# Scientific Inference and How We Come to Know Stuff - Comments

• Insights
Exactly. And this is where the problem of induction comes in: how are you able to know whether your knowledge will continue to be useful? Any expectation that it will be useful for some period of time presumes certain regularities about the universe. The challenge is identifying what these regularities are in every instance so that we can bolster our inductive reasoning.
It is fascinating to me that my favorite definition of energy (Noetherian energy) relies on the assumption of such regularities in the universe. This is so true, that to some extent modern scientific models are based on this underlying Lagrangian path. In other words, since the real (as in true) path's derivative is (classically) defined as zero, any changes would show up as energy changes in the model.

Thus, to some extent, irregularities do exist as energy changing form. Of course we observe these changes and account for them in our models. Whenever we find a new change, we account for it as a new form of energy. Thus we change our model to match our changing universe.

atyy
Is the principle of equivalence a form of induction, ie. the local laws of physics are everywhere the same?

Dr. Courtney
Gold Member
Science cannot really prove the constancy of the laws of nature. Science assumes the constancy of natural law.

Stephen Jay Gould put it this way:

Begin Exact Quote (Gould 1984, p. 11):

METHODOLOGICAL PRESUPPOSITIONS ACCEPTED BY ALL SCIENTISTS

1) The Uniformity of law - Natural laws are invariant in space and time. John Stuart Mill (1881) argued that such a postulate of uniformity must be invoked if we are to have any confidence in the validity of inductive inference; for if laws change, then an hypothesis about cause and effect gains no support from repeated observations - the law may alter the next time and yield a different result. We cannot "prove" the assumption of invariant laws; we cannot even venture forth into the world to gather empirical evidence for it. It is an a priori methodological assumption made in order to practice science; it is a warrant for inductive inference (Gould, 1965).

End Exact Quote (Gould 1984, p. 11)

Gould, Stephen Jay. "Toward the vindication of punctuational change."Catastrophes and earth history (1984): 9-16.
also see:
Gould, Stephen Jay. "Is uniformitarianism necessary?" American Journal of Science 263.3 (1965): 223-228.
Gould, Stephen Jay. Time's arrow, time's cycle: Myth and metaphor in the discovery of geological time. Harvard University Press, 1987.

Is the principle of equivalence a form of induction, ie. the local laws of physics are everywhere the same?
Any physical law that is a generalization through time or space (or both) of individual observed instances is an induction. So, yeah, the equivalence principle is a great example!

Dr. Courtney
Gold Member
Is the principle of equivalence a form of induction, ie. the local laws of physics are everywhere the same?
Someone more of an expert in GR may adjust my answer, but there are some specific assertions in the principle of equivalence beyond the local laws of physics being the same everywhere. These assertions could potentially be falsified:

1. Gravitational mass is equal to inertial mass.
2. There is no experiment that can possibly distinguish a uniform acceleration from a uniform gravitational field.

Dr. Courtney