bluuebunny/crossref_metadata_2025 huggingface dataset:
Republican Schoolmaster: The U.S. Supreme Court, Public Opinion, and Abortion
Authors: Franklin Charles H. , Kosaki Liane C.
Published: May 2006

The United States Supreme Court has a historical role as a “republican schoolmaster,” inculcating virtues in the citizenry. The role as teacher to the republic also serves the interests of the Court. As the “weakest branch,” the Supreme Court needs public support if its decisions are to be effective. We investigate the Court's ability to win popular support for its rulings, specifically in the case of Roe v. Wade. The analysis shows that the Court's decision did affect public attitudes but not as previous work would predict. While support for abortions to protect health increased as a result of the Court's decision, the public became more polarized over “discretionary” abortions. The puzzle is what process can account for these disparate reactions. We develop a theory resting on interpersonal influences to explain these results, arguing that the social interpretation of events drives the differing outcomes. This theory is then tested against a purely psychological alternative. The closing discussion considers how these results can be extended to the general problem of public decisions and popular responses, including presidential actions and the influence of the media.
The 1928–1936 Partisan Realignment: The Case for the Conversion Hypothesis
Authors: Erikson Robert S. , Tedin Kent L.
Published: May 2006

An unresolved question concerning the New Deal realignment is the extent to which the Democratic surge in the vote resulted from either the conversion of former Republicans or the mobilization of newly active voters. Analyzing survey data from the Literary Digest straw polls and from early Gallup polls, we find evidence supporting the conversion hypothesis. New voters in 1928, 1932 and 1936 were only slightly more Democratic in their voting behavior than were established voters. Between 1924 and 1936, the vote among established voters was extremely volatile, largely accounting for the Democratic gains. After 1936, however, vote shifts became minimal and party identification had become highly consistent with presidential voting, suggesting a crystallization of the New Deal realignment by the late 1930s rather than a gradual evolution due to generational replacement.
The Return to the State: Critiques
Authors: Nordlinger Eric A. , Lowi Theodore J. , Fabbrini Sergio
Published: May 2006

This symposium features three critiques of Gabriel Almonds argument—by Eric A. Nordlinger of Brown University, Theodore J. Lowi of Cornell University, and Sergio Fabbrini of the University of Trento.
Measuring Policy Change in the U.S. Supreme Court
Authors: Baum Lawrence
Published: May 2006

Measuring the U.S. Supreme Court's policy changes is complicated by change in the content of the cases that come before the Court. I adapt from earlier scholarship a method to correct for changes in case content and use this method to measure change in the Court's support for civil liberties in the 1946–85 terms. Analysis based on this method indicates that because of changes in case content, the average difficulty of reaching a pro-civil liberties result varied during that period. With corrections for case difficulty, the Warren Court of the 1950s appears to have been more conservative, and the Burger Court more liberal, than patterns of case outcomes themselves suggest. This method, while imperfect, has utility for the measurement of policy change in the Supreme Court and other institutions and thus can serve as a building block in analyses of the processes and determinants of change.
Crisis Bargaining, Escalation, and MAD
Authors: Powell Robert
Published: May 2006

Although incomplete information is recognized to be an essential feature of crises, game-theoretic formulations have not generally modeled this explicitly. This paper models a mutually assured destruction (MAD) crisis as a game of sequential bargaining with incomplete information, sufficiently simple that its equibria may be found. These provide better game-theoretic foundations for the notions of resolve and critical risk and their role in crises and also make it possible to compare the bargaining dynamics of this model with those of descriptively richer, but incompletely specified models, revealing several inconsistencies: several analyses of MAD conclude that the state with the greatest resolve in this contest of resolve will prevail. Many models based on critical risks suggest that a state is less likely to escalate, the greater its adversary's resolve. In our model, however, the state with the weakest resolve sometimes prevails, and some states prove more likely to escalate if their adversaries' resolve is greater.
Stacking the Deck: Bureaucratic Missions and Policy Design
Authors: Bendor Jonathan , Taylor Serge , Van Gaalen Roland
Published: May 2006

Empirical studies suggest that mission-oriented bureaucrats bias their design of program alternatives to increase the odds that a superior will choose the kind of program the officials want. However, political executives may anticipate this manipulation and try to reassert control. These struggles are examined in three models. In Model 1 a senior bureaucrat is interested only in missions; the bureaucrat's political superior controls him or her by rejecting inferior proposals and entertaining new options from other policy specialists. Model 2 is a principal-agent analysis. Here the official is interested only in budgets; the official's superior reduces search bias by creating an ex ante incentive scheme. In Model 3 the bureaucrat cares about both budgets and programs; the superior uses both his or her final review authority and ex ante incentives to reduce agenda manipulation. The models' contrasting implications for the political control of bureaucracy are examined.
Why are Congressional Committees Powerful?
Authors: Krehbiel Keith , Shepsle Kenneth A. , Weingast Barry R.
Published: May 2006

In “The Institutional Foundations of Committee Power” (this Review, March 1987) Kenneth Shepsle and Barry Weingast made the case that congressional committees are powerful not so much because of members' deference to them as because of the committees' ex post veto, a potential negative committees might deliver, say, at the conference committee stage of lawmaking. But Keith Krehbiel argues that congressional committees have, in fact, never possessed an uncircumventable ex post veto and are very much constrained by their parent chambers. In response, Shepsle and Weingast defend their model of the foundations of committee power.
Concrete Theory: An Emerging Political Method
Authors: Lane Ruth
Published: May 2006

Concrete theory is defined by a cluster of attributes—emphasis on governmental and other political elites, on strategic decision-making processes freed from narrow notions of economic rationality, and on a concern with the environment and institutions within which choice occurs. The approach has been observed recently in all research-oriented subfields within political science. Eight exemplars are discussed. Concrete theory demonstrates a novel combination of strong interest in empirical political processes, formalized through models that emphasize logical structure and depth explanation. Its effect is to bridge the gap between behavioral and institutional approaches.
Feminism and Liberal Theory
Authors: Sinopoli Richard C. , Hirschmann Nancy J.
Published: May 2006

In her article on “Freedom, Recognition, and Obligation: A Feminist Approach to Political Theory,” published in the December 1989 issue of this Review, Nancy J. Hirschmann argued that a feminist methodology could breathe new and useful life into liberal political theory, relieving it of its structural sexism. In this Controversy, Richard C. Sinopoli takes issue with key claims made by Hirschmann. In turn, Hirschmann elaborates her case.
Defense Expenditures, Economic Growth, and the “Peace Dividend”
Authors: Mintz Alex , Huang Chi
Published: May 2006

Recent developments in Eastern Europe have created expectations of a “peace dividend” associated with reduced levels of U.S. defense expenditures. We present and empirically estimate a two-equation model for assessing the direct and indirect, immediate and delayed effects of changes in defense spending on economic growth in the United States.
The Public Hearing as an Effective Citizen Participation Mechanism: A Case Study of the General Revenue Sharing Program
Authors: Cole Richard L. , Caputo David A.
Published: May 2006

Students of citizen participation in public affairs disagree as to the effectiveness of such citizen involvement. Using the General Revenue Sharing program as a case study and applying techniques of both cross-sectional and longitudinal analysis, this article examines the effectiveness of one form of citizen participation, the public hearing. It is found that in the revenue-sharing program, the public hearing did have an immediate, but only short-term, impact on levels of public interest and citizen involvement. Evidence to support some short-term and some long-term effects on reported expenditure decisions is presented; however, these impacts generally are found to be inconsequential and not statistically significant. It is concluded that, as a form of citizen participation, the public hearing—at least as demonstrated in the General Revenue Sharing program—has not had much of an impact on citizen behavior or policy choices.
The Just and the Advantageous in Thucydides: The Case of the Mytilenaian Debate
Authors: Orwin Clifford
Published: May 2006

As no passage in Thucydides is more important, so none is more dramatic than the Mytilenaian Debate. Having resolved to punish harshly a rebel city, the Athenians repent and reconsider. Exhorted by Kleon to maintain their original decision and by Diototos to abandon it, the Athenians must scrutinize the relationship between justice and expediency. Diodotos, who professes to argue from interest only, narrowly prevails in the debate. There is, however, much more to his speech than meets the eye. For it proves misleading to say that he is arguing merely from interest—and then, on a deeper level, to say that he is arguing from justice. In fact no passage in Thucydides, including the Melian Dialogue, raises starker questions about the status of political justice.
Measuring Political Violence and Land Inequality in Central America
Authors: Brockett Charles D.
Published: May 2006

The value of cross-national quantitative studies of the relationship between mass political violence and land inequality is challenged along three lines. First, gross and systematic errors in the political violence data of theWorld Handbook of Political and Social Indicators(the usual data source for empirical studies) render them worthless for Central America at least and probably much of the Third World as well. Second, conceptualizations of land inequality have been too simplistic to be of much theoretical value. Third, the temporal nature of this relationship has been inadequately considered. Responding to such deficiencies, I elaborate a broader understanding of land inequality and provide a fuller discussion of the temporal nature of its relationship to political violence. Throughout, the five nations of Central America are utilized for appropriate case material.
POLI: An Expert System Model of U.S. Foreign Policy Belief Systems
Authors: Taber Charles S.
Published: May 2006

One of the more fruitful systematic approaches to the study of foreign policy views nations as information processors and explains foreign policy as a function of information and processing thereon. Much of such processing depends on the prior beliefs of decision makers, but for a variety of reasons these systems of prior beliefs are very difficult to analyze using “standard” empirical and modeling techniques. Computational modeling, including expert system technology, provides an alternative methodology that allows such analysis. I present Policy Arguer (POLI), an expert system model of U.S. foreign policy making in Asia. Poli has been very successful in reproducing actual U.S. responses to events in Asia from the 1950s. More important, POLI recreates policy debate in the form of the arguments and counterarguments used to justify policy alternatives. The model explains foreign policy outputs in terms of a complete process from foreign policy beliefs, through debate, to choice.
Policy-Making and Secretariat Influence in the U. N. General Assembly: The Case of Public Information
Authors: Gordenker Leon
Published: May 2006

During the annual sessions of the General Assembly of the United Nations the policy and budget of the Office of Public Information (OPI) of the organization have been the perennial center of a complex debate. Instructions first given the Secretariat in 1946 provide some elements of this debate, while others depend on the professional expertise of the international civil service and on its influence and support in a General Assembly divided several ways. As a whole, the outcome demonstrates once more both the durable force of an attractive idea and the truth of the maxim that secretariats have great weight in the policy processes of international, as of other, organizations. For despite repeated debate and attack OPI has proved enduring and resilient.

During the last 15 years the many-faceted program of the agency has shrunk somewhat, to be sure, under the economizer's knife. In particular, it was under unusually severe criticism in 1957, when the General Assembly established an expert committee to investigate UN public information activities, and also in 1958, when the results of the inquiry were discussed. This committee, appointed with the unenthusiastic concurrence of the Secretary General, and made up of six governmental nominees not all of whom had experience with public information, directly challenged some of the working assumptions of OPI and called attention to difficulties with others. Their report struck a blow, too, at the internal balance of OPI, accused it of substantive failures and urged it to design new programs.
Degrees of Power and Freedom
Authors: Oppenheim Felix E.
Published: May 2006

Basic concepts in political science have been used in a purely classificatory way ever since Aristotle established the sixfold classification of the forms of government: monarchy, aristocracy, constitutional government, and their respective “perversions”: tyranny, oligarchy, democracy. Similarly, a modern writer distinguishes among four types of political systems: the Anglo-American, the Continental European, the pre-industrial (or partially industrial), and the totalitarian. All these are categorical concepts; a political system is either monarchical or not, either of the Anglo-American or of another type. Such key terms as influence, control, authority, power, and freedom also tend to function categorically: one actor either has or lacks power over some activity of another actor; with respect to one actor, another is either free or unfree to act in a certain way.

However, concrete political situations exhibit such characteristics to different degrees. Just as the substances we encounter in nature have varying degrees of hardness (rather than being either hard or soft), so a given political system is more, or less, totalitarian (or of the Anglo-American or of the pre-industrial type) than another. The United States and Soviet Russia have at present more power than any other country, and both are perhaps about equally powerful. Soldiers in general have less freedom than civilians, but they have more than prisoners. There can (or there cannot) be equal freedom for all.

Since we do make such assertions, the question arises whether it is possible to give them precise empirical meaning. To do so, we must replace such categorical concepts as power and freedom by the corresponding comparative concepts, e.g., “more power than,” “as much freedom as,” and provide operational definitions for these expressions.
Political Philosophy and Poetry
Authors: Bloom Allan
Published: May 2006

Sigurd Burckhardt has rendered a service in providing the occasion for a thematic presentation of the principles underlying the interpretations of Shakespearean drama by Jaffa and me, to which he has taken such exception. The issue does not primarily concern literary criticism but rather has to do with the relation of art to political philosophy and, in turn, with their relation to life. Burckhardt, however, has not joined the debate on the level of the issues. He does not argue against the substance of our interpretations, and does not say wherein and why they are in error. Characteristic of his method is his offer of three statements “admittedly out of context” from my article for which he then proposes the following test: “Choose,” he says, “a jury of widely read, intelligent men, show them these statements (with the information that they are meant to describe two main characters in a play known to all of them), and then make them guess who is being talked about.” Burckhardt thinks he is “safe in claiming that there will not be a single correct identification.” The moment seems somewhat inappropriately chosen for suggesting the method of a quiz program for deciding a matter of validity. But seriously, does any scholar, however he may wish for public acceptance, make this his standard? Agreement may produce peace, but it can never by itself be a criterion of truth. In presenting my conclusions, I have a right to ask that they be tested in the light of my evidence and my arguments. In the court of scholarly judgment it is a weak argument that rests on the number of witnesses who can be summoned to support an opinion.
Money Talks: Deterring Quality Challengers in Congressional Elections
Authors: Epstein David , Zemsky Peter
Published: May 2006

We examine the role of incumbent fundraising in deterring strong challengers. We construct a signaling model in which incumbents can use fundraising strategically to ward off quality challengers. We show, however, that only under very limited circumstances will there be an observable relationship between fundraising and challenger quality. Therefore, previous empirical tests for deterrence have systematically underestimated the effects of fundraising in decreasing electoral competition. Our analysis also suggests that by making fundraising easily observable, Federal Election Commission regulations may encourage candidates to overinvest time and resources accumulating large war chests instead of governing.
Report from the Laboratory: The Influence of Institutions on Political Elites' Democratic Values in Germany
Authors: Rohrschneider Robert
Published: May 2006

The unification of Germany revives several questions about the future of Germany's democracy. Given the socialist-authoritarian background, how supportive are East Germany's elites of liberal democratic rights? Has the socialist-democratic experience instilled into elites a social egalitarian conception of democracies? In what ways, if at all, do elites support direct democracy procedures? I examine political elites' conceptions of democracies in the united Germany in 1991, using a survey of 168 parliamentarians from the united parliament in Berlin. I find that the socialist and parliamentary institutions in the East and the West, respectively, have substantially influenced elites' conceptions of democracies in Germany, leading to a value divergence across the East-West boundary. Yet the findings also suggest that a partial value convergence in terms of liberal democratic rights among postwar elites has taken place. The results support an institutional learning theory, but they also suggest that support for liberal democratic values has been diffused into East Germany.
The Citizen as Respondent: Sample Surveys and American Democracy Presidential Address, American Political Science Association, 1995
Authors: Verba Sidney
Published: May 2006

Citizen participation is the main way in which the public communicates its needs and preferences to the government and induces the government to be responsive. Since participation depends on resources and resources are unequally distributed, the resulting communication is a biased representation of the public. Thus, the democratic ideal of equal consideration is violated. Sample surveys provide the closest approximation to an unbiased representation of the public because participation in a survey requires no resources and because surveys eliminate the selection bias inherent in the fact that participants in politics are self-selected. The contrast between the participatory process and the sample survey is used to highlight the nature of the bias in the former. Surveys, however, are not seen as a practical way of providing more equal representation.
The Ethical Individual: An Historical Alternative to Contemporary Conceptions of the Self
Authors: McCready Amy R.
Published: May 2006

In this article I offer an historically situated model of the self as an alternative to liberal, communitarian, and Foucauldian conceptions. Through the example of John Milton, I show that the conscience gave rise to a self that was jointly individual and ethical. By participating in public debates at the behest of his conscience, Milton recognized himself as an individual possessor of moral authority. Conscience thus liberated Milton from traditional identifications and beliefs as it bound him to act for his society. The self founded on conscience therefore differs from both communitarian and liberal variants. Moreover, whereas conscience in the Foucauldian account renders the self docile, it empowers the self in my account. I conclude that the self predicated on conscience challenges the divisions between private and public realms, self-regarding and prosocial actions, and self-creating and culturally determined persons.
On the interpretation of the sign ‘⊃’
Authors: Myhill John
Published: May 2006

The sign ‘⊃’ (or ‘→’ or ‘C’) functions in many logical systems in a way which precludes its interpretation as either strict or material implication. For example, in the systems of Heyting, Johansson, Fitch and Bernays (positive logic), the following are theorems:

Now if ‘⊃’ were interpreted as strict implication, ⊃2 would mean ‘if p is true, then p is strictly implied by every proposition’, i.e. ‘if p is true, it is necessarily true’, which is false for contingently true p. If on the other hand ‘⊃’ were interpreted as material implication, ⊃1 would reduce to ‘~p ∨ p’, i.e. to the law of excluded middle, which is conspicuously lacking in the systems mentioned. The reader is likely in practice to veer between these two interpretations. Thus in Fitch or Heyting on realizing that ‘~p⊃▪ p⊃q’ is a theorem, one thinks of it as meaning ‘a false proposition implies everything’ and regards the implication as material; but the presence of ‘p⊃p’ as a theorem, even for choices of p which do not satisfy excluded middle, inclines one again to the strict interpretation. This vacillation, while it need not lead to the commission of any formal fallacies, tends to hamstring one's intuition and thus waste time. The purpose of this paper is to suggest an interpretation of ‘⊃’ which will prevent such havering.

Let two formulae A and B be called interdeducible if A ⊢ B and B ⊢ A.
A test for the existence of tautologies according to many-valued truth-tables
Authors: Kalicki Jan
Published: May 2006

Theorem. There is an effective procedure to decide whether the set of tautologies determined by a given truth-table with a finite number of elements is empty or not.

Proof. Let W(P) be a w.f.f. with a single variable P and n a given n-valued truth-table with elements (values)

Substitute 1, 2, 3, …, n in succession for P. By the usual contraction process let W(P) assume the truth-values w1, w2, w3, …, wn respectively. The sequence

will be called the value sequence of W(P).

Value sequences consisting of designated elements of exclusively will be called designated; others will be called undesignated.

All the W(P)'s will be classified in the following way:

(a) to the first class CL1 of W(P)'s there belongs the one element P,

(b) to the (t + 1)th class CLt + 1 belong all the w.f.f. which can be built up by means of one generating connective from constituent w.f.f. of which one is an element of CLt and all the others (if any) are elements of CLn ≤ t.

For example, if N and C are the connectives described by a truth-table

etc.

Let ∣CLn∣ stand for the set of value sequences of the elements of CLn.
A reduction in the number of primitive ideas of arithmetic
Authors: Myhill John R.
Published: May 2006

Let

We shall show that every formula in the elementary arithmetic of positive integers may be constructed out of matrices of the form ϕ(x, y) by means of quantifiers and the stroke. For Julia Robinson has shown that the successor function and the relation of divisibility are sufficient to define addition and multiplication; but from elementary considerations

and
On Universals
Authors: Quine W. V.
Published: May 2006

The philosophical dispute over whether there are universale, or abstract entities, is not a dispute over the admissibility of general terms. Both sides will agree that general terms, e.g. ‘man,’ and perhaps even abstract singular terms such as ‘mankind’ and ‘7’, are meaningful, in the sense at least of participating in statements which as wholes are true or false. Where the platonists (as I shall call those who accept universale) differ from their opponents, the nominalists, is in positing a realm of entities, universals, corresponding to such general or abstract words.

The platonist is likely to regard the word ‘man’ as naming a universal, the class of men or the property of being a man, much as the word ‘Caesar’ names the concrete object Caesar. Actually, however, this is an extraneous detail. The platonist could equally well concur with the nominalist in the view that general terms, though meaningful in context, are not names at all.
An extension of basic logic
Authors: Fitch Frederic B.
Published: May 2006

A logical calculus Κ was defined in a previous paper and then shown in a subsequent paper to contain within itself a representation of every constructively definable subclass of expressions of a certain infinite class U of expressions, where Κ itself is one such subclass. (The former paper will be referred to as BL and the latter paper as RC.) The calculus Κ was called a “basic calculus” and its theorems were thought of as expressing the asserted propositions of a “basic logic,” that is, of a logic within which is definable every constructively definable system of logic and indeed every constructively definable class or relation. The notion of constructive definability was essentially equated with the notion of recursive enumerability.
The theory of quaternialty
Authors: Gottschalk W. H.
Published: May 2006

It is well-known that every involution in a logical or mathematical system gives rise to a theory of duality; for example, negation in the sentential calculus and predicate calculus, complementation in the calculus of classes, complementation and conversion in the calculus of relations, etc. The purpose of this note is to call attention to the fact that every involution in a logical or mathematical system gives rise to a theory of quaternality and that the square of quaternality, of which the classical squares of opposition are special cases, provides a diagrammatic representation for much of the theory of quaternality. For the sake of definiteness we expose the theory of quaternality in the context of the lower predicate calculus.

Let ϕ and ψ be formulas of the lower predicate calculus. The constants {T and F} {∧ and ∨} {→ and ⇷} {← and ⇸}{↔ and ⇹} {↑ and ↓} {∧ (all) and ∨ (some)} are dual. The constant ~ is self-dual. The negational of ϕ, denoted ϕN, is the formula obtained from ϕ by interchanging negated and unnegated variables (that is, sentence variables and predicate variables) and by interchanging dual constants. The contradual of ϕ, denoted ϕC, is the formula obtained from ϕ by interchanging negated and unnegated variables. The dual of ϕ, denoted ϕD, is the formula obtained from ϕ by interchanging dual constants. The four formulas ϕ, ϕN, ϕC, ϕD, are quaternals of each other.
Note on a paradox
Authors: Stanley Robert L.
Published: May 2006

The usual logical paradoxes, which stem from Russell's class R0 (i.e., and its relatives R1, R2, and so on (i.e., , , and so on, correspondingly), are contradictions (Ri ϵ Ri) ≡ ~(Ri ϵ Ri), derivable under unrestricted rules of inference. No contradiction appears to obtain.
New notes on simplicity
Authors: Goodman Nelson
Published: May 2006

The treatment of simplicity in my book and in earlier articles needs one important amplification and certain minor amendments. The basic method for computing complexity values nevertheless remains the same.

New studies show that so to adjust the actual technique of computation as to take full account of the factor of reflexivity would result in unwieldy rules. Fortunately, however, this is unnecessary; for the method already prescribed works for thoroughly irreflexive predicates, and every other predicate is replaceable by such predicates. Thus we need only require that before the complexity of a basis is evaluated every primitive be replaced by the simplest adequate set of irreflexive predicates.

Consider, for example, two-place predicates that are not irreflexive. Any two-place (or indeed any n-place) predicate that is satisfied only by identity pairs (or identity n-ads) can obviously be replaced by a one-place predicate. Any two-place predicate that is satisfied by some non-identity pairs and that is either exactly reflexive (i.e. satisfied also by just the identity pairs of elements in such non-identity pairs) or totally reflexive (i.e. satisfied also by all identity pairs) can be replaced by a two-place irreflexive predicate. In the former case, for instance, we replace “P” by “Q”, so explained that Qx, y if and only if Px, y and x ≠ y; and then define:

Finally, a non-irreflexive two-place predicate “P” that is of none of these three kinds can be replaced by a one-place and an irreflexive two-place predicate as follows:—let Qx if and only if Px,x, and let Rx,y if and only if Px,y andx ≠ y; then define:

Predicates of more than two places offer much greater variety since they may exhibit any sort of reflexivity with respect to any selection of places.
Conditions affecting the application of symbolic logic
Authors: Berkeley Edmund C.
Published: May 2006

In 1513 the Spanish adventurer Balboa discovered an ocean three times bigger than any other ocean in the world. When he returned to Europe at the end of the year and told the Spaniards, they probably did not fully believe him. Like Balboa, the symbolic logicians have recently discovered a new vast ocean of thought, and like the Europeans of his day, many people are hardly aware of the discovery or its full implications.

The newly discovered ocean, symbolic logic, is, in its broadest sense, a new science which studies through use of efficient symbols the nature and properties of all nonnumerical relations, seeking precise meanings and necessary conclusions. As an applied science, it holds immense promise. For example, it may give us an unambiguous language for political, economic, and social fields, which will conveniently reflect the structure of these fields and make discussion and analysis easy.
Models of logical systems
Authors: Kemeny John G.
Published: May 2006

The purpose of this paper is to show that some of the difficulties confronting logicians are caused by too narrow an interpretation of the function of mathematical logic. I hope to show that very fruitful results can be obtained by considering a much wider range of problems than usually found in the literature.

I believe that the function of mathematical logic is to study all logical systems. The problems now considered usually concern some particular system or set of systems. Of course we would have to agree first on what a logical system is. I shall suggest a tentative definition. The rest of my paper will proceed on the assumption that we have agreed on this question. However, it is only necessary for this paper that some definition should be accepted, it is not necessary that it should be the one I suasest.
On confirmation
Authors: Hosiasson-Lindenbaum Janina
Published: May 2006

Taking for the relation of confirmation the following obvious axioms, we obtain several more or less well-known theorems and are able to solve in a definite and strict manner several problems concerning confirmation.

Let a, b, and c be variable names of sentences belonging to a certain class, the operations a·b, a + b, and ā the (syntactical) product, the sum, and the negation of them. Let us further assume the existence of a real non-negative function c(a, b) of a and b, when b is not self-contradictory. Let us read ‘c(a, b)’ ‘degree of confirmation of a with respect to b' and take the following axioms:

Axiom I. If a is a consequence of b, c(a, b) = 1.

Axiom II. If is a consequence of c,

Axiom III. c(a·b, c) = c(a, c)·c(b, a·c).

Axiom IV. If b is equivalent to c, c(a, b) = c(a, c).

As may be easily seen, the interval of variation for c is (0, 1); this is quite conventional.
A demonstrably consistent mathematics—Part I
Authors: Fitch Frederic B.
Published: May 2006

This paper continues the exposition of a demonstrably consistent foundation for mathematics begun in An extension of basic logic (hereafter referred to as EBL) and in The Heine-Borel theorem in extended basic logic (hereafter referred to as HB). Still earlier papers related to these are A basic logic (referred to as BL) and Representations of calculi (referred to as RC). The main conventions and results of all the above papers will be presupposed in what follows. The numbering of sections and paragraphs will be a continuation of that of EBL and HB.
On the axiom of extensionality – Part I
Authors: Gandy R. O.
Published: May 2006

In part I of this paper it is shown that if the simple theory of types (with an axiom of infinity) is consistent, then so is the system obtained by adjoining axioms of extensionality; in part II a similar metatheorem for Gödel-Bernays set theory will be proved. The first of these results is of particular interest because type theory without the axioms of extensionality is fundamentally rather a simple system, and it should, I believe, be possible to prove that it is consistent.

Let us consider — in some unspecified formal system — a typical expression of the axiom of extensionality; for example:

where A(h) is a formula, and A(f), A(g) are the results of substituting in it the predicate variagles f, g for the free variable h. Evidently, if the system considered contains the predicate calculus, and if h occurs in A(h) only in parts of the form h(t) where t is a term which lies within the range of the quantifier (x), then 1.1 will be provable. But this will not be so in general; indeed, by introducing into the system an intensional predicate of predicates we can make 1.1 false. For example, Myhill introduces a constant S, where ‘Sϕψχω’ means that (the expression) ϕ is the result of substituting ψ for χ in ω.
A new symbolism for the propositional calculus
Authors: Parry William Tuthill
Published: May 2006

This paper reviews various symbolisms for the two-valued propositional calculus, and introduces a new set of signs which embodies the principles of Leśniewski's symbolism, yet resembles better known signs. This type of symbolism, serving as a diagram, may be used either in place of or as auxiliary to the usual symbolisms.
Toward a calculus of concepts
Authors: Quine W. V.
Published: May 2006

By concepts will be meant propositions (or truth-values), attributes (or classes), and relations of all degrees. The degree of a concept will be said to be 0, 1, or n (> 1), and the concept will be said to be medadic, monadic, or n-adic, according as the concept is a proposition, an attribute, or an n-adic relation. The common procedure in systematizing logistic is to treat these successive degrees as ultimately separate categories. The partition is not rested upon properties of the thus classified elements within the formal system, but is imposed rather at the metamathematical level, through stipulations as to what combinations of signs are to be accorded or denied meaning. Each function of the formal system is restricted, thus metamathematically, to one degree for its values and to one for each of its arguments. The theory of types imports a further scheme of infinite partition, imposed by metamathematical stipulations as to the relative types of admissible arguments of the several functions and stipulations as to the types of the values of the functions relative to the types of the arguments.

The elaborateness of the metamathematical grillwork which thus underlies formal logistic accounts in part for the tendency of those interested in logistic less for the matters treated than for the structures exemplified to limit their attention to the propositional calculus and the Boolean calculus of attributes (or classes), which, taken separately, are independent of the partitioning. A second reason for the algebraic appeal of these departments is their freedom from bound (apparent) variables: for use of bound variables fuses systematic considerations with notational or metamathematical ones in a way which resists ordinary formulation in terms of fixed functions and their arguments. Freedom from bound variables may be regarded, indeed, as the feature distinguishing algebra from analysis.
A note on universal sets
Authors: Lachlan A. H.
Published: May 2006

In this note is proved the following:

Theorem.Iƒ A × B is universal and one oƒ A, B is r.e. then one of A, B is universal.

Letα, τbe 1-argument recursive functions such thatxgoes to (σ(χ), τ(χ)) is a (1–1) map of the natural numbers onto all ordered pairs of natural numbers. A set A of natural numbers is calleduniversalif every r.e. set is (many-one) reducible to A; A × B is calleduniversalif the set
A simplified account of validity and implication for quantificational logic
Authors: Leblanc Hugues
Published: May 2006

As those of us who instruct him are well aware, customary accounts of validity and implication for quantificational logic often bewilder the novice. For his benefit, I present here an account of validity, due (in effect) to the late E. W. Beth, and two accounts of implication, one my own, the other Jaakko Hintikka's, which add up to what the better textbooks say, but, making no mention whatever of domains, say it far more simply.
A splitting theorem for simple Π11 Sets
Authors: Owings James C.
Published: May 2006

As was first mentioned in [3, §5], if A is any – set, A is the union of two disjoint – sets B(0), B(1). In metarecursion theory this is proven as follows. Let ƒ be a one-to-one metarecursive function whose range is A, let R be an unbounded metarecursive set whose complement is also unbounded, and set B(0) = f(R), B(1) = f(). The corresponding fact of ordinary recursion theory, namely that any r.e. but not recursive set can be split into two other such sets, was proved by Friedberg [2, Theorem 1], using a clever priority argument. Sacks [7, Corollary 2] then showed that any r.e. but not recursive set is the union of two disjoint r.e. sets neither of which was recursive in the other, a much stronger result. In this paper we attempt to prove the analogous result for – sets A, but succeed only in the case A is simple; i.e., the complement of A contains no infinite subset. As a corollary we show the metadegrees are dense, a fact already announced by Sacks [8, Corollary 1], but only proven by him for nonzero metadegrees.
A quasi-intumonistic set theory
Authors: Tharp Leslie H.
Published: May 2006

It is natural, given the usual iterative description of the universe of sets, to investigate set theories which in some way take account of the unfinished character of the universe. We do not here consider any arguments aimed at justifying one system over another, or at clarifying the basic philosophy. Rather, we look at an obvious candidate which is similar to a system discussed by L. Pozsgay in [1]. Pozsgay sketched the development of the ordinary theorems in such a system and attempted to show it equiconsistent with ZF. In this paper we show that the consistency of the system we call IZF can be proved in the usual ZF set theory.
The post correspondence problem
Authors: Cudia Dennis F. , Singletary Wilson E.
Published: May 2006

The correspondence decision problem was first formulated and shown to be recursively unsolvable in Post (1946). The method of proof was to reduce the known unsolvable decision problem for the class of normal systems on a, b to the correspondence decision problem. In the present paper the concept of a standard Post normal system is used so as to obtain some equivalence reductions of combinatorial systems. In particular the following main result is obtained.
A generalisation of productive set
Authors: Mitchell R.
Published: May 2006

The purpose of the present paper is to introduce a generalisation of the concept of productive set introduced by Post (2) and studied by Dekker (3) and others. Throughout the paper we shall use small Latin letters to denote both non-negative integers (referred to as numbers) and functions (both partial and total) from numbers to numbers. Sets of numbers will be denoted by small Greek letters and classes of such sets by capital Latin letters. ωη is the range of the ηth partial recursive function.
Initial segments of the degrees of unsolvability Part II: minimal degrees
Authors: Yates C. E. M.
Published: May 2006

The first of this sequence of papers [21] surveyed the progress that has been made in embedding partially ordered sets as initial segments of the uncountable upper semilattice D of degrees of unsolvability. The principal concern of the present and subsequent parts will be with initial segments of the countable upper semilattice D (≦0(1)) of degrees ≦0(1); a summary appeared in [21].
The strong homogeneity conjecture
Authors: Feiner L.
Published: May 2006

The strong homogeneity conjecture asserts that, for any Turing degree, a, there is a jump preserving isomorphism from the upper semilattice of degrees to the upper semilattice of degrees above a. Rogers [3, p. 261] states that this problem is open and notes that its truth would simplify many proofs about degrees. It is, in fact, false. More precisely, let 0 be the smallest degree and let 0(n) be the nth iterated jump of 0, as defined in [3, pp. 254–256].
Countable vector spaces with recursive operations Part I1
Authors: Dekker J. C. E.
Published: May 2006

We use the word “number” for “nonnegative integer” and “set” for collection of numbers. The set of all numbers is denoted by ε and the empty set by ο. We write ⊂ for the relation of inclusion and ⊆ for that of proper inclusion. If ƒ is a function from a subset of ε into ε, its domain and range are denoted by δƒ and ρƒ respectively. For any collection Γ of entities, card Γ or card (Γ) stands for the cardinality of Γ. The cardinality of the continuum is denoted by c.
An undecidable two sorted predicate calculus
Authors: Slomson A. B.
Published: May 2006

Let L be a first order predicate language with two sorts of variables and a single dyadic predicate letter whose first place is to be filled by variables of one sort and whose second place is to be filled by variables of the other sort. In answer to a question of M. H. Löb we show that there is no decision procedure for determining whether or not a sentence of L is universally valid.
A note on many·one reducibility
Authors: Liu Shih-Chao
Published: May 2006

In this note we partly answer a question left open in [1, p. 52] by proving the following theorem.

Theorem. Supposep0≧2, ωn+1·p0≦σ<ωn+1(p0+1). Then W(σ) is uniformly many-one reducible to W(τ) for τ≧(ωn+1·p0)+1.

To prove this theorem we need only show that there is a recursive function f(e) such that if ∣e∣<σ, then ∣f(e)<(ωn+1·p0)+1, while if ∣e∣ ≮ σ, f(e)∉W. (For the notations see [2].)
The system CΔ of combinatory logic
Authors: Fitch Frederic B.
Published: May 2006

The system of combinatory logic to be presented in this paper will be called CΔ. It may be compared to various systems of combinatory logic constructed by Schonfinkel [11], Curry [1], Rosser [10], and Curry and Feys [2], and to the author's systems K′ [3] and S [5], and to extensional modifications of K′ [6], [7], [8], [9]. The present system falls within this latter category of extensional or semi-extensional systems, but it is more perspicuous than the others, and the proof of its consistency is more direct. It contains the theory of combinators in full strength. It also contains operators for disjunction, conjunction, negation, existence (that is, non-emptiness), and universality. A considerable part of classical mathematical analysis can be shown to be derivable in CΔ, just as in K′ [4], but with the added advantage of the availability of a limited extensionality principle.
Replacement in some modal systems
Authors: Thomas Ivo
Published: May 2006

In the original formulations of Lewis's S1–S5 in [1], Feys's S1°, S2° in [2], and Sobociński's S3°, S4° in [3], a primitive rule is that of replacement for strict equivalents which it is enough to express formally as:

RI: where γ′ is like γ except for having β at one place where γ has α.
Recursion theory and formal deducibility
Authors: Kleinberg E. M.
Published: May 2006

The enumeration, given a first-order sentence , of all sentences deducible from in the first-order predicate calculus, and the enumeration, given a non-negative integer n, of the recursively enumerable set Wn, are two well-known examples of effective processes. But are these processes really distinct? Indeed, might there not exist a Gödel numbering of the sentences of first-order logic such that for each n, if n is the number assigned to the sentence , then Wn is the set of numbers assigned to all sentences deducible from ? If this were the case, the first sort of enumeration would just be a particular instance of the second.
Ten modal models
Authors: Thomas Ivo
Published: May 2006

We consider the results of adding to a basic modal system T0the axioms G1.CLpp;Pn.CLnpLn+1p; Bn.CpLnMp, where n ≧ 11, in all combinations. The method of Meredith's [7] will be extended to get models of these systems in lower predicate calculus (LPC) with a constant binary relation,U. Most of the results were already obtained in [1]–[6], though systems as in (i) and (ii) below were not investigated, except that S40in (ii) was mentioned in [1]. However some repetition may be excused in view of the simplicity with which the results are obtained by the present method.
Simplicity of recursively enumerable sets
Authors: Robinson Robert W.
Published: May 2006

In §1 is given a characterization of strongly hypersimple sets in terms of weak arrays which is in appearance more restrictive than the original definition. §1 also includes a new characterization of hyperhypersimple sets. This one is interesting because in §2 a characterization of dense simple sets is shown which is identical in all but the use of strong arrays instead of weak arrays. Another characterization of hyperhypersimple sets, in terms of descending sequences of sets, is given in §3. Also a theorem showing strongly contrasting behavior for simple sets is presented. In §4 a r-maximal set which is not contained in any maximal set is constructed.
Proof of the law of infinite conjunction using the perfect disjunctive normal form
Authors: Thomson James
Published: May 2006

The law of infinite conjunction (Quine's name, see Methods of logic, rev. ed., Holt & Co., New York, p. 254) says that a set of truthfunctional formulas is satisfiable provided every finite subset is. We give a proof of the law which uses some properties of the perfect disjunctive normal form.

Any satisfiable formula can be written as a disjunction of conjunctions of literals (a literal is a statement-letter or the negation of one) in which a statement-letter which occurs in any conjunction occurs exactly once in each; a literal by itself counts as a conjunction and a conjunction by itself as a disjunction.