That’s how the scientific theories should be: simple, explanatory, predictive. Paul Steinhardt expressed it in these terms in an interview with John Horgan recently. Peter Woit reported it and I wanted to report it here as well.
I could not resist quoting Paul Steinhardt’s answer to one of Horgan’s questions. This has nothing to do with the subject of my post today but I could not resist:
Horgan: “Are you religious? Can you be a physicist and also believe in God?”
Steinhardt: “I never answer the first question because I consider religion to be a private matter. My scientific views stand on their own and I would like them to be evaluated independent of my private views about religion. In answer to your second question, it is a demonstrated fact that successful physicists can believe in God.”
I thank Paul Steinhardt for expressing the sentiment of the majority of scientists. In a similar sentiment I wrote a post titled “Not all scientists are atheists.”
One objection to the criterion of simplicity would be the fact that “simple” is a relative term. What is difficult and complex to me may be simple to you or vica versa. Sometimes, what looks difficult becomes simple when we study the subject. In defense of simplicity, a related criterion known as the Occam’s Razor has been accepted by the majority of scientists. I recommend the text found in  for an explanation of “Occam’s Razor .” I would like to quote some of those definitions from 
“when you have two competing theories that make exactly the same predictions, the simpler one is the better.”
“If you have two theories that both explain the observed facts, then you should use the simplest until more evidence comes along.”
“The simplest explanation for some phenomenon is more likely to be accurate than more complicated explanations.”
“If you have two equally likely solutions to a problem, choose the simplest.”
“The explanation requiring the fewest assumptions is most likely to be correct.”
When I was in graduate school in the 1980’s and working as a professional physicist in the 1990’s the mathematical elegance of a physical theory was used as a criterion too. If the mathematics of the theory was “elegant” then Nature must have preferred it. In the 2010’s I don’t hear the word “elegance” any more. In the 2010’s the scene is dominated by the inelegant theories such as the Standard Model (SM) of particles. SM is not elegant but that’s the best we can do at this time. Elegance as a criterion for truth remains as wishful thinking.
The “new and improved” theory must explain all the known facts in a quantitative way. The term “quantitative” means “mathematical.” The explanation has to be mathematical. This is the current dogma in science but it is a type of dogma that will serve humanity for many years to come. Eventually when the definition of “mathematics” expands (it has been expanding continuously) then we will express this principle in a different way. For the time being “quantitative” is the best word. There are conceptual (qualitative) models. They explain a lot but they are not mathematical and therefore not considered by scientists. An example is my “Prometheus and Chronos” model. It has explanatory power but it is not quantitative yet. My other model titled “Golden Biquaternions, 3 Generations and Spin” is mathematical (quantitative) but it needs to be developed further to explain all the known facts. Not conflicting with the known facts is important too. It is extremely difficult to come up with a “new and improved” theory of physical reality because it is almost impossible to explain all known facts with a single theory.
Minimum number of free parameters
The goal is to have a theory with minimum number of free parameters.
In the Standard Model (SM) of particle physics there are 18 free parameters. There will be 7 more free parameters if the neutrino rest-masses turn out to be non-zero. In SM the rest-masses of the elementary particles are free parameters. The “free parameter” means that we measure the rest-mass and set the “free parameter” to the measured value without any fundamental understanding.
The simplest and the most efficient (yielding to calculations) theory with the smallest number of free parameters will be accepted as the most worthy.
In this context the term “predictive” is used to mean
(a) predicting the future outcome
(b) pointing to an aspect of Nature that was not known before
(c) explaining some aspects of Nature from more fundamental principles.
The case (a) mentioned above is the most difficult problem in life. Predicting the future is very hard. We have no choice but to use the past events to make a prediction about the future events. If we can detect a trend or cycle then the job gets easier but sometimes there is neither a trend nor a cycle. Even when there is a trend or cycle it may be impossible to detect it using a short look-back period. Besides, in the microscopic world “predicting the future outcome” has no meaning. Quantum Mechanics computes probabilities of possible outcomes. This is very different from “predicting the future outcome.”
The cases (b) and (c) are also very difficult and getting more difficult every day. The difficulty implicit in cases (b) and (c) are sometimes expressed with the aphorism “Nature loves to hide.”
My model “Golden Biquaternions, 3 Generations and Spin” is predictive in the (c) sense but not relevant in the (a) or (b) sense.
Simple, explanatory, predictive! What about falsifiable? Paul Steinhardt mentions this criterion as well in his interview with John Horgan. The “falsifiability criterion” was proposed by Karl Popper.
Paul Steinhardt is concerned about the multiverse, string, and inflationary theories because in their current form they seem to be non-falsifiable. He qualifies his assessment by saying that the string theory may still be the best hope for a unified theory.
Horgan: “In a recent essay on Edge.org, you criticized multiverse and string as well as inflationary theories. Can you summarize your concerns?”
Steinhardt: “My concern was that the multiverse is a ‘theory of anything’, a proposal that allows all possible cosmological outcomes (smooth or not smooth, curved or flat, etc.) and, consequently, is not subject to empirical tests. Some claim that superstring theory allows exponentially many (or perhaps infinitely many) possibilities for the fundamental laws (masses of particles, types of forces, etc.) and that there is no guiding principle to determine which set of physical laws is more probable. The sets of laws comprise what is called the “string landscape.” Combine the inflationary multiverse with the string landscape, and now one has a ‘supertheory of anything’: both the cosmological properties and the microphysical properties of the universe are accidental and unpredictable.”
Steinhardt: “I share Edward’s view that string theory represents our best hope at present for a unified theory. However, I think success requires that the string landscape issue be resolved and that we find some empirical evidence for supersymmetry. As we understand superstring theory better, I truly hope we find that there are sound reasons why the physical laws we observe are naturally selected. Superstring theory, combined with an improved cosmological picture, may then lead to a powerfully explanatory and predictive theory.”
The multiverse, string, and inflationary theories cannot explain all the known facts. and they cannot “predict” in the (a), (b) sense but they are still valuable in my opinion because they provide new perspectives. I suspect that the “multiverse” and the “string landscape” approaches are motivated by the atheist perspective but that’s alright. I would not dismiss these theoretical approaches.
Science cannot provide a single “Theory of Everything.” Science will provide multiple perspectives on Nature. Examples of these perspectives are many: reductionist and wholistic perspectives, Field Theory perspective, String Theory perspective and many more. In the far future we may have a scientific perspective of the Microvita theory. I try to provide new perspectives in this blog too (see index).