A note on the system of propositional calculus with primitive rule of extensionality

Summary The present paper deals with a systemS of propositional calculus, conjunction, equivalence and falsum being its primitive terms. The only primitive rule inS is the rule of extensionality defined by the scheme:      

Formalization of functionally complete propositional calculus with the functor of implication as the only primitive term

The most difficult problem that Leniewski came across in constructing his system of the foundations of mathematics was the problem of defining definitions, as he used to put it. He solved it to his satisfaction only when he had completed the formalization of his protothetic and ontology. By formalization of a deductive system one ought to understand in this context the statement, as precise and unambiguous as possible, of the conditions an expression has to satisfy if it is added to the system as a new thesis. Now, some protothetical theses, and some ontological ones, included in the respective systems, happen to be definitions. In the present essay I employ Leniewski's method of terminological explanations for the purpose of formalizing ukasiewicz's system of implicational calculus of propositions, which system, without having recourse to quantification, I first extended some time ago into a functionally complete system. This I achieved by allowing for a rule of implicational definitions, which enabled me to define any propositionforming functor for any finite number of propositional arguments.To the memory of Jerzy Supecki     

A contribution to the history of propositional calculus

Summary The anonimous scholiumOn all forms of syllogism was copied in 1884 from the Paris Codex 2064 by E. Richter. In 1899 M. Wallies published it in the preface to Ammonius' commentary on the Prior Analytics of Aristotle. There appear in that scholium, apart from the complex figure of Galenos, other characteristic forms of inference.Among these forms I found five so-called non-demonstrable stoic syllogisms, three modifications of the law of transposition of which the third is not mentioned by the authors of Princ pia Mathematica, and a modification of the form of inference known as Euclid's law. This form of inference was applied by Euclid in mathematics and by Saccherius in syllogistics; it is mentioned for the first time by Cardan in a treatise of 1570 and later by Clavius in his commentary of 1574 on the Elements of Euclid and in the commentary on Theodosius'Sphaerica of the year 1586.In 1658 Erhard Weigel made the first attempt at refuting the logical law of Euclid as formulated by Cardan and Clavius and in 1686 James Bernoulli tried to prove it.     

A cognitive model in which representations are images

Interpretations of images of the brain are starting to reveal the conceptual tasks in which the person was engaged at the time of imaging. Existing mathematical models can explain the patterns of activity observed in such images in terms of the coherent activity of large populations of neurons, but not in terms of cognition. This paper is an early investigation into how such patterns might provide the internal representations for a cognitive system. Probes, working memories and memories are all represented as images. The accompanying process model describes how attention is set according to the contents of working memory, how attention determines what parts of the probe are memorised, how memories are activated according to similarity to the probe in areas in attention, and how working memory is managed. The model is demonstrated on re-creations of classic simulations of recognition memory and categorisation.     

Worlds are colliding! Explaining the fictional in terms of the real

I discuss Gregory Currie’s taxonomy of explanations of the fictional. On the one hand, there is an important kind of relation between internal and external explanations of some fictional truths that Currie leaves out, where both are salient and yet in a relation of harmony with each other. On the other hand, I do not see that he has established that there is a genuine relation of tension between some pairs of internal and external explanations, and thus I question the usefulness of the category of collapse. I also consider a further kind of explanation: the exterior explanation.

Processing category terms in context: Instantiations as inferences

Three experiments were conducted to isolate conditions in which readers make their representations of text more concrete by instantiating (inferring a specific instance of) category terms. In previous research using single-sentence contexts and a modified Stroop task as an on-line measure of comprehension, no evidence for instantiation was obtained. In the present experiments, the modified Stroop task was used to test for instantiation when category terms were referred to anaphorically in subsequent sentences and when the category terms served as the subjects of single-sentence contexts. The pattern of the Stroop effects was dependent upon whether typical or atypical exemplars were suggested by the context. Facilitation of color naming was obtained in the former case, and interference was obtained in the latter case when the instances followed the appropriate biasing contexts. The results highlight the role of foregrounding and context in guiding the use of elaborative inferences.     

Personality terms of abuse in three cultures: type nouns between description and insult

In this study terms of abuse are investigated in three different cultures. Spontaneous verbal aggression is to a certain extent reminiscent of the values of a certain culture. One hundred and ninety‐two male subjects from Spain, Germany and the Netherlands were asked to write down terms of abuse that they would use given a certain stimulus situation, and in addition to give their rating of the offensive character of those terms. A total set of 830 useful expressions was thus collected. The frequencies of the expressions were established, and the total list of expressions was categorized in terms of what they were about. In Spanish abusive language is typically about family and relations, in Germany it is typically about anal aspects, and in the Netherlands it is mainly about genitals. Explanations are provided in terms of dimensions on which the three cultures differ. Copyright © 2004 John Wiley & Sons, Ltd.     

Whole-word units are used before orthographic knowledge in perceptual development

A visual search task for target letters in multiletter displays was used to investigate information-processing differences between college students and presecond-grade children (mean age = 7 years, 4 months). The stimulus displays consisted of single words, pronounceable pseudowords, and unpronounceable nonwords varying in length from three to five letters. The mean response times for indicating whether or not a target letter occurred in the display increased with the number of display letters for both groups, although there were apparent differences between groups in the rate of search and type of search strategy used. Pre-second-grade children responded faster to word displays than to pseudoword and nonword displays, indicating that familiar letter strings could be processed faster than unfamiliar strings regardless of whether or not the latter were consistent with rules of English orthography. In contrast, college students processed words and pseudowords about equally well, and both resulted in faster responses than nonwords. As reading skills develop, children apparently come to process familiar words differently from other letter strings. Only after a significant sightword vocabulary is established do children seem to recognize the regularities of standard English orthography and make use of this knowledge to facilitate perceptual processes.     

A critical evaluation of coercive persuasion as used in the assessment of cults

An intense controversy regarding new and unpopular religious movements, or cults, continues to involve professionals at the juncture of psychiatry, religion, and the law. As the cults come under increasingly critical scrutiny, the concept most often used for assessing them is that of coercive persuasion. Briefly, such persuasion is seen as a means of psychological manipulation that leaves individuals without the normal control of their own minds. Considering recent pertinent cases and literature, the authors find major weaknesses in this theory. When applied it proves elastic, and it is regularly identified in cults for conduct that, on close examination, is similar to that of established religious groups. The concept of coercive persuasion as a means of thought control fails to pass scientific muster, and it serves poorly as a means of evaluating the connection between alleged harm and the cults. Instead, the authors suggest that a search for an alternative theory might well begin with one based on the individual as competent or not to make a choice regarding religion.     

Leader election outcomes as contextual moderators explaining the different frequencies of action-oriented terms and negation terms used in inaugural speeches of effective versus ineffective leaders and charismatic versus non-charismatic leaders: Evidence from 30 U.S. presidents

Psychologists have increasingly employed dictionary-based text analysis to examine the language of leadership, as leadership is embedded in a web of negotiated meanings and contextual factors. This research seeks to embed leaders’ rhetorical influence in leader–follower relationships and identify contextual factors that explain the different patterns of effective versus ineffective leaders’ and charismatic versus non-charismatic leaders’ uses of action-oriented terms and negation terms in their inaugural speeches. By analyzing data of 30 U.S. presidents’ inaugural addresses, presidential election outcomes, and leadership styles, I found that effective leaders used action-oriented terms more frequently in their inaugural speeches than ineffective leaders only when follower participation was low, whereas charismatic leaders used negation terms more frequently in their inaugural speeches than non-charismatic leaders only when follower endorsement was low. These findings suggest that effective leaders are attuned to action-related situational cues whereas charismatic leaders are attuned to value-related situational cues.     

A test of Durkheim's theory of suicide in primitive societies.

Primitive societies were classified as high, moderate, or low on independent measures of social integration and social regulation to test Durkheim's theory of suicide. The estimated frequency of suicide did not differ between those societies predicted to have high, moderate, and low suicide rates. Thus, Durkheim's theory was not confirmed. Possible reasons for these results are discussed.     

A method of factor analysis by means of which all coordinates of the factor matrix are given simultaneously

In general, the methods of factor analysis developed during the past five years are based on the reduction of the correlational matrix by successive steps. The first factor loadings are determined and eliminated from the correlational matrix, giving a residual matrix. This process is continued for successive factor loadings until the elements of the last obtained residual matrix may be regarded as due to chance. The method outlined in this paper assumes the maximum number of factorsm in the correlational matrix. Them factor vectors are solved for simultaneously. Once them factor vectors are found, any vectors having only negligible factor loadings may be discarded.