Faithful representation,physical extensive measurement theory and Archimedean axioms

The formal methods of the representational theory of measurement (RTM) are applied to the extensive scales of physical science, with some modifications of interpretation and of formalism. The interpretative modification is in the direction of theoretical realism rather than the narrow empiricism which is characteristic of RTM. The formal issues concern the formal representational conditions which extensive scales should be assumed to satisfy; I argue in the physical case for conditions related to weak rather than strong extensive measurement, in the sense of Holman 1969 and Colonius 1978. The problem of justifying representational conditions is addressed in more detail than is customary in the RTM literature; this continues the study of the foundations of RTM begun in an earlier paper. The most important formal consequence of the present interpretation of physical extensive scales is that the basic existence and uniqueness properties of scales (representation theorem) may be derived without appeal to an Archimedean axiom; this parallels a conclusion drawn by Narens for representations of qualitative probability. It is concluded that there is no physical basis for postulation of an Archimedean axiom.     

Make up your mind: octopus cognition and hybrid explanations

In order to argue that cognitive science should be more accepting of explanatory plurality, this paper presents the control of fetching movements in the octopus as an exemplar of a cognitive process that comprises distinct and non-redundant representation-using and non-representational elements. Fetching is a type of movement that representational analyses can normally account for completely—but not in the case of the octopus. Instead, a comprehensive account of octopus fetching requires the non-overlapping use of both representational and non-representational explanatory frameworks. What this need for a pluralistic or hybrid explanation implies is that cognitive science should be more open to using both representational and non-representational accounts of cognition, depending on their respective appropriateness to the type of cognition in question.

     

Estimation ofJ scales for unidimensional unfolding

In Coombs' unidimensional unfolding theory each individual ranks all stimuli, often in terms of preference judgments. These ranks, calledI scales, are used to infer the latent continuum called aJ scale which is presumed to have generated theI scale rankings. A major problem concerns the inference of theJ scale given a set ofI scales because anI scale is not unique to any oneJ scale. This paper presents a procedure for estimatingJ scale probabilities given a set ofI scales. Models for three and four or more stimuli are presented. Results of computer tests are reported.     

Tolerant enactivist cognitive science

Enactivist (Embodied, Embedded, etc.) approaches in cognitive science and philosophy of mind are sometimes, though not always, conjoined with an anti-representational commitment. A weaker anti-representational claim is that ascribing representational content to internal/sub-personal processes is not compulsory when giving psychological explanations. A stronger anti-representational claim is that the very idea of ascribing representational content to internal, sub-personal processes is a theoretical confusion. This paper criticises some of the arguments made by Hutto and Myin (2013, 2017) for the stronger anti-representational claim and suggests that the default Enactivist view should be the weaker non-representational position.     

Binary action based estimation of propensities

An observer is to make inference statements about a quantityp, called apropensity and bounded between 0 and 1, based on the observation thatp does or does not exceed a constantc. The propensityp may have an interpretation as a proportion, as a long-run relative frequency, or as a personal probability held by some subject. Applications in medicine, engineering, political science, and, most especially, human decision making are indicated. Bayes solutions for the observer are obtained based on prior distributions in the mixture of beta distribution family; these are then specialized to power-function prior distributions. Inference about logp and log odds is considered. Multiple-action problems are considered in which the focus of inference shifts to theprocess generating the propensitiesp, both in the case of a process parameter known to the subject and unknown. Empirical Bayes techniques are developed for observer inference aboutc when is known to the subject. A Bayes rule, a minimax rule and a beta-minimax rule are constructed for the subject when he is uncertain about.This research was partially supported by the Defense Advanced Research Projects Agency of the Department of Defense and was monitored by ONR under Contract No. N00014-77-C-0095. Any opinions, findings, conclusions or recommendations expressed herein are those of the author and do not necessarily reflect the views of the Defense Advanced Research Projects Agency, the Office of Naval Research, or Carnegie-Mellon University.     

On the general theory of meaningful representation

The numerical representations of measurement, geometry and kinematics are here subsumed under a general theory of representation. The standard theories of meaningfulness of representational propositions in these three areas are shown to be special cases of two theories of meaningfulness for arbitrary representational propositions: the theories based on unstructured and on structured representation respectively. The foundations of the standard theories of meaningfulness are critically analyzed and two basic assumptions are isolated which do not seem to have received adequate justification: the assumption that a proposition invariant under the appropriate group is therefore meaningful, and the assumption that representations should be unique up to a transformation of the appropriate group. A general theory of representational meaningfulness is offered, based on a semantic and syntactic analysis of representational propositions. Two neglected features of representational propositions are formalized and made use of: (a) that such propositions are induced by more general propositions defined for other structures than the one being represented, and (b) that the true purpose of representation is the application of the theory of the representing system to the represented system. On the basis of these developments, justifications are offered for the two problematic assumptions made by the existing theories.Material from this paper was presented at a conference on meaningfulness in the theory of measurement held at New York University in December 1984, hosted by J. C. Falmagne. I would like to thank Patrick Suppes for arranging my invitation to this conference, and David Krantz, R. Duncan Luce, and Fred Roberts for helpful comments. I would also like to thank an anonymous referee for extremely detailed and helpful comments and suggestions, the most important of which are acknowledged in footnotes.     

The impossibility of a bivalent truth-functional semantics for the non-Boolean propositional structures of quantum mechanics

Summary The general fact of the impossibility of a bivalent, truth-functional semantics for the propositional structures determined by quantum mechanics should be more subtly demarcated according to whether the structures are taken to be orthomodular latticesP _L or partial-Boolean algebrasP _A; according to whether the semantic mappings are required to be truth-functional or truth-functional ; and according to whether two-or-higher dimensional Hilbert spaceP structures or three-or-higher dimensional Hilbert spaceP structures are being considered. If the quantumP structures are taken to be orthomodular latticesP _L, then bivalent mappings which preserve the operations and relations of aP _L must be truth-functional . Then as suggested by von Neumann and Jauch-Piron and as proven in this paper, the mere presence of incompatible elements in aP _L is sufficient to rule out any semantical or hidden-variable proposal which imposes this strong condition, for anytwo-or-higher dimensional Hilbert spaceP _L structure. Thus from the orthomodular lattice perspective, the peculiarly non-classical feature of quantum mechanics and the peculiarly non-Boolean feature of the quantum propositional structures is the existence of incompatible magnitudes and propositions. However, the weaker truth-functionality condition can instead be imposed upon the semantic or hidden-variable mappings on theP _L structures, although such mappings ignore the lattice meets and joins of incompatibles and preserve only the partial-Boolean algebra structural features of theP _L structures. Or alternatively, the quantum propositional structures can be taken to be partial-Boolean algebrasP _A, where bivalent mappings which preserve the operations and relations of aP _A need only be truth-functional (c). In either case, the Gleason, Kochen-Specker proofs show that any semantical or hidden variable proposal which imposes this truth-functionality (c) condition is impossible for anythree-or-higher dimensional Hilbert spaceP _A orP _L structures. But such semantical or hidden-variable proposals are possible for any two dimensional Hilbert spaceP _A orP _L structures, in spite of the presence of incompatibles in these structures, in spite of the fact that Heisenberg's Uncertainty Principle applies to the incompatible elements in these structures, and in spite of the fact that these structures are non-Boolean in the Piron sense. The present paper is a sequel of the proceedings of theSociety of Exact Philosophy annual meeting, published in our issue 9:2, pp. 187–278. — Ed. I am indebted to my supervisor, Dr. Edwin Levy, for many hours of helpful discussion on the drafts leading to this paper.     

Gestural imitation and limb apraxia in corticobasal degeneration

Limb apraxia is a common symptom of corticobasal degeneration (CBD). While previous research has shown that individuals with CBD have difficulty imitating transitive (tool-use actions) and intransitive non-representational gestures (nonsense actions), intransitive representational gestures (actions without a tool) have not been examined. In the current study, eight individuals with CBD and eight age-matched healthy adults performed transitive, intransitive representational and intransitive non-representational gestures to imitation. The results indicated that compared to controls, individuals with CBD were significantly less accurate in the imitation of transitive and intransitive non-representational gestures but showed no deficits for the imitation of intransitive representational gestures. This advantage for intransitive representational gestures was thought to be due to fewer demands being placed on the analysis of visual-gestural information or the translation of this information into movement when imitating these gestures. These findings speak to the importance of context and the representation of gestures in memory in gesture performance.     

Radicalizing numerical cognition

In recent decades, non-representational approaches to mental phenomena and cognition have been gaining traction in cognitive science and philosophy of mind. In these alternative approach, mental representations either lose their central status or, in its most radical form, are banned completely. While there is growing agreement that non-representational accounts may succeed in explaining some cognitive capacities (e.g. perception), there is widespread skepticism about the possibility of giving non-representational accounts of cognitive capacities such as memory, imagination or abstract thought. In this paper, I will critically examine the view that there are fundamental limitations to non-representational explanations of cognition. Rather than challenging these arguments on general grounds, I will examine a set of human cognitive capacities that are generally thought to fall outside the scope of non-representational accounts, i.e. numerical cognition. After criticizing standard representational accounts of numerical cognition for their lack of explanatory power, I will argue that a non-representational approach that is inspired by radical enactivism offers the best hope for developing a genuine naturalistic explanatory account for these cognitive capacities.

     

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.     

Outline of a general model of measurement

Measurement is a process aimed at acquiring and codifying information about properties of empirical entities. In this paper we provide an interpretation of such a process comparing it with what is nowadays considered the standard measurement theory, i.e., representational theory of measurement. It is maintained here that this theory has its own merits but it is incomplete and too abstract, its main weakness being the scant attention reserved to the empirical side of measurement, i.e., to measurement systems and to the ways in which the interactions of such systems with the entities under measurement provide a structure to an empirical domain. In particular it is claimed that (1) it is on the ground of the interaction with a measurement system that a partition can be induced on the domain of entities under measurement and that relations among such entities can be established, and that (2) it is the usage of measurement systems that guarantees a degree of objectivity and intersubjectivity to measurement results. As modeled in this paper, measurement systems link the abstract theory of measuring, as developed in representational terms, and the practice of measuring, as coded in standard documents such as the International Vocabulary of Metrology.     

Elementary categorial logic,predicates of variable degree,and theory of quantity

Developing some suggestions of Ramsey (1925), elementary logic is formulated with respect to an arbitrary categorial system rather than the categorial system of Logical Atomism which is retained in standard elementary logic. Among the many types of non-standard categorial systems allowed by this formalism, it is argued that elementary logic with predicates of variable degree occupies a distinguished position, both for formal reasons and because of its potential value for application of formal logic to natural language and natural science. This is illustrated by use of such a logic to construct a theory of quantity which is argued to be scientifically superior to existing theories of quantity based on standard categorial systems, since it yields realvalued scales without the need for unrealistic existence assumptions. This provides empirical evidence for the hypothesis that the categorial structure of the physical world itself is non-standard in this sense.I would like to thank my collegue Mark Brown and an anonymous referee for helpful comments on an earlier draft of this paper.     

Congruence and Career Change in Employed Adults

Holland's theory of congruence was applied to adults changing careers. Forty-two nontraditional students attending college to attain a new occupation were surveyed. The group's average experience in the work force was 14.5 years, and their average age was 34.4 years. Using theCindex (Brown & Gore, 1994) and Kwak and Pulvino's (1982) K-P index to measure congruence, data supported the hypothesis that employed adults in the process of changing their careers move in a direction of greater congruence. Further, job satisfaction was correlated significantly with congruence as operationalized by theCindex (r= .33,p< .03) and the K-P index (r= .32,p< .04).     

The enactive computational basis of cognition and the explanatory cognitive basis for computing

The computational theory of cognition, or computationalism, holds that cognition is a form of computation. Two issues related to this view are comprised by the goal of this paper: A) Computing systems are traditionally seen as representational systems, but functional and enactive approaches support non-representational theories; B) Recently, a sociocultural theory against computationalism was proposed with the aim of ontologically reducing computing to cognition. We defend, however, that cognition and computation are in action, thus cognition is just a form of computing and that cognition is the explanatory basis for computation. We state that: 1. Representational theories of computing recurring to intentional content run into metaphysical problems. 2. Functional non-representational theories do not incur this metaphysical problem when describing computing in terms of the abstract machine. 3. Functional theories are consistent with enactive in describing computing machines not in a strictly functional way, but especially in terms of their organization. 4. Enactive cognition is consistent with the computationalism in describing Turing machines as functionally and organizationally closed systems. 5. The cognitive explanatory basis for computing improves the computational theory of cognition. When developed in the human linguistic domain, computer science is seen as a product of human socionatural normative practices, however, cognition is just an explanatory, not ontological, basis for computing. The paper concludes by supporting that computation is in action, that cognition is just one form of computing in the world and the explanatory basis for computation.     

Comparatal dispersion,a measure of accuracy of judgment

It is suggested that the ambiguity of aset of paired comparison judgments may be measured by the quantity _i ² + _j ² – 2r _{ij ii}, This quantity is termed thecomparatal dispersion. A simultaneous solution for scale values and ratios of comparatal dispersions has been presented and applied to some data on food preferences.This research was jointly supported in part by Princeton University, the Office of Naval Research under contract Nonr-1858(15), and the National Science Foundation under grant NSF G-642, and in part by Educational Testing Service. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

Muscular Imaginings—A Phenomenological and Enactive Model for Imagination*

A phenomenological model (labeled ‘EC’) is developed as an alternative to current analyses of the imagination in sport philosophy, heirs to an Enlightenment notion that conceptualizes imaginings as abstract, eidetic, and representational. EC describes how Eidetic and Corporeal Imaginings (EIs & CIs) phenomenologically structure our imaginative undertakings. EIs keep the ‘ideal’ aspect, but CIs—enacted, corporeal, non-representational—are more fundamental and foundational. Sports are particularly suited to express CIs’ muscular imaginings, which result in novel performances. An enactive framework theorizes CIs as non-representational interactions.     

A more powerful method for testing for agreement between a judge and a known standard

We assume that a judge's task is to categorize each ofN subjects into one ofr known classes. The design of primary interest is employed if the judge is presented withs groups, each containingr subjects, such that each group of sizer consists of exactly one subject of each of ther types. The probability distribution for the total number of correct choices is developed and used to test the null hypothesis that the judge is guessing in favor of the alternative that he or she is operating at a better than chance level. The power of the procedure is shown to be superior to two other procedures which appear in the literature.The authors are grateful for the suggestions of the referees and for computer funding provided by the Northeast Regional Data Center at the University of Florida.