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Chapter
Why the Book of Nature is Written in the Language of Mathematics
The essay traces the following idea from the presocratic philosopher Heraclitus, to the Pythagoreans, to Newton’s Principia: Laws of nature are laws of proportion for matter in motion. Proportions are expressed b...
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Book Series
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Chapter
It’s Complicated: The Relationship between Physics and Mathematics
A joke is never good if one has to explain the punchline. But since I have limited comedic ambitions, I am going to do exactly that. The dispersion of heat in a volume, such as your living room, is a thermodyn...
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Chapter
Special Science Laws
This chapter will address the special sciences, in particular the reduction of special science laws to microphysical laws.
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Chapter
The Structure of Typicality
The following chapter is rather technical and can be skipped without great loss if the reader is eager to get to the meat, namely, applications of typicality in physics. Its main goal is to further disentangle...
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Chapter
Boltzmann’s Statistical Mechanics
This chapter will discuss statistical mechanics in the manner of Ludwig Boltzmann (1844–1906). I will focus, in particular, on Boltzmann’s account of thermodynamic irreversibility and the second law of thermod...
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Chapter
Boltzmann Equation and the H-Theorem
Although the formula engraved on Boltzmann’s tombstone is Eq. (8.1), connecting the entropy of a system with the measure associated with its macrostate, his name i...
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Chapter
Causality and the Arrow of Time
While causal intuitions are integral to our experience of the world, corresponding relations between states or events are conspicuously absent in its micro-physical description. If the fundamental laws are bi-...
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Chapter
Other Applications of Typicality
In this short chapter, I will discuss applications of typicality beyond statistical mechanics and probability theory. On the one hand, this will emphasize the wide scope and philosophical potential of typicali...
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Chapter
Typicality and the Metaphysics of Laws
Over the past few decades, the best system account has developed into a popular, maybe even dominant, position regarding the metaphysics of the laws of nature. In a nutshell, this view holds that the laws of n...
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Chapter
Introduction
These regularities are all of a different kind. C is a statistical regularity. B is a mechanical phenomenon. A turns out to be an instance of the second law of thermodynamics. All three regularities strike us ...
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Book
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Chapter
Cournot’s Principle
The second premise could be denied by admitting something like propensities into the physical ontology. But we can replace the word “facts” with “empirical facts” and end up with an analogous conclusion: logic...
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Chapter
The Mentaculus: Typicality Versus Humean Chances
The objective probabilities we encounter in the world are the results of physical processes. Grounding them in the fundamental micro-physical laws is thus the task of statistical mechanics, broadly construed. ...
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Chapter
From the Universe to Subsystems
Any fundamental physical theory is a theory of the universe as a whole. Its laws describe the evolution of the entire configuration of matter. Thus, in classical mechanics, where the forces range over all physica...
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Chapter
Past Hypothesis and the Arrow of Time
In what seems like a terminological nod to David Chalmers’s (1995) problems of consciousness, Sheldon Goldstein (Boltzmann’s Approach to Statistical Mechanics. In Bricmont, J., Dürr, D., Galavotti, M. C., Ghir...
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Chapter
Quantum Mechanics
Our discussions have been based almost exclusively on deterministic laws. Some might object that this is not very naturalistic. Aren’t our best physical theories, viz. quantum theories, indeterministic? The sh...
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Chapter
Typicality in Probability Theory
Although one of this book’s primary goals is to clarify the formal, conceptual, and metaphysical differences between typicality and probability, I will start by discussing typicality in the context of standard...
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Chapter
A Typicality Theory of Probability
It is also in this chapter that we begin to decouple the notion of typicality from that of “very high probability” and free it from unnecessary connotations of ignorance or chanciness. What is typical is simpl...
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Article
The Point of Primitive Ontology
Bohmian mechanics grounds the predictions of quantum mechanics in precise dynamical laws for a primitive ontology of point particles. In an appraisal of the de-Broglie–Bohm theory, the paper discusses the cruc...
