seif M. , de Mesquita Bruce Bueno , Lalman David
Published: May 2006

The appropriate model of international conflict and war has been much discussed in recent years, and considerable progress has been made in modeling. Nevertheless the assumptions, conditions, and specifications for international conflict models remain eminently debatable. In the December 1986 issue of this Review, Bruce Bueno de Mesquita and David Lalman presented a generalized expected utility model of international conflict. Here Seif Hussein takes issue with their model in various particulars, aiming to perfect and strengthen the model. Bueno de Mesquita and Lalman respond.
Constitution-Making: Alignment and Realignment in the Federal Convention of 1787
Authors: Jillson Calvin C.
Published: May 2006

This study offers an empirical description of the voting alignments that dominated the American Constitutional Convention as the delegates struggled to produce the final report of that historic assembly. Its conceptual roots are firmly planted in the theoretical traditions of Schattschneider on conflict and cleavage, and of Key, Burnham and Sundquist on critical realignment of the American party system. I demonstrate that dynamic processes analogous to Key's conception of “critical elections” at the macro-level of national politics can also be identified and analyzed at the micro-level of the constituent assembly. Therefore, I argue that one of the “mainsprings of American politics,” as Burnham calls the critical election phenomenon, permeates all levels of the American political system and not simply the national level of electoral mass politics. More specifically, this clear description of coalition alignment, operation and realignment in the Constitutional Convention, when informed and enlightened by the “critical realignment” model, greatly facilitates the more traditional discussion of debate, conflict and ultimate decision on the central issues before that body—representation, federalism, senatorial authority, and the nature of the executive in a republican government.
Soviet Political Culture and “Covert Participation” in Policy Implementation
Authors: DiFranceisco Wayne , Gitelman Zvi
Published: May 2006

Our study of political participation in the Soviet Union, based on interviews with recent emigres, leads us to conclude that Soviet political culture is neither a “subject” nor a “subject-participant” one. There are meaningful forms of participation in the system, but they take place either outside the nominally participatory institutions, or within those institutions but in nonprescribed ways. The citizen may participate covertly, utilizing unsanctioned or blatantly illegal methods in attempts to influence policy implementation, not policymaking. The findings support the concept that traditional, prerevolutionary modes of citizen-state interactions are reinforced by the pattern of Soviet socioeconomic development and by a highly centralized and hierarchical administrative structure, itself a continuation of tsarist patterns. This study describes how different types of Soviet citizens try to influence policy implementation, and how they differentiate among the bureaucracies. Analysis of this activity leads us to reformulate our conception of Soviet political culture.
Some Social and Political Dimensions of Nuclear Power: Examples from Three Mile Island
Authors: Nelkin Dorothy
Published: May 2006

Public concerns about the social and political implications of energy choices have found expression in the nuclear debate. The Three Mile Island accident, in its complexity and far-reaching consequences, served to focus criticism of nuclear power that had been building up for a decade. It revealed with striking clarity that technology is a social concept to be understood in terms of social and political relationships if it is to be brought under public control. The ramifications of the accident revealed the conceptual difficulties of assessing social risks and the political difficulties in managing them. This article draws examples from the Three Mile Island accident to review several characteristics of nuclear technology, its scale and costs, its complexity, its uncertain and unpredictable physical effects, and its indirect risks. It then explores the implications for social, political and administrative institutions as they grope for ways to manage the risks of nuclear power in the context of critical public scrutiny. Finally it identifies a range of issues calling for policy research.
America'sDepartmentsof State: Irregular and Regular Syndromes of Policy Making
Authors: Rockman Bert A.
Published: May 2006

This article (1) sketches a general explanation for the growth of coordinative machinery and of irregular personnel in modern governments; (2) identifies both general and specific reasons for this phenomenon in the United States with special reference to foreign policy making; (3) identifies within the American foreign policy-making context the modal characteristics of irregular and regular syndromes of policy making, and the conjunction between personnel and institutional base; (4) traces the implications arising from these different policy syndromes; and (5) evaluates some proposals for improving the coherence and knowledge base of American foreign policy making. The problems of defining foreign policy authority, assuring an integrated perspective, and effectively using specialized expertise are best seen in terms of the larger problem of governance in Washington against which all proposals for reform must be abraded.
Political Commentary on the History of Political Theory
Authors: Baumgold Deborah
Published: May 2006

The phrasing of the title telegraphs the thesis of this essay: study of the history of political theory ought to be understood and approached as a branch of political studies. Prior to the postwar success of empirical political science, the view would have seemed unexceptional. But the need for a defense against the empiricist attack impelled many theorists to turn to theories of interpretation in search of a philosophical and methodological identity. A preoccupation with issues of interpretation now threatens the customary, political study of the tradition. This essay, written in defense of a political understanding of the field, identifies fundamental propositions distinguishing “political commentary” and suggests critical standards appropriate to the enterprise. It also criticizes two currently fashionable applications of interpretative theory to the study of politics, historicist commentary and hermeneutical political science.
Constituency Opinion and Congressional Policy Making: The Reagan Defense Buildup
Authors: Bartels Larry M.
Published: May 2006

Rrepresentatives' votes on a series of defense budget roll calls in the first year of the Reagan administration's Pentagon buildup are related to constituency opinions on defense spending during the 1980 election campaign. The strong aggregate constituency demand for increased defense spending in 1980 is estimated to have added almost $17 billion (about 10%) to the total fiscal year 1982 Pentagon appropriation. The impact of constituency opinion was largely independent of specific political circumstances: differential responsiveness in districts with partisan turnover, intense districtlevel competition, and strong presidential coattails together accounted for less than $1 billion in additional appropriations, with the remaining $16 billion attributable to across-the-board responsiveness by even the most safely incumbent representatives.
Is Work Special? Justice and the Distribution of Employment
Authors: Arneson Richard J.
Published: May 2006

I investigate from an egalitarian welfarist standpoint the issue of whether state-guaranteed employment should be offered as a matter of right to able-bodied poor citizens who suffer chronic or persistent unemployment. An affirmative answer is defended. One consideration supporting this right to work is that provision of transfer aid in the form of jobs rather than cash screens “nonneedy bohemians” from the class of beneficiaries. The main conclusion of the essay is defended from one objection based on efficiency wage models of the labor market and from another based on the alleged impossibility of maintaining the self-respect and self-esteem of able-bodied individuals who fail to earn their own keep independently in a market economy.
The Moral Force of Political Obligations
Authors: Klosko George
Published: May 2006

Political obligations vary in force. Though we have strong obligations to obey certain laws, our obligations to obey others appear to be considerably weaker. Because the weakness of the obligations to obey certain laws has been employed as an argument against the existence of general prima facie political obligations, an adequate theory of political obligation must account for this. By employing the obligation to keep promises as a model, I sort out the factors that contribute to the force of prima facie political obligations. Their varying force can be explained according to a general theory of political obligation founded on the principle of fairness.
Evolutionary Biology and Political Theory
Authors: Masters Roger D.
Published: May 2006

The traditional emphasis on human nature as the foundation of politics needs to be reexamined from the perspective of contemporary biology. Because biological processes operate independently on the individual, the social group, and the species, an evolutionary approach to both observational research and cost-benefit analysis does not entail reductionism. Selfishness and altruism, participation in social groups, languages and cultures, and the rise and fall of centralized states can all be illuminated by empirical evidence and theories in the life sciences. For political philosophy, a new “naturalism” points to a return to the Aristotelian view that values or standards of judgment have rationally intelligible foundations, thereby challenging the relativist or nihilistic orientation that has characterized most contemporary thought.
Moral Education and the “Tie that Binds” in Liberal Political Theory
Authors: Paris David C.
Published: May 2006

I examine the search for a “tie that binds, “ or “core” values, in liberal political theory, specifically Rawls's recent arguments, and in proposals concerning moral education in the public schools. Both Rawls and the proponents of moral education appeal to consensus or shared values, but the search for core values in both theory and practice is only partly successful. Specifically, this search is misguided insofar as it does not reflect how values are embedded in specific institutions and practices. The various forms of moral education in the public schools, both implicit and explicit, illustrate a consensus about a range of moral and intellectual virtues that is broader and more complex than arguments for core values allow. Comparing arguments concerning core values in political theory and moral education suggests how liberal political theory might deal with questions of consensus, justification, and the task of political theory generally.
Politics and the Problem of Technology: An Essay on Heidegger and the Tradition of Political Philosophy
Authors: Weinberger Jerry
Published: May 2006

I examine Heidegger's postmodern interpretation of technology, with an eye to exposing its weaknesses. I do this by showing that his view entails an understanding of the tradition of political philosophy that cannot do justice to that tradition's own understanding of the character of technology. I consider first Plato and Aristotle and then Hobbes and Locke in order to suggest that Heidegger's view that modern politics are stamped by technological metaphysics can be challenged on two related grounds: (1) it assumes incorrectly that the tradition is dominated by dogmatic metaphysics; (2) it prevents us from seeing how some in the tradition both understood and doubted the possibility of a technological stamp. I then suggest an alternative view of technology that might account better for the character of technology and political life.
Serving God and Mammon: The Lockean Sympathy in Early American Political Thought
Authors: Dienstag Joshua Foa
Published: May 2006

This paper seeks to revive the old theory of a “Lockean consensus” in early American political thought against the prevailing “republican” view. The language of “virtue” and “slavery,” which was pervasive at the time of the founding, and which many have been eager to take as evidence for the influence of civic humanism, in fact has a perfectly plain Lockean provenance. This is established first through a reexamination of Locke that links his account of virtue to a Christian asceticism (i.e., the Protestant Ethic) rather than republican philosophy. That the founders understood virtue in this way is then established through an exploration of Adams and Jefferson. In both cases, it was a Lockean slavery which they feared and a Lockean virtue which they sought. A Lockean sympathy did exist among the founders; in order to understand it, however, it must be distinguished from modern liberalism, with which it has only tenuous connections.
Riding Waves or Making Waves? The Services and the U.S. Defense Budget, 1981–1993
Authors: Lebovic James H.
Published: May 2006

Bureaucratic politics is the favored explanation of those addressing the perversities of defense budgeting. But it is arguably devoid of politics, given its dependence on either aggregate top-down or horizontal models. I seek to redirect analysis. I disaggregate defense spending (by service and weapon type) and study budget sensitivity to program pressures in the buildups and builddowns of the Reagan-Bush eras. Applying a two-equation model to time-series cross-sectional data, the analysis shows weapon budgets increasing with program diversification and a commitment to defense spending. In turn, it shows programs diversifying to accomodate service objectives: when turning to missions, the services increased program varieties while concentrating program resources.
Comparative Democracy: The Economic Development Thesis
Authors: Burkhart Ross E. , Lewis-Beck Michael S.
Published: May 2006

In comparative politics, an established finding—that economic development fosters democratic performance—has recently come under challenge. We counter this challenge with a dynamic pooled time series analysis of a major, but neglected data set from 131 nations. The final generalized least squares-autoregressive moving averages estimates (N = 2,096) appear robust and indicate strong economic development effects, dependent in part on the nation's position in the world system. For the first time, rather hard evidence is offered on the causal relationship between economics and democracy. According to Granger tests, economic development “causes” democracy, but democracy does not “cause” economic development. Overall, the various tests would seem to advance sharply the modeling of democratic performance.
The calculus of individuals and its uses
Authors: Leonard Henry S. , Goodman Nelson
Published: May 2006

An individual or whole we understand to be whatever is represented in any given discourse by signs belonging to the lowest logical type of which that discourse makes use. What is conceived as an individual and what as a class is thus relative to the discourse within which the conception occurs. One task of applied logic is to determine which entities are to be construed as individuals and which as classes when the purpose is the development of a comprehensive systematic discourse.

The concept of an individual and that of a class may be regarded as different devices for distinguishing one segment of the total universe from all that remains. In both cases, the differentiated segment is potentially divisible, and may even be physically discontinuous. The difference in the concepts lies in this: that to conceive a segment as a whole or individual offers no suggestion as to what these subdivisions, if any, must be, whereas to conceive a segment as a class imposes a definite scheme of subdivision—into subclasses and members.

The relations of segments of the universe are treated in traditional logistic at two places, first in its theorems concerning the identity and diversity of individuals, and second in its calculus of membership and class-inclusion. But further relations of segments and of classes frequently demand consideration. For example, what is the relation of the class of windows to the class of buildings? No member of either class is a member of the other, nor are any of the segments isolated by the one concept identical with segments isolated by the other. Yet the classes themselves have a very definite relation in that each window is a part of some building. We cannot express this fact in the language of a logistic which lacks a part-whole relation between individuals unless, by making use of some special physical theory, we raise the logical type of each window and each building to the level of a class—say a class of atoms—such that any class of atoms that is a window will be included (class-inclusion) in some class that is a building. Such an unfortunate dependence of logical formulation upon the discovery and adoption of a special physical theory, or even upon the presumption that such a suitable theory could in every case be discovered in the course of time, indicates serious deficiencies in the ordinary logistic. Furthermore, a raising of type like that illustrated above is often precluded in a constructional system by other considerations governing the choice of primitive ideas.
A formulation of the simple theory of types
Authors: Church Alonzo
Published: May 2006

The purpose of the present paper is to give a formulation of the simple theory of types which incorporates certain features of the calculus of λ-conversion. A complete incorporation of the calculus of λ-conversion into the theory of types is impossible if we require that λx and juxtaposition shall retain their respective meanings as an abstraction operator and as denoting the application of function to argument. But the present partial incorporation has certain advantages from the point of view of type theory and is offered as being of interest on this basis (whatever may be thought of the finally satisfactory character of the theory of types as a foundation for logic and mathematics).

For features of the formulation which are not immediately connected with the incorporation of λ-conversion, we are heavily indebted to Whitehead and Russell, Hilbert and Ackermann, Hilbert and Bernays, and to forerunners of these, as the reader familiar with the works in question will recognize.

The class of type symbols is described by the rules that ı and o are each type symbols and that if α and β are type symbols then (αβ) is a type symbol: it is the least class of symbols which contains the symbols ı and o and is closed under the operation of forming the symbol (αβ) from the symbols α and β.
On the definition of negation by a fixed proposition in inferential calculus
Authors: Curry Haskell B.
Published: May 2006

It is well known that negation can be defined by postulating a fixed proposition F and specifying that

where “≡” indicates identity by definition. I propose to discuss this way of introducing negation in relation to the inferential systems of my Notre Dame lectures of 1948. Acquaintance with these lectures is presupposed; they will be referred to as TFD. The definition (1) was used there, essentially, in connection with the T-systems; but it was not used in connection with the L-systems because of a certain difficulty which I was not able to overcome at that time. This paper contains proofs of results concerning L-systems which have been announced elsewhere.
Arithmetical problems and recursively enumerable predicates
Authors: Davis Martin
Published: May 2006

It is an immediate consequence of results of Church and Gödel that there exist arithmetical recursively unsolvable problems, that is, recursively unsolvable problems of the form [M](P = Q) where P and Q are polynomials and [M] is some finite sequence of existential and universal quantifiers. A question which is immediately raised by this result is whether there exist unsolvable problems of this form where [M] is some finite sequence of existential quantifiers only. As a matter of fact this question is easily seen to be closely related to the tenth problem in the famous list proposed by Hilbert in 1900.

In this paper, we prove the existence of recursively unsolvable problems of the form

where P and Q are polynomials with non-negative integral coefficients. As a matter of fact we show that every recursively enumerable predicate is of the form (1), and conversely that every predicate of the form (1) is recursively enumerable. While our result does not yield the recursive unsolvability of Hilbert's tenth problem, it is easily seen that any considerable improvement of our result would yield this unsolvability.

The author wishes to take this opportunity to express his gratitude to Professors Alonzo Church and E. L. Post with whom he has had the privilege of discussing some of the questions involved in this paper. He also wishes to thank his friends Melvin Hausner and Jacob Schwartz who have made valuable suggestions.
A Note on Quine's principles of quantification
Authors: Wang Hao
Published: May 2006

In his Mathematical logic Quine characterizes the theorems of quantification theory by six principles:
On the rules of proof in the pure functional calculus of the first order
Authors: Mostowski Andrzej
Published: May 2006

We consider here the pure functional calculus of first order as formulated by Church.

Church, l.c., p. 79, gives the definition of the validity of a formula in a given set I of individuals and shows that a formula is provable in if and only if it is valid in every non-empty set I. The definition of validity is preceded by the definition of a value of a formula; the notion of a value is the basic “semantical” notion in terms of which all other semantical notions are definable.

The notion of a value of a formula retains its meaning also in the case when the set I is empty. We have only to remember that if I is empty, then an m-ary propositional function (i.e. a function from the m-th cartesian power Im to the set {f, t}) is the empty set. It then follows easily that the value of each well-formed formula with free individual variables is the empty set. The values of wffs without free variables are on the contrary either f or t. Indeed, if B has the unique free variable c and ϕ is the value of B, then the value of (c)B according to the definition given by Church is the propositional constant f or t according as ϕ(j) is f for at least one j in I or not. Since, however, there is no j in I, the condition ϕ(j) = t for all j in I is vacuously satisfied and hence the value of (c)B is t.
On the paradox of grounded classes
Authors: Montague Richard
Published: May 2006

Mr. Shen Yuting, in this Journal, vol. 18, no. 2 (June, 1953), stated a new paradox of intuitive set-theory. This paradox involves what Mr. Yuting calls the class of all grounded classes, that is, the family of all classes a for which there is no infinite sequence b such that … ϵ bn ϵ … ϵ b2ϵb1 ϵ a.

Now it is possible to state this paradox without employing any complex set-theoretical notions (like those of a natural number or an infinite sequence). For let a class x be called regular if and only if (k)(x ϵ k ⊃ (∃y)(y ϵ k · ~(∃z)(z ϵ k · z ϵ y))). Let Reg be the class of all regular classes. I shall show that Reg is neither regular nor non-regular.

Suppose, on the one hand, that Reg is regular. Then Reg ϵ Reg. Now Reg ϵ ẑ(z = Reg). Therefore, since Reg is regular, there is a y such that y ϵ ẑ(z = Reg) · ~(∃z)(z ϵ z(z = Reg) · z ϵ y). Hence ~(∃z)(z ϵ ẑ(z = Reg) · z ϵ Reg). But there is a z (namely Reg) such that z ϵ ẑ(z = Reg) · z ϵ Reg.

On the other hand, suppose that Reg is not regular. Then, for some k, Reg ϵ k · [1] (y)(y ϵ k ⊃ (∃z)(z ϵ k · z ϵ y)). It follows that, for some z, z ϵ k · z ϵ Reg. But this implies that (ϵy)(y ϵ k · ~(ϵw)(w ϵ k · w ϵ y)), which contradicts [1].

It can easily be shown, with the aid of the axiom of choice, that the regular classes are just Mr. Yuting's grounded classes.
Closure and Quine's *101
Authors: Fitch Frederic B.
Published: May 2006

The purpose of this paper is to suggest two alternatives to Quine's definition of closure. These new definitions have two advantages over Quine's definition, and they probably are the simplest definitions having both advantages. The two advantages are:

(1). Principle *101 becomes superfluous and may be dropped from Quine's set of principles for quantification. (In the case of my second definition, however, the dropping of *101 must be balanced by a slight change in *104.)

(2). Closure is made independent of the alphabetical order of variables.

The second of these advantages turns on the fact that the “alphabetical order” possessed by variables in virtue of their respective positions in the alphabet (or arbitrarily assigned to them) is a mere convention and not of genuine logical significance. It seems therefore desirable to consider some alternatives to Quine's definition of closure, since according to his definition the closure of a given formula will be one statement or another, depending upon whether or not one letter of the alphabet is alphabetically prior to a certain other letter. It is interesting that the removal of this minor artificiality also enables us to dispense with *101.

According to Quine, the closure of a formula containing n free variables is obtained by prefixing to it in alphabetical order the n universal quantifiers formed from these variables by enclosing each in a pair of parentheses. (If n = 0 the formula is its own closure and is a “statement” rather than a “matrix.”) Thus the statement ‘(x)(y)(z)(xϵy ▪ yϵz)’ would be the closure of ‘xϵy ▪ yϵz’, but ‘(z)(x)(y)(xϵy ▪ yϵz)’ would not be its closure. Now there is no reason why ‘(z)(x)(y)(xϵy ▪ yϵz)’ or (y)(z)(x)(xϵy ▪ yϵz) and so on, could not just as well be regarded as “the” closure of ‘(xϵy ▪ yϵz’ as ‘(x)(y)(z)(xϵy ▪ yϵz)’. I therefore propose to allow to each formula not merely one closure, but as many closures as can be obtained by permuting in various ways the n prefixed universal quantifiers. In this way alphabetical order becomes irrelevant and no preference is given to one order of prefixed quantifiers in contrast to other orders which seem equally good. This constitutes my first redefinition of closure.
Undecidable sentences generated by semantic paradoxes
Authors: Wang Hao
Published: May 2006

In applying the method of arithmetization to a proof of the completeness of the predicate calculus, Bernays has obtained a result which, when applied to set theories formulated in the predicate calculus, may be stated thus.

1.1. By adding an arithmetic sentence Con(S) (expressing the consistency of a set theory S) as a new axiom to the elementary number theory Zμ (HB II, p. 293), we can prove in the resulting system arithmetic translations of all theorems of S.

It then follows that things definable or expressible in S have images in a simple extension of Zμ, if S is consistent. Since S can be a “strong” system, this fact has interesting consequences. Some of these are discussed by me and some are discussed by Kreisel. Kreisel finds an undecidable sentence of set theory by combining 1.1 and the Cantor diagonal argument. I shall prove below, using similar methods, a few further results, concerned with the notions of truth and designation. The method of numbering sets which I use (see 3.1 below) is different from Kreisel's. While the method used here is formally more elegant, Kreisel's method is much more efficient if we wish actually to calculate the numerical values.
The use of dots as brackets in Church's system
Authors: Turing A. M.
Published: May 2006

Any logical system, if its use is to be carried beyond a rather elementary stage, needs powerful conventions about abbreviations: in particular one usually wants to modify the bracketing so as to make the formulae more readable, and also possibly shorter. The present note has been written in the belief that Church's formulation of the simple theory of types is particularly suitable as a basis for work on that theory, and that it is therefore worth while introducing special conventions which take into account the needs of this particular system. The conventions which I shall describe are ones which I have used a good deal myself, and have always found adequate. I intend to make use of them in forthcoming papers. They may be regarded as an extension of Curry's conventions.

I shall begin with a general discussion of punctuation by means of groups of dots. This general theory is applicable, with some modifications, to Russell's, Quine's, and Curry's bracketing systems as well as to the present one.
Logic based on inclusion and abstraction
Authors: Quine W. V.
Published: May 2006

All notions of mathematical logic, as measured e.g. by Principia mathematica, can be constructed from a basis which embraces variables and just two further primitives: the familiar notions of inclusion and abstraction. Inclusion will be expressed by the usual form of notation “(x⊂y)”, which may be read “x is included in y.” Abstraction will be expressed by the form of notation “x3 …” as with Peano, the blank being filled by any formula (statement or statement form); the whole may be read “the class of all objects x such that ….”

A system of logic based on these primitives will be presented in this paper. The system involves the familiar theory of class types, which, for metamathematical convenience, will be recorded in the system by use of distinctive styles of variables; thus the variables “x”, “y”, and “z”, also with subscripts when further variety is needed, will take individuals as values; the variables “x′”, “y′”, and “z′”, also with subscripts, will take classes of individuals as values; the variables “x″”, “y″”, and “z″”, also with subscripts, will take classes of classes of individuals as values; and so on. The metamathematical notion of term, covering all variables and also all expressions of abstraction, is now describable recursively thus: a variable is a term, and the number of accents which it bears is called its rank; and if terms of equal rank are put for “ζ” and “η” and a variable of rank n is put for “α” in “α3(ζ ⊂ η)”, the result is a term of rank n+1. A formula finally, is any result of putting terms of equal rank for “ζ” and “η” in “(ζ ⊂ η)”.
Formal systems of constructive mathematics
Authors: Löb M. H.
Published: May 2006

In the present paper we investigate in some detail two systems closely related to those contained in [4]. The system K1 of [4] is simplified by eliminating conjunction and disjunction, giving rise to a system Σ whose primitives are two individuals, concatenation, identity, existential and limited universal quantification. Any relation expressible in Σ may be expressed in the form (Eα1)(β)α1(Eα2)…(Eαn)(γ = δ). A further reduction of primitives leads to a system Σμ, which differs from Σ by containing the operator μ (i.e. “the first string, such that” with respect to a certain ordering) in place of the quantifiers. Reasons are given for restricting Myhill's definition of constructive ideas to those expressible in Σμ.

Acquaintance with [4], [5], [6] is assumed. We deviate from [4] by dropping concatenation-signs and parentheses in chain matrices from the official notation, and, furthermore, by using Greek and German letters as metalinguistic variables standing for chain matrices and chains, respectively, while retaining small Roman letters (excluding a, b) for use as variables of the systems.
A theorem about infinite-valued sentential logic
Authors: McNaughton Robert
Published: May 2006

In this paper we shall use a logic with truth values ranging over all the real numbers x such that 0 ≦ x ≦ 1.1 will be “complete truth” and 0 will be “complete falsity.” The primitive sentential connectives are ‘⊃’ and ‘∼’; other connectives are ‘∨’ and ‘·’. Assume that ‘p’ and ‘q’ are sentential variables, whose truth values are respectively x and y. Then

1.1. ‘p ⊃ q’ has the value min(1 − x + y, 1),

1.2. ‘∼p’ has the value 1 − x,

1.3. ‘p∨q’ has the value max(x, y), and

1.4. ‘p·q’ has the value min (x, y).

‘∨’ and ‘·’ can be defined as follows:

It is the purpose of this paper to prove a theorem which will be stated in the next section. The following symbolism and convention will be used throughout the paper:

S is a logical formula.

ν (S) is the value of S.

‘p’, ‘pi1, ’p2, …, ‘q’, are sentential variables.

ν(p) = x and ν(x1) = x1, etc.

ν(S) = σ and ν(S1) = σ1, etc.

If S contains the sentential variables ‘p1’, ‘p2’, …, then we write for S, S(p1, P2, …). Also ν{S(p1, p2, …)) = σ(x1, x2, …).

A logical formula is defined in the usual manner. 1. A sentential variable is a logical formula; 2. if S is a logical formula then ·S is a logical formula; and 3. if S and S′ are logical formulae then (S ⊃ S′) is a logical formula.
The Heine-Borel theorem in extended basic logic
Authors: Fitch Frederic B.
Published: May 2006

A demonstrably consistent theory of real numbers has been outlined by the writer in An extension of basic logic1 (hereafter referred to as EBL). This theory deals with non-negative real numbers, but it could be easily modified to deal with negative real numbers also. It was shown that the theory was adequate for proving a form of the fundamental theorem on least upper bounds and greatest lower bounds. More precisely, the following results were obtained in the terminology of EBL: If С is a class of U-reals and is completely represented in Κ′ and if some U-real is an upper bound of С, then there is a U-real which is a least upper bound of С. If D is a class of (U-reals and is completely represented in Κ′, then there is a U-real which is a greatest lower bound of D.
Finite sequences of classes
Authors: Robinson Raphael M.
Published: May 2006

Consider an axiomatic set theory in which there is a distinction between “sets” and “classes,” only sets being allowable as elements. How can one define a finite sequence of classes? This problem was proposed to me by A. Tarski, and a solution is given in this note. We shall assume the axiom system Σ used by Godei in his study of the continuum hypothesis, and shall use the same notation.1
Symbols, signs, and signals
Authors: Ducasse C. J.
Published: May 2006

In this address, no attempt to deal with any problem of symbolic technique will be made, for even if a problem of this kind should be found that was suitable to the present occasion, I should probably lack sufficient competence in the handling of symbols to deal with it satisfactorily. It occurred to me, however, that it might be interesting to consider the nature of symbols in general, to point out certain characteristics peculiar to the symbols used by logicians and mathematicians, and to say something concerning the relations of these symbols to the knowledge of Nature. Although developments in the science of logic are not dependent on such an inquiry, it yet provides us with a perspective on the nature and importance of that science which we cannot gain so long as we attend only to the problems arising inside its field.

The symbolic relation. Our attempt to gain this perspective may well begin with the trite remark that nothing is intrinsically a symbol, but that anything is a symbol if and only if it symbolizes. Moreover, the relation called symbolizing is not a dyadic but rather a tetradic relation. That is, in order for something A to be a symbol of something B, there must be in addition C, a mind trained in a special way, and D, a certain manner in which that mind is occupied at the time. For although we do say, for instance, that a mark consisting of a little cross is the symbol of addition, the fact is of course that at times when that mark is not present to a mind, it does not symbolize addition or anything else. Moreover, even when it is present to a mind, it does not symbolize addition unless that mind has been trained in a certain manner; for obviously such a mark does not symbolize addition to the mind of a Hottentot or other wholly illiterate person.
A basic logic
Authors: Fitch Frederic B.
Published: May 2006

This paper is concerned with finding a fairly simple system of logic which is “basic” in the sense that every system of logic is definable in it. If a “system”is regarded as being a class of propositions, rather than a class of sentences, then every class of propositions which is a system should be definable in the basic logic. The system of logic proposed in this paper will not be proved to be a basic logic, but strong evidence that it is basic will be given at the end of the paper. Evidence will also be given that the class of propositions which are not provable in the system is not definable in any system of logic. It will be established that the decision problem is unsolvable for the system. Notable characteristics of the system are its lack of negation and universal quantification, and its similarity to systems proposed by Church, Curry, and Rosser.

By a “system” will be meant a class of propositions the membership of which can be specified by ordinary recursive methods, so that if the membership of a given proposition in the class can be established at all, such membership can be established in a finite number of steps. (This is not the same as demanding that a criterion must exist for determining, in a finite number of steps, whether or not some given proposition is a member of the class. Such a demand would require a solution of the decision problem for every system.)
Syntactical and semantical properties of generalized quantifiers
Authors: Yasuhara Mitsuru
Published: May 2006

In the first-order language, quantifiers (∀x) and (∃#) are understood “to say” that “for all elements” and “there is at least one element such that …”, respectively. We are interested in changing the interpretation to “for all elements with fewer than κ exceptions” and “there are at least κ elements such that”, respectively, where κ is a cardinal. We call this the κ-interpretation of the quantifiers.1 The first question which presents itself is “What is the relationship between the κ-interpretation and the λ-interpretation?” For instance, is a formula valid under one interpretation also valid in all other interpretations? In the second section, it will be shown that as far as infinite interpretations, i.e. κ-interpretations for infinite cardinals κ, are concerned, the validity of a formula is preserved. Actually, a more general result is obtained there by model theoretic methods.
Two additions to positive implication
Authors: Prior A. N.
Published: May 2006

Let LIC be the implicational fragment of Dummett's LC, axiomatised by Bull in [1] by adding the axiom (L) CCCpqrCCCqprr to positive implication. The system which Bull in [2] calls OIC, i.e. positive implication plus (0) CCCCpqqrCCCpqrr, is contained in LIC (it is thesis 34 in [1], p. 193); but it does not contain it, as the following matrix (due to Bull)

verifies OIC but not (L) (CCC342CCC4322 = 2). Nor is (L) deducible in OIC supplemented by intuitionist axioms for negation, since the latter are all verified by the above matrix with Cp5 for Np.