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Some Perspectives on Godelian Philosophy
Title
Some Perspectives on Godelian Philosophy.
Creator
Servais, Sondra, Solomon, Martin K., Florida Atlantic University, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description
We characterize Godel's philosophy of mathematics, as presented in his published works, with possible clarification and support provided by his posthumously published drafts, as being formulated by Godel as an optimistic neo-Kantian epistemology superimposed on a Platonic metaphysics. We further consider that Godel's more general philosophical worldview can also be characterized as such. We provide a philosophical interpretation of Godel's rotating universe solutions to Einstein's field...
Show moreWe characterize Godel's philosophy of mathematics, as presented in his published works, with possible clarification and support provided by his posthumously published drafts, as being formulated by Godel as an optimistic neo-Kantian epistemology superimposed on a Platonic metaphysics. We further consider that Godel's more general philosophical worldview can also be characterized as such. We provide a philosophical interpretation of Godel's rotating universe solutions to Einstein's field equations that is contrary to Godel's own philosophical interpretation. We compare Godel's worldview with our materialistic worldview. Our materialistic worldview developed from interpreting Godelian type results, but stands in contrast to Godel's worldview. Finally, our materialistic worldview serves to further explicate, by contrast , Godel's Platonic world view.
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Date Issued
2007
PURL
http://purl.flvc.org/fau/fd/FA00012550
Subject Headings
Mathematics--Philosophy, Logic, Symbolic and mathematical, Gödel, Kurt--Criticism and Interpretation
Format
Document (PDF)
Mathematical model of the dynamics of psychotherapy
Title
Mathematical model of the dynamics of psychotherapy.
Creator
Norman, Michael D., Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
Abstract/Description
This is a novel attempt to produce a rigorous mathematical model of a complex system. The complex system under study is the relationship between therapists and their clients. The success of psychotherapy depends on the nature of the relationship between a therapist and a client. We use dynamical systems theory to model the dynamics of the emotional interaction between a therapist and client. We determine how the therapeutic endpoint and the dynamics of getting there depend on the parameters...
Show moreThis is a novel attempt to produce a rigorous mathematical model of a complex system. The complex system under study is the relationship between therapists and their clients. The success of psychotherapy depends on the nature of the relationship between a therapist and a client. We use dynamical systems theory to model the dynamics of the emotional interaction between a therapist and client. We determine how the therapeutic endpoint and the dynamics of getting there depend on the parameters of the model. ... We describe the emotional state of both the therapist and client with coupled, first order, nonlinear ordinary differential equations (ODE's). The rate of change of the emotional state of the therapist and client is proportional to their previous state, their uninfluenced state when alone, and an influence function which depends on the state of the other person. We formulated influence functions based on the research literature on psychotherapy and the therapeutic alliance. We then determined the critical points from the intersection of the nullclines and used a numerical ODE solver (Matlab ODE113) to compute the trajectories from different initial conditions. ... The results validate this prototypical approach to psychotherapy ; we have shown that human interaction (in the context of psychotherapy) can be quantified and modeled using differential equations.
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Date Issued
2012
PURL
http://purl.flvc.org/FAU/3358758
Subject Headings
Psychotherapist and patient, Mathematical models, Counselor and client, Mathematical models, Therapeutic alliance, Mathematical models, Psychotherapy, Philosophy, Mathematical models, Evidence-based psychotherapy, Transference (Psychology), Countertransference (Psychology)
Format
Document (PDF)
Brain dynamics and behavioral basis of a higher level cognitive task
Title
Brain dynamics and behavioral basis of a higher level cognitive task: number comparison.
Creator
Ballan, Meltem., Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
Abstract/Description
Number perception, its neural basis and its relationship to how numerical stimuli are presented have been challenging research topics in cognitive neuroscience for many years. A primary question that has been addressed is whether the perception of the quantity of a visually presented number stimulus is dissociable from its early visual perception. The present study examined the possible influence of visual quality judgment on quantity judgments of numbers. To address this issue, volunteer...
Show moreNumber perception, its neural basis and its relationship to how numerical stimuli are presented have been challenging research topics in cognitive neuroscience for many years. A primary question that has been addressed is whether the perception of the quantity of a visually presented number stimulus is dissociable from its early visual perception. The present study examined the possible influence of visual quality judgment on quantity judgments of numbers. To address this issue, volunteer adult subjects performed a mental number comparison task in which two-digit stimulus numbers (Arabic number format), among the numbers between 31 and 99 were mentally compared to a memorized reference number, 65. Reaction times (RTs) and neurophysiological (i.e. electroencephalographic (EEG) data) responses were acquired simultaneously during performance of the two-digit number comparison task. In this particular quantity comparison task, the number stimuli were classified into three distance factors. That is, numbers were a close, medium or far distance from the reference number (i.e., 65). In order to evaluate the relationship between numerical stimulus quantity and quality, the number stimuli were embedded in varying degrees of a typical visual noise form, known as "salt and pepper noise" (e.g., the visual noise one perceives when viewing a photograph taken with a dusty camera lens). In this manner, the visual noise permitted visual quality to be manipulated across three levels: no noise, medium noise (approximately 60% degraded visual quality from nonoise), and dense noise (75% degraded visual quality from no-noise)., The RTs provided the information about the overt responses; however, the temporal relationship of visual quality (starts earlier than quantity perception) and quantity were examined using eventrelated potentials (ERPs) extracted from continuous EEG recordings. The analysis of the RTs revealed that the judgment of number quantity is dependent upon visual number quality. In addition, the same effect was observed over the ERP components occurring between 100 ms and 300 ms after stimulus onset time over the posterior electrodes. Principal components analysis (PCA) and independent component analysis (ICA) methods were used to further analyze the ERP data. The consistent results of the PCA and ICA were used to represent the spatial brain dynamics, as well as to obtain temporal dynamics. The overall conclusion of the present study is that ERPs, ICs and PCs along with RTs suggested a strategy of quantitative perception (i.e., number comparison) based on the qualitative attributes of the stimuli highlighting the importance of the design of the task and the methodology
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Date Issued
2010
PURL
http://purl.flvc.org/FAU/2867328
Subject Headings
Cognitive neuroscience, Learning, Physiological aspects, Visual perception, Information visualization, Mathematics, Philosophy
Format
Document (PDF)