bluuebunny/crossref_metadata_2025_split huggingface dataset:
Mass Movement and Democracy: Sokagakkai in Japanese Politics
Authors: White James W. 
Published: May 2006

With a claimed membership of over 12 million members, possession of over 1000 seats in local and national legislative assemblies, a widespread domestic reputation, and a sensationalistic treatment in the foreign press, the Sokagakkai has come in recent years to be a subject of some academic, and much religious and political interest in both Japan and the United States. An organization of lay believers of the Sho sect of Nichiren Buddhism (noted for its intolerance and vigorous propagation methods), the Sokagakkai has gone into Japanese politics with a striking degree of success; the extent to which it has brought its religious characteristics into the political sphere and the question of whether such religious groups should be in that sphere at all are at present the focus of considerable debate in Japan.Most criticisms of the Sokagakkai have to date concentrated upon its religious activities, its doctrinal truth or falsehood, its alleged militaristic tendencies, and the proper place of religion in the political system of a secular state, I would like to touch on some of the social (or antisocial) functions performed by the Sokagakkai in Japanese society, as proclaimed by the Gakkai itself and as evidenced in the Gakkai's performance, and on the implications of these social functions for the Japanese political process.As its name, the “Value-Creation Society,” suggests, the Sokagakkai postulates pursuit of absolute happiness by means of the creation of certain values in one's life as the proper direction of human life. So that all men may be able to achieve this happiness, the Gakkai emphasizes equality of all men; so that they may be fully able to enjoy their values, the Gakkai stresses freedom. Absolute freedom, equality, and happiness may be sought by the individual through religious faith; the agency for the realization of these ideals for society and the world is the political system.
Conditions for Party Leadership: The Case of the House Democrats
Authors: Froman Lewis A. , Ripley Randall B. 
Published: May 2006

Political power in Congress, all observers agree, is highly decentralized. The factors chiefly responsible for this are also well known: weak national parties (in the Congress this results in strong constituency ties and weak leadership sanctions over members) and a highly developed division of labor through the committee system. A leadership endowed with few opportunities to punish and reward, coupled with specialization by policy area, inevitably produces an institution with numerous and disparate centers of power. Just as inevitably the politics of such an institution is compounded of persuasion, bargaining, and log-rolling.As weak as the legislative parties are, however, they still provide the major organizing force in Congress. Roll-call vote analyses have demonstrated this, and a recent study of the House Whip organizations also bears it out. Generally speaking, the single most important variable explaining legislative outcomes is party organization.
On an implication function in many-valued systems of logic
Authors: Dienes Z. P. 
Published: May 2006

In a paper J. Łukasiewicz and A. Tarski study the systems arising out of the implication function C (x, y) = min(1, 1 – x + y) and the negation function Nx = 1 – x, where x, y are real numbers between 0 and 1 inclusive. Let us then write
Сxy = min(1, 1 – x + y) and Nx = 1 – x. (1)In this note we shall consider another implication function, namely
С′xy = ССNxyy, (2)
The elimination theorem when modality is present
Authors: Curry Haskell B. 
Published: May 2006

The present paper contains an emendation to the theory of formal deducibility which was presented in lectures at the University of Notre Dame in the spring of 1948 [4]. The method of proof developed in these lectures for the elimination theorem, which corresponds to the “Hauptsatz” of Gentzen's thesis [6], failed when modal connectives were present. This deficiency was remedied soon thereafter; but it was not possible to include the new proof in those lectures. This new proof is presented below.Before proceeding to this proof, the elimination theorem will be formulated, and its proof outlined, in an abstract form. Certain general conditions on the rules are formulated in §1; then, in §2, it is shown that the first two stages of the elimination theorem go through for any rules satisfying the conditions. The modifications necessary to extend this proof to cases where modal rules are present will then be taken care of in the later sections. A section on the extension of the elimination theorem to the singular form of LC is added at the end.
Elimination of extra-logical postulates
Authors: Quine W. V. , Goodman Nelson 
Published: May 2006

Under certain circumstances a postulate can be eliminated in favor of a mere definition, or convention of notational abbreviation. Suppose e.g. that a given system presupposes the machinery of ordinary logic and contains in addition a single extra-logical primitive: the relation Pt, “is a spatial part of.” Suppose this relation is governed by a single extra-logical postulate, to the effect that Pt is transitive:Now instead of Pt, the relation O of spatial overlapping might be taken as primitive; Pt could then be defined in terms of O as follows:The transitivity of Pt then follows by purely logical principles from the definition. The statement (1) with its ‘Pt’ clauses expanded according to (2) is a purely logical theorem, demonstrable independently of any stipulations or assumptions concerning the properties of O. Thus, through a change involving neither increase nor decrease of primitive ideas, the need of adopting (1) as a postulate is removed.Or again, consider a system comprising ordinary logic and the sole extra-logical primitive S, the relation of simultaneity, governed by a sole postulate to the effect that S is symmetrical:Here instead of S the relation N, “is no later than” might be taken as primitive; S could then be defined in terms of N as follows:Postulation of (3) then becomes unnecessary, for (3) is an abbreviation, according to (4), of a theorem which is demonstrable within pure logic.
Proof that there are infinitely many modalities in Lewis's system S2
Authors: McKinsey J. C. C. 
Published: May 2006

In this note I show, by means of an infinite matrix M, that the number of irreducible modalities in Lewis's system S2 is infinite. The result is of some interest in view of the fact that Parry has recently shown that there are but a finite number of modalities in the system S2 (which is the next stronger system than S2 discussed by Lewis).I begin by introducing a function θ which is defined over the class of sets of signed integers, and which assumes sets of signed integers as values. If A is any set of signed integers, then θ(A) is the set of all signed integers whose immediate predecessors are in A; i.e., , so that n ϵ θ(A) is true if and only if n − 1 ϵ A is true.Thus, for example, θ({−10, −1, 0, 3, 14}) = {−9, 0, 1, 4, 15}. In particular we notice that θ(V) = V and θ(Λ) = Λ, where V is the set of all signed integers, and Λ is the empty set of signed integers.It is clear that, if A and B are sets of signed integers, then θ(A+B) = θ(A)+θ(B).It is also easily proved that, for any set A of signed integers we have . For, if n is any signed integer, then
Solution of a problem of Leon Henkin
Authors: Löb M. H. 
Published: May 2006

If Σ is any standard formal system adequate for recursive number theory, a formula (having a certain integer q as its Gödel number) can be constructed which expresses the proposition that the formula with Gödel number q is provable in Σ. Is this formula provable or independent in Σ? [2].One approach to this problem is discussed by Kreisel in [4]. However, he still leaves open the question whether the formula (Ex)(x, a), with Gödel-number a, is provable or not. Here (x, y) is the number-theoretic predicate which expresses the proposition that x is the number of a formal proof of the formula with Gödel-number y.In this note we present a solution of the previous problem with respect to the system Zμ [3] pp. 289–294, and, more generally, with respect to any system whose set of theorems is closed under the rules of inference of the first order predicate calculus, and satisfies the subsequent five conditions, and in which the function (k, l) used below is definable.The notation and terminology is in the main that of [3] pp. 306–326, viz. if is a formula of Zμ containing no free variables, whose Gödel number is a, then ({}) stands for (Ex)(x, a) (read: the formula with Gödel number a is provable in Zμ); if is a formula of Zμ containing a free variable, y say, ({}) stands for (Ex)(x, g(y)}, where g(y) is a recursive function such that for an arbitrary numeral the value of g() is the Gödel number of the formula obtained from by substituting for y in throughout. We shall, however, depart trivially from [3] in writing (), where is an arbitrary numeral, for (Ex){x, ).
The completeness of the first-order functional calculus
Authors: Henkin Leon 
Published: May 2006

Although several proofs have been published showing the completeness of the propositional calculus (cf. Quine (1)), for the first-order functional calculus only the original completeness proof of Gödel (2) and a variant due to Hilbert and Bernays have appeared. Aside from novelty and the fact that it requires less formal development of the system from the axioms, the new method of proof which is the subject of this paper possesses two advantages. In the first place an important property of formal systems which is associated with completeness can now be generalized to systems containing a non-denumerable infinity of primitive symbols. While this is not of especial interest when formal systems are considered as logics—i.e., as means for analyzing the structure of languages—it leads to interesting applications in the field of abstract algebra. In the second place the proof suggests a new approach to the problem of completeness for functional calculi of higher order. Both of these matters will be taken up in future papers.The system with which we shall deal here will contain as primitive symbolsand certain sets of symbols as follows:(i) propositional symbols (some of which may be classed as variables, others as constants), and among which the symbol “f” above is to be included as a constant;(ii) for each number n = 1, 2, … a set of functional symbols of degree n (which again may be separated into variables and constants); and(iii) individual symbols among which variables must be distinguished from constants. The set of variables must be infinite.
A syntactical characterization of S5
Authors: Bergmann Gustav 
Published: May 2006

This note should be considered as an appendix to a paper by McKinsey. Familiarity with this paper is assumed; its terminology and notation will be used without explanation. McKinsey's main result (theorem 1) is that every class of sentences fulfilling P1–P5, with a set of substitutions satisfying A1–A4, is a system of modal logic in the sense that the “associated” set, T2, contains all theorems of S4. It is also proved (theorem 2) that for T2 to contain all theorems of S5, it is sufficient that the elements of S form a group. The basic idea of the construction is the formalization, by means of D5, of our intuitive notion of possibility.In view of the great generality of S, it may be of some interest to give a condition that is both necessary and sufficient for T2 to contain S5 after some restriction suggested by our intuitive notions about modalities has first been imposed upon S. The following postulate is related to the idea that if a sentence is possible, then its negation is not necessary. Informally speaking, it requires that S be sufficiently “comprehensive” for this idea to become formalizable in terms of S.P. If ♢α is in T1, then there exists an element sm of S such that ♢∼sm(α) is not in T1.I shall now prove that if P is satisfied, the following condition is both necessary and sufficient for T2 to contain all theorems of S5.C. If α is in T1, then ♢s(α) is in T1 for all elements s of S.
A solution of the decision problem for the Lewis systems S2 and S4, with an application to topology
Authors: McKinsey J. C. C. 
Published: May 2006

In this paper I shall give a solution of the decision problem for the Lewis systems S2 and S4; i.e., I shall establish a constructive method for deciding whether an arbitrary given sentence of one of these systems is provable. The method is laborious to apply, since, in order to decide by means of it whether a given sentence is provable, it is necessary to construct a (usually very large) finite matrix. The argument will perhaps be of general interest, however, because it does not seem to depend too closely on the special features of these particular systems, so that it may be possible to apply it in order to solve the decision problem for other such systems.Section II presents the decision method for S2, and Section III for S4. In Section IV, I shall establish a certain correspondence between S4 and topology, which will provide a solution for a decision problem in topology; this correspondence also enables us to settle a previously unsolved problem with regard to the Lewis systems.In treating of this system, I shall use the notation of Lewis, with the single exception that I shall use the symbol “≣”, instead of Lewis's symbol “=”, for strict equivalence. I shall use the symbol “=” to denote identity. Thus “p≣q” is a formula of S2, while “x=y” is the statement asserting that x and y are identical. I shall refer to the rules, primitive sentences and theorems of S2 by the names and numbers used by Lewis. Whenever a theorem stated by Lewis involves the symbol “=”, I shall of course suppose that this symbol has been replaced throughout by “≣”: thus, for example, I shall take 19.82 to be “(◇p∨◇q) ≣ ◇(p∨q)”, instead of “(◇p∨◇q) ≣ ◇(p∨q)”.
Strict implication, deducibility and the deduction theorem
Authors: Marcus Ruth Barcan 
Published: May 2006

Lewis and Langford state, “… it appears that the relation of strict implication expresses precisely that relation which holds when valid deduction is possible. It fails to hold when valid deduction is not possible. In that sense, the system of strict implication may be said to provide that canon and critique of deductive inference which is the desideratum of logical investigation.” Neglecting for the present other possible criticisms of this assertion, it is plausible to maintain that if strict implication is intended to systematize the familiar concept of deducibility or entailment, then some form of the deduction theorem should hold for it. The purpose of this paper is to analyze and extend some results previously established which bear on the problem.We will begin with a rough statement of some relevent considerations. Let the system S contain among its connectives an implication connective ‘I’ and a conjunction connective ‘&’. Let A1, A2, …, An ⊦ B abbreviate that B is provable on the hypotheses A1, A2, …, An for a suitable definition of “proof on hypotheses”, where A1, A2, …, An, B are well-formed expressions of S.
Systems of syntactic analysis
Authors: Chomsky Noam 
Published: May 2006

During the past several decades, linguists have developed and applied widely techniques which enable them, to a considerable extent, to determine and state the structure of natural languages without semantic reference. It is of interest to inquire seriously into the formality of linguistic method and the adequacy of whatever part of it can be made purely formal, and to examine the possibilities of applying it, as has occasionally been suggested, to a wider range of problems. In order to pursue these aims it is first necessary to reconstruct carefully the set of procedures by which the linguist derives the statements of a linguistic grammar from the behaviour of language users, distinguishing clearly between formal and experimental in such a way that grammatical notions, appearing as definienda in a constructional system, will be formally derivable for any language from a fixed sample of linguistic material upon which the primitives of the system are experimentally defined. The present paper will be an attempt to formalize a certain part of the linguist's generalized syntax language.From another point of view, this paper is an attempt to develop an adequate notion of syntactic category within an inscriptional nominalistic framework. The inscriptional approach seems natural for linguistics, particularly in view of the fact that an adequate extension of the results of this paper will have to deal with the problem of homonymity, i.e., with a statement of the conditions under which tokens of the same type must be assigned to different syntactic classes.
On finite and infinite modal systems
Authors: Churchman C. West 
Published: May 2006

In Oskar Becker's Zur Logik der Modalitäten four systems of modal logic are considered. Two of these are mentioned in Appendix II of Lewis and Langford's Symbolic logic. The first system is based on A1–8 plus the postulate,From A7: ∼◊p⊰∼p we can prove the converse of C11 by writing ∼◊p for p, and hence deriveThe addition of this postulate to A1–8, as Becker points out, allows us to “reduce” all complex modal functions to six, and these six are precisely those which Lewis mentions in his postulates and theorems: p, ∼p, ◊p, ∼◊p, ∼◊∼p, and ◊∼p This reduction is accomplished by showingwhere ◊n means that the modal operator ◊ is repeated n times; e.g., ◊3p = ◊◊◊p. Then it is shown thatBy means of (1), (2), and (3) any complex modal function whatsoever may be reduced to one of the six “simple” modals mentioned above.It might be asked whether this reduction could be carried out still further, i.e., whether two of the six “irreducible” modals could not be equated. But such a reduction would have to be based on the fact that ◊p = p which is inconsistent with the set B1–9 of Lewis and Langford's Symbolic logic and independent of the set A1–8. Hence for neither set would such a reduction be possible.
Logical paradoxes for many-valued systems
Authors: Shaw-Kwei Moh 
Published: May 2006

As we know, the system of material implication is led into an inconsistency by the Russellian class, defined as λx. Nϵxx. This class, however, does no harm to many other systems, for example, the three-valued system L3 given by J. Łukasiewicz. A natural question is whether or not there exist classes which affect some of these other logical systems. The main result of the present paper is to answer this question affirmatively. At the end of this paper we point out that the interpretation given by J. Łukasiewicz for the system L3 is not satisfactory, and propose a new interpretation.B. Russell deduced the mentioned inconsistency by the aid of the notion of negation. Later on, H. B. Curry pointed out that we could get the same result without the aid of that notion. None of these results affects the system L3 and other similar systems. But these systems may be involved.To show this, we need the following definitions.A function of two variables Cpq will be called an implication when the following “implication rule” is valid:Under this definition we should note that material equivalence Epq, for example, is an implication.Let C be such an implication. Then the symbol “(Cp)iq” is defined recursively byThe class an is defined as λx. (Cϵxx)np, where p is a propositional variable. The rule of absorption of order n, denoted by (An), is:
Some theorems about the sentential calculi of Lewis and Heyting
Authors: McKinsey J. C. C. , Tarski Alfred 
Published: May 2006

In this paper we shall prove theorems about some systems of sentential calculus, by making use of results we have established elsewhere regarding closure algebras and Brouwerian albegras. We shall be concerned mostly with the Lewis system and the Heyting system. Some of the results here are new (in particular, Theorems 2.4, 3.1, 3.9, 3.10, 4.5, and 4.6); others have been stated without proof in the literature (in particular, Theorems 2.1, 2.2, 4.4, 5.2, and 5.3).The proofs to be given here will be found to be mostly very simple; generally speaking, they amount to drawing conclusions from the theorems established in McKinsey and Tarski [10] and [11]. We have thought it might be worth while, however, to publish these rather elementary consequences of our previous work—so as to make them readily available to those whose main interest lies in sentential calculus rather than in topology or algebra.
Note on a property of matrices for Lewis and Langford's calculi of propositions
Authors: Dugundji James 
Published: May 2006

The object of this note is to show that there is no finite characteristic matrix for any one of Lewis and Langford's systems.Theorem I. There is no finite characteristic matrix for any one of the systems S1–S5.Proof. Let M be a matrix with less than n elements for which all the provable formulas in S1, or S2, or S3, or S4, or S5, are satisfied. Let Fn represent the formulawhere ∑ stands for a ∨-chain, and the pi, are variables in any one of the calculi. Using M, there is always at least one summand in Fn where pi and pk have the same value. Therefore, Fn can always be written in the form (a = a)∨ B, and thus will give, for any B, a “designated” value, since the formula (p = p) ∨ q is provable in any one of the systems S1–S5.Give to any one of the systems S1–S5, the following matrix, due to Henle:1. Elements: all possible classes formed from the integers 1, 2, 3, …, n.2. “Designated” element: the class {1, 2, 3, …,n}.3. Boole-Schröder algebra on the elements.4. ◊N = N (N the null class)◊A = {1, 2, …, n} (A any non-null class).5
Definability and simplicity
Authors: Svenonius Lars 
Published: May 2006

In the following pages we wish to clarify some questions concerning definitions of relations in terms of other relations. A study is made of how a definition of a relation R1 in terms of another relation R2 works in a given specified universe U. The definition is regarded as a correlation rule between the “possible extensions” of R1 and R2. There are no difficulties in formulating necessary, and in a certain sense also sufficient, formal conditions for the existence of a definition relation between R1 and R2.In particular, we are concerned with questions such as: “Is every relation of the form s1 definable in terms of some relation of the form s2?” (§ IV) A related question concerns the criterion used by Goodman1 for degrees of complexity, namely, whether for every relation R2 of the form s1 there is some relation R2 of the form s2 such that R1 and R2 are mutually definable (§ V). Some concrete results concerning this condition are stated in the theorems 22–24.The “complexity function” which is defined (definition 17) and which very naturally suggests itself from the discussion of the definability conditions, seems to furnish an adequate measure of the sort of complexity discussed by Goodman.