Remarks on the Theory of Quasi-sets

Quasi-set theory has been proposed as a means of handling collections of indiscernible objects. Although the most direct application of the theory is quantum physics, it can be seen per se as a non-classical logic (a non-reflexive logic). In this paper we revise and correct some aspects of quasi-set theory as presented in [12], so as to avoid some misunderstandings and possible misinterpretations about the results achieved by the theory. Some further ideas with regard to quantum field theory are also advanced in this paper.     

The Structural Metaphysics of Quantum Theory and General Relativity

The paper compares ontic structural realism in quantum physics with ontic structural realism about space–time. We contend that both quantum theory and general relativity theory support a common, contentful metaphysics of ontic structural realism. After recalling the main claim of ontic structural realism and its physical support, we point out that both in the domain of quantum theory and in the domain of general relativity theory, there are objects whose essential ways of being are certain relations so that these objects do not possess an intrinsic identity. Nonetheless, the qualitative, physical nature of these relations is in the quantum case (entanglement) fundamentally different from the classical, metrical relations treated in general relativity theory.     

Elementary Particles,Hidden Variables,And Hidden Predicates

We recently showed that it is possible to deal withcollections of indistinguishable elementary particles (in thecontext of quantum mechanics) in a set-theoretical framework, byusing hidden variables. We propose in the presentpaper another axiomatics for collections of indiscernibleswithout hidden variables, where hidden predicates are implicitlyassumed. We also discuss the possibility of a quasi-settheoretical picture for quantum theory. Quasi-set theory, basedon Zermelo-Fraenkel set theory, was developed for dealing withcollections of indistinguishable, but, not identical objects.     

Working memory for relations among objects

Across many areas of study in cognition, the capacity of working memory (WM) is widely agreed to be roughly three to five items: three to five objects (i.e., bound collections of object features) in the literature on visual WM or three to five role bindings (i.e., objects in specific relational roles) in the literature on memory and reasoning. Three experiments investigated the capacity of observers’ WM for the spatial relations among objects in a visual display, and the results suggest that the “items” in WM are neither simply objects nor simply role bindings. The results of Experiment 1 are most consistent with a model that treats an “item” in visual WM as an object, along with the roles of all its relations to one other object. Experiment 2 compared observers’ WM for object size with their memory for relative size and provided evidence that observers compute and store objects’ relations per se (rather than just absolute size) in WM. Experiment 3 tested and confirmed several more nuanced predictions of the model supported by Experiment 1. Together, these findings suggest that objects are stored in visual WM in pairs (along with all the relations between the objects in a pair) and that, from the perspective of WM, a given object in one pair is not the same “item” as that same object in a different pair.     

Proficient performance of a conjunctive, recursive task by an African gray parrot (Psittacus erithacus).

The comprehension skills of an African gray parrot (Psittacus erithacus), Alex, were tested on a taks that included a conjunctive condition. For each trial, Alex was shown different collections of 7 items, each collection chosen from among 100 objects of various combinations of shapes, colors, and materials, and he was asked to provide (vocally) information about the specific instance of one category of an item that was uniquely defined by the conjunction of two other categories (e.g., "What color is the [object defined by shape and material]?"). Other objects exemplified one, but not both, of these defining categories. Alex responded with an accuracy of 76.5%, which indicated that he understood all the elements in the question, including the conjunctive condition, and that he used these elements to guide his search for the one object in the collection that provided the requested information.     

A theory of variability discrimination: Finding differences

Visual variability discrimination requires an observer to categorize collections of items on the basis of the variability in the collection; such discriminations may be vital to the adaptive actions of both humans and other animals. We present a theory of visual variability discrimination that aggregates localized differences between nearby items, and we compare this finding differences model with a previously proposed positional entropy model across several data sets involving both people and pigeons. We supplement those previously published data sets with four new experiments, three of which involve arrays comprising items entailing systematic, quantitative differences. Although both theories provide strong and similar fits of the published data sets, only the finding differences model is applicable to investigations involving quantitative item differences, providing excellent fits in these new experiments.     

Many entities, no identity

The aim of this paper is to argue that some objections raised by Jantzen (Synthese, 2010) against the separation of the concepts of ‘counting’ and ‘identity’ are misled. We present a definition of counting in the context of quasi-set theory requiring neither the labeling nor the identity and individuality of the counted entities. We argue that, contrary to what Jantzen poses, there are no problems with the technical development of this kind of definition. As a result of being able to keep counting and identity apart for those entities, we briefly suggest that one venerable tradition concerning the nature of quantum particles may be consistently held. According to that tradition, known as the Received View on particles non-individuality, quantum particles may be seen as entities having both features: (i) identity and individuality do not apply to them, (ii) they may be gathered in collections comprising a plurality of them.     

Identity,Indiscernibility, and Philosophical Claims

The concept of indiscernibility in a structure is analysed with the aim of emphasizing that in asserting that two objects are indiscernible, it is useful to consider these objects as members of (the domain of) a structure. A case for this usefulness is presented by examining the consequences of this view to the philosophical discussion on identity and indiscernibility in quantum theory.     

ORDER FROM VIRTUAL STATES: A DIALOGUE ON THE RELEVANCE OF QUANTUM THEORY TO RELIGION

Abstract. Lothar Schäfer has written a poetic tribute pointing out the relevance of quantum theory to religious beliefs. Two items in his article trouble me greatly. First are the excessive claims about the relevance of quantum mechanisms for the creation and evolution of life. Schäfer's claim that “everything that can happen must happen” can be dangerously misleading. The quantum rules predict that most outcomes have a near‐zero chance of occurring. Although “anything can happen” can be a wonderful metaphor for living life, it can be dangerous if taken literally. It can also be misleading when applied to Darwinian mechanisms. My second trouble was with Schäfer's desire to extract moral values from quantum principles in a literalist manner. Extracting ethics from science has always been problematic. Luckily, Schäfer provides balance to these objections by including many wonderful passages that in my opinion correctly point out how quantum theory should change the way we conceive of our place in the universe. I list twelve points in which the quantum ontology differs from our normal Newtonian ontology. Awareness of these aspects is typically missing from our usual appreciation of nature, so Schäfer's poetry on a number of these points is well appreciated.     

Divided attention: Storing and classifying briefly presented objects

Although in many studies divided attention has been examined by having people perform the same task (e.g., report or search) with a large number of objects, in few studies have people had to perform two logically independent tasks involving the same brief display. In two experiments, subjects saw 200-msec arrays of characters. In dual-task blocks, theyclassified the color of some or all of the items (making an immediate response) andstored the shape of some of the items for a later recognition test. There was not much mutual interference between classifying and storing per se. However, the tasks were by no means independent: there was substantial interference whendifferent objects from the array had to be stored for one task and classified for the other. The results confirm that wholly unrelated visual tasks depend on the same input-attention system and suggest that attending to an object for any purpose may entail storing a representation of it in visual short-term memory.     

Classes and collections: Internal organization and resulting holistic properties

This work presents an analysis of a type of concept, the collection, not readily characterized by class inclusion models. Collections, the referents of collective nouns (e.g., pile, family, bunch), are argued to differ from classes in (a) how membership can be determined, (b) part-whole relationships, (c) internal structure, and (d) the nature of the higher order units they form. From this analysis, it is hypothesized that the psychological integrity of collections is greater than that of classes. Collections and objects, in contrast to classes, both require specified relationships among the parts and both result in a coherent psychological unit. It was suggested that objects form a relatively more stable unit than collections. Corresponding to this analysis the degree of psychological integrity is hypothesized to lead to different degrees of difficulty in making part-whole comparisons for objects, collections, and classes in modified Piagetian class-inclusion paradigms. The hypothesized difference in performance was found for collections and classes and an alternative linguistic explanation for the greater success with collections was eliminated. However, children performed equally well on tasks involving collections and objects, raising the possibility that when elements are organized into collections, they form psychological units which are as coherent as objects.     

Quantum information in an evolutionary perspective

An approach to quantum phenomena is reviewed that deals with the possibility of their realistic interpretation in the sense that they represent manifestations of hermeneutic circles between quantum “objects” and their experimental boundary conditions. Quantum cybernetics provides an evolutionary perspective in that all higher‐level organizations like molecules, cells, living systems, etc., can be discussed under one and the same systemic viewpoint: a hermeneutic circularity between a “core” (or “nucleus") and a relevant “periphery” (or “environment") which constitutes the systems’ organization and information potential.

Generally, in realistic theories, an individual quantum system is analyzable into a local “particle‐like” nonlinearity of a generally nonlocal “wave‐like” mode of some sub‐quantum structure of the vacuum ("Dirac ether"). In this view, a “particle” can be considered as being “guided” along one specific route by the (generally nonlocal) configurations of superimposed waves, which spread along all possible paths of an experimental setup. Moreover, in the approach of Quantum Cybernetics, an additional focus is given on the fact that the energy and momentum of a particle also determine the wave behavior. Thus, “waves” and “particles” are mutually and self‐consistently defined, and Quantum Cybernetics puts particular emphasis on the circular relationship—mediated by plane waves—between a quantum system and its macroscopically defined boundary conditions.     

Transfer of signed responses in American Sign Language from vocal English stimuli to physical object stimuli by a chimpanzee (Pan)

A chimpanzee was taught 10 signs of Ameslan (American Sign Language) using only vocal English words as stimuli. The corresponding physical objects were items found in the subject's home environment, and which he frequently encountered during daily activities. Reference was not made to these items during teaching sessions. Each teaching session was followed by a test session in which the objects were silently presented to the subject and the question What that? was signed to him. The subject acquired all 10 signs in response to the English word stimuli and then successfully transferred these signs to their physical object referents during testing.     

Distinguishing different strategies of across-dimension attentional selection

Selective attention in multidimensional displays has usually been examined using search tasks requiring the detection of a single target. We examined the ability to perceive a spatial structure in multi-item subsets of a display that were defined either conjunctively or disjunctively. Observers saw two adjacent displays and indicated whether the to-be-selected items within the two displays matched in terms of their spatial structure (the identity of the corresponding items within these subsets was not relevant to the task). The observers in our study could readily perceive conjunctively defined subsets, but had great difficulty with disjunctively defined subsets. The results pose a challenge to the popular idea that attention is guided by a "priority map" that sums bottom-up and top-down factors, whereas they are directly predicted by Boolean map theory of visual attention.     

Schrödinger logics

Schrödinger logics are logical systems in which the principle of identity is not true in general. The intuitive motivation for these logics is both Erwin Schrödinger's thesis (which has been advanced by other authors) that identity lacks sense for elementary particles of modern physics, and the way which physicists deal with this concept; normally, they understandidentity as meaningindistinguishability (agreemment with respect to attributes). Observing that these concepts are equivalent in classical logic and mathematics, which underly the usual physical theories, we present a higher-order logical system in which these concepts are systematically separated. A classical semantics for the system is presented and some philosophical related questions are mentioned. One of the main characteristics of our system is that Leibniz' Principle of the Identity of Indiscernibles cannot be derived. This fact is in accordance with some authors who maintain that quantum mechanics violates this principle. Furthermore, our system may be viewed as a way of making sense some of Schrödinger's logical intuitions about the nature of elementary particles.The authors very much would like to thank the anonymous referee for his quite interesting suggestions, which contributed significantly to improve the paper.Presented byJan Zygmunt;     

What is a visual object? Evidence from target merging in multiple object tracking

The notion that visual attention can operate over visual objects in addition to spatial locations has recently received much empirical support, but there has been relatively little empirical consideration of what can count as an 'object' in the first place. We have investigated this question in the context of the multiple object tracking paradigm, in which subjects must track a number of independently and unpredictably moving identical items in a field of identical distractors. What types of feature clusters can be tracked in this manner? In other words, what counts as an 'object' in this task? We investigated this question with a technique we call target merging: we alter tracking displays so that distinct target and distractor locations appear perceptually to be parts of the same object by merging pairs of items (one target with one distractor) in various ways - for example, by connecting item locations with a simple line segment, by drawing the convex hull of the two items, and so forth. The data show that target merging makes the tracking task far more difficult to varying degrees depending on exactly how the items are merged. The effect is perceptually salient, involving in some conditions a total destruction of subjects' capacity to track multiple items. These studies provide strong evidence for the object-based nature of tracking, confirming that in some contexts attention must be allocated to objects rather than arbitrary collections of features. In addition, the results begin to reveal the types of spatially organized scene components that can be independently attended as a function of properties such as connectedness, part structure, and other types of perceptual grouping.     

The twofold role of diagrams in Euclid’s plane geometry

Proposition I.1 is, by far, the most popular example used to justify the thesis that many of Euclid??s geometric arguments are diagram-based. Many scholars have recently articulated this thesis in different ways and argued for it. My purpose is to reformulate it in a quite general way, by describing what I take to be the twofold role that diagrams play in Euclid??s plane geometry (EPG). Euclid??s arguments are object-dependent. They are about geometric objects. Hence, they cannot be diagram-based unless diagrams are supposed to have an appropriate relation with these objects. I take this relation to be a quite peculiar sort of representation. Its peculiarity depends on the two following claims that I shall argue for: (i) The identity conditions of EPG objects are provided by the identity conditions of the diagrams that represent them; (ii) EPG objects inherit some properties and relations from these diagrams.     

Tropes in space

Tropes are particular features of concrete objects. Properties—the extensions of predicates—are primitive resemblance classes of tropes. Friends of tropes have been criticized for failing to answer three questions. First, are there fundamental items other than tropes? Second, what criteria determine whether some tropes are all and only the features of some one object? Third, can trope classes be formed adequately using only primitive resemblance? Trading on the spatiotemporal status of tropes, this essay offers new responses to each of these questions. The novel thesis is that there is a sui generis property called ‘markedness’, whose tropes “mark” certain locations in an ontologically basic way. The spatiotemporal distribution of markedness tropes fixes the distribution of familiar characterizing tropes like mass and charge, and characterizing tropes are bundled by being co-contained in the location of a maximally connected markedness trope. This novel theory of trope bundling is defended by appeal to theoretical utility: it is ontologically parsimonious and solves outstanding problems involving co-location and resemblance class construction.