Mandelstam's interpretation of quantum mechanics in comparative perspective

In his 1939 Lectures, the prominent Soviet physicist L. I. Mandelstam proposed an interpretation of quantum mechanics that was understood in different ways. To assess Mandelstam's interpretation, we classify contemporary interpretations of quantum mechanics and compare his interpretation with others developed in the 1930s (the Copenhagen interpretation and the statistical interpretations proposed by K. R. Popper, H. Margenau, and E. C. Kemble). We conclude that Mandelstam's interpretation belongs to the family of minimal statistical interpretations and has much in common with interpretations developed by American physicists. Mandelstam's characteristic message was his theory of indirect measurement, which influenced his discussion of the “reduction of the wave packet” and the Einstein, Podolsky, and Rosen argument. This article also reconstructs what lay behind Mandelstam's interpretation of quantum mechanics. This was his operationalism, by virtue of which his interpretation resembled Kemble's, in which the statistical and Copenhagen views had been combined. Like Popper and Margenau, Mandelstam followed R. von Mises's empirical conception of probability. Mandelstam, like the other proponents of the statistical approach to quantum mechanics, was affected by the culture of macroscopic experimentation with its emphasis on statistical (collective) measurement.     

Tarski ‐ a dilemma

Tarski's correspondence theory of truth (which he spells out in his semantic conception of truth) is open to two interpretations. This ambiguity in the theory has led philosophers to find support in it for metaphysical reali sm. In fact, Tarski's theory turns out to support a form of ontological relativism. In different passages Tarski himself gives support to each of these interpretations. The first interpretation leads to ontological relativism, while the second sacrifices the connection between language and the world. I clarify the dilemma that I see in having to choose between these two interpretations, explain how these interpretations have their source in different problems which occupied Tarski, and consider a possible solution to the dilemma. Finally, finding good reasons to claim that Tarski's theory is indeed a correspondence theory of truth, I argue in favour of the first interpretation with its relativistic implications.     

TOWARD THE DEVELOPMENT OF STRUCTURED CRITERIA FOR INTERPRETATION OF FUNCTIONAL ANALYSIS DATA

Using functional analysis results to prescribe treatments is the preferred method for developing behavioral interventions. Little is known, however, about the reliability and validity of visual inspection for the interpretation of functional analysis data. The purpose of this investigation was to develop a set of structured criteria for visual inspection of multielement functional analyses that, when applied correctly, would increase interrater agreement and agreement with interpretations reached by expert consensus. In Study 1, 3 predoctoral interns interpreted functional analysis graphs, and interrater agreement was low (M = .46). In Study 2, 64 functional analysis graphs were interpreted by a panel of experts, and then a set of structured criteria were developed that yielded interpretive results similar to those of the panel (exact agreement = .94). In Study 3, the 3 predoctoral interns from Study 1 were trained to use the structured criteria, and the mean interrater agreement coefficient increased to .81. The results suggest that (a) the interpretation of functional analysis data may be less reliable than is generally assumed, (b) decision-making rules used by experts in the interpretation of functional analysis data can be operationalized, and (c) individuals can be trained to apply these rules accurately to increase interrater agreement. Potential uses of the criteria are discussed.     

Aristotle's Metaphysics: Form,Matter and Identity

ABSTRACT

The example of the Spanish poet’s amnesia, mentioned by Spinoza in the scholium of proposition 39 of part IV of the Ethics in order to elucidate his conception of death, has given rise to many controversies in the scholarly interpretations, which in most cases maintain that the poet dies and that Spinoza himself thought this way. However, the matter is more complex than it at first appears and in this article I take a different path by reconstructing this scholium anew and providing an alternative interpretation. The comparison with selected passages of part V highlights the presence of a bi-conditional between the ratio of motion and rest that a body possesses, and its aptitude to be affected and affect in many more ways. In particular, the latter allows us to acknowledge the continuity of the poet’s individuality, expressed in his mind–body union grounded by the parallelism theory. As a result, the poet case has a crucial explanatory role for Spinoza’s theory of the eternity of the human mind and if one misunderstands the former, the latter is also misconceived.     

Using e-learning modules to teach ongoing-visual inspection of functional analyses

Despite the effectiveness of function-based treatments, most clinicians do not conduct functional analyses (FA). The time required to conduct an FA is a major barrier preventing their use. One way to increase FA efficiency is to discontinue the analysis as soon as it has produced clear results. Saini et al. (2018) evaluated a structured procedure for ongoing-visual inspection of FAs and found that it produced accurate interpretations while averaging 40% fewer sessions than author interpretation. This study evaluated the efficacy of an e-learning module for training registered behavior technicians (RBTs) to implement ongoing visual inspection of FAs. Following training, 5 of the 6 participants showed mastery of ongoing visual inspection, and the final participant did so with the addition of supplemental procedures. We discuss how this training may increase the efficiency of FAs by teaching individuals who are less experienced in FA methodology when to seek supervision from a supervising Board Certified Behavior Analyst® (BCBA).     

The Concept of Number: Multiplicity and Succession between Cardinality and Ordinality

Abstract

This article sets out to analyse some of the most basic elements of our number concept - of our awareness of the one and the many in their coherence with multiplicity, succession and equinumerosity. On the basis of the definition given by Cantor and the set theoretical definition of cardinal numbers and ordinal numbers provided by Ebbinghaus, a critical appraisal is given of Frege’s objection that abstraction and noticing (or disregarding) differences between entities do not produce the concept of number. By introducing the notion of subject functions, an account is advanced of the (nominalistic) reason why Frege accepted physical, kinematic and spatial properties (subject functions) of entities, but denied the ontic status of their quantitative properties (their quantitative subject function). With reference to intuitionistic mathematics (Brouwer, Weyl, Troelstra, Kreisel, Van Dalen) the primitive meaning of succession is acknowledged and connected to an analysis of what is entailed in the term ‘Gleichzahligkeit’ (‘equinumerosity’). This expression enables an analysis of the connections between ordinality and cardinality on the one hand and succession and wholeness (totality) on the other. The conceptions of mathematicians such as Frege, Cantor, Dedekind, Zermelo, Brouwer, Skolem, Fraenkel, Von Neumann, Hilbert, Bernays and Weyl, as well as the views of the philosopher Cassirer, are discussed in order to arrive at an assessment of the relation between ordinality and cardinality (also taking into account the relation between logic and arithmetic) - and on the basis of this evaluation, attention is briefly given to the definition of an ordered pair in axiomatic set theory (with reference to the set theory of Zermelo-Fraenkel) and to the defmition of an ordered pair advanced by Wiener and Kuratowski.     

Two interpretations of the discrimination parameter

In this paper we propose two interpretations for the discrimination parameter in the two-parameter logistic model (2PLM). The interpretations are based on the relation between the 2PLM and two stochastic models. In the first interpretation, the 2PLM is linked to a diffusion model so that the probability of absorption equals the 2PLM. The discrimination parameter is the distance between the two absorbing boundaries and therefore the amount of information that has to be collected before a response to an item can be given. For the second interpretation, the 2PLM is connected to a specific type of race model. In the race model, the discrimination parameter is inversely related to the dependency of the information used in the decision process. Extended versions of both models with person-to-person variability in the difficulty parameter are considered. When fitted to a data set, it is shown that a generalization of the race model that allows for dependency between choices and response times (RTs) is the best-fitting model.     

Biased interpretation in perfectionism and its modification

Perfectionism is a transdiagnostic construct associated with a range of diagnoses, including depression, eating disorders and obsessive compulsive disorder. Treatments that directly target perfectionist cognitions have been shown to successfully reduce associated pathologies. However, the way in which they do this is not clear. We set out to assess the role of one candidate mechanism of action, namely the cognitive process of interpretation of ambiguity. In one experiment we looked for associations between biased interpretation and perfectionism. In a second, we manipulated interpretations, thereby providing a strong test of their aetiological significance. Results from the first experiment confirmed the presence of biased interpretation in perfectionism and demonstrated that these are highly specific to perfection relevant information, rather than reflecting general negativity. The second experiment succeeded in manipulating these perfection relevant interpretations and demonstrated that one consequence of doing so is a change in perfectionist behaviour. Together, these data experimentally demonstrate that biased interpretation of perfection relevant ambiguity contributes to the maintenance of perfectionism, but that it is also possible to reverse this. Clinical implications include the identification of one likely mechanism of therapeutic change within existing treatments, as well as identification of an appropriate evidence-based focus for future treatment development. Targeting underlying functional mechanisms, such as biased interpretation, has the potential to offer transdiagnostic benefits.     

Kant,Neo‐Kantians,and Transcendental Subjectivity

This article discusses an interpretation of Kant's conception of transcendental subjectivity, which manages to avoid many of the concerns that have been raised by analytic interpreters over this doctrine. It is an interpretation put forward by selected C19 and early C20 neo‐Kantian writers. The article starts out by offering a neo‐Kantian interpretation of the object as something that is constituted by the categories and that serves as a standard of truth within a theory of judgment (I). The second part explicates transcendental subjectivity as the system of categories, which is self‐referential and constitutes objects (II), in order to then evaluate this conception by means of a comparison with Hegel's absolute subject (III). Rather than delineating the differences between neo‐Kantian writers, the article systematically expounds a shared project, which consists in providing the ultimate foundation for judgments by means of an anti‐psychologist and non‐metaphysical interpretation of transcendental subjectivity.     

Radical Interpretation and The Aggregation Problem

This paper takes issue with Lewis’ influential argument for the supervenience of the semantic on the non-semantic based on the possibility of radical interpretation. Radical interpretation is possible only if an ideal being, who is omniscient about the non-semantic truths, can deduce the semantic truths a priori. The radical interpreter appeals to a set of criteria of interpretation choice, such as most notably some kind of Principle of Charity. It is argued in this paper that the radical interpreter faces an insoluble aggregation problem: the radical interpreter must jointly apply several criteria for evaluating interpretations in order to determine which interpretation is best overall. First, the situation of the radical interpreter is formally modeled using the machinery of social choice theory. Second, it is argued that either Arrow's impossibility theorem or a variant of it applies to the situation of the radical interpreter. The upshot is that radical interpretation is impossible, and Lewis’ argument for semantic supervenience fails.     

A theory of belief

A theory of belief is presented in which uncertainty has two dimensions. The two dimensions have a variety of interpretations. The article focusses on two of these interpretations.The first is that one dimension corresponds to probability and the other to “definiteness,” which itself has a variety of interpretations. One interpretation of definiteness is as the ordinal inverse of an aspect of uncertainty called “ambiguity” that is often considered important in the decision theory literature. (Greater ambiguity produces less definiteness and vice versa.) Another interpretation of definiteness is as a factor that measures the distortion of an individual's probability judgments that is due to specific factors involved in the cognitive processing leading to judgments. This interpretation is used to provide a new foundation for support theories of probability judgments and a new formulation of the “Unpacking Principle” of Tversky and Koehler.The second interpretation of the two dimensions of uncertainty is that one dimension of an event A corresponds to a function that measures the probabilistic strength of A as the focal event in conditional events of the form A|B, and the other dimension corresponds to a function that measures the probabilistic strength of A as the context or conditioning event in conditional events of the form C|A. The second interpretation is used to provide an account of experimental results in which for disjoint events A and B, the judge probabilities of A|(A∪B) and B|(A∪B) do not sum to 1.The theory of belief is axiomatized qualitatively in terms of a primitive binary relation ? on conditional events. (A|B?C|D is interpreted as “the degree of belief of A|B is greater than the degree of belief of C|D.”) It is shown that the axiomatization is a generalization of conditional probability in which a principle of conditional probability that has been repeatedly criticized on normative grounds may fail.Representation and uniqueness theorems for the axiomatization demonstrate that the resulting generalization is comparable in mathematical richness to finitely additive probability theory.     

Interface Problems: Structural Constraints on Interpretation?

Five experiments investigated the interpretation of quantified noun phrases in relation to discourse structure. They demonstrated, using questionnaire and on-line reading techniques, that readers in English prefer to give a quantified noun phrase in (VP-external) subject position a presuppositional interpretation, in which the noun phrase limits or restricts the interpretation of an already available set, rather than giving it a nonpresuppositional or existential interpretation, in which it introduces completely new entities into the discourse. Experiment 1 showed that readers prefer a presuppositional interpretation of three ships over the existential interpretation in Five ships appeared on the horizon. Three ships sank. Experiment 2 showed longer reading times in sentences that are disambiguated toward the existential interpretation than in sentences that permit the presuppositional interpretation. Experiment 3 suggested that the presuppositional preference is greater when the phrase three ships occurs outside the verb phrase than when it occurs inside the verb phrase. Experiment 4 showed that Korean subjects marked with a topic marker received more presuppositional interpretations than subjects marked with a nominative marker. Experiment 5 showed that German subjects in VP-external (but nontopic) position received more presuppositional interpretations than VP-internal subjects. The results suggest the syntactic position of a phrase is one determinant of its interpretation, as expected according to the mapping hypothesis of Diesing (1992).This research was supported in part by grants HD-18708 and HD-17246 to the University of Massachusetts. Rayner was also supported by a Research Scientist Award (MH01255).     

Butter Knives and Screwdrivers: An Intentionalist Defense of Radical Constructivism

Robert Stecker has posed a dilemma for the constructivist theory of interpretation: either interpretations consist of statements with truth values or they do not. Stecker argues that either way, they cannot change the meaning of an artwork. In this article, I argue contra Stecker that if interpretations consist of meaning declarations rather than statements, they can change the meanings of the objects toward which they are directed, where whether they so consist is largely a function of the interpreter's intentions. Hence, the second horn of Stecker's dilemma is defeated.     

J. S. Mill on Coolie Labour and Voluntary Slavery

This article discusses John Stuart Mill's voluntary slavery argument in On Liberty. The author shows that standard interpretations of the argument rely on the assumption that part of Mill's objection to voluntary slavery is the permanent nature of the decision. However, in correspondence, Mill also objects to voluntary ‘coolie’ labour contracts, which he regards as a form of slavery. This produces difficulties for standard interpretations of the voluntary slavery argument. Finally, the author provides a revised interpretation of Mill's argument to solve this problem.     

A functional theory of the McCollough effect

Pattern-contingent color aftereffects, or McCollough effects (MEs), are used to probe the visual brain's operations psychophysically. Their neural substrate is unknown, however, and theories about them are weak. Our theory proposes a strong functional role for MEs and a neuropsychological basis that accounts for "top-down" (global) constraints ignored by other theories. The functional aspect of the theory is based on the concept of contingent adaptation level, following Helson (1964), and on the "error-correcting device" of Andrews (1964), which tracks and adjusts internal representation to external-world contingencies. The neuropsychological part of the theory postulates that global properties are the result of MEs being generated not at the individual detector level but in vectorfields of which the detectors are elements. It is an implementation of Lie transformation group theory (Hoffman, 1966). Evidence for this model is assessed.     

Preposition-phrase attachment in noun phrases

This paper examines the ambiguity of noun phrases (NPs) with postmodifying preposition phrases (PPs), such as the triangle next to the circle below the square. This ambiguity is attributable in part to the difference in attachment sites for the second PP. If it attaches low, it modifies just the NP that is the object of the first preposition, and the resulting structure is right branching. If it attaches high, it modifies the entire preceding NP, and the resulting structure is left branching. However, each of these structures itself has two distinct interpretations. In the case of the high-attachment structure, these different interpretations have been previously noted; we call them stacking and coordinating. In the stacking interpretation, each PP modifies the entire NP to its left, whereas in the coordinating interpretation, it modifies just the head noun to its left (the first noun in the construction). In the case of the low-attachment structure, only the interpretation corresponding to the coordinating one has been noted; we call it alternating. However, a fourth distinct interpretation is possible, which corresponds to the stacking interpretation of the highattachment structure; we call it stuffing. In the alternating interpretation, each preposition has scope only over the head of the NP that is its complement. In the stuffing interpretation, each preposition has scope over its entire complement. In a pilot study, we found that the interpretations based on low attachment are preferred to those based on high attachment by a 21 ratio. Of the two low-attachment interpretations, alternating is preferred to stuffing by a 201 ratio. However, of the two high-attachment interpretations, coordinating is preferred to stacking by only a 21 ratio. In a second pilot study, we examined the pattern of interpretations of phrases with four PP postmodifiers of an NP, which in principle have 112 distinct interpretation types. Eleven of these types were noted in the experimental materials. We provide a detailed analysis of these types and note that the relative preference of the various interpretations found in the first study is preserved.     

Mikhail Lifshits and the Soviet image of Giambattista Vico

Mikhail Lifshits’ interpretation of the scholarly work of the Italian philosopher Giambattista Vico is analysed against the background of other Soviet interpretations. M. Lifshits authored the introductory article for the first complete translation of Vico’s Scienza Nuova in 1940. In the second half of the 1930s, interest in Vico’s ‘historical theory of knowledge’ was important for the struggle against so-called ‘vulgar sociology’ in the field of aesthetics and literary criticism. Besides this, Vico’s theory of the ‘historical cycle’ was close to the interests M. Lifshits and G. Lukács and their circle in Stalin-era Moscow. This interest was connected with discussions about the preservation of the revolutionary impulse under the conditions of state socialism. However, such an interpretation of Vico (considering him only as a predecessor of Hegel’s and Marx’s philosophy of history) restricted a wide spectrum of his scholarly work. In particular, Lifshits, as an opponent of social-constructivism tradition, ignored Vico’s well-known doctrine of verum factum.

     

Consciousness and Hegel's Solution to the Problem of the Criterion

Traditional epistemological interpretations have portrayed Hegel as offering a coherentist solution to the problem of the criterion in the introduction to The Phenomenology of Spirit. In this paper, I criticize the coherentist interpretation and present an alternative reading that emphasizes the central role of conscious experience in Hegel's argument. In the first part of the paper, I show how the passages commonly used to support the coherentist interpretation ultimately fail to do so and argue that coherence by itself cannot be the lynchpin for an adequate solution to the problem of the criterion. In the second part, I then develop a novel interpretation of Hegel's argument by drawing attention to the fact that Hegel formulates both the problem of the criterion and his solution to it in terms of consciousness.     

Truths qua Grounds

A number of philosophers have recently found it congenial to talk in terms of grounding. Grounding discourse features grounding sentences that are answers to questions about what grounds what. The goal of this article is to explore and defend a counterpart‐theoretic interpretation of grounding discourse. We are familiar with David Lewis's applications of the method of counterpart theory to de re modal discourse. Counterpart‐theoretic interpretations of de re modal idioms and grounding sentences share similar motivations, mechanisms, and applications. I shall explain my motivations and describe two applications of a counterpart theory for grounding discourse. But, in this article, my main focus is on counterpart‐theoretic mechanisms.     

The functional theory of counterfactual thinking.

Counterfactuals are thoughts about alternatives to past events, that is, thoughts of what might have been. This article provides an updated account of the functional theory of counterfactual thinking, suggesting that such thoughts are best explained in terms of their role in behavior regulation and performance improvement. The article reviews a wide range of cognitive experiments indicating that counterfactual thoughts may influence behavior by either of two routes: a content-specific pathway (which involves specific informational effects on behavioral intentions, which then influence behavior) and a content-neutral pathway (which involves indirect effects via affect, mind-sets, or motivation). The functional theory is particularly useful in organizing recent findings regarding counterfactual thinking and mental health. The article concludes by considering the connections to other theoretical conceptions, especially recent advances in goal cognition.