Kant,the Third Antinomy and Transcendental Arguments

In this paper, I consider whether a reading of Kant's solution to the Third Antinomy can offer material for devising a new model of transcendental argument. The problem that this form of argument is meant to address is an antinomy between two apparently contradictory claims, q and ¬q, where we seem equally justified in holding both. The model has the following form: p; q is a necessary condition of p; the only justification we have for q is that it is a necessary condition of p; p is justified only in domain X (where X is a domain of objects of cognition); therefore, q is justified only in domain X. Because the argument shows that our justification for q is valid only in X, it also establishes that there is conceptual space to hold ¬q outside of X.     

Some properties of the communality in multiple factor theory

Several theorems concerning properties of the communaltiy of a test in the Thurstone multiple factor theory are established. The following theorems are applicable to a battery ofn tests which are describable in terms ofr common factors, with orthogonal reference vectors.1. The communality of a testj is equal to the square of the multiple correlation of testj with ther reference vectors.2. The communality of a testj is equal to the square of the multiple correlation of testj with ther reference vectors and then—1 remaining tests. Corollary: The square of the multiple correlation of a testj with then—1 remaining tests is equal to or less than the communality of testj. It cannot exceed the communality.3. The square of the multiple correlation of a testj with then—1 remaining tests equals the communality of testj if the group of tests containsr statistically independent ests teach with a communality of unity.4. With correlation coefficients corrected for attenuation, when the number of tests increases indefinitely while the rank of the correlational matrix remains unchanged, the communality of a testj equals the square of the multiple correlation of testj with then—1 remaining tests.5. With raw correlation coefficients, it is shown in a special case that the square of the multiple correlation of a testj with then—1 remaining tests approaches the communality of testj as a limit when the number of tests increases indefinitely while the rank of correlational matrix remains the same. This has not yet been proved for the general case.The author wishes to express his appreciation of the encouragement and assistance given him by Dr. L. L. Thurstone.     

Circle graphs and monadic second-order logic

This article is part of a project consisting in expressing, whenever possible, graph properties and graph transformations in monadic second-order logic or in its extensions using modulo p cardinality set predicates or auxiliary linear orders. A circle graph is the intersection graph of a set of chords of a circle. Such a set is called a chord diagram. It can also be described by a word with two occurrences of each letter, called a double occurrence word. If a circle graph is prime for the split (or join) decomposition defined by Cunnigham, it has a unique representation by a chord diagram, and this diagram can be defined by monadic second-order formulas with the even cardinality set predicate. By using the (canonical) split decomposition of a circle graph, we define in monadic second-order logic with auxiliary linear orders all its chord diagrams. This construction uses the fact that the canonical split decomposition of a graph can be constructed in monadic second-order logic with help of an arbitrary linear order. We prove that the order of first occurrences of the letters in a double occurrence word w that represents a connected circle graph determines this word in a unique way. The word w can be defined by a monadic second-order formula from the word of first occurrences of letters. We also prove that a set of circle graphs has bounded clique-width if and only if all the associated chord diagrams have bounded tree-width.     

Semantic Information and the Correctness Theory of Truth

Semantic information is usually supposed to satisfy the veridicality thesis: p qualifies as semantic information only if p is true. However, what it means for semantic information to be true is often left implicit, with correspondentist interpretations representing the most popular, default option. The article develops an alternative approach, namely a correctness theory of truth (CTT) for semantic information. This is meant as a contribution not only to the philosophy of information but also to the philosophical debate on the nature of truth. After the introduction, in Sect. 2, semantic information is shown to be translatable into propositional semantic information (i). In Sect. 3, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in Sect. 4, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + A]. This completes the reduction of the truth of i to the correctness of A. In Sects. 5 and 6, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates Q by verifying and validating it (in the computer science’s sense of “verification” and “validation”); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of “proxy”) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of “commutation”); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. Sect. 7 provides some further clarifications about CTT, in the light of semantic paradoxes. Section 8 draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. In the course of the article all technical expressions from computer science are explained.     

Knowledge despite falsehood

I examine the claim, made by some authors, that we sometimes acquire knowledge from falsehood. I focus on two representative cases in which a subject S infers a proposition q from a false proposition p. If S knows that q, I argue, S's false belief that p is not essential to S's cognition. S's knowledge is instead due to S's belief that p′, a proposition in the neighbourhood of p that S (dispositionally) believes (and knows). S thus knows despite her false belief. The widely accepted and plausible principle that inferential knowledge requires known premises is unscathed.     

The Point of Scientificity,the Fall of the Epistemological Dominos,and the End of the Field of Educational Administration

The point of scientificity, or pos,represents a place in history whereeducational administration was founded as ascience. A pos creates a field of memoryand a field of studies. A pos isepistemologically sustained in its claim forscientific status by a line of demarcation orlod. A lod is supported by truthclaims based on various forms ofcorrespondence. As these forms have beeninterrogated and abandoned, correspondence hasgiven way to coherentism and finally to testsof falsification. As falsification has shownto contain serious flaws when compared to theactual history of scientific discoveries, theentire project of a distinct and unitaryfield known as educational administration isseriously cast into doubt. Contemporaryexaminations in educational administrationdiscourse show that even when the lod hasbeen undermined by epistemological shifts, theinitial pos has remained to supportclaims regarding the project of a ``science ofleadership.' The analysis contained in thisarticle show, however, that when claims of thelod are demonstrably unsustainable, theinitial pos must be similarly abandoned. With that collapse the concept of a fieldis likewise effaced. The epistemologicalalternative is to envision fields ofstudy which do not require a lod, excepton a longitudinal basis to ascertain whether aresearch program shaped and sustained by it isprogressive or regressive. In short, there areno aprori meta-criteria to separate sciencefrom non-science in educationaladministration.     

General theory and methods for matric factoring

Methods are developed for factoring an arbitrary rectangular matrixS of rankr into the formFP, whereF hasr columns andP hasr rows. For the statistical problem of factor analysis,S may be the score matrix of a population of individuals on a battery of tests. ThenF is a matrix of factor loadings,P is a matrix of factor scores, andr is the number of factor variates. (As in current procedures, there remains a subsequent problem of rotation of axes and interpretation of factors, which is not discussed here.) Methods are also developed for factoring an arbitrary Gramian matrixG of rankr into the formFF, whereF hasr columns andF denotesF transposed. For the statistical problem of factor analysis,G may be the matrix of intercorrelations,R, of a battery of tests, with unity, communalities, or other parameters in the principal diagonal.R is proportional toSS, and it is shown thatS can be factored by factoringR. This may usually be the most economical procedure in practice; it should not be overlooked, however, thatS can be factored directly. The general methods build up anF (andP) in as many stages as desired; as many factors as may be deemed computationally practical can be extracted at a time. Perhaps it will usually be found convenient to extract not more than three factors at a time. Current procedures, like the centroid and principal axes, are special cases of a general method presented here for extracting one factor at a time.     

A simplification of a result by zellini on the maximal rank of symmetric three-way arrays

Zellini (1979, Theorem 3.1) has shown how to decompose an arbitrary symmetric matrix of ordern ×n as a linear combination of 1/2n(n+1) fixed rank one matrices, thus constructing an explicit tensor basis for the set of symmetricn ×n matrices. Zellini's decomposition is based on properties of persymmetric matrices. In the present paper, a simplified tensor basis is given, by showing that a symmetric matrix can also be decomposed in terms of 1/2n(n+1) fixed binary matrices of rank one. The decomposition implies that ann ×n ×p array consisting ofp symmetricn ×n slabs has maximal rank 1/2n(n+1). Likewise, an unconstrained INDSCAL (symmetric CANDECOMP/PARAFAC) decomposition of such an array will yield a perfect fit in 1/2n(n+1) dimensions. When the fitting only pertains to the off-diagonal elements of the symmetric matrices, as is the case in a version of PARAFAC where communalities are involved, the maximal number of dimensions can be further reduced to 1/2n(n–1). However, when the saliences in INDSCAL are constrained to be nonnegative, the tensor basis result does not apply. In fact, it is shown that in this case the number of dimensions needed can be as large asp, the number of matrices analyzed.     

EMOTION IN SIKH MUSICOLOGY

Recent studies in Sikh musicology have focused on its history and theory. However, there is an absence of theoretical research which focuses on the role of emotions in Sikh music. In this paper, we contribute to this research by investigating key issues relating to emotions in Sikh musicology. We explore theories which propose that a rāga will evoke a particular emotion/mood in the listener and that there are a number of factors which influence this process. In particular, we focus on two parallel theories which we term the ‘one rāga one emotion’ and the ‘one rāga multiple emotions’ theories. We consider these theories within the context of the shabads (We are adding an ‘s’ for Punjabi plural words such as shabads and rāgas although the plural in Punjabi in this case would be Shabad or rāga. By Anglicising the words in this way we hope that it makes the paper easier to read), in particular rāgas of the Guru Granth Sahib which convey a number of emotions/moods. In this paper, we explore the problem of how to approach the interpretation of rāgas within the context of the emotions/moods presented in the shabads of those rāgas whilst adhering to the musical structure of the rāga. We use rāga Sirī to exemplify and focus the discussion. We challenge the ‘one rāga one emotion’ theory and propose that a rāga can be performed to evoke a number of emotions/moods but that certain considerations have to be taken into account by the performer during the rendition of the rāga.     

On the use of the term ‘frequency’ in applied behavior analysis

There exists a terminological problem in applied behavior analysis: the term frequency has been used as a synonym for both rate (the number of responses per time) and count (the number of responses). To guide decisions about the use and meaning of frequency, we surveyed the usage of frequency in contemporary behavior‐analytic journals and textbooks and found that the predominant usage of frequency was as count, not rate. Thus, we encourage behavior analysts to use frequency as a synonym for count.     

The PIG in sPrInG: Evidence on letter grouping from the reading of buried words

We introduce a novel procedure for investigating factors that determine selective attention to letters in words. Participants were presented with words (in Experiments 1 and 3) and nonwords (in Experiment 2) that contained a buried word whose letters differed in color relative to the other letters present (e.g.,pig, in spring). The strings were presented in single case or mixed case, keeping the letters of the buried words in one case (SpRiNg). The time in which the whole stimulus was named was shorter for same-case than for mixed-case strings (forspring: spring < SpRiNg). In contrast, the time in which buried words were named was shorter in mixed- than in same-case strings (forpig: spring > SpRiNg). Across items, the effects of case mixing were negatively correlated across the two tasks. The positive effect of case mixing for buried words also occurred irrespective of whether the whole string was a word or a nonword, and there were contributions from similarity of both letter size and case. The results suggest that case mixing can facilitate selective attention to letters, which is otherwise disrupted by size- and case-based grouping across letter strings. The study provides evidence for letter grouping using size and case information.     

Wittgenstein’s Picture Theory and the Distinction between Representing and Depicting

In this paper, I draw attention to the often-overlooked Tractarian distinction between representing (darstellen) and depicting (abbilden), provide a clear account of it and examine how it affects our understanding of the notions of ‘being a picture’, meaningfulness, truth, and falsity in the Tractatus. I also look at the recent debate in the literature on the notion of truth and show that Glock’s claim that the official theory of the Tractatus is to be accounted in terms of obtainment only and deflationary accounts such as Hacker’s derive from a failure to notice the distinction between representing and depicting (in the case of Glock) or a misconception of depicting (in the case of Hacker). Finally, I argue against the idea that either representing or depicting should be dispensed with. Both are necessary for Wittgenstein to account for every case of a proposition being a picture of reality.     

Patterns of Aggression in Parents and their Children

In this research, we examined children's awareness of inconsistencies in messages that are meaningful for children, instructions for games. In the first experiment, kindergarten (n = 25) and second- (n = 25) and fourth-grade (n = 26) children were individually read the instructions for two games, each of which included two inconsistent statements. Chi-square analyses yielded a significant effect for grade for one game (p < .05) and a marginally significant effect for a second game (p < .10). In a second experiment, second- (n = 40), fourth- (n = 40), and sixth-grade (n = 40) children were read the instructions for two games, each of which included two statements that were inconsistent. An analysis of variance demonstrated that with an increase in grade, there was a significant increase (p < .001) in awareness that a message contained an inconsistency. The analysis also indicated that the subjects were more willing (p < .08) to question an adult than they were to question a child about an inconsistency. Moreover, a regression analysis indicated that awareness of inconsistencies in the rules for games was significantly related to memory (p < .001) and to one's ability to note inconsistencies in shorter, simpler messages (p < .001).     

What is a fourdimensionalist to do about temporally extended properties?

Some properties and relations take time to be instantiated. They are not instantiated at a time, but through a temporal interval. Cognitive properties and relations such as understanding and thinking are like this, but also many biological, chemical, and microphysical properties and relations such as absorbing, freezing, radiating, and decaying. In this paper, I make a case for taking seriously such temporally extended properties (TEPs). I argue that they are ubiquitous and that our current theories of persistence would do well to make room for them in their ontology. The focus here is on fourdimensionalism and different ways it can accommodate TEPs. I explore four different ways of dealing with TEPs within a fourdimensionalist framework. These are: (a) to make the objects that bear apparent TEPs temporally more extended or “chunky,” while giving TEPs a reductive or eliminativist treatment in favor of instantaneous properties (IPs); (b) to make a series of objects the bearer of TEP predicates, while, again, holding only to IPs; (c) to endorse TEPs in their own right and take them to be temporally extended in a literal sense; and (d) to hold on to TEPs as atemporal properties and make the exemplification relation temporally extended. I discuss each of these options and highlight the types of problems that a fourdimensionalist faces in attempting to accommodate TEPs. I conclude that fourdimensionalists do not yet have a satisfactory account of TEPs in their hands.     

De-idealizing Disagreement,Rethinking Relativism

Relativism is often motivated in terms of certain types of disagreement. In this paper, we survey the philosophical debates over two such types: faultless disagreement in the case of gustatory conflict, and fundamental disagreement in the case of epistemic conflict. Each of the two discussions makes use of a (largely) implicit conception of judgement: brute judgement in the case of faultless disagreement, and rule-governed judgement in the case of fundamental disagreement. We show that the prevalent accounts work with unreasonably high levels of idealization. We defend two claims. First, philosophical discussions of disagreement need to be de-idealized. Second, once a less idealized account of disagreement is available, both our conception of judgement and our understanding of relativism need to be revised. Our example is a case study in the Sociology of Scientific Knowledge: Steven Shapin and Simon Schaffer’s classic Leviathan and the Air-Pump (1985). This case study gives a less idealized account of disagreement that conceptualizes judgements as situated (rather than brute or rule-governed). We argue that this conception can and should be applied to cases of gustatory and epistemic disagreement. The payoff will be a reformulation of relativism in terms of rationally resolvable yet contingent disagreements.     

How to eliminate self-reference: a précis

We provide a systematic recipe for eliminating self-reference from a simple language in which semantic paradoxes (whether purely logical or empirical) can be expressed. We start from a non-quantificational language L which contains a truth predicate and sentence names, and we associate to each sentence F of L an infinite series of translations h ₀(F), h ₁(F), ..., stated in a quantificational language L ^*. Under certain conditions, we show that none of the translations is self-referential, but that any one of them perfectly mirrors the semantic behavior of the original. The result, which can be seen as a generalization of recent work by Yablo (1993, Analysis, 53, 251–252; 2004, Self-reference, CSLI) and Cook (2004, Journal of Symbolic Logic, 69(3), 767–774), shows that under certain conditions self-reference is not essential to any of the semantic phenomena that can be obtained in a simple language.     

Difference to One: A Nuanced Early Chinese Account of Tong

The graph tong同and its associated concepts, such as da-tong (Great tong大同) and xuan-tong (mystic or dark tong玄同), have played important roles in the development of Chinese philosophy. Yet tong has received scant attention from either western or eastern scholarships. This paper is a first attempt to remedy such regret. Unlike usual understandings of tong as sameness or unity, this paper presents a nuanced account from early China, that is, ‘difference to one,’ a definition from the Mozi墨子. This definition can be supported from etymological, textual, and lexical evidence. ‘Difference to one’ should not be solely attributed to a Mohist understanding; it in fact represents a common understanding of tong across philosophical streams in early China. This nuanced account provides new insights into the concept of tong in early philosophical texts, and furthermore breaks solid grounds for further studies of tong and its associated concepts.     

Personality and Fears

The contribution to self-reported fears of individual differences in extraversion-introversion (E) and neuroticism (N) was studied in 102 female college students. Four groups of 20 Ss each were constituted - high E high N, high E low N, low E high N, and low E low N. A fear survey schedule and the Eysenck Personality Inventory were employed. By analysis of variance, total fear scores were a significant function of N but not E. Extreme or phobic fears were a significant function of neither personality dimensions, though the N effect approached conventional significance levels. Correlational analyses on the full sample confirmed these findings, except that a statistically significant though slight (6 percent) proportion of extreme fear variance was accountable by N.