Ramifications of a population model forκ as a coefficient of reliability

Coefficient is generally defined in terms of procedures of computation rather than in terms of a population. Here a population definition is proposed. On this basis, the interpretation of as a measure of diagnostic reliability in characterizing an individual, and the effect of reliability, as measured by, on estimation bias, precision, and test power are examined. Factors influencing the magnitude of are identified. Strategies to improve reliability are proposed, including that of combining multiple unreliable diagnoses.This investigation was supported in part by the National Institute of Mental Health Specialized Research Center Grant # MH-30854.     

Complete Infinitary Type Logics

For each regular cardinal , we set up three systems of infinitary type logic, in which the length of the types and the length of the typed syntactical constructs are < . For a fixed , these three versions are, in the order of increasing strength: the local system ₍₎, the global system g₍₎ (the difference concerns the conditions on eigenvariables) and the -system ₍₎ (which has anti-selection terms or Hilbertian -terms, and no conditions on eigenvariables). A full cut elimination theorem is proved for the local systems, and about the -systems we prove that they admit cut-free proofs for sequents in the -free language common to the local and global systems. These two results follow from semantic completeness proofs. Thus every sequent provable in a global system has a cut-free proof in the corresponding -systems. It is, however, an open question whether the global systems in themselves admit cut elimination.     

Variations in use of the term “or”

Two studies showed that adults' responses to questions involving the term or varied markedly depending upon the type of question presented. When presented with various objects (A's and B's) and asked to circle all things which are A or B subjects tended to circle A's as well as B's, whereas when asked to circle all the A's or B's subjects showed a relatively stronger tendency to circle one or the other. Moreover the nature of the sets of objects (As and Bs) influenced behavior as well. There was also evidence that the effects due to question wording or set type transferred.     

The influence of verbal specifications on ratings of relative properties of pictures

Summary Sixty subjects were shown pictures each containing two objects (A and B). The objects were unobtrusive with respect to relative properties such as long — short, big — small, etc. The pictures were preceded by sentences referring either to objects A and B or only to object A. Object A was dimensionally specified: The same object was called, e.g., long for one and short for a different subject. Ratings during a later test (without presentation of the pictures) revealed that not only were objects A remembered according to the verbal specification provided during the presentation but ratings of objects B also changed in line with the specification of A. This was true even when object B had not been mentioned verbally during the presentation. In this way, verbal specifications had an effect beyond the referential bond. It is concluded that models based on the assumption that the semantic interpretation of an event depends on the application of syntactic rules — rules indicating, e.g., to which object an adjective refers — lack an important clue.     

Elementary Extensions of External Classes in a Nonstandard Universe

In continuation of our study of HST, Hrbaek set theory (a nonstandard set theory which includes, in particular, the ZFC Replacement and Separation schemata in the st--language, and Saturation for well-orderable families of internal sets), we consider the problem of existence of elementary extensions of inner "external" subclasses of the HST universe.We show that, given a standard cardinal , any set R * generates an "internal" class S(R) of all sets standard relatively to elements of R, and an "external" class L[S(R)] of all sets constructible (in a sense close to the Gödel constructibility) from sets in S(R). We prove that under some mild saturation-like requirements for R the class L[S(R)] models a certain -version of HST including the principle of +-saturation; moreover, in this case L[S(R)] is an elementary extension of L[S(R)] in the st--language whenever sets R R satisfy the requirements.     

Third Men: The Logic of the Sophisms at Arist. SE 22, 178b36–170a10

This article aims at elucidating the logic of Arist. SE 22, 178b36–179a10 and, in particular, of the sophism labelled "Third Man" discussed in it. I suggest that neither the sophistic Walking Man argument, proposed by ancient commentators, nor the Aristotelian Third Man of the , suggested by modern interpreters, can be identified with the fallacious argument Aristotle presents and solves in the passage. I propose an alternative reconstruction of the Third Man sophism and argue that an explanation of the lines regarding the identity of Coriscus and Coriscus the musician (178b39–179a3) is indispensable for its correct understanding, since they hint at another sophism in some important aspects analogous. Finally, I show that two contradictions concerning spotted by scholars in the passage are only apparent and can be dissolved once the assumption that the anti-Platonic Third Man argument is at stake here is discarded, and once the passage is read in the light of its agonistic context.     

A modification of kendall's tau for measuring association in contingency tables

A coefficient of association is described for a contingency table containing data classified into two sets of ordered categories. Within each of the two sets the number of categories or the number of cases in each category need not be the same.=+1 for perfect positive association and has an expectation of 0 for chance association. In many cases also has –1 as a lower limit. The limitations of Kendall's _a and _b and Stuart's _c are discussed, as is the identity of these coefficients to' under certain conditions. Computational procedure for is given.     

Some results on the Kripke sheaf semantics for super-intuitionistic predicate logics

Some properties of Kripke-sheaf semantics for super-intuitionistic predicate logics are shown. The concept ofp-morphisms between Kripke sheaves is introduced. It is shown that if there exists ap-morphism from a Kripke sheaf ₁ into ₂ then the logic characterized by ₁ is contained in the logic characterized by ₂. Examples of Kripke-sheaf complete and finitely axiomatizable super-intuitionistic (and intermediate) predicate logics each of which is Kripke-frame incomplete are given. A correction to the author's previous paper Kripke bundles for intermediate predicate logics and Kripke frames for intuitionistic modal logics (Studia Logica, 49(1990), pp. 289–306 ) is stated.Dedicated to Professor Takeshi Kotake on his 60th birthdayThis research was partially supported by Grant-in-Aid for Encouragement of Young Scientists No. 03740107, Ministry of Educatin, Science and Culture, Japan.     

Frege,Boolos, and Logical Objects

In this paper, the authors discuss Frege's theory of logical objects (extensions, numbers, truth-values) and the recent attempts to rehabilitate it. We show that the eta relation George Boolos deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the eta relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses unrestricted Comprehension for Logical Objects and banishes encoding (eta) formulas from Comprehension for Properties. The relative mathematical and philosophical strengths of the two theories are discussed. Along the way, new results in the theory of abstract objects are described, involving: (a) the theory of extensions, (b) the theory of directions and shapes, and (c) the theory of truth values.     

Letter Writing and the Performativity of Intimacy in Female Pedagogical Relations: Recuperating Derridean Amnesia,Writing Back to Madame de Maintenon

Performativity and performance of language are the subject of this re-writing of Derrida's position on the gift. Here the source of performativity is Althusser's while the source of the gift is not only Marcel Mauss, but also both the opening of Derrida's Given Time: I, Counterfeit Money and the signing through letters of Madame de Maintenon, wife of Louis XIV and founder of a school for girls. A third writing plays a role, that of a 1910 biography of Madame. The paper is a relay, a re-play of the positions of the central characters, -- Derrida and Maintenon -- and a semiology of their writings. Out of this a new gift of pedagogy is evoked in a conception of pedagogical retreat.     

A reduction rule for Peirce formula

A reduction rule is introduced as a transformation of proof figures in implicational classical logic. Proof figures are represented as typed terms in a -calculus with a new constant P ⁽⁽⁾⁾. It is shown that all terms with the same type are equivalent with respect to -reduction augmented by this P-reduction rule. Hence all the proofs of the same implicational formula are equivalent. It is also shown that strong normalization fails for P-reduction. Weak normalization is shown for P-reduction with another reduction rule which simplifies of (( ) ) into an atomic type.This work was partially supported by a Grant-in-Aid for General Scientific Research No. 05680276 of the Ministry of Education, Science and Culture, Japan and by Japan Society for the Promotion of Science. Hiroakira Ono     

La Evolucion de la filosofia de Wittgenstein

Summary The author claims that there is a basic difference between theTractatus and thePhilosophical Investigations; despite Bernstein's and O'Brien's claims to the contrary, there are, indeed, two Wittgensteins. Yet, to ascertain the difference between both we must look at Wittgenstein's conceptions of philosophy rather than at his views on logic and language. Wittgenstein's different, and even divergent, views on logic and language are grounded on his two views on philosophy and not the other way around. At the same time, Wittgenstein's views on philosophy are caused by his ways of conceiving the scope of philosophical activity in regard to language. Both in theTractatus and in thePhilosophical Investigations, Wittgenstein points out what is important in language for philosophy, but in each case he reaches very different conclusions. Now, when all is said, there remains one unifying factor in all of Wittgenstein's investigations: it is the question of the logic of language, which shifts positions from theTractatus to theInvestigations, so that what was earlier a hidden structure becomes later the grammar of its indefinitely complexe uses.     

Argumentative aspects of indirect proof

While direct proof is widely considered the paradigm of the acquisition of knowledge by deductive means, indirect proof has traditionally been criticized as showing merely that its conclusion is true and not why it is true. This paper accounts for the traditional objection by emphasizing the argumentative role in indirect proof of logical principles such as excluded middle and non-contradiction.     

From negation to “notion”: Cognitive processes and argumentative strategies

Summary This article deals with the role of negation as a language and cognitive operation. Such a topic is treated here within the framework of the argumentative strategies which consist in making certain cognitive landmarks of the discourse flip over with the intent of imposing the necessity to choose between two types of notions, aiming at the transformation of this choice into an implication. The reference here to the Aristotelian logic of Prior Analytics appears to be more efficient than any other contemporary logic and the author intends to give account of the role of negation as contrary coming into play on an operational and cognitive basis in all the argumentative strategies which oscillate reciprocally from universal to particular.     

A New Representation Theorem for Contranegative Deontic Logic

The logic of an ought operator O is contranegative with respect to an underlying preference relation if it satisfies the property Op & (¬p)(¬q) Oq. Here the condition that is interpolative ((p (pq) q) (q (pq) p)) is shown to be necessary and sufficient for all -contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & OqO(p&q)) and disjunctive division (O(p&q) Op Oq).     

On the logic of conscious belief

In this paper we are discussing a version of propositional belief logic, denoted by LB, in which so-called axioms of introspection (B BB and B B B) are added to the usual ones. LB is proved to be sound and complete with respect to Boolean algebras equipped with proper filters (Theorem 5). Interpretations in classical theories (Theorem 4) are also considered. A few modifications of LB are further dealt with, one of which turns out to be S5.     

On a new property of partially balanced association schemes useful in psychometric structural analysis

In an earlier paper [Psychometrika,31, 1966, p. 147], Srivastava obtained a test for the HypothesisH ₀ : = ₀₀ + ... + _ll, where i are known matrices,i are unknown constants and is the unknown (p ×p) covariance matrix of a random variablex (withp components) having ap-variate normal distribution. The test therein was obtained under (p ×p) covariance matrix of a random variablex (withp components) the condition that ₀, ₁, ..., l form a commutative linear associative algebra and a certain vector, dependent on these, has non-negative elements. In this paper it is shown that this last condition is always satisfied in the special situation (of importance in structural analysis in psychometrics) where ₀, ₁, ..., l are the association matrices of a partially balanced association scheme.This research was partially supported by the U. S. Air Force under Grant No. AF33(615)-3231, monitored by the Aero Space Research Labs.Now at Colorado State University.     

A deontic logic of action

The formal language studied in this paper contains two categories of expressions, terms and formulas. Terms express events, formulas propositions. There are infinitely many atomic terms and complex terms are made up by Boolean operations. Where and are terms the atomic formulas have the form = ( is the same as ), Forb ( is forbidden) and Perm ( is permitted). The formulae are truth functional combinations of these. An algebraic and a model theoretic account of validity are given and an axiomatic system is provided for which they are characteristic.The closure principle, that what is not forbidden is permitted is shown to hold at the level of outcomes but not at the level of events. In the two final sections some other operators are considered and a semantics in terms of action games.     

Happiness and virtue in Socrates' moral theory

Conclusion In Section IV above we start with texts whose prima facie import speaks so strongly for the Identity Thesis that any interpretation which stops short of it looks like a shabby, timorous, thesis-saving move. What else could Socrates mean when he declares with such conviction that no evil can come to a good man (T19), that his prosecutors could not harm him (T16(a)), that if a man has not been made more unjust he has not been harmed (T20), that all of happiness is in culture and justice (T16(a)), that living well is the same as living justly (T15)? But then doubts begin to creep in. Recalling that inflation of the quantifier is normal and innocuous in common speech (that job means everything to him, he'll do anything to get it, will stick at nothing) we ask if there is really no chance at all that no evil in T19, not harmed in T20 might be meant in the same way? The shift from no harm at T16(a) to no great harm at T16(b), once noticed, strengthens the doubt. It gets further impetus in T21(b) when to explain how all of happiness is in culture and justice he depicts a relation (that recurs more elaborately in T22) which, though still enormously strong, is not quite as strong as would be required by identity. The doubt seeps into T15 when we note that current usage did allow just that relation as a respectable use of the same.At that point we begin to wonder if resort to the Identity Thesis might not be just a first approximation to a subtler, more finely nuanced, doctrine which would give Socrates as sound a foundation for what we know he wants to maintain at all costs - the Sovereignty of Virtue - without obliterating the eudaemonic value of everything else in his world. We cast about for a credible model of such a relation of virtue to happiness and hit on that multicomponent pattern sketched on p. 9 above. We ascertain that this will afford a comprehensively coherent eudaemonist theory of rational action, while its rival would not, and will fit perfectly a flock of texts in Section V which the latter will not fit at all. Are we not entitled to conclude that this is our best guide to the true relation of virtue to happiness in Socrates' thought - the one for which he would have declared if he had formulated explicitly those two alternative theses and made a reasoned choice between them?The Socrates of this paper is the protagonist of Plato's earlier dialogues. I list these (by self-explanatory abbreviations), borrowed from T. Irwin, Plato's Moral Theory [1974] (hereafter PMT): Ap., Ch., Cr., Eud., Eu., G., HMa., HMi, Ion, La., Ly., Pr., R., I. I assume, but shall not argue here, that in this segment of his corpus, Plato aims to recreate the doctrines and arguments of his teacher in dramatic scenes, all of which (except for the Ap.) may be, and most of which undoubtedly are, fictional; I shall be referring these works, under this proviso, as Plato's Socratic dialogues. (I did not include the Menexenus in the above list, since the parody of a funeral oration in this dialogue is implicitly dissociated from Socrates.)     

Natural deduction rules for English

A system of natural deduction rules is proposed for an idealized form of English. The rules presuppose a sharp distinction between proper names and such expressions as the c, a (an) c, some c, any c, and every c, where c represents a common noun. These latter expressions are called quantifiers, and other expressions of the form that c or that c itself, are called quantified terms. Introduction and elimination rules are presented for any, every, some, a (an), and the, and also for any which, every which, and so on, as well as rules for some other concepts. One outcome of these rules is that Every man loves some woman is implied by, but does not imply, Some woman is loved by every man, since the latter is taken to mean the same as Some woman is loved by all men. Also, Jack knows which woman came is implied by Some woman is known by Jack to have come, but not by Jack knows that some woman came.