On Holland's Dutch identity conjecture

The manifest probabilities of observed examinee response patterns resulting from marginalization with respect to the latent ability distribution produce the marginal likelihood function in item response theory. Under the conditions that the posterior distribution of examinee ability given some test response pattern is normal and the item logit functions are linear, Holland (1990a) gives a quadratic form for the log-manifest probabilities by using the Dutch Identity. Further, Holland conjectures that this special quadratic form is a limiting one for all smooth unidimensional item response models as test length tends to infinity. The purpose of this paper is to give three counterexamples to demonstrate that Holland's Dutch Identity conjecture does not hold in general. The counterexamples suggest that only under strong assumptions can it be true that the limits of log-manifest probabilities are quadratic. Three propositions giving sets of such strong conditions are given.     

On a property of BCK-identities

A BCK-algebra is an algebra in which the terms are generated by a set of variables, 1, and an arrow. We mean by aBCK-identity an equation valid in all BCK-algebras. In this paper using a syntactic method we show that for two termss andt, if neithers=1 nort=1 is a BCK-identity, ands=t is a BCK-identity, then the rightmost variables of the two terms are identical.This theorem was conjectured firstly in [5], and then in [3]. As a corollary of this theorem, we derive that the BCK-algebras do not form a variety, which was originally proved algebraically by Wroski ([4]).To prove the main theorem, we use a Gentzen-type logical system for the BCK-algebras, introduced by Komori, which consists of the identity axiom, the right and the left introduction rules of the implication, the exchange rule, the weakening rule and the cut. As noted in [2], the cut-elimination theorem holds for this system.Presented byJan Zygmunt     

On a derivation of the necessity of identity

The source, status, and significance of the derivation of the necessity of identity at the beginning of Kripke’s lecture “Identity and Necessity” is discussed from a logical, philosophical, and historical point of view.     

Native and alien. On ethnic identity]

Freud's theory of the antagonism between family and culture provides the point of departure for this study, which sets out to rehabilitate the concepts "ethnic" and "ethnic identity". The family represents the locus of established tradition and familiar ritual and seeks to make each new generation identify with "us and ours". Culture, by contrast, is dependent on contact and confrontation with things alien and foreign. Between these extremes and the potential dangers specific to each of them, ethnicity--which is neither biological nor cultural--represents a mediating factor. In adolescence, a phase of dis- and re-orientation, the individual needs to draw upon his ethnic identity to reconcile the disturbing contradiction between familial and cultural claims, between the native and the alien.     

On two arguments for the indeterminacy of personal identity

Both arguments are based on the breakdown of normal criteria of identity in certain science-fictional circumstances. In one case, normal criteria would support the identity of person A with each of two other persons, B and C; and it is argued that, in the imagined circumstances, A=B and A=C have no truth value. In the other, a series or spectrum of cases is tailored to a sorites argument. At one end of the spectrum, persons A and B are such that A=B is clearly true; at the other end, A and B are such that the identity is clearly false. In between, normal criteria of identity leave the truth or falsehood of A=B undecided, and it is argued that in these circumstances A=B has no truth value.These arguments are to be understood counterfactually. My claim is that, so understood, neither establishes its conclusion. The first involves a pair of counterfactual situations that are equally possible or tied. If A=B and A=C have no truth value, a counterfactual conditional with one of them as consequent and an antecedent that is true in circumstances in which either is true should have no truth value. Intuitively, however, any such counterfactual is false. The second argument can be seen to invite an analogous response. If this is right, however, there is an important disanalogy between this and the classical paradox of the heap. If the disanalogy is only apparent, the argument shows at most that the existence of persons can be indeterminate.     

Personal identity is social identity

Phenomenology and the Cognitive Sciences - The question of the identity or persistence of the self through time may be interesting for philosophers, but it is hardly a burning question for most...     

Martin Heidegger's principle of identity: On belonging and Ereignis

This article discusses Martin Heidegger's interpretation of Parmenides given in his last public lecture “The Principle of Identity” in 1957. The aim of the piece is to illustrate just how original and significant Heidegger's reading of Parmenides and the principle of identity is, within the history of philosophy. Thus the article will examine the traditional metaphysical interpretation of Parmenides, and consider G. W. F. Hegel and William James’ account of the principle of identity in light of this. It will then consider Heidegger's contribution, his return to and re-interpretation of Parmenides in his last lecture. Heidegger will, through the Parmenidean claim that “Thinking and Being are one”, deconstruct the traditional metaphysical understanding of the principle of identity, and in its place offer a radically different conception of how our relationship, our “belonging together” with Being can be understood.     

On what matters. Personal identity as a phenomenological problem

Phenomenology and the Cognitive Sciences - This paper focuses on the connection between meaning, the specific field of phenomenological philosophy, and mattering, the cornerstone of personal...     

On boredom and social identity: a pragmatic meaning-regulation approach

People who feel bored experience that their current situation is meaningless and are motivated to reestablish a sense of meaningfulness. Building on the literature that conceptualizes social identification as source of meaningfulness, the authors tested the hypothesis that boredom increases the valuation of ingroups and devaluation of outgroups. Indeed, state boredom increased the liking of an ingroup name (Study 1), it increased hypothetical jail sentences given to an outgroup offender (Study 2 and Study 3), especially in comparison to an ingroup offender (Study 3), it increased positive evaluations of participants' ingroups, especially when ingroups were not the most favored ones to begin with (Study 4), and it increased the appreciation of an ingroup symbol, mediated by people's need to engage in meaningful behavior (Study 5). Several measures ruled out that these results could be explained by other affective states. These novel findings are discussed with respect to boredom, social identity, and existential psychology research.     

On maximal intermediate logics with the disjunction property

For intermediate logics, there is obtained in the paper an algebraic equivalent of the disjunction propertyDP. It is proved that the logic of finite binary trees is not maximal among intermediate logics withDP. Introduced is a logicND, which has the only maximal extension withDP, namely, the logicML of finite problems.