Rational scientific thought is inductive.
Empiricism is guided by experiment and mathematics.In experiment, the scientist sets up an unambiguous aparatus (note: all physical apparatus are necessarily unambigous since something must happen but not two contradictory things at once!). He then observes and records the outcome of his "do" and, to the best of his ability, interprets it in the light of "known" facts, i.e. the standard scientific corpus.
If he understands what he is about, new knowledge results which can be added to the corpus (without contradiction) - it is placed in the hierarchy of the corpus, under a previously known concept but never above it (induction).
One may also deduce by the mechanism of mathematics.The aforementioned corpus is coincidental with its mathematical description. That mathematics may drift off into its own never-never land seemingly divorced from physical reality only to return with a new "physically appropriate equation".
The mathematical physicist who drifts off with such mathematics may then, in a philosophically sober moment, design an experiment to test his meta-knowledge against the Final Arbiter.
We here accept tacitly that all physical knowledge can be rendered mathematically but that not all mathematics corresponds to physical entities and their behaviors.Chain of mathematical deduction:
Inductive reasoning (Rationalization) obtains from the following
If lines ... find the circles.
e.g. ... Dirac anticipates the positron.Symmetry analysis is also the fastest method of disproof. We may prove a hypothesis false by violation of some symmetry rule (or its related conservation law) and never have to bother with actual quantification (we don't have to calculate the "how much" if we know that the hypothesis is qualitively untenable).
Alternatively, if no proof by the foregoing is possible, it may then be necessary to laboriously calculate the damn thing out to see if it fails by way of not enough or too much.
Induction by dimensional analysisThis I believe is the least dependable mechanism for finding "new concepts". For if all physical systems have mathematical analogs but not all mathematical systems have physical analogs ... then dimensional analysis is frought with possible missteps.
A good example is the Planck Scale.
To date, there is absolutely no direct physical evidence that the Planck scales have any correspondence at all to physical reality. The very idea of such scales is rooted in the belief that all physical and mathematical systems are absolutely congruent (if we can show that a mathematical system leads to a certain magic number ... then that physics corresponding to the magic must be existentially valid).
Note: I personally subscribe to this view. I simply do not trust it. It seems to need a clarification such that physical reality would not be a "logical whore", i.e. granting physical validation to any mathematical proposition whatsoever.Obviously, if we obtain a measure and give it dimensions expressed in length-mass-time then we may take any number of such expressions and "monkey them" in order to construct an equation which yields:
Do you see what I mean? No matter how you cut it, you get some sort of Planck length or Johnstone-Stoney scale ... you will always get something. Are all such derivables physically meaningful? I have doubts.
The Planck scales may be chimera but dimensional analysis is still an incredibly useful tool much of the time.