Update to “A Survey of Abstract Algebraic Logic”

A definition and some inaccurate cross-references in the paper A Survey of Abstract Algebraic Logic, which might confuse some readers, are clarified and corrected; a short discussion of the main one is included. We also update a dozen of bibliographic references. Presented by Jacek Malinowski     

Frege’s Anti-Psychologism about Logic : the Relationship between Logic and Judgment

Philosophia - Frege is an anti-psychologist about logic who takes logic to be sharply distinguished from psychology. However, Frege also takes judgment, which seems to be a subject of psychology,...     

Numerical representation: Abstract or nonabstract?

Until now it has been a commonly held view that numbers are represented abstractly in the human brain. However, a recent imaging study challenged the existence of an abstract representation at least of digits and number words, at the brain level, and argued that previous studies and paradigms were not sensitive enough to detect deviations from abstract representation at the behavioural level. The current study addressed this issue with an analysis of distance and sequential effects in magnitude classification. Previous studies that used this paradigm did not find deviation from abstract representation for digits and number words (e.g., Dehaene, 1996 Dehaene, S. 1996. The organization of brain activations in number comparison: Event-related potentials and the additive-factors method. Journal of Cognitive Neuroscience, 8: 47–68. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Schwarz & Ischebeck, 2000 Schwarz, W. and Ischebeck, A. 2000. Sequential effects in number comparison. Journal of Experimental Psychology: Human Perception and Performance, 26: 1606–1621. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). However, in the current study a short stimulus–response interval was used, which reduced subjective expectancy and increased automatic processing. The current results showed deviation from abstract representation in both reaction time and accuracy and therefore support the idea that nonabstract representations of numbers do exist.     

Unification of Two Approaches to Quantum Logic: Every Birkhoff – von Neumann Quantum Logic is a Partial Infinite-Valued Łukasiewicz Logic

In the paper it is shown that every physically sound Birkhoff – von Neumann quantum logic, i.e., an orthomodular partially ordered set with an ordering set of probability measures can be treated as partial infinite-valued ?ukasiewicz logic, which unifies two competing approaches: the many-valued, and the two-valued but non-distributive, which have co-existed in the quantum logic theory since its very beginning.     

Logic and eloquence: A Ramusian revolution?

Logic and eloquence: A Ramusian revolution?     

Categorical perception of tonal intervais: Musicians can’t tellsharp fromflat

Six musicians with relative pitch judged 13 tonal intervals in a magnitude estimation task. Stimuli were spaced in .2-semitone increments over a range of three standard musical categories (fourth, tritone, fifth,). The judged magnitude of the intervals did not increase regularly with stimulus magnitude. Rather, the psychophysical functions showed three discrete steps cor-responding to the musically defined intervals. Although all six subjects had identified in-tune intervals with >95% accuracy, all were very poor at differentiating within a musical category— they could not reliably tell “sharp” from “flat.” After the experiment, they judged 63% of the stimuli to be “in tune,” but in fact only 23% were musically accurate. In a subsequent labeling task, subjects produced identification functions with sharply defined boundaries between each of the three musical categories. Our results parallel those associated with the identification and scaling of speech sounds, and we interpret them as evidence for categorical perception of music.     

Logic and Reasoning: do the facts matter?

Modern logic is undergoing a cognitive turn, side-stepping Frege’s ‘antipsychologism’. Collaborations between logicians and colleagues in more empirical fields are growing, especially in research on reasoning and information update by intelligent agents. We place this border-crossing research in the context of long-standing contacts between logic and empirical facts, since pure normativity has never been a plausible stance. We also discuss what the fall of Frege’s Wall means for a new agenda of logic as a theory of rational agency, and what might then be a viable understanding of ‘psychologism’ as a friend rather than an enemy of logical theory. Edited by Hannes Leitgeb     

Abstract conceptualization in schizophrenia: a fundamental psychological deficit?

Wright (1975) has recently argued that impairment in abstract conceptualization is an important schizophrenic deficit. We contend that the data to which he refers are insufficient support for that conclusion. Although schizophrenics' performance on sorting tasks may be less efficient than that of some other groups, the significance of this finding is debatable. A differential deficit in conceptual ability has not been shown and the confounding effects of third variables have not been ruled out. In addition, the validity of sorting techniques in measuring abstraction has not been adequately established. These methodological issues have a more general applicability to the study of psychopathology. Appreciation of them and a more specific definition of "acceptable evidence" would reduce considerably the continuing state of confusion in research on psychological deficit.     

Behavioral Gerontology Research: Where are the Male Participants?

It has been reported that females are underrepresented in several areas of psychological research, which may have significant clinical and theoretical implications. No one has reported, however, whether women are underrepresented in behavioral gerontology research. To make this determination we recorded the gender of participants in behavioral gerontology studies published in six journals. In 129 published studies that included older adults (i.e. people 55 or more years of age) there were a total of 3070 participants, and most (69%) were female. Underrepresentation of men is significant insofar as treatment effects are sometimes gender specific, making it inappropriate to generalize results from females to males (or vice versa). Moreover, underrepresentation of older men suggests that their behavioral needs may not be generating the attention they deserve. Copyright © 2015 John Wiley & Sons, Ltd.     

Categorical perception of facial expressions: Evidence for a “category adjustment” model

Four experiments probed the nature of categorical perception (CP) for facial expressions. A model based on naming alone failed to accurately predict performance onthese tasks. The data are instead consistentwith an extension of the category adjustment model (Huttenlocher et al., 2000), in which the generation of a verbal code (e.g., "happy") activated knowledge ofthe expression category's range andcentral tendency (prototype) in memory, which was retained as veridical perceptual memory faded.Further support for amemory bias toward the category center came from a consistently asymmetric pattern of within-category errors. Verbal interference in the retention interval selectively removed CP for facial expressions, under blocked, but not under randomized presentation conditions. However, verbal interference at encoding removed CPeven under randomized conditions and these effects were shown to extend even to caricatured expressions, which lie outside the normal range of expression categories.     

Extending Łukasiewicz Logics with a Modality: Algebraic Approach to Relational Semantics

This paper presents an algebraic approach of some many-valued generalizations of modal logic. The starting point is the definition of the [0, 1]-valued Kripke models, where [0, 1] denotes the well known MV-algebra. Two types of structures are used to define validity of formulas: the class of frames and the class of ? _n -valued frames. The latter structures are frames in which we specify in each world u the set (a subalgebra of ? _n ) of the allowed truth values of the formulas in u. We apply and develop algebraic tools (namely, canonical and strong canonical extensions) to generate complete modal n + 1-valued logics and we obtain many-valued counterparts of Shalqvist canonicity result.     

Acceptance in Cognitive Behavioral Psychotherapies: Different or the Same?

Acceptance is a key construct in both rational emotive behavior therapy (REBT) and acceptance and commitment therapy (ACT). The objectives of this study were to assess and compare the properties of ACT acceptance with those of REBT acceptance in predicting emotions. A sample of 112 subjects, comprising different educational and occupational status, completed three measures of acceptance (REBT and ACT), two of mindfulness, as well as completing depression and anxiety scales. Both ACT acceptance as process and REBT acceptance could predict significant ACT acceptance as outcome. Mindfulness as a trait also predicted the level of ACT outcome acceptance as well as the level of REBT acceptance, but mindfulness as process predicted only ACT outcome acceptance. The results show that REBT acceptance, ACT acceptance and mindfulness can explain anxiety and depression in different ways. The results show that the difference between ACT acceptance and REBT acceptance primary concern the process of acceptance, most likely due to the underlying cognitive processing. The outcome acceptance and emotional level are similar in the two conditions. Future research should employ multiple cognitive measurements.     

Behavioral obesity research: Where have all the single subjects gone?

Many recent reviews of the literature concerning behavioral treatments of obesity have concluded that behavioral methods have not been as successful in treating this problem as might have been predicted in the early years of behavior modification. Among the many potential reasons for this lack of success is the growing trend to utilize group statistical designs rather than single subject designs to examine the problem of obesity, in spite of the fact that single case methodology has provided the foundation for applied behavior analysis and behavior therapy. Several behavioral journals were surveyed to determine more precisely the trends in types of research strategies utilized in obesity studies. The potential relationship between research methodology and the development of effective treatments is discussed.     

Husserl and the Algebra of Logic: Husserl’s 1896 Lectures

In his 1896 lecture course on logic–reportedly a blueprint for the Prolegomena to Pure Logic–Husserl develops an explicit account of logic as an independent and purely theoretical discipline. According to Husserl, such a theory is needed for the foundations of logic (in a more general sense) to avoid psychologism in logic. The present paper shows that Husserl’s conception of logic (in a strict sense) belongs to the algebra of logic tradition. Husserl’s conception is modeled after arithmetic, and respectively logical inferences are viewed as analogical to arithmetical calculation. The paper ends with an examination of Husserl’s involvement with the key characters of the algebra of logic tradition. It is concluded that Ernst Schr?der, but presumably also Hermann and Robert Grassmann influenced Husserl most in his turn away from psychologism.     

Modal Logic for Other-World Agnostics: Neutrality and Halldén Incompleteness

The logic of ‘elsewhere,’ i.e., of a sentence operator interpretable as attaching to a formula to yield a formula true at a point in a Kripke model just in case the first formula is true at all other points in the model, has been applied in settings in which the points in question represent spatial positions (explaining the use of the word ‘elsewhere’), as well as in the case in which they represent moments of time. This logic is applied here to the alethic modal case, in which the points are thought of as possible worlds, with the suggestion that its deployment clarifies aspects of a position explored by John Divers un-der the name ‘modal agnosticism.’ In particular, it makes available a logic whose Halldén incompleteness explicitly registers the agnostic element of the position – its neutrality as between modal realism and modal anti-realism.