Dear Alwielland Q. Bello , some people say that physics is the epitome of the use of the scientific method, and I guess using the scientific method somehow is the also the epitome of critical thought, no?

There are so very many extremely counter-intuitive results in Physics that it enjoins its students to not mistake ideas based on common sense or conventional wisdom for the truth : it demolishes cognitive bias and cognitive dissonance.

It mathematically and logically demonstrates that many wildly counter-intuitive results are in fact correct, and that many 'self-evident truths' (to borrow a phrase from the US Constitution) are in fact utterly wrong.

Despite all this - cognitive biases die very hard, even in this day and age. I keep seeing hidden assumptions in many instances, and theories built on unrecognized cognitive biases.

Critical thinking means that any facts or results are judged on their proven logical validity, not on the basis of their apparent common sense. Physics demonstrates that results that look impossible or far out can in fact be true : by doing so, it helps develop critical thinking, rather than easy thinking based on the acceptance of unproven, albeit seemingly obvious inference.

Dear H Chris Ransford , would you say that for example theories of cosmology or string theory are proven on their logical validity? Also, doesn't physics differ from math in that aside from logical validity (which in physics is a problem itself as i think from what little I know, our most successful theories, special relativity and quantum mechanics are incompatible) you also need experimental success?

Greetings @Haris Shekeris,

A number of questions here.

First - of course experimental confirmation is always required, and there is a purely mathematical, theoretical reason for it : many different and contradictory mathematical solutions can seamlessly fit experimental results. All that we ever have is a number of data points (whether finite or not, at most aleph 0) , but since there exists an aleph 2 infinity of mathematical functions, there is an infinity of mathematical functions that can fit any set of data points (to illustrate this: what is the next point in the series y= 1,2,3,4,5,6,7,8 ? To figure that out, plot out these points on an (x,y) graph at (x=1,y=1), (x=2,y=2) etc., and you immediately see that you can draw an infinity of curves that go through all these points and any possible next value after the 8: there is no way to know the value Y of the next point at (x=9,y=Y) without experimentation - for instance, by lifting the lid on the last Y point.) That’s what experimental physicists do: they narrow the number of possible real-world solutions to a given real-world problem down from the infinity of possible, legitimate math-only solutions, through experimentation.

Second - Our two most successful theories are not incompatible, despite what many believe (I deem this belief to simply stem from cognitive dissonance), here's why : 2a - cutting a long story short, the apparent contradiction stems from divisions by naught in the formalism when trying to reconcile the 2 theories (which is ultimately what gave rise to the speculations of string theory, thereby avoiding dimensionless point-like elements), but 2b as Marcelo Gleisner convincingly argued, there is no reason whatsoever why they should be physically compatible - which would mean that we've finally nailed a TOE yet there is no reason why a physical TOE should exist at all and indeed 2c - this is a mathematical universe, and the TOE lies in plain sight : in the fact that the same mathematics seamlessly describes both theories.

Last but not least - different theories , in cosmology, or string, etc. are all WIPs and the final word has not been written yet. In the specific case of string, or rather M theory, we fall into the above trap : every new set of data gives rise to new variables that subsume what has gone before - which is why we end up, in some renditions of M theory, with over 500 dimensions : anything goes if we are to house all results under a same roof, but of course all meaning and all predictive power are lost

Dear H Chris Ransford ,

Good morning, many thanks for your very insightful answer!

Regarding your first point, glad to see there's a mathematical formulation of something called 'the underdetermination of theory by data', i think it's exactly the same thing, don't know what came first, the mathematicians or the philosophers of science (probably the former, not that it matters much though).

Regarding your second point, can you elucidate a bit more (or give a reference) what you mean by 'cognitive dissonance'? Cognitive dissonance by whom, by physicists? I would hesitate to attribute that to a whole class of scientist on their topic, but you may have a better view of the field. However, from my own low-level studies in the subject, i also came to the conclusion that having point particles would only lead to trouble, hence I'm actually glad that your conclusions are similar (also the divisions by zero).

However I'm not sure I understand your point about the TOE, are you saying that it's enough that any theories are written in math sufficient to call them TOE, because ultimately it's the math (if i could stretch it further, as i know an author in philosophy who argued sth similar, under the title of 'ontic structuralism' where he argued that 'structure' is mathematical structure). The above feels a bit misguided, or out of step with the history of the concept of TOE. It *feels* to me that a TOE should be a physics theory, not a math one.

Finally, about your last point about theories being WIPs, I think your claim seems to take away something from the authority of science, no? Even though there were people saying this about the natural science theories in the '60s and '70s (Lakatos, Popper maybe mainly), i feel that the way you put your point across then somebody could legitimately resort to other sources which do provide final words, such as religion or, to a lesser extent, psychology or the law.

Best Wishes,

Haris