On the completeness of first degree weakly aggregative modal logics

This paper extends David Lewis result that all first degree modal logics are complete to weakly aggregative modal logic by providing a filtration-theoretic version of the canonical model construction of Apostoli and Brown. The completeness and decidability of all first-degree weakly aggregative modal logics is obtained, with Lewiss result for Kripkean logics recovered in the case k=1.     

Axiomatisation and decidability ofF andP in cyclical time

We present a Hilert style axiomatisation for the set of formulas in the temporal language withF andP which are valid over non-transitive cyclical flows of time.We also give a simpler axiomatisation using the slightly controversial irreflexivity rule and go on to prove the decidability of any temporal logic over cyclical time provided it uses only connectives with first-order tables.     

Truth and reflection

Conclusion Many topics have not been covered, in most cases because I don't know quite what to say about them. Would it be possible to add a decidability predicate to the language? What about stronger connectives, like exclusion negation or Lukasiewicz implication? Would an expanded language do better at expressing its own semantics? Would it contain new and more terrible paradoxes? Can the account be supplemented with a workable notion of inherent truth (see note 36)? In what sense does stage semantics lie between fixed point and stability semantics? In what sense, exactly, are our semantical rules inconsistent? In what sense, if any, does their inconsistency resolve the problem of the paradoxes?The ideals of strength, grounding, and closure together define an intuitively appealing conception of truth. Nothing would be gained by insisting that it was the intuitive conception of truth, and in fact recent developments make me wonder whether such a thing exists. However that may be, until the alternatives are better understood it would be foolish to attempt to decide between them. Truth gives up her secrets slowly and grudgingly, and loves to confound our presumptions.     

Decidability,partial decidability and sharpness relation for L-subsets

If X is set and L a lattice, then an L-subset or fuzzy subset of X is any map from X to L, [11]. In this paper we extend some notions of recursivity theory to fuzzy set theory, in particular we define and examine the concept of almost decidability for L-subsets. Moreover, we examine the relationship between imprecision and decidability. Namely, we prove that there exist infinitely indeterminate L-subsets with no more precise decidable versions and classical subsets whose unique shaded decidable versions are the L-subsets almost-everywhere indeterminate.This research was supported by M. P. I. of Italy (60% and 40% 1986).     

Naive and refined truth approximation

The naive structuralist definition of truthlikeness is an idealization in the sense that it assumes that all mistaken models of a theory are equally bad. The natural concretization is a refined definition based on an underlying notion of structurelikeness.In Section 1 the naive definition of truthlikeness of theories is presented, using a new conceptual justification, in terms of instantial and explanatory mistakes.In Section 2 general constraints are formulated for the notions of structurelikeness and truthlikeness of structures.In Section 3 a refined definition of truthlikeness of theories is presented, based on the notion of structurelikeness, using a sophisticated version of the conceptual justification for the naive definition.In Section 4 it is shown that idealization and concretization is a special kind of potentially refined truth approximation.I would like to acknowledge that van Benthem (1987) played in several respects a crucial role in the research for a new refined definition. Moreover, I like to thank David Miller, Ilkka Niiniluoto, and two referees for their comments on an earlier version. One of the referees notes that the Miller version of the naive approach (in model-theoretic terms, and identifying the truth with the truth about the actual world) has been criticised on several occasions for its failure to accommodate likeness between structures by Oddie (notably Oddie, 1986). The idea that likeness between structures should be a guiding idea behind truthlikeness is said to be a constant theme of Oddie's work. All this may well be true, but I should add however that Oddie's publications did not play any role in my research. The local references to Oddie are based on the suggestions by the referee.     

Think Before You Speak: Utterances and the Logic of Indexicals

This essay discusses some aspects of the logical behaviour of sentences in languages containing indexical and demonstrative expressions. After some preliminary remarks in section one, sections two and three focus on instances of logically true sentences that may be uttered falsely, and on cases of logically equivalent sentences whose utterances may have distinct truth-values. The logical and semantic problems taken into consideration include the validity of a Principle of Translation, the so-called puzzle of addressing, and examples related to measurement and approximation. Section four discusses the complementary phenomenon of sentences that may presumably always be uttered truly, but that do not qualify as logically true. In particular, I argue against the widespread tendency to consider I am here now or I exist as truths of the logic of indexicals.     

Formal systems of dialogue rules

Section 1 contains a survey of options in constructing a formal system of dialogue rules. The distinction between material and formal systems is discussed (section 1.1). It is stressed that the material systems are, in several senses, formal as well. In section 1.2 variants as to language form (choices of logical constants and logical rules) are pointed out. Section 1.3 is concerned with options as to initial positions and the permissibility of attacks on elementary statements. The problem of ending a dialogue, and of infinite dialogues, is treated in section 1.4. Other options, e.g., as to the number of attacks allowed with respect to each statement, are listed in section 1.5. Section 1.6 explains the concept of a chain of arguments.From section 2 onward four types of dialectic systems are picked out for closer study: D, E, Di and Ei. After a preliminary section on dialogue sequents and winning strategies, the equivalence of derivability in intuitionistic logic and the existence of a winning strategy (for the Proponent) on the strength of Ei is shown by simple inductive proofs.Section 3 contains a — relatively quick — proof of the equivalence of the four systems. It follows that each of them yields intuitionistic logic.     

Toulmin on Ideals of Natural Order

In this paper I criticize Toulmin's concept of Ideals of Natural Order and his account of the role these Ideals play in scientific explanation as given in his book, Foresight and Understanding. I argue that Toulmin's account of Ideals of Natural Order as those theories taken to be self evident by scientists at a given time introduces an undesirable subjectivism into his account of scientific explanation. I argue also that the history of science, especially the recent history of microphysics, does not support Toulmin's contentions about the supposed self-evidence of the basic explanatory theories in science.     

On Davidson and interpretation

Davidson's theory of interpretation, I argue, is vulnerable to a number of significant difficulties, difficulties which can be avoided or resolved by the more Quinean approach which I develop. In Section 1 I note difficulties which apply to T-theories but are avoided by translation manuals. In Section 2 I show how to construct what I call T-manuals, which are like T-theories in requiring Tarskian structure, but like translation manuals in avoiding the difficulties discussed in Section 1. In Section 3 I show that the approach using T-manuals does at least as well as Davidson's with respect to a number of other concerns of his. In Section 4 I show that it does better than Davidson's with respect to reporting interpretations, especially where demonstrative utterances are concerned. In Section 5 I argue for (somewhat modified) Quinean empirical constraints, which go with manuals, as superior to the empirical constraints Davidson imposes, which go with T-theories. In Section 6 I show that Davidson is unable to offer an adequate account of what an interpreter knows; and propose a more acceptable theory of language mastery which gives a central role to the requirement that the interpreter's language usage satisfy the refined and amplified Quinean empirical constraints of Section 5.I wish to thank Susan Haack for her help in turning a draft into the present paper.     

The Traditional Regression Model for Measuring Test Bias is Incorrect and Biased Against Minorities

For 25 years psychologists have measured systematic measurement bias in terms of regression lines. According to this traditional approach a test is an unbiased predictor of a criterion for all subgroups if all subgroups have identical Y regression lines (i.e., identical slopes and identical Y intercepts). This paper shows that the traditional model is fundamentally incorrect and identical Y regression lines are not expected to occur with an unbiased test in a testing situation in which one group score lower than another group on both the test and criterion. This is the case even if the test is perfectly reliable. The traditional model for measuring bias actually results in a consistent error or bias against groups which score lower than average on both the test and criterion. In practice this bias operates against minority groups. Tests now thought to be unbiased or even biased in favor of minority groups may in fact be biased against minority groups. A new model of test bias, which is based solely on measurement principles, is briefly introduced. In this model unbiased tests produce groups with identical test-criterion common-factor axes having a slope of S _YC/S _XC and with each axis intersecting the group centroids.     

An alternative approach to the method of correct matching

The correct matching method is treated in a new way which increases its power and enables the results to be expressed by a correlation coefficient. Tables for 3n7 are included.I wish to express my thanks and indebtedness to Professor Louis Guttman for his assistance and guidance. Also I am grateful for helpful discussions with Dr. D. Kahneman, O. E. Schild, and J. Norman.     

Are Knowledge Claims Indexical?

David Lewis, Stewart Cohen, and Keith DeRose have proposed that sentences of the form S knows P are indexical, and therefore differ in truth value from one context to another.¹ On their indexical contextualism, the truth value of S knows P is determined by whether S meets the epistemic standards of the speakers context. I will not be concerned with relational forms of contextualism, according to which the truth value of S knows P is determined by the standards of the subject Ss context, regardless of the standards applying to the speaker making the knowledge claim. Relational contextualism is a form of normative relativism. Indexical contextualism is a semantic theory. When the subject is the speaker, as when S is the first person pronoun I, the two forms of contextualism coincide. But otherwise, they diverge. I critically examine the principal arguments for indexicalism, detail linguistic evidence against it, and suggest a pragmatic alternative.     

Consistent Fragments of Grundgesetze and the Existence of Non-Logical Objects

In this paper, I consider two curious subsystems ofFrege's Grundgesetze der Arithmetik: Richard Heck's predicative fragment H, consisting of schema V together with predicative second-order comprehension (in a language containing a syntactical abstraction operator), and a theory T in monadic second-order logic, consisting of axiom V and ¹ ₁-comprehension (in a language containing anabstraction function). I provide a consistency proof for the latter theory, thereby refuting a version of a conjecture by Heck. It is shown that both Heck and T prove the existence of infinitely many non-logical objects (T deriving,moreover, the nonexistence of the value-range concept). Some implications concerning the interpretation of Frege's proof of referentiality and the possibility of classifying any of these subsystems as logicist are discussed. Finally, I explore the relation of T toCantor's theorem which is somewhat surprising.     

Semantic indeterminacy and the realist stance

Semantic Indeterminacy and Scientific Realism are perhaps the two most ubiquitous and influential doctrines of the Quinean corpus. My concern is to argue against neither in isolation, but against their joint compatibility. Scientific Realism, I argue, when understood as Quine's realistic attitude toward the posits of physical theory, is essentially intentional in character. Thus, Realism requires Intentionality. In Section 1, I provide some necessary exegesis. In Section 2, I attempt to show how this Realism/Intentionality connection arises, surprisingly, within Quine's own mature work to create a tension in his views which he does not himself resolve. In Section 3, I examine the source of the Realism/Intentionality connection more deeply, and respond to possible Quinean objections to my account. In Section 4, I consider the consequences of the connection for various debates in recent analytic philosophy.     

Running in Circles about Begging the Question

In a published exchange, Richard Robinson and Roy A. Sorenson debate the matter of whether begging the question is a fallacy; Robinson thinks it is not, but Sorenson argues that it is. Norman Ten attempts to resolve this debate by making a distinction between begging the question and fallaciously begging the question. While Teng is right to note that Robinson and Sorenson are talking past each other, he incorrectly diagnoses the source of this miscommunication. In this paper, then, I offer what I take to be a more illuminating distinction 3; viz. that between logical and rhetorical fallacies 3; and employ that distinction to resolve the debate.     

The percentage bend correlation coefficient

A well-known result is that the usual correlation coefficient,, is highly nonrobust: very slight changes in only one of the marginal distributions can alter by a substantial amount. There are a variety of methods for correcting this problem. This paper identifies one particular method which is useful in psychometrics and provides a simple test for independence. It is not recommended that the new test replace the usual test ofH ₀: = 0, but the new test has important advantages over the usual test in terms of both Type I errors and power.     

An Essay In The Aid Of Writing History: Fictions Of Historiography

In what follows I explore the question of fictionality in history writing. First, I venture into the unfamiliar genre of ego-histoire and make my own professional training in the tenets of positivist or realist historiography an object of theoretical reflection and critical analysis. Then as a way of dealing with the literary dimension of written history, I make a canonical work in history of education an object of rhetorical analysis. Finally, as another way of coming to terms with the fictions of historiography, I revisit one of my own productions and make it an object of metacritical consideration. My central theme is that historiographical realism alone will not suffice , that historians are as dependant upon literary invention as upon documents, that history cannot be written without the aid of the fictions of historiography, and that the difference between the historian and the novelist is narrower than we may have been accustomed to think. I further argue that attention to the literary or rhetorical dimension of history is long overdue in history of education, where it flourishes unacknowledged. I conclude that historical writing is not just a literary pastime and the issue remains: how to come to grips with fictionalizing and the truth claims of historiography.     

Female delinquency in the emancipation era: A review of the literature

By the mid-1970s studies began to indicate that the era of women's emancipation had been accompanied by changes in the volume and character of female lawbreaking. In this paper, I critically review the growing literature that has attempted to measure and explain the alleged changes in female delinquency. I examine whether females have remained traditional in their delinquency patterns, whether the observed changes (if they exist at all) are real or the result of changing societal reactions, and whether female delinquents have been masculinized or in other ways influenced by the women's liberation movement or changing gender roles. I also review explanations of female delinquency that are derived from social control, power-control, strain, and subcultural theories. Finally, I argue that more attention needs to be given to understanding the role strain inherent in females' attempts to negotiate ambiguous or contradictory gender roles, and that the concept of role strain offers a promising explanation of contemporary patterns of female delinquency.Portions of this paper were adapted from R. J. Berger (Ed.), The Sociology of Juvenile Delinquency, Chicago: Nelson-Hall, 1990 forthcoming.     

Paradox,truth and logic part I: Paradox and truth

Conclusion The discussion of the semantics of inconsistent truth theories now comes to a pause. The preceding is of course but a sketch; many interesting questions remain to be answered. The second part of this essay, however, will not seek to answer them. Rather, I will turn to the discussion of the proof theory of truth theory: the local and global logic of truth.Under the first heading, I show how to replace the inductive construction of models with an appropriate infinitary proof theory, and relate this on the one hand to the so-called dependence approach to inductive truth theories (Davis, 1979; Yablo, 1982) and on the other to van Fraassen's fact semantics for relevance logic.Under the second heading, I offer formals systems which capture the inferences valid in all approximate models. Not surprisingly, these turn out to be relevant logics.With formalism in hand, I discuss finally the extent to which the gap and/or glut approach can in fact be said to solve the paradoxes; that is, to allow us to say that the very language we are speaking is of the sort described in our theory.     

On sensitive rank tests for comparing the effects of two treatments on a single group

The rank testR _n of Cronholm and Revusky [1965] in effect doubles the number of comparisons carried out in the Mann-Whitney test between Treated and Control subjects chosen from a single group ofn and triples the asymptotic Pitman efficiency against shift alternatives by using a series ofn — 1 subexperiments. However, the full series can be too costly or time-consuming. It is shown thatj appropriately chosen subexperiments will permit one to make at leastj/(j+1) of the number of comparisons possible underR _n, with large sample efficiency ofj/(j+2) relative toR _n against shift alternatives and small sample efficiency greater than that,j=2, 3, ...,n — 2. The resulting test criterion is a sum ofj independent Mann-Whitney test statistics. Its null distribution is tabulated forn10 and small sample efficiency comparisons are carried out forn=10.