bluuebunny/crossref_metadata_2025 huggingface dataset:
Hegel's Theory of Modern Bureaucracy
Authors: Shaw Carl K. Y.
Published: May 2006

I make three contentions. First, Hegel's theory of bureaucracy is as comprehensive as Weber's ideal type of bureaucratic organization. I argue this by making a sociological reformulation of Hegel's model and comparing it with the Weberian paradigm. Second, Hegel adapts the Aristotelian category of practical judgment in characterizing the bureaucratic activity assubsumption. This characterization is contrary to the dominant view that bureaucracy embodies mere instrumental rationality and solves some difficulties in Hegel's political thought. Third, Hegel's conceptualization can contribute to a liberal theory of bureaucracy that apprehends modern political reality more adequately than the skepticism of classical liberals and contemporary libertarians about bureaucratic organization.
Covenants with and without a Sword: Self-Governance Is Possible
Authors: Ostrom Elinor , Walker James , Gardner Roy
Published: May 2006

Contemporary political theory often assumes that individuals cannot make credible commitments where substantial temptations exist to break them unless such commitments are enforced by anexternalagent. One such situation may occur in relation tocommon pool resources, which are natural or man-made resources whose yield is subtractable and whose exclusion is nontrivial (but not necessarily impossible). Examples include fisheries, forests, grazing ranges, irrigation systems, and groundwater basins. Empirical evidence, however, suggests that appropriators in common pool resources develop credible commitments in many cases without relying on external authorities. We present findings from a series of experiments exploring (1) covenants alone (both one-shot and repeated communication opportunities); (2) swords alone (repeated opportunities to sanction each other); and (3) covenants combined with an internal sword (one-shot communication followed by repeated opportunities to sanction each other).
Superior Orders, Nuclear Warfare, and the Dictates of Conscience: The Dilemma of Military Obedience in the Atomic Age
Authors: Lewy Guenter
Published: May 2006

When Francis Gary Powers was asked by the presiding judge of the Soviet military tribunal trying him for espionage whether he had not considered the possibility that his U-2 flight might provoke armed conflict, the captured pilot answered, “The people who sent me should think of these things. My job was to carry out orders. I do not think it was my responsibility to make such decisions.” This article deals with a similar problem, a predicament which to this day, fortunately, has remained hypothetical, but which may become distressingly real at some time in the future. It concerns the unenviable position of the military subordinate commanded to use nuclear weapons, who may be punished today if he disobeys and prosecuted tomorrow if he obeys. The discussion initially evolves around three issues in international law: (1) the validity of the plea of superior orders as a defense in war crimes trials; (2) the question of the legality of using nuclear weapons; and (3) the present status and future of the law of war. That these problem areas are intimately related should become clear as we proceed.

The disregard for humanitarian and moral considerations which has increasingly characterized the conduct of war in the twentieth century, and, more recently, the development of nuclear weapons—the tools of mass extermination par excellence—have led many students of international law to conclude that the laws of war are dead. Grotius' doctrine of the temperamenta belli, requiring belligerents to conduct hostilities with regard for the principles of humanity and chivalry, as well as the many conventions drawn up prior to World War I in order to regulate the use of violence, are said to have become largely obsolete.
Parliamentarism in Western Germany: The Functioning of the Bundestag
Authors: Loewenberg Gerhard
Published: May 2006

Although universal male suffrage as the basis for a representative assembly existed in Germany half a century earlier than in Great Britain, the Reichstag never occupied as important a position in the German constitutional order as the House of Commons did in the British. Neither in its representative function of integrating the community (in Friedrich's terms), nor in its deliberative function as a lawmaking and supervisory body, did the Reichstag ever achieve the significance that would warrant describing the German system of government, either under the Second Empire or the first Republic, as a parliamentary system. The popularly elected Reichstag under Bismarck, in form so advanced for its time, existed under a constitutional system whose “artfully manufactured chaos” permitted, in reality, the exercise of authoritarian government with little parliamentary interference. When, during the latter years of the first World War, the Reichstag demonstrated an increasing ability to call governments to account, this apparent development of a parliamentary system gained a fleeting constitutional recognition during the last days of the Empire and paved the way for the provisions of the Weimar Constitution under which the Government was to be responsible to the Reichstag. Nevertheless, the republican Reichstag never actually fulfilled its constitutional functions, and in difficult times fell victim to the habits of the authoritarian past, manifesting themselves in the autonomy of the army and the bureaucracy, and the irresponsible behavior of the political parties and the President. “Surely the new constitution granted the Reichstag unquestioned leadership in the formation of policy,” a political analyst of the Weimar epoch has written.
The Constitution, the Supreme Court, and Religion
Authors: Carroll William A.
Published: May 2006

The Supreme Court of the United States, whose decisions not only define constitutional law but vitally affect national policy, has long held both an honored and a controversial place in American life. In no area do its decisions bring it more honor or more controversy than in the field of religion; for, as a member of the First Congress under the Constitution said, “the rights of conscience are, in their nature, of peculiar delicacy, and will little bear the gentlest touch of governmental hand. … Thus, the same decision of the Court may be hailed by some as a great landmark in the struggle for religious liberty, and denounced by others as a serious invasion of liberty of conscience. For although it may be pleasant to dream of religion insulated from governmental touch, the dual membership of citizens in the state and in religious bodies insures that conscience and government will touch at some points with inevitable friction, and, to the conscience so touched, it makes little difference whether the governmental hand is that of a local school board, the Congress, or the Supreme Court of the United States.

The Court has recently been attacked as antireligious, or at least as callous to our religious heritage, because of its decisions invalidating a state-prescribed prayer and state-prescribed Bible reading in public schools. The first of these decisions prompted the more excited outcry, but the two, at first singly and then together, have precipitated a renewed debate about the proper constitutional relationship between the state and religion.
Class Struggle and Socialist Justice: The Case of Czechoslovakia
Authors: Ulč Otto
Published: May 2006

This article represents an attempt to assess the degree of legal certainty in post-February 1948 Czechoslovakia and, more specifically, the intervention of political bias in the work of the courts. This conflict will be viewed and evaluated through an analysis of the class struggle, a process most appropriate for testing the interaction between political pressures and judicial integrity. The study of basic laws, published court decisions, and legal literature support the contention that the Communist Party has not given up the discriminatory concept of class justice which subordinates law to politics, and that the absence of legal “definiteness” is a conditio sine qua non of a totalitarian mode of government. It should be added that my first hand experience with the Czechoslovak judicial system is limited to the period 1953–1959. As far as the sixties are concerned (Part VI), it has been necessary to rely exclusively on the published and available sources. Without benefit of “hard evidence,” the conclusions in that section must be regarded as merely interpretative and inferential.
Politics and Pseudopolitics: A Critical Evaluation of Some Behavioral Literature
Authors: Bay Christian
Published: May 2006

A curious state of affairs has developed within the academic discipline that bravely calls itself Political Science—the discipline that in a much-quoted phrase has been called “a device, invented by university teachers, for avoiding that dangerous subject politics, without achieving science.” A growing and now indeed a predominant proportion of leading American political scientists, the behavioralists, have become determined to achieve science. Yet in the process many of them remain open to the charge of strenuously avoiding that dangerous subject, politics.

Consider a recent essay on the behavioral persuasion in politics. The conclusion stresses the purpose of political inquiry: “The Goal is Man.” There is to be a commitment to some humane purpose after all. But what kind of man? A democratic kind of man, a just man, or perhaps a power-seeking man? The answer follows: “These are philosophical questions better left to the philosophers.”
Contested Elections and Voter Turnout in a Local Community: A Problem in Spurious Correlation
Authors: Beyle Thad L.
Published: May 2006

This paper presents an attempt, in a case study, to infer causal relationships between contests for local elective office and voter turnout—an attempt which required, in turn, the use of a recently developed mathematical technique for identifying and eliminating spurious correlations. The method no doubt has wider applications.

The case study involves a small New England town and its annual February town elections over the period 1947–1963. The town was chosen as one of the six affected by the newly established Cape Cod National Seashore. The time period was chosen to cover the interval during which the town was faced with the rapid increase in tourism which transformed it from a declining agricultural town to a service-based town. The policies and methods by which the town dealt with this basic change in its economic structure were of immediate interest, especially in the latter years when the National Park Service became involved in the problems the Cape has faced in this postwar period.
Issue Conflict and Consensus among Party Leaders and Followers
Authors: McClosky Herbert , Hoffmann Paul J. , O'Hara Rosemary
Published: May 2006

American political parties are often regarded as “brokerage” organizations, weak in principle, devoid of ideology, and inclined to differ chiefly over unimportant questions. In contrast to the “ideological” parties of Europe—which supposedly appeal to their followers through sharply defined, coherent, and logically related doctrines—the American parties are thought to fit their convictions to the changing demands of the political contest. According to this view, each set of American party leaders is satisfied to play Tweedledee to the other's Tweedledum.
Confusion, Diffusion, and Innovation
Authors: Eyestone Robert
Published: May 2006

The apparent fact that interactive effects are more common in policy innovations taking a long time to diffuse among the states, contrary to the presumed effects of interaction, suggests the existence of alternate diffusion mechanisms. Some policies diffuse directly from a federal model, while others diffuse among states via a segmented pattern of emulations. The order of state adoption of fair employment practices legislation is compared with the adoption order for three labor policies and two civil rights policies. Fair employment practice, by this test, is identified as a civil rights policy and not as a labor policy. State minimum wage legislation is discussed as a case of federal influence in the diffusion process. A first wave of diffusion was followed by a period of federally inspired court rescission. Federal legislation in 1938 began another wave of diffusion. In a third wave of innovations, states with existing laws amended those laws by emulating the new federal legislation.
The Stability and Reliability of Political Efficacy: Using Path Analysis to Test Alternative Models
Authors: McPherson J. Miller , Welch Susan , Clark Cal
Published: May 2006

The reliability and stability of survey items designed to measure political attitudes are important to the study of political behavior. Several past studies have examined the reliability and stability of items measuring one construct, that of political efficacy. The results of this prior research have been contradictory, in part because of the limitations of the methodologies used. In this article, the authors employ path analysis to examine more closely the stability and reliability of the four SRC items commonly used to measure political efficacy. The American Panel Study (1956–1960), in which efficacy is measured at two points in time, is used as the data base. The authors conclude that two of the four items (NO CARE and NO SAY) seem to measure best what is meant by political efficacy. These two items are more stable and reliable than previously thought, while the other items are relatively unstable and unreliable, and they display systematic differences from each other and from the NO CARE and NO SAY items.
Political Literature and the Response of the Reader: Experimental Studies of Interpretation, Imagery, and Criticism
Authors: Brown Steven R.
Published: May 2006

The influence of political literature has often proved elusive to empirical political science, partly because of the subjectivity of literary response, and partly because of social science methods which are largely incapable of dealing with subjective phenomena in a satisfactory way. A distinction is made between the experimental methods of expression which focus on objective responses, and the methods of impression which focus on subjective responses. Experimental methods are then applied to interpretations of Golding's Lord of the Flies, to the effects on imagery of reading Mazlish's In Search of Nixon, and to reactions to Burdick's The Ninth Wave. An illustration is also given of the experimental study of literary response in the single case.
The Georges' Wilson Reexamined: An Essay on Psychobiography
Authors: Tucker Robert C.
Published: May 2006

Psychobiography interprets a life-course in terms of a consciously thought-out interpretation of the subject's personality. There are criteria for judging the relative merit of differing lines of interpretation. The Georges' Woodrow Wilson and Colonel House, rightly recognized as a psychobiographical classic, proceeds from Harold Lasswell's formula for “political man” as one who seeks power to overcome a low self-estimate. The formula is in some respects questionable. The Georges' generally effective application of it falls short of full success. An alternative interpretation, based on the view that Wilson's life exemplified the neurotic search for glory as described by Karen Horney, is explored. The two different lines of interpretation are compared with respect to what Alexander George has called the “self-defeating pattern” in Wilson's career as a leader.
The Politics of Property Rights
Authors: Firmin-Sellers Kathryn
Published: May 2006

The study of land tenure polarizes the field of development. Neoclassical scholars lobby for a move toward private property rights, while other economists and historians defend the maintenance of customary land tenure. I argue that the development scholars' focus on the structure of property rights obscures a more fundamental problem of land reform—that of enforcement. Property rights will not inspire individual investment and economic growth unless political institutions give the ruler of a local community or nation-state sufficient coercive authority to silence those who advocate an alternative, more distributionally favorable property rights system. At the same time, political institutions must force the ruler to establish a credible commitment to that property rights system. I illustrate this theoretical argument through an analysis of property rights institutions in Akyem Abuakwa, a traditional state in colonial Ghana.
Nature or Nurture? Sources of Firm Preference for National Health Reform
Authors: Martin Cathie Jo
Published: May 2006

I shall explore the process by which firms develop their political preferences, using the case of national health reform. Although rising health costs have heavily burdened many companies, I argue that economic interests alone are unable to account for the variation in firm response to the national reform effort. Rather, institutional factors, shown elsewhere to shape government decision making, also influence corporate preferences. These are (1) the institutionalization of private policy expertise within the firm, (2) firm participation in policy groups, and (3) policy legacies. These findings challenge conventional views of business political mobilization that suggest largely autonomous agents acting on the basis of easily recognized self-interests. Preference formation and corporate mobilization transpire in collective settings as a new stratum of corporate policy managers search for solutions to social problems. The primacy of economic concerns is very real. But institutional analysis explains how these economic concerns are interpreted and acted upon.
“The Slow Boring of Hard Boards”: Methodical Thinking and the Work of Politics
Authors: Dietz Mary G.
Published: May 2006

From the perspective of quite different theoretical traditions, Simone Weil and Hannah Arendt present nearly identical and equally powerful critiques of technological determinism in modernity. Yet unlike Arendt, Weil develops a concept of work that draws a distinction between technology and instrumental action as “methodical thinking.” As a result, Weil's theory of action embraces something that Arendt's theatrical politics rejects—a concept of liberatory instrumentality, or purposeful performance. I shall reassess some of the inadequacies of Arendt's concept of work and develop Simone Weil's concept of methodical thinking in order to argue for a more neighborly affinity between work:interaction and purposeful:theatrical performance than Arendtian public realm theory, for all its power, currently allows. If such an affinity is possible, then public realm theory might be more adequately equipped to deliver on what I take to be its promise as an emancipatory project in late modernity.
The Partisan Basis of Procedural Choice: Allocating Parliamentary Rights in the House, 1789–1990
Authors: Binder Sarah A.
Published: May 2006

Conventional accounts of the institutional development of Congress suggest that expansion of the size and workload of the House led members to distribute parliamentary rights narrowly: Majority party leaders accrued strong procedural powers while minority parties lost many of their parliamentary rights. I offer an alternative, partisan basis of procedural choice. Using an original data set of changes in House rules, I present a statistical model to assess the influence of partisan and nonpartisan factors on changes in minority procedural rights in the House between 1789 and 1990. I find that short-term partisan goals—constrained by inherited rules—shape both the creation and suppression of rights for partisan and political minorities. Collective institutional concerns and longer-term calculations about future parliamentary needs have little impact on changes in minority rights. The findings have important theoretical implications for explaining both the development of Congress and the nature of institutional change more generally.
Culture and Preferences in the International Cooperation Two-Step
Authors: Legro Jeffrey W.
Published: May 2006

Rational choice analyses of international cooperation have slighted the effect of state preference formation and the influence of cultural forces in that process. This article addresses these gaps by developing an explanation that specifies howorganizational culturesof bureaucracies shape state aims and international outcomes. This approach is evaluated in a set of least likely cases—decisions on the use of force in war—where the conventional wisdom expects external material, not internal cultural, concerns to dominate. Before World War II, countries agreed to limit the use of three types of warfare, but during that conflict mutual restraint was maintained in only one. I show how this variation is best understood as a product of state preference dynamics, shaped largely by the collective beliefs and customs of military services. This result suggests ways to rethink the use of the preferences-interaction model and the role of cultural factors in that framework.
Dynamic Representation
Authors: Stimson James A. , Mackuen Michael B. , Erikson Robert S.
Published: May 2006

If public opinion changes and then public policy responds, this is dynamic representation. Public opinion is the global policy preference of the American electorate. Policy is a diverse set of acts of elected and unelected officials. Two mechanisms of policy responsiveness are (1) elections change the government's political composition, which is then reflected in new policy and (2) policymakers calculate future (mainly electoral) implications of current public views and act accordingly (rational anticipation). We develop multiple indicators of policy activity for the House, Senate, presidency, and Supreme Court, then model policy liberalism as a joint function of the two mechanisms. For each institution separately, and also in a global analysis of “government as a whole,” we find that policy responds dynamically to public opinion change. This responsiveness varies by institution, both in level and in mechanism, as would be expected from constitutional design.
The Advantage of Being Moderately Cooperative
Authors: Morikawa Tomonori , Orbell John M. , Runde Audun S.
Published: May 2006

We use computer simulation to identify a process by which cooperation evolves without iteration, and evolves better in large than in small societies. It is based on an empirically supported heuristic for deciding whether to enter noniterated prisoner's dilemma games, namely,Expect others to have the same dispositions as yourself. Players are assigned a probability of cooperating that also defines their expectations about others' behavior and thus their willingness to play. The carrying capacity of the ecology is 10,000. Players multiply by 2 if their aggregate payoff in a given round (1) places them among the more successful 5,000 and (2) is more than zero. We find that the most adaptive disposition is toward the mean of the population. That is where individuals have the optimal mix of consummated plays with more cooperative players and unconsummated plays with less cooperative ones. When encounters occur by proximity, fortuitous clusters toward the cooperative tail will grow and dominate the society. Such clusters are more likely in large societies.
Party Cleavages and Welfare Effort in the American States
Authors: Brown Robert D.
Published: May 2006

Attempts to determine the impact of party control on state welfare policy have produced mixed and inconclusive results, in part due to our inability to account for variations in the state partisan environments. I used CBS/New York Times surveys combined over the period 1976–88 to offer a detailed examination of the state party systems, resulting in a description of the dominant social group partisan cleavage in each state. This information is then used to examine the impact of party control on state welfare benefits. The findings show that the coalitional bases of the parties vary in important ways, both within and across the states. These differences in the state party systems have an important influence on the relationship between party control and state welfare effort. Specifically, party control has a significantly greater impact in states where partisan divisions reflect class-based New Deal-type coalitions. When examined in the context of state partisan environments, party control has a much greater impact on state welfare effort than has been suggested by previous studies.
On the semantic non-completeness of certain Lewis calculi
Authors: Halldén Sören
Published: May 2006

I intend to show that for S1, S2, and S3 the class of true formulas cannot coincide with the class of theorems. This is to hold irrespective of the meaning assigned to “◊”. when only “∼”, “▪”, and the variables are interpreted in the customary manner.

The idea of the proof is extremely simple and can be illustrated by the following argument concerning S3. The formula ~(◊(p▪~p)⥽▪p▪~p) ∨ (◊(q▪~q)⥽▪q▪~q) is a theorem of S3. Suppose now that all S3-theorems are true. Then either ~(◊(p▪~p)⥽▪p▪~p) is true (for every p) or (◊(q▪~q)⥽▪q▪~q) is true (for every q). But none of these formulas is an S3-theorem. Then some true S3-formula is not an S3-theorem. Hence, if all S3-theorems are true, some true S3-formula is not an S3-theorem. Then the class of S3-theorems cannot be identical with the class of true S3-formulas.
Postulates for the calculus of binary relations
Authors: McKinsey J. C. C.
Published: May 2006

The theory of relations was discussed, along with the theory of classes, by Peirce and Schröder. While the calculus of classes has subsequently been presented (by Couturat, and by Huntington) as an abstract mathematical system, no similar formulation has been published of the calculus of relations. Professor Alfred Tarski has proposed to me, the problem of developing a similar formulation for the theory of relations. In this paper I present a set of postulates for the calculus of relations.

The postulates have been chosen so as to enable us to prove Theorem A, below, which asserts a kind of completeness of the system. A set of postulates is called semi-categorical, if every two realizations which involve the same number of elements are isomorphic. From Theorem A one can easily prove that my postulates are semi-categorical, if one assumes the following theorem from Mengenlehre: if α and β are cardinal numbers such that , then α=β. This theorem has not been proved, however, except on the assumption of the axiom of choice and the generalized continuum hypothesis, and is not assumed in the present paper.

It should be pointed out, that the sort of completeness I have chosen is not the only sort, or even necessarily the most interesting sort, of completeness which a set of postulates for the calculus of relations could possess. For example, the question arises, whether it would be possible to find a set of postulates from which all true equations (involving free variables and the operations used by Schröder) could be derived, and which was the weakest possible such set. The present work should therefore be regarded only as a first step in the investigation of the axiomatization of the calculus of relations.
Proofs of non-deducibility in intuitionistic functional calculus
Authors: Mostowski Andkzej
Published: May 2006

It has been proved by S. C. Kleene and David Nelson that the formula

is intuitionistically non-deducible, i.e., non-deducible within the intuitionistic functional calculus.

The aim of this note is to outline a general method which permits us to establish the intuitionistic non-deducibility of many formulas and in particular of the formula (1).
The identity of individuals in a strict functional calculus of second order
Authors: Barcan Ruth C.
Published: May 2006

In previous papers we developed two functional calculi of first order based on strict implication which we called S2 and S4. In the present paper, these systems will be extended to include a functional calculus of second order with the purpose of introducing the relation of identity of individuals.

Primitive symbols. ̂ {the abstraction operator, the blank space to be replaced by an appropriate variable}.
A system of axiomatic set theory—Part II
Authors: Bernays Paul
Published: May 2006

For the formulation of the remaining axioms we need the notions of a function and of a one-to-one correspondence.

We define a function to be a class of pairs in which different elements always have different first members; or, in other words, a class F of pairs such that, to every element a of its domain there is a unique element b of its converse domain determined by the condition 〈a, b〉ηF. We shall call the set b so determined the value of F for a, and denote it (following the mathematical usage) by F(a).

A set which represents a function—i.e., a set of pairs in which different elements always have different first members—will be called a functional set.

If b is the value of the function F for a, we shall say that F assigns the set b to the set a; and if a functional set f represents F, we shall say also that f assigns the set b to the set a.

A class of pairs will be called a one-to-one correspondence if both it and its converse class are functions. We shall say that there exists a one-to-one correspondence between the classes A and B (or of A to B) if A and B are domain and converse domain of a one-to-one correspondence. Likewise we shall say that there exists a one-to-one correspondence between the sets a and b (or of a to b) if a and b respectively represent the domain and the converse domain of a one-to-one correspondence. In the same fashion we speak of a one-to-one correspondence between a class and a set, or a set and a class.
A system of axiomatic set theory—Part VI
Authors: Bernays Paul
Published: May 2006

Comparability of classes. Till now we tried to get along without the axioms Vc and Vd. We found that this is possible in number theory and analysis as well as in general set theory, even keeping in the main to the usual way of procedure.

For the considerations of the present section application of the axioms Vc, Vd is essential. Our axiomatic basis here consists of the axioms I—III, V*, Vc, and Vd. From V*, as we know, Va and Vb are derivable. We here take axiom V* in order to separate the arguments requiring the axiom of choice from the others. Instead of the two axioms V* and Vc, as was observed in Part II, V** may be taken as well.
On direct products of theories
Authors: Mostowski Andrzej
Published: May 2006

This paper deals with the notion of direct product in the theory of decision problems.

Elementary mathematical theories are always concerned with certain functions defined in a set I (called the universe of discourse of the theory) and certain relations with the common domain I. The notions of functions and relations are known to be reducible to each other. To avoid duplication of definitions and proofs we shall eliminate the former notion in favor of the latter and consider only theories in which all the primitive terms are of the type of relations (with an arbitrary number of arguments).

It is easy to define for relations the notion of a direct product in the way which is usual in abstract algebra. We are led to this definition in a very natural way when we reflect that relations are but a particular case of functions, and the direct product of an arbitrary number of functions is defined in algebra.

A relation which is representable as a product of an arbitrary number of pairwise identical relations is called the power-relation, and the relations which occur as factors are called the base-relations.

The content of the present paper can now be characterized more precisely as follows.

We shall discuss a theory of which the primitive notions are representable as powers of certain base-relations, and shall try to reduce all the problems concerning this theory (in particular the decision problem) to problems concerning the theory of the base-relations. It will be seen that this reduction is in fact possible, and that several particular cases of the decision problem, the solutions of which are known from the literature, can be included in the general scheme established in the present paper.
A minimum calculus for logic
Authors: Fitch Frederic B.
Published: May 2006

A logical calculus will be presented which not only is a formulation of a “basic logic” in the sense of the writer's previous papers, but which has the additional property that no weaker calculus can be a formulation of a basic logic. A sort of minimum logical calculus is thus attained, which has nothing superfluous about it for achieving the purpose for which it is designed.

In the case of some logical calculi the question can arise as to whether certain of the postulates are really logically valid and necessary. Sometimes a test is available, such as the truth-table test, enabling us to distinguish between logically valid sentences and others, but often no such test is available, especially where quantifiers are involved. Is or is not the axiom of infinity, for example, to be regarded as logically valid? Or is the principle of double negation really acceptable, even though it satisfies the truth-table test?
A system of axiomatic set theory. Part IV. General set theory
Authors: Bernays Paul
Published: May 2006

Our task in the treatment of general set theory will be to give a survey for the purpose of characterizing the different stages and the principal theorems with respect to their axiomatic requirements from the point of view of our system of axioms. The delimitation of “general set theory” which we have in view differs from that of Fraenkel's general set theory, and also from that of “standard logic” as understood by most logicians. It is adapted rather to the tendency of von Neumann's system of set theory—the von Neumann system having been the first in which the possibility appeared of separating the assumptions which are required for the conceptual formations from those which lead to the Cantor hierarchy of powers. Thus our intention is to obtain general set theory without use of the axioms V d, V c, VI.

It will also be desirable to separate those proofs which can be made without the axiom of choice, and in doing this we shall have to use the axiom V*—i.e., the theorem of replacement taken as an axiom. From V*, as we saw in §4, we can immediately derive V a and V b as theorems, and also the theorem that a function whose domain is represented by a set is itself represented by a functional set; and on the other hand V* was found to be derivable from V a and V b in combination with the axiom of choice. (These statements on deducibility are of course all on the basis of the axioms I–III.)
On existence conditions for elements and classes
Authors: Quine W. V.
Published: May 2006

In the middle of myMathematical logicI defined a certain class of formulae as “stratified,” and conjectured that exclusion from this class is a feature “shared, presumably, by all the untenable statements(p. 157). This ushered in a set of axioms of class-membership which Rosser has since shown to be inconsistent. Accordingly, inElement and numberI dropped the principle*200, in which had been assembled axioms to the effect, roughly, that “stratified functions of elements are elements.” In lieu of*200 I set forth alternatives in which no appeal is made to stratification. The system ofMathematical logicexclusive of*200 carries over as an unchanging framework; and this framework admits, we know, of a simple consistency proof. My concern in the present paper is to draw attention to certain relationships between this framework and earlier theories.
The decision problem for some classes of sentences without quantifiers
Authors: McKinsey J. C. C.
Published: May 2006

In this paper we shall be concerned with questions regarding decision problems for certain classes of sentences (without quantifiers) of various kinds of algebra. In the first section we shall establish a result of a general nature, which enables one, in a number of cases, to reduce a decision problem of the type considered to a somewhat simpler problem. In the second section we formulate a rather broad sufficient condition for the existence of a decision method for sentences without quantifiers; and in the last section we show that this condition holds of lattices.
Weak simplest normal truth functions
Authors: Nelson Raymond J.
Published: May 2006

In certain applications of truth-functional logic it is of interest to determine classes of formulas equivalent to a given formula Φ under the hypothesis that certain conjunctions of letters of Φ are always false. Of especial interest is the case where the class to be determined is that of simplest normal truth functions. The problem of giving a calculation procedure for this question is evidently a more general form of the simplification problem as considered in [1] and [2]. The purpose of this note is to indicate how the procedure of [1] applies.

Let Π, Π′, Π″, … be fundamental formulas, in the sense of [2], such that every literal of Π, etc., is a literal of Φ and such that Π, Π′, Π″, … are all false for all values of the constituent literals. Then we say that Ψ is a weak simplest disjunctive normal equivalent of Φ if and only if Ψ ≡ Φ, under the hypothesis, and there is no Ψ′ such that Ψ′ is simpler than Ψ and Ψ′ ≡ Φ, under the hypothesis. Similarly, under exactly the same hypothesis, we say that X is a weak simplest conjunctive normal equivalent of Φ. When the class of always false fundamental formulas is empty, as in [1] and [2], we may speak of strong simplest forms and hence of the more general problem of strong simplification.
The þ-function in λ-K-conversion
Authors: Turing A. M.
Published: May 2006

In the theory of conversion it is important to have a formally defined function which assigns to any positive integer n the least integer not less than n which has a given property. The definition of such a formula is somewhat involved: I propose to give the corresponding formula in λ-K-conversion, which will (naturally) be much simpler. I shall in fact find a formula þ such that if T be a formula for which T(n) is convertible to a formula representing a natural number, whenever n represents a natural number, then þ(T, r) is convertible to the formula q representing the least natural number q, not less than r, for which T(q) conv 0.2 The method depends on finding a formula Θ with the property that Θ conv λu·u(Θ(u)), and consequently if M→Θ(V) then M conv V(M). A formula with this property is,

The formula þ will have the required property if þ(T, r) conv r when T(r) conv 0, and þ(T, r) conv þ(T, S(r)) otherwise. These conditions will be satisfied if þ(T, r) conv T(r, λx·þ(T, S(r)), r), i.e. if þ conv {λptr·t(r, λx·p(t, S(r)), r)}(þ). We therefore put,

This enables us to define also a formula,

such that (T, n) is convertible to the formula representing the nth positive integer q for which T(q) conv 0.
Über eine Art von Unvollständigkeit des Prädikatenkalküls der ersten Stufe
Authors: Hasenjaeger Gisbert
Published: May 2006

Nach Gödel ist der Prädikatenkalkül der ersten Stufe vollständig in dem Sinne, daβ alle identischen Ausdrücke dieses Kalküls ableitbar sind. Für den einstelligen Prädikatenkalkül gilt darüber hinaus, daβ zwei Ausdrücke deduktionsgleich (HB I, p. 149) sind, wenn sie für dieselben Individuenbereiche identisch bzw. nicht identisch sind. Solche Ausdrücke mögen identitätsverbunden heiβen. Daβ umgekehrt deduktionsgleiche Ausdrücke identitätsverbunden sind, gilt auch für den vollen Prädikatenkalkül. Dagegen gibt es dort Ausdrücke, die identitätsverbunden, aber nicht deduktionsgleich sind. Solche Ausdrücke sind die in HB I, p. 123, 124 angegebenen und , die beide genau im Endlichen identisch, also identitätsverbunden sind. Die Frage der gegenseitigen Ableitbarkeit bleibt dort allerdings noch unentschieden. Ich werde im Folgenden die gegenseitige Nichtableitbarkeit von und im Prädikatenkalkül der ersten Stufe beweisen. Daraus folgt dann, daβ für den vollen Prädikatenkalkül die Bernayssche Deduktionsgleichheit nicht mit der Identitätsverbundenheit zusammenfällt. Es sei erwähnt, daβ die Identitätsverbundenheit sich zwar in der “Protosyntax” (d.h. metasprachliches “Alle” und “Es gibt” beschränkt auf Zeichenreihen) definieren läβt. Trotzdem kann man nicht von einer verschärften Vollständigkeit des Prädikatenkalküls sprechen; denn es läβt sich zeigen, daβ die Identitätsverbundenheit keine Beziehung vom Typ der Beweisbarkeit ist.
Modalities and Quantification
Authors: Carnap Rudolf
Published: May 2006

The purpose of this article is to give a survey of some results I have found in investigations concerning logical modalities. The results refer: (1) to semantical systems, i.e., symbolic language systems for which semantical rules of interpretation are laid down; (2) to corresponding calculi, i.e., syntactical systems with primitive sentences and a rule of inference; (3) to relations between a semantical system and the corresponding calculus.

The semantical systems to be dealt with are the following: pro positional logic (PL), functional logic (FL), and the corresponding modal systems, viz. modal propositional logic (MPL) and modal functional logic (MFL).
A partial model for Quine's “New foundations”
Authors: Beneš Václav Edvard
Published: May 2006

1. In this paper we construct a model for part of the system NF of [4]. Specifically, we define a relation R of natural numbers such that the R-relativiseds of all the axioms except P9 of Hailperin's finitization [2] of NF become theorems of say Zermelo set theory. We start with an informal explanation of the model.

2. Scrutiny of P1-P8 of [2] suggests that a model for these axioms might be constructed by so to speak starting with a universe that contained a “universe set” and a “cardinal 1”, and passing to its closure under the operations implicit in P1-P7, viz., the Boolean, the domain, the direct product, the converse, and the mixtures of product and inverse operations represented by P3 and P4. To obtain such closure we must find a way of representing the operations that involve ordered pairs and triples.

We take as universe of the model the set of natural numbers ω; we let 0 represent the “universe set” and 1 represent “cardinal 1”. Then, in order to be able to refer in the model to the unordered pair of two sets, we determine all representatives of unordered pairs in advance by assigning them the even numbers in unique fashion (see d3 and d25); we can now define the operations that involve ordered pairs and triples, and obtain closure under them using the odd numbers. It remains to weed out, as in d26, the unnecessary sets so as to satisfy the axiom of extensionality.
Improved decision procedures for Lewis's calculus S4 and von Wright's calculus M
Authors: Anderson Alan Ross
Published: May 2006

The decision procedures to be described in this paper constitute simplifications of methods previously developed by G. H. von Wright. The decision problems for both the systems under consideration have already been solved, but the known solutions are hopelessly impractical. Our methods for S4 and M, while not “practical” in the sense that they can be applied quickly and easily to any formula, do constitute a vast improvement over any other known methods. It appears, for example, that our methods (with the aid of very little ingenuity) will yield decisions readily when applied to modal functions of degree two (or less) with three (or fewer) distinct propositional variables.
Report on some investigations concerning the consistency of the axiom of reducibility
Authors: Myhill John
Published: May 2006

The purpose of this paper is to construct a non-finitary system of logic S, based on the theory of types, in which classical quantification theory holds without restriction and the axiom of reducibility holds with such slight restriction as is perhaps unlikely to interfere with the construction of classical mathematics. The system will be shown to be consistent.

For purposes of orientation, a rough description of the ontology of the system will first be given. The ‘individuals’ are expressions built up in the following way: ‘0’ is an individual, and if ϕ and ψ are individuals, so is ˹*ϕψ˺. The usual apparatus of truth functional connectives and quantifiers is employed, and one primitive four place predicate ‘S’. ˹Sϕψχω˺ says that ϕ is the result of writing ψ for all occurrences of χ in ω, where ϕ, ψ, χ and ω may be formulae, individuals, or members of a wider category called ‘expressions’ which includes individuals, formulae, and other things as well. (At first sight this looks like a confusion of use and mention, but the formation rules and rules of inference are so phrased that no ambi
guity arises.)

The individuals are divided into types concentrically, so that type 0 has them all as members and type n includes type m for m > n. There is no highest type, but we shall find it convenient from the point of view of exposition to construct an infinity of ‘auxiliary’ systems Q(k), restricted to types ≦ k, before presenting the system S.
On the use of dots as brackets in logical expressions
Authors: Curry H. B.
Published: May 2006

The Peanese convention for the use of dots as brackets has the disadvantage that it gives only an awkward method for representing chains of indefinite length, such as the compound implication

Such chains occur frequently in logical investigations of a metatheoretic nature, and it is convenient to have a systematic method of abbreviating them. The most obvious method of doing this would be to leave the parentheses out entirely, and to understand that in such cases the implication sign or other operation appearing on the extreme left is the most inclusive; but this method, which has been followed by Quine, is at variance with our ordinary algebraic usage, in which we write a − b + c − d for ((a − b) + c) − d, and consequently leads to confusion. It is desirable to have a modification of the Peanese convention which gives a simple method of representing such chain implications, and at the same time avoids this difficulty.

Such a modification is easily obtained by generalizing somewhat a procedure of Church. The latter author uses only a single dot, which he writes on the right of an operator to signify a bracket extending from that point to the end of the formula (or parenthesized expression). If dots are used only on the right of operations this is all that can be desired. But the essential idea of this device can be extended to the case where dots are used also on the left, as follows: let us suppose that a group of dots on the right of an operation or prefix denotes the beginning of a bracket which extends to the right until it meets a group with an equal or larger number of dots on the left of an operation; and that the scope of a group of dots on the left of an operation shall extend to the left until it reaches a larger group of dots on the right of some operation.
Emch's calculus and strict implication
Authors: Lewis C. I.
Published: May 2006

In a previous number of this Journal, Dr. Arnold F. Emch argues that the mathematical properties of the system of strict implication preclude the interpretation of p⊰q as synonymous with “q is deducible from p” and of ◊(pq), or p o q, as “p and q are consistent.” He proposes a new calculus of propositions in which the primitive ideas of the system of strict implication are retained but an additional idea, “logical consistency,” Op, is introduced, and two new relations, “logical implication,” p∾q, and “logical equivalence,” p = q, are denned. He believes that the properties of this new system are in accord with the facts about deducibility, consistency, and independence of propositions where those of p⊰q and ◊(pq) fail of such accord.

Not all of the objections which Dr. Emch advances against strict implication are given due consideration in what follows. Concerning one especially important point, something will be said at the end of this paper. For the rest, discussion will here be limited to certain formal properties of the two systems, and certain consequences for the interpretation of them.

For brevity, the system of strict implication will be referred to, in what follows, as the “system S,” or merely as S; and Dr. Emch's calculus as the “system L,” or as L.