Posts Tagged With: Steven Weinberg

knowledge/evidence not captured by mathematical prob.

Mayo mirror

Equivocations between informal and formal uses of “probability” (as well as “likelihood” and “confidence”) are responsible for much confusion in statistical foundations, as is remarked in a famous paper I was rereading today by Allan Birnbaum:

“It is of course common nontechnical usage to call any proposition probable or likely if it is supported by strong evidence of some kind. .. However such usage is to be avoided as misleading in this problem-area, because each of the terms probability, likelihood and confidence coefficient is given a distinct mathematical and extramathematical usage.” (1969, 139 Note 4).

For my part, I find that I never use probabilities to express degrees of evidence (either in mathematical or extramathematical uses), but I realize others might. Even so, I agree with Birnbaum “that such usage is to be avoided as misleading in” foundational discussions of evidence. We know, infer, accept, and detach from evidence, all kinds of claims without any inclination to add an additional quantity such as a degree of probability or belief arrived at via, and obeying, the formal probability calculus.

It is interesting, as a little exercise, to examine scientific descriptions of the state of knowledge in a field. A few days ago, I posted something from Weinberg on the Higgs particle. Here are some statements, with some terms emphasized:

The general features of the electroweak theory have been well tested; their validity is not what has been at stake in the recent experiments at CERN and Fermilab, and would not be seriously in doubt even if no Higgs particle had been discovered.

I see no suggestion of a formal application of Bayesian probability notions. Continue reading

Categories: philosophy of science, Philosophy of Statistics | Tags: , , , | 10 Comments

Scalar or Technicolor? S. Weinberg, “Why the Higgs?”

CERN’s Large Hadron Collider under construction, 2007

My colleague in philosophy at Va Tech, Ben Jantzen*, sent me this piece by Steven Weinberg on the Higgs. Even though it does not deal with the statistics, it manages to clarify some of the general theorizing more clearly than most of the other things I’ve read. (See also my previous post.)

Why the Higgs?
August 16, 2012
Steven Weinberg

The New York Times Review of Books

The following is part of an introduction to James Baggott’s new book Higgs: The Invention and Discovery of the “God Particle,” which will be published in August by Oxford University Press. Baggott wrote his book anticipating the recent announcement of the discovery at CERN near Geneva—with some corroboration from Fermilab—of a new particle that seems to be the long-sought Higgs particle. Much further research on its exact identity is to come.

It is often said that what was at stake in the search for the Higgs particle was the origin of mass. True enough, but this explanation needs some sharpening.

By the 1980s we had a good comprehensive theory of all observed elementary particles and the forces (other than gravitation) that they exert on one another. One of the essential elements of this theory is a symmetry, like a family relationship, between two of these forces, the electromagnetic force and the weak nuclear force. Electromagnetism is responsible for light; the weak nuclear force allows particles inside atomic nuclei to change their identity through processes of radioactive decay. The symmetry between the two forces brings them together in a single “electroweak” structure. The general features of the electroweak theory have been well tested; their validity is not what has been at stake in the recent experiments at CERN and Fermilab, and would not be seriously in doubt even if no Higgs particle had been discovered. Continue reading

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