Repository of Arcane Knowledge

Science and Mathematics

Natural science, such as physics, chemistry, and biology, was originally conceived as a philosophical endeavor, but from the time of Galileo it has increasingly focused on quantitative analysis to the neglect of other aspects of being. Despite this narrower scope, modern scientific inquiry often engages profound philosophical and social questions that defy quantification. In the essays below, we subject some of these issues to philosophical scrutiny, and also address some purely quantitative problems.

Essays

• Causality and Physical Laws (2010) [Parts I-II only]
  Examines whether so-called "laws of physics" truly explain phenomena or merely constitute higher-order descriptions.
• Vitalism and Psychology (2010)
  Examines modern misconceptions about vitalism and shows how an immaterial psyche is necessary for a logically and empirically sound psychology.
• Intensive and Extensive Magnitudes (2007)
  A meta-mathematical analysis of the notions of number, counting and addition. Re-examines Henri Bergson's contention that intensive magnitudes are not true quantities.
• Limitations of Statistical Analysis without Error Bars (2007)
  Shows how analysis-of-variance (ANOVA) as used in the biological and social sciences inadequately tests against the null hypothesis, limiting the explanatory value of these studies.
• Ontological Interpretations of Quantum Mechanics(2006)
  Argues that most quantum paradoxes can be resolved by distinguishing the actuality of eigenstates from the potentiality of mixed states, following the theories of Werner Heisenberg and Karl Popper.
• A Critique of the Anthropic Principle (2006)
  Shows how use of the anthropic principle as a cosmological explanation conflates a priori and a posteriori reasoning.
• Critique of Humanistic Psychotherapy (2005)
  Examines the cultural and philosophical assumptions of humanistic psychotherapy.
  • Related Reading: Discussion of the Medicalization of Behavior (President's Council on Bioethics, 2003)
  • Related Reading: Prozac Backlash by J. Glenmullen, MD
• Monkeys, Fairness and Anthropomorphism (2005)
  Critique of a 2003 Nature article exemplifying common fallacies of evolutionary behavioralism.
• Does a "religion of science" exist? (2004)
  Examines the extent to which scientists attempt to pose as moral authorities, notwithstanding the epistemic limitations of physical science.
• Has "science" supplanted "religion"?: A Deconstruction of the Warfare Hypothesis (2004)
  The popular hypothesis of historic warfare between "science" and "religion," long abandoned by serious historians, is briefly critiqued, while questioning the utility of "science" and "religion" as constructs for historical analysis.
• Ehrenfest Urn Problem with Applications (1997)
  A mathematical discussion of the Ehrenfest model of dissipation, considered as a random walk on a hypercube and a Markov chain, followed by an analytic solution of the generalized problem.

Special Feature

• Number of Humans in Space (1961-Present)
  A unique graphical depiction of the human population of space by nationality. Updated through Oct. 22, 2009.

Future Essays

• The Ontology of General Relativity
  Proposes that Einstein's theory conclusively divorces physico-mathematical descriptions of the universe from ontological reality.
• The Statistics and Metaphysics of Emergent Properties
  Examines whether mathematical or physical emergent properties truly violate the metaphysical requirement that an effect be contained in its cause in potentia.
• Linguistic, Anthropological, and Logical Perspectives on the Existence of the Self
  Critically examines the hypothesis that the reification of the self is an artifact of particular linguistic or anthropological developments.
• Stochastic and Entropic Considerations of Evolutionary Biology
  Attempts to address several major evolutionary questions from the perspectives of mathematical probability and thermodynamics.

© 2005-2010 Daniel J. Castellano. All rights reserved.