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What if, like me, you don't think that the probability calculus is
the One, True Logic of Induction? Then you want to know what other
logics are possible. Here I map out a large class of inductive logics
that originate in the idea that the inductive support B affords A,
that is "[A|B]," is defined in terms of the deductive relations among
propositions. I demonstrate some very general properties for these
logics. In large algebras of propositions, for example, inductive
independence is generic in all of them. A no-go result forces all the
logics to supplement the deductive relations among propositions with
intrinsically inductive structures. |
"Deductively Definable Logics of Induction" Download. |
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While Bayesian analysis has enjoyed notable success with many
particular problems of inductive inference, it is not the one true
and universal logic of induction. I review why the Bayesian approach
fails to provide this universal logic of induction. Some of the
reasons arise at the global level through the existence of competing
systems of inductive logic. Others emerge through an examination of
the individual assumptions that, when combined, form the Bayesian
system: that there is a real valued magnitude that expresses
evidential support, that it is additive and that its treatment of
logical conjunction is such that Bayes' theorem ensues. |
“Challenges to Bayesian Confirmation Theory,”
Prepared for Prasanta S. Bandyopadhyay and Malcolm Forster (eds.),
Philosophy of Statistics: Vol. 7 Handbook of the Philosophy of
Science. Elsevier. Download draft. |
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Here's a chance to look over Einstein's shoulder and watch him in
line by line detailed calculations as he is making the greatest
discovery of his scientific career, the general theory of
relativity |
A Peek into Einstein's Zurich Notebook. Goodies. |
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Elsewhere, I have
urged that science is not grounded in a factual principle of
causality. Matthias Frisch, however, in "Causal
Reasoning in Physics," has identified a computation in the
physics of scattering theory that, according to standard text books,
requires a principle of causality for its completion. I argue that
this supposed application is merely the adding of causal labels to an
already presumed fact; and that the principle called upon is either
false or too vague and ambiguous to be serviceable. |
"Is There an Independent Principle of Causality in
Physics?" Download. |
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Constructivists, such as Harvey Brown, must believe that the
geometry of spacetime can be inferred from the properties of matter
without recourse to spatiotemporal presumptions. I show that the
construction project only succeeds if constructivists antecedently
presume the essential commitments of a realist conception of
spacetime. |
"Why Constructive Relativity Fails," Manuscript |
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Forming the dual is a familiar operation in logic and mathematics.
Truth is the dual of falsity; and (A or B) is the dual of (A and B).
Here I develop the corresponding notion for additive measures, such
as probability measures. The resulting dual additive measures are
degrees of disbelief and turn out to obey their own peculiar
calculus. An ignorance state is conveniently characterized as one
that is self-dual. |
"Disbelief as the Dual of Belief" Download. |
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This paper illustrates how the material theory of induction can be
used to assess evidence claims made historically in science. Two
cases are considered: Einstein's 1905 thermodynamic argument for
light quanta and his 1915 recovery of the anomalous perihelion motion
of Mercury. |
"History of Science and the Material Theory of
Induction: Einstein's Quanta, Mercury's Perihelion." Download. |
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A simple indeterministic system is displayed and it is urged that
we cannot responsibly infer inductively over it if we presume that
the probability calculus is the appropriate logic of induction. The
example illustrates the general thesis of a material theory of
induction, that the logic appropriate to a particular domain is
determined by the facts that prevail there. |
"Induction without Probabilities." Download.
See also "Induction without
Probabilities" in Goodies.
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Because of the specific shape of the dome at its apex, Newton's
equations of motion tell us that a mass at rest at the apex can
spontaneously be set into motion. It has been suggested that this
indeterminism should be discounted since it draws on an incomplete
rendering of Newtonian physics; or it is "unphysical"; or it employs
illicit idealizations. I analyze and reject each of these reasons.
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"The Dome: An Unexpectedly Simple Failure of
Determinism," download.
See also "The Dome: A Simple Violation
of Determinism in Newtonian Mechanics" in Goodies. |
