Anthony F. Peressini

Confirming Mathematical Theories: an Ontologically Agnostic Stance

The Quine/Putnam indispensability approach to the confirmation of mathematical theories in recent times has been the subject of significant criticism. In this paper I explore an alternative to the Quine/Putnam indispensability approach. I begin with a van Fraassen-like distinction between accepting the adequacy of a mathematical theory and believing in the truth of a mathematical theory. Finally, I consider the problem of moving from the adequacy of a mathematical theory to its truth. I argue that the prospects for justifying this move are qualitatively worse in mathematics than they are in science.

Development of a Synchronization Coefficient for Biosocial Interactions in Groups and Teams

Body movements, autonomic arousal, and electroencephalograms (EEGs) of group members are often coordinated or synchronized with those of other group members. Linear and nonlinear measures of synchronization have been developed for pairs of individuals, but little work has been done on measures of synchronization for groups. We define a new synchronization coefficient, SE, for a group based on pairwise correlations in time series data and employing the notions of a group driver, who most drives the group’s responses, and empath, who is most driven by the group. SE is developed here in the context of emotional synchronization based on galvanic skin response time series. A simulation study explores its properties, the balance between strong versus weak autocorrelational effects, transfer, group size, and direct versus oscillatory functions. Distributions of SE are not affected by group size up to 16 members. Norms for interpreting the coefficient are presented along with directions for new research.

Generalizing Evolutionary Altruism

Although accounts of evolutionary altruism which leave the question of whether altruism can evolve in nature open to empirical confirmation/refutation have been worked out for special (two-trait) cases, no real effort has been made to work out such accounts for general (N-trait) cases. It is tempting to take this lack of attention as evidence for an inextricably conventional element, which precludes such accounts from being of practical scientific value. I argue that such accounts do generalize in a natural way. As is often the case in science, generalizing theoretically simplified notions is not straightforward because of issues hidden in the special case. These issues do not, however, turn out to be essentially conventional.

Blurring two conceptions of subjective experience: Folk versus philosophical phenomenality

Philosophers and psychologists have experimentally explored various aspects of peoples understandings of subjective experience based on their responses to questions about whether robots “see red” or “feel frustrated,” but the intelligibility of such questions may well presuppose that people understand robots as experiencers in the first place. Departing from the standard approach, I develop an experimental framework that distinguishes between “phenomenal consciousness” as it is applied to a subject (an experiencer) and to an (experiential) mental state and experimentally test folk understandings of both subjective experience and experiencers. My findings (1) reveal limitations in experimental approaches using “artificial experiencers” like robots, (2) indicate that the standard philosophical conception of subjective experience in terms of qualia is distinct from that of the folk, and (3) show that folk intuitions do support a conception of qualia that departs from the philosophical conception in that it is physical rather than metaphysical. These findings have implications for the “hard problem” of consciousness.

Causation, Probability, and the Continuity Bind

Analyses of singular (token-level) causation often make use of the idea that a cause increases the probability of its effect. Of particular salience in such accounts are the values of the probability function of the effect, conditional on the presence and absence of the putative cause, analysed around the times of the events in question: causes are characterized by the effect’s probability function being greater when conditionalized upon them. Put this way, it becomes clearer that the ‘behaviour’ (continuity) of probability functions in small intervals about the times in question ought to be of concern. In this article, I make an extended case that causal theorists employing the ‘probability raising’ idea should pay attention to the continuity question. Specifically, if the probability functions are ‘jumping about’ in ways typical of discontinuous functions, then the stability of the relevant probability increase is called into question. The rub, however, is that sweeping requirements for either continuity or discontinuity are problematic and, as I argue, this constitutes a ‘continuity bind’. Hence more subtle considerations and constraints are needed, two of which I consider: (1) utilizing discontinuous first derivatives of continuous probability functions, and (2) abandoning point probability for imprecise (interval) probability. 1 Introduction 2 Probability Trajectories and Continuity   2.1 Probability trajectories   2.2 Causation as discontinuous jumps   2.3 Against systematic discontinuity 3 Broader Discontinuity Concerns 4 The Continuity Bind   4.1 Retaining continuity with discontinuous first derivatives   4.2 Imprecise (interval) probability trajectories 5 Concluding Remarks  Appendix 1 Introduction 2 Probability Trajectories and Continuity   2.1 Probability trajectories   2.2 Causation as discontinuous jumps   2.3 Against systematic discontinuity 3 Broader Discontinuity Concerns 4 The Continuity Bind   4.1 Retaining continuity with discontinuous first derivatives   4.2 Imprecise (interval) probability trajectories 5 Concluding Remarks  Appendix

There is nothing it is like to see red: holism and subjective experience

The Nagel inspired “something-it-is-like” (SIL) conception of conscious experience remains a dominant approach in philosophy. In this paper I criticize a prevalent philosophical construal of SIL consciousness, one that understands SIL as a property of mental states rather than entities as a whole. I argue against thinking of SIL as a property of states, showing how such a view is in fact prevalent, under-warranted, and philosophically pernicious in that it often leads to an implausible reduction of conscious experience to qualia. I then develop a holistic conception of SIL for entities (not states) and argue that it has at least equal pre-empirical warrant, is more conservative philosophically in that it decides less from the a priori “armchair,” and enjoys a fruitful two-way relationship with empirical work.

Determining Optimization-Risk Profiles for Individual Decision Makers

Investment funds typically vary with regard to the emphasis that the managers place on acceptable risk and expected returns on investment. This chapter highlight a nonlinear analytic strategy, orbital decomposition (ORBDE) for identifying and extracting patterns of categorical events from time series data. The contributing constructs from symbolic dynamics, chaos, and entropy are described in conjunction with the central ORBDE algorithm. A study in task switching, which can alleviate or induce cognitive fatigue, is used an illustrative example of the basic mode of analysis. The aggregate more of ORBDE allows category codes from multiple variables to be assigned to each event in a time series. An illustrative example of the aggregate mode is presented for risk profile analysis in financial decisions. The results open up many possibilities for studying sequences of decisions made by fund managers and individual investors to determine profiles of risk acceptance, expected returns, and other features of portfolio management.

Philosophy of Mathematics and Mathematics Education

In this paper we explore how the naturalistic perspective in philosophy of mathematics and the situative perspective in mathematics education, while on one level are at odds, might be reconciled by paying attention to actual mathematical practice and activity. We begin by examining how each approaches mathematical knowledge, and then how mathematical practice manifest itself in these distinct research areas and gives rise to apparently contrary perspectives. Finally we argue for a deeper agreement and a reconciliation in the perspectives based on the different projects of justification and explanation in mathematics.