Ultimately the business of "definition" is one of those things that is never resolved, and in fact cannot be permanently resolved using any language, mathematical expression or model.  As an example, philosophers debated for centuries -- and still have not solved -- such things as "the nature of being, the nature of time, the nature of life, the nature of mind, etc."  What each school did was find a very clever way to say their "position", and took up positions.  There is still no adequate definition of any of those, and in spite of centuries of arduous work, the philosophers never solved their own problems and have not solved them today.  They will not solve them tomorrow either.  Simple reason: intelligence itself ultimately involves "adaptation" or "adaptive ability", and it is never perfect.

 Ultimately there are no fast and fixed Aristotelian-type definitions, and there cannot be, since Aristotelian logic is incomplete.

 But to prevent debating how many angels can dance on the head of a pin -- which they indeed debated -- the philosophers finally realized that there were only interpretations.

 The physicists, for example, have never solved the "wave-or-particle" duality problem, and it cannot be solved in Aristotelian logic (see that "or" I stuck in there).  Ultimately one faces the "bane" of the philosophers: what they called the "accursed necessity for the identity of opposites".

 And that is still what we are stuck with in physics, and always will be.  There are NO firm definitions of mass, time, energy, action, space, spacetime, "physical", potential, field, etc.  There are no firm definitions of the physicist's use of "be" in its various forms either.  There are, however, accustomed usages, and they can be and often are contradictory.  The term "field", e.g., is used in two completely contradictory fashions in electrodynamics, and no such thing as the classical "definition" of field (force per unit charge) exists in space devoid of such unit point charges, and cannot "a priori", to use another "customary" phrase.  Feynman (and Wheeler) pointed out that only the potential for such a field existed in space, in case we place a unit point static charge at every point in space we desire to find the "field".  In short, the interaction of the charge with the "field-causing entity in space" is what generates (detects, observes) a field and a force.  But that is on the "effect" end of the reaction, not on the "causal" end.  Similarly in particle vs. wave: the particle can make a wave, and a wave can make a particle.  Or a wave can make a wave, and a particle can make a particle.  So what is it "before it gets made?"

 The physicist's answer finally was: "Whatever is useful and predicts the measured results".  That is what physics had to go to  -- the scientific method, which substitutes experimental demonstration for the incessant, unending, strident arguments of philosophy.  At least that is supposed to be what physics uses!  These days, there is again a great deal of fuss and fury in defending status quo models, as if they were "absolute".  There are really no laws of nature, as is well-known to most great physicists; instead, there are models of behavior, that predict such behavior across a very great range of phenomena.  But it only takes a single exception to prove it is not absolute, hence not a "law".  No "law of nature" is greater than the most accurate experiment that has been performed to test it, and found it acceptable.

 As an example, nobody seemed to notice that mass and charge are components of the force field, in the prevailing "definition," because of their "customary" usages (mistakenly called definitions).  Yet the notion of fields has been one of the most productive "non sequiturs" in history.  Newtonian physics does not work in many cases, but it is still very, very useful.  To build a house, one does not need quantum chronodynamics!  But one definitely needs Newton.

 So I'm not really interested in the various interpretations of terms one uses in common interpretations -- but do admit that there is always an interpretation.  And he is right, that the interpretation can change as situations change (or as what is being discussed changes, as does the term "field", or even as the interpreter changes.).  Much of the fuss and fury in scientific and philosophical debates is due to the argument over differing interpretations.  Such as, time always moves forward, which is not true.  It is generally true in the macro world, not true in the microscopic world, and if we have properly understood the Priore effect, it is not universally true in the macro universe, where one can time-reverse a cell or a group of cells called a human body.  In biology it is also known but under the name "dedifferentiation".  Becker already showed that cells (specifically, red blood cells) can be dedifferentiated and redifferentiated all over the map; his system of treating otherwise intractable bone fractures depends on that effect, and it works, as witnessed by the fact that this treatment is successfully used in hospitals in some intractable bone fracture cases.

 I guess a humorous approach is to realize that one can always get away with a "little bit of sinning" against the hoary old staid "laws of nature".  Want to go superluminal, use quantum tunneling -- and watch all the pundits argue all over the place.  Simply put, it "goes in here" and "gets out there" before ordinary light in space can travel from "here" to "there".  Now what is added or brought up after that, is interpretation.  And yes, it can indeed "transport information", such as one of Mozart's symphonies.

 A good illustration is the term "be", which has about as many "interpretations" as there are interpreters to argue over it.

 It also gets in the interpretations that the conscious mind, being a sensing thing, never can "know" anything directly, but only a "sensing" of it, which after all is an interpretation from the getgo.  And the "unconscious" turns out to be totally conscious, just a massively parallel processor, while the conscious mind is a serial processor.  Yet most philosophical arguments are based on only how the conscious mind interprets something.  Or even mistaking the serial process for the being itself.  Etc.

 We've only had a modern science for a few centuries.  That is still but a moment in time, and we still know very little about nature's deepest surprises.  The more we think we learn and know, the more we confront a vaster vision of what we do not yet know.  For every problem we solve, 10 new problems rear up in its place.  We progress, yes, but there is always much more progress yet to be made.

 So we just use the English language, as precisely as possible, but it will never be totally precise.  In many centuries of bitter debate, the philosophers have also not succeeded in getting it precise, or in finding the "ultimate answers".  Neither will we.

 Also, neither has a single textbook, university professor, philosopher, pundit, skeptic, supporter, whatever, ever solved any of the so-called "fundamental philosophical" problems.  The scientist long ago found he had to bow out of that unending and incessant debate.  Instead, he simply stated, "the truth is whatever is found to experimentally work", and that suffices for physics.

 So the terms "rigor" and "a priori" are indeed to an extent arbitrary and interpretative.  So is everything else.  There isn't even a definition of randomness in physics; a "random" series is random only the first time one writes it down.  And so on.

 All these things have been debated for centuries.  They will continue to be debated centuries from now.  Language is after all a model, and as Godel showed, there  is never going to be a perfect model -- in physics, language, mathematics, whatever.

  I felt it was worth writing this down once, but not again.  In the language of the scientist and engineer, "There's too much useful physics to get done, instead of debating interpretations of various schools of thought on the meaning of the terms."  If the prevailing usage of the terms (even sloppy usage, which much of it still is)  predicts something that can be physically checked at least in some major part, and does that prediction reliably, then it is useful as an experimental model and an experimental "truth", at least as best we understand at the time.

 What I do like to do is surface new notions that fit something already established in physics, or in one part of it.  Such a notion, basing it on the accepted notion that observation is totally 3-spatial, is that no observable can exist in time, or persist, a priori.  We use the demonstration of observation being a time-derivative of LLLT spacetime, producing a single frozen LLL snapshot at that instant.  At the next instant, that former observation is gone, and a new one has occurred.  So observation can recur repeatedly, but that is not persistence.  A waterfall (Van Flandern's beautiful analogy) may be so perfect as to appear absolutely static  and persisting in 3-space.  But it is doing no such thing; at any point in it, from instant to instant that is a different piece of water and a different observation.  I like his analogy so much that it's good to quote it.  So here it is:

 “To retain causality, we must distinguish two distinct meanings of the term ‘static’.  One meaning is unchanging in the sense of no moving parts.  The other meaning is sameness from moment to moment by continual replacement of all moving parts.  We can visualize this difference by thinking of a waterfall.  A frozen waterfall is static in the first sense, and a flowing waterfall is static in the second sense.  Both are essentially the same at every moment, yet the latter has moving parts capable of transferring momentum, and is made of entities that propagate.

            As this applies to gravitational fields for a fixed source, if the field were static in the first sense, there would be no need of aberration, but also no apparent causality link between source and target.  If the field were static in the second sense, then the propagation speed of the entities carrying momentum would give rise to aberration; and the observed absence of aberration demands a propagation speed far greater than lightspeed.