scholarly journals Probability Theory and Its Models

2019 ◽  
pp. 168-181
Author(s):  
Paul Humphreys
Keyword(s):  
Probability Theory ◽  
Mathematical Models ◽  
Mathematical Theory ◽  
Scientific Theory ◽  
Formal Theory ◽  
Empirical Content ◽  
Formal Models ◽  
The Status ◽  
Historical Transition ◽  
Abstract Probability

This paper argues for the status of formal probability theory as a mathematical, rather than a scientific, theory. Some remarks are made about the historical transition from Hilbert’s view of probability as a scientific theory to Kolmogorov’s view of probability as a mathematical theory. A process is provided that bridges abstract probability theory with concrete systems via mathematical models. This demonstrates that empirical content is injected into formal models via the mapping from those formal models on to elements of the concrete systems. David Freedman and Philip Stark’s concept of model-based probabilities is examined and is used as a bridge between the formal theory and applications.

Philosophical Papers

2019 ◽  
Author(s):  
Paul Humphreys
Keyword(s):  
Probability Theory ◽  
Computer Simulations ◽  
Social Dynamics ◽  
Scientific Explanation ◽  
Contemporary Literature ◽  
Unpublished Paper ◽  
Agent Based ◽  
Philosophical Investigations ◽  
The Status ◽  
Original Presentation

Paul Humphreys pioneered philosophical investigations into the methodological revolution begun by computer simulations. He has also made important contributions to the contemporary literature on emergence by developing the fusion account of diachronic emergence and its generalization, transformational emergence. He is the discoverer of what has come to be called “Humphreys” Paradox in probability theory and has also made influential contributions to the literature on probabilistic causality and scientific explanation. This collection contains fourteen of his previously published papers on topics ranging from numerical experiments to the status of scientific metaphysics. There is also and a previously unpublished paper on social dynamics. The volume is divided into four parts on, respectively, computational science, emergence, probability, and general philosophy of science. The first part contains the seminal 1990 paper on computer simulations, with three other papers arguing that these new methods cannot be accounted for by traditional methodological approaches. The second part contains the original presentation of fusion emergence and three companion papers arguing for diachronic approaches to the topic, rather than the then dominant synchronic accounts. The third part starts with the paper that introduced the probabilistic paradox followed by a later evaluation of attempts to solve it. A third paper argues, contra Quine, that probability theory is a purely mathematical theory. The final part includes papers on causation, explanation, metaphysics, and an agent-based model that shows how endogenous uncertainty undermines utility maximization. Each of the four parts is followed by a comprehensive postscript with retrospective assessments.

scholarly journals A Logic of Comparative Support: Qualitative Conditional Probability Relations Representable by Popper Functions

2017 ◽  
Author(s):  
James Hawthorne
Keyword(s):  
Probability Theory ◽  
Decision Theory ◽  
Classical Logic ◽  
Scientific Theory ◽  
Classical Probability ◽  
Open Questions ◽  
Classical Setting ◽  
Alternative Approaches ◽  
Popper Functions ◽  
Self Reference

Revising classical logic—to deal with the paradoxes of self-reference, or vague propositions, for the purposes of scientific theory or of metaphysical anti-realism—requires the revision of probability theory. This chapter reviews the connection between classical logic and classical probability, clarifies nonclassical logic, giving simple examples, explores modifications of probability theory, using formal analogies to the classical setting, and provides two foundational justifications for these ‘nonclassical probabilities’. There follows an examination of extensions of the nonclassical framework: to conditionalization and decision theory in particular, before a final review of open questions and alternative approaches, and an evaluation of current progress.

scholarly journals International conflict and strategic games

2019 ◽  
Vol 14 (1) ◽  
pp. 80-102
Author(s):  
Enzo Lenine Lima
Keyword(s):  
Mathematical Models ◽  
Armed Conflict ◽  
International Conflict ◽  
Strategic Interaction ◽  
Model Testing ◽  
Formal Models ◽  
Strategic Games ◽  
Interaction Game

The pervasiveness of international conflict makes of it one of the main topics of discussionamong IR scholars. The discipline has extensively attempted to model the conditions andsettings under which armed conflict emerges, at sometimes resorting to formal models as toolsto generate hypotheses and predictions. In this paper, I analyse two distinct approaches toformal modelling in IR: one that fits data into mathematical models and another that derivesstatistical equations directly from a model’s assumption. In doing so, I raise the followingquestion: how should maths and stats be linked in order to consistently test the validity offormal models in IR? To answer this question, I scrutinise James Fearon’s audience costsmodel and Curtis Signorino’s strategic interaction game, highlighting their mathematicalassumptions and implications to testing formal models. I argue that Signorino’s approachoffer a more consistent set of epistemological and methodological tools to model testing,for it derives statistical equations that respect a model’s assumptions, whereas the data-fitapproach tends to ignore such considerations.

Preferences-Based Performance Measurement Models

2013 ◽  
pp. 62-84
Keyword(s):  
Probability Theory ◽  
Performance Measurement ◽  
Mathematical Theory ◽  
Utility Functions ◽  
Subjective Expectations ◽  
Von Neumann ◽  
Measurement Models

It is shown that the human subjective expectations for the uncertainty events can be described mathematically with the terms of the probability theory and can be inserted into the mathematical theory of von Neumann and Morgenstern. Some examples of utility functions are shown.

scholarly journals Response to Johnson: A random sample versus the radical event

2016 ◽  
Vol 2 (2) ◽  
pp. 205-16
Author(s):  
Elie Ayache
Keyword(s):  
Probability Theory ◽  
Random Sample ◽  
Derivative Pricing ◽  
Working Hypothesis ◽  
Abstract Probability ◽  
Sample Versus

Timothy Johnson’s working hypothesis in his review of my latest book, The Medium of Contingency, is that I (as well as the ‘quants’ involved in the derivative pricing industry) do not understand the foundations of abstract probability theory. In this response, I show that this is not the case. On the contrary, rules and protocols which are common in the derivative pricing industry, the result of which can be an extension of abstract probability theory as it now stands, seem to elude Johnson. To address these failings, I provide theoretical reflections on probability theory and its formalisms.

scholarly journals Ada Unseen // Invisible Ada

2019 ◽  
Vol 10 (1) ◽  
pp. 216-219
Author(s):  
Frances Presley
Keyword(s):  
Wave Function ◽  
Mathematical Theory ◽  
Scientific Theory ◽  
Natural Phenomena ◽  
Poetic Form ◽  
Forthcoming Book

      These poems are from a forthcoming book based on the life of Ada Lovelace.  They combine mathematical theory with landscape through innovative poetic form.  I have chosen two themes-wave function and will o' the wisp, both in terms of complex scientific theory and unpredictable natural phenomena. They are rooted in landscapes which are significant for Lovelace and in my own life. Resumen      Estos poemas son de un libro pendiente de publicación sobre la vida de Ada Lovelace. Combinan la teoría matemática con el paisaje en una innovadora forma poética. He escogido dos temas-función de onda y fuegos fatuos, ambos en términos de teoríca cinetífica compleja y de fenómenos naturales impredecibles. Están enraizados en paisajes que son significativos para Lovelace y para mi propia vida.

scholarly journals Safety of transport processes of the trucks determined by reliability.

2015 ◽  
Vol 2015 (2) ◽  
pp. 88-92
Author(s):  
Владимир Самусенко ◽  
Vladimir Samusenko ◽  
Наталия Сакович ◽  
Nataliya Sakovich ◽  
Евгений Христофоров ◽  
...  
Keyword(s):  
Probability Theory ◽  
Mathematical Models ◽  
Russian Federation ◽  
Transport Processes ◽  
The Russian Federation

In article questions of safety of transport processes on roads of the Russian Federation of the vehicles caused by reliability are considered. Authors considered activities on safety of the movement at design stages of the created car. For a solution authors used mathematical models on the basis of probability theory.

Formal Models in Narrative Analysis

2012 ◽  
Author(s):  
David Herman
Keyword(s):  
Mathematical Models ◽  
Narrative Analysis ◽  
Permutation Groups ◽  
Formal Models ◽  
Structural Linguistics ◽  
Modeling Practices ◽  
And Mathematics ◽  
Models And Modeling

This chapter considers formal models of narrative and the nature of the theory of narrative. After discussing the diachronic and synchronic approaches to investigating the role of formal models in narrative analysis, the chapter looks at those ideas about models and modeling as a kind of bridge between humanistic and technoscientific discourse. It then evaluates descriptive and functional classifications of models, along with a range of perspectives on mathematical models and modeling. It also presents a case study in metanarratology, with a particular focus on modeling practices that have been brought to bear on focalization. It also analyzes some instances of the confluence of the formal study of narrative and mathematics, including the use of permutation groups, as well as the synergy between mathematically based theories of structural linguistics and early work on story grammars.

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