Pretend I said "rules" rather than "laws".
Thank you. I will take that as a grumbling concession.
which normally seek to provide deeper and broader explanations to observed phenomena, laws
of physics (in the strictest sense) are essentially exceptionless regularities. They are universal generalizations
(UG, an inference rule in predicate logic) from thousands of observations, amassed throughout the history of physics, that have repeatedly and consistently displayed certain conditionalities ('if x
, then y'
properties) under widely differing contexts. Over the course of time, owing to their seeming inviolability, they have become validated as 'laws'.
If, however, UG is applied simplistically, these generalizations are vulnerable to what is called 'the Johnson-Carnap continuum': (infinite) universal generalizations have zero probability
In other words, not only is it the obvious case (taught in almost every introductory course of first-order logic) that a consistent finite number of black raven observations, no matter how numerous, does not logically follow that all future ravens observed will be black. But, in fact, having observed n
black ravens, it logically follows from k
successive applications of the rule of succession that the probability the next k
ravens are also black approaches zero
as the succession tends to infinity.
This elegant argument, however, is premised on infinite succession. It stumbles upon non-zero probabilities in actual physics, inherently associated with a finite succession of confirming observations resulting in 1 (100 % probability). Take the following formulation of the Law of Conservation of Energy as an example:
In a closed a system the total energy of the system is conserved.
This law is a logical inference from thousands upon thousands of observations whereby, invariably, 'the more closed the physical system, the more it conserves energy'. If we assume, as seems reasonable, that the universe has a finite number of systems (despite being an enormous number), then every new observation of energy-conservation being conditional upon a system's level of openness further confirms
the Law of Conservation of Energy. Every single positive instance increases the probability of the law applying to future instances closer to 1. This conclusion can be made even before applying your favourite Bayesian models that add further credence to the law.
is a good analysis on UG and its proper application for those who wish to geek out on philosophical logic further.
Oh, "philosophy strikes right back".