The notion that physics is searching for absolute truth has been long rejected by both contemporary philosophers of science and, I believe, by physicists themselves.  Philosophers of physics (and physicists) speak about the development models regarding fundamental physical reality.  Such models are not evaluated or judged on the basis of whether they are possibly absolutely true but on their renormalizability, coherence, simplicity, elegance, fruitfulness, how well they contribute to the unification of received theories, and other pragmatic (and aesthetic) criteria.  So, it's not about absolute truth.  For example, with the acceptance of the Weinberg-Salam model as the prototype of gauge theories in the mid-1970's, the consensus was reached that all physical theories should be renormalizable.  However, even when this criterion is met, it's possible that Model A might do better with regard to fruitfulness while Model B does better with regard to coherence.   One cannot determine a priori which of the two (or more) models will be accepted.  Scientific consensus is reached by weighing all of the criteria and seeing which model works best overall in light of the currently dominant paradigm. At times, as with the Higg's boson, physicists are fortunate enough to have their hypotheses confirmed by data.  However, in most cases and particularly when theoretical entities are involved, the decision of which model to accept is a pragmatic one.

I share you this job, I think it could be usefull in this brainstorming:  

https://www.researchgate.net/publication/266737490_Aplicaciones_tericas_sobre_consistencia_lingstica_y_contradiccin_lgica_en_sistemas_de_generadores_afines_o_derivados_de_Principia_Mathematica

Conference Paper Aplicaciones teóricas sobre consistencia lingüística y contr...

Any thing we humans do are from the perspectives of our observations, imaginations or mathematical abstract constructions of nature from what we assumed as axioms or basis of a fundamental theory and therefore are variants. Results of our search are temporary approximates and proximity to certain degrees of truth of nature. Physics and other natural sciences study empirical approximations of nature, not the absolute truth of nature. 

As some of you have pointed out, only laws of nature are invariant to some degree as we can change the nature of things through scientific modifications.  But what is invariant is the nature of variability and continuous changes nature makes and the expansion of the universe, until a different kind of regression and a sudden big collapse happens.

Therefore the non existence of an absolute truth is what the only and absolute truth is. 

I know a lot of absolute truths in mathematics: equations of degree bigger than 4 are not solvable by radicals, planar maps are colorable with 4 colors, 8 and 9 are unique integer powers differing by 1, there is no algorithm to determine the truth of arithmetic formulae with quantifiers, etc... On the other side I know some absolute truths in physics, like those concerning the elastic collision, or the perfect gas, or the incompressible fluid, the closed systems, the perfect vacuum, the black body, etc. The only thing is that those objects do not exist. It looks like those objects have been introduced by physicists in order to do mathematics. If someone makes a theory of the Universe starting with the hypothesis "Let U be a perfect universe" - then how far away from the reality will be the predictions of this theory? HOW IMPERFECT IS OUR REALLY EXISTING UNIVERSE? 

Gyan: you say: "But all the systems of the universe are changing, so the nature is not the truth."  The truth about nature is precisely that, we live in a universe with a well established "truth" : it is evolving. Evolution is then the most important property of the universe: it started from an initial expansion until the physical properties in evolution, getting more and more complex, made possible for life to appear. So, I do think that nature is the truth. We have science, the scientific method, to keep cheking the validity of our findings, the laws of physics, until they become invalid due to new experiments and a new (more evolved and complex) theory is able to be validated by a never ending chain of more and more experiments.

I am not a physicist but I think that physicists may be a bit more lenient than mathematicians. Example: a product of two negative numbers is positive. A physicist ought to say "Yes, certainly", and do not think about it,  but for a mathematician it is an axiom.  

Are we certain with no degree of error that the theory of elastic collision describes princely what is happening, so the theory is complete? The unit apart numbers 8 and 9 are based on the axioms used to develop the theory in which such arithmetic is valid and has some meaning to our lives. Mathematical truths are absolute truths within their bound, they are rigid, consistent and logically stable within their establishments.

But are they absolute from a wider perspective or from outside. Something that is absolute has to be complete and unchangeable but Godel's result indicates that any mathematical theory is incomplete, indicating the availability of space to augment, modify or change an existing working mathematical structure. The insolubility of higher degree equations using radicals is based on the principles developed from an apriori set of axioms put forward. There might be a different set of axioms and a better mathematical structure with a wider capability including solvabilty  of equations that were not possible before, which we call them now truths.

For example it was an absolute truth of mathematics that there is no a square of a negative number. But because of a wider and better set of axioms developed to enable us to make such numbers as valid, true and exist naturally.  

I think the role of physics is to find a set of simple laws and descriptors that are broad enough to encode the observable world and evolve them.  My own passion has been to develop more general formalisms that encode these observations in more subtle ways in a search for unification possibilities.  There are also derivative results for composite higher level systems like hydrodynamics where the results may seem to follow from a different set of rules with more limited applicability but to more practical effect.  

Quantum theory has a big hole in it from the above point of view.  Some say it is fine as it is and some of us say it must be brought into accord with these conditions.  

Hello Dejenie!

""Godel's result indicates that any mathematical theory is incomplete, indicating the availability of space to augment, modify or change an existing working mathematical structure. """

Not really... Gödel's result says that Peano Arithmetic and any other tentative recursively enumerable axiomatization of arithmetic is incomplete. It says also that the theory of (N, +, x) is not recursively axiomatizable. This theory is complete but not algorithmically decidable, and this is the true content of Gödel. It does not say anything about other theories. Indeed, the theory of densely ordered sets without endpoints (like (Q,

Werner Heisenberg

Gyan: About the constancy of some physical properties of nature, this constancy has to be validated from time to time as any physical law needs too.  As far as "geometrical points of nature....." My opinion is that there are no geometrical points, nor lines nor volumes in nature..... These concepts have been created by our minds and they are very useful, that is all. In nature may be the physical important items that exist are mass, energy, electric charge....and certainly no point masses nor electrical charges and so on.

Thank you Remi,

"mathematics cannot bootstrap itself".  That statement is profound. Singularly, it has motivated me in the work I do for quite some years.  But does the same not apply to machines?  A machine cannot bootstrap itself?  OR  A Universe cannot bootstrap itself? I hate going off topic, but this is a compelling point -- I wonder if accident has a role in mathematics?  Can mathematical conditions occur accidentally under a set of axioms?

Again thanks.

Thank you Mihai,

You are coming from the direction I am trying to highlight.

""A big problem of physics is that there is no axiomatic system for any significant physical theory. Maybe something TO STRIVE FOR (as is asked in this thread) is a good foundation for physics. We have to discuss in order to establish what were a good foundation, from different points of view.""

Thank you.

There is a mathematics of truth, after Tarski's formalisation of semantics. Truth is defined relatively to a language and to a class of models for sentences of that language. Since there are many languages, with different expressive resources, and there are many classes of models that can be associated with each language, any question about truth must be carefully formulated. Otherwise, saying "p is true" (where p stays for a sentence) is like "saying "b is at rest" (where b stays for a body), without specifying any reference system. This does not foster any relativism, exactly as relativity theory does not. The question concerns invariance. So it's unclear what Stabler's claim can mean. On one side it's trivially correct, on the other side it presupposes the notion of "absolute" is meaningful. My impression is that his claim is notably informal. Unfortunately, after the existence of metamathematics (and the notion of truth for mathematical statements is a meta-mathematical one) this can be only done for popular papers and books. As far as physics is expressed in mathematical language, it inherits the issues concerning the formalised notion of truth for mathematics and, of course, adds further issues. But I can't see which scientific gain can be achieved by talking informally about formal theories. The result is just a sort of naive philosophy of mathematics and physics, which skips centuries of foundational discussion.

Steve  --  I think you gave the answer in your initial discussion of the question. In physics we aren't looking for truth but for theories or models that "explain"  large domains of empirical data. "Explain" means using mathematics to show that calculated results are consistent with the assumptions of the theory or model and agree with measurements. Just one part of necessary assumptions in every theory so far is the physical constants which are supplied independently of the theory but whose values are derived through use of simpler or more established theory. All of this amounts to a very complex structure from a logical standpoint.

Dear Mihai,

The point here is not the specific wordings but the over all idea about the existence of a thing in a logical system that can not be proven in that system. For instance the consistency of a logical system can not be proven within that system, not topological behaviors of completeness or otherwise. 

Indeed still mathematics is the true means in which we communicate with nature as we always say nature's lingua franca is mathematics. The reason is because the basic axioms, up on which the current mathematics is built are valid and responsive to  behaviors of nature positively. 

 " The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word", Galileo, an astute observation and description of a mathematical universe, I like it. 

But I will also say that  conservation laws of physics are consistently true principles of nature. For instance energy can not be destroyed or created, but transferable between forms -true. 

Mathematics can never be absolute because relativity is a necessity for this science to exist. Without multiplicity there cannot be any mathematics. Absolute truth cannot be more than one. If there are two absolute truths than one will be greater and another lesser and again there will be relativity, so it cannot be called absolute. So the absolute truth has to be one without a second. All the greatest theories of physics are based on relativity and yield all kind of dualistic knowledge dependent on subject object duality. For example the observer of general relativity is a subject and all observed phenomenon in physics are the objects. So the physics can never get over this subject object duality. Therefore physics can only yield dualistic relative knowledge.

The kind of knowledge that would yield absolute truth has to be non-dual absolute knowledge. This is possible only when the distinction between subject and object disappear. Such knowledge is not possible in physics but it is possible in Metaphysics and many have experienced it. When a subject looks at the universe he/she splits up the universe into miriads of objects and gets entangled in the maze and enjoys the multiplicity. But the man who has acquired the non-dual absolute knowledge perceives the one undivided fundamental substance underlying all multiplicity of objects in the universe which happens to be his own Self. Therefore non-dual absolute knowledge is also called Self knowledge.

The above can be explained with following example. When you see a motion picture, you see various colorful characters and objects moving on the screen and in order to enjoy the movie you must see them as distinct entities interacting with each other. But you know in the back of your mind that all this is unreal. So then what is real? The real thing is the white movie screen in the background and the white light. The film between the screen and the light is the veiling power of delusion which causes the apparent multiplicity on the screen. But without this delusion the enjoyment is not possible. So all the enjoyments in this universe are possible because of the ignorance of the reality. The moment the reality is perceived, the enjoyment of universe will not be possible. This reality is one without a second, and of the nature of absolute truth.

Akira, Welcome to physics!  ha ha!  This is the reason we have made essentially no progress on fundamental problems in the last 60+ years.  Low bars and big egos and the sensible people skulk out of the room before the sparks fly.  

There is at least one group of researchers professionally trying an axiomatization for physics or particular physical theories. See: 

http://www.renyi.hu/conferences/lrb15/

There is a fuzzy notion of mathematics being put forward here: fuzzy because it's intuitive.  Mathematics is not one thing it's many. We know for example that if you use an elliptic geometry when the metric has a different curvature, you'll get the wrong answer. The kind of truth you get in math is a rather low level of truth: tautological truth. Physicists use math as a tool. To whatever extent they are able to put truth in at the beginning, math allows one to derive consistent results. The choice of what math to use has to be part of the input, an empirical choice. For 200 years most physicists believed they were deriving truth from Newtons gravitation, only a few still knew that Newtons gravitation was non-causal (including Newton himself). And they had good reason to believe this: it agreed with (most) observations. But Einstein revealed the reason it was non-causal and from then on Newton's gravitation was recognized as an approximation, quite good, even adequate, in non-relativistic cases. Special relativistic math and local general relativistic math use Minkowski geometry, not Euclidean as for Newtonian gravity.

Akira  --  Perhaps you've never heard of Noether's theorem. Since we take physical systems to be independent of position and time, it results that the systems energy and momentum are conserved.

The absolute requirement in Mathematics is self-consistency: Your building must be consistent with its basement and no exception is being accepted.

The absolute requirement in Physics is experimental certification: Your theory, despite if it is or not mathematically beautiful, has to be experimentally be proven to be valid, otherwise it has to be dropped away.

But, during last century, the above requirement has slightly been modified as:

• The requirement for a physical theory in order to be broadly accepted is that its base on a rigorous mathematical concept (like algebra or differential geometry) and its ability to explain the largest set of the experiments: A rather big percentage of unexplained phenomena are (quietly) been accepted without the need to reform the theory.

So, we have put a large amount of water in our wine and probably this is the reason of our sufferings...

People following this thread could be happy to read also some answers given in a parallel (and some weeks older) thread here:

https://www.researchgate.net/post/Is_Max_Tegmarks_Mathematical_Universe_Hypothesis_true/2

As always, extremist points of view, as Tegmark's theory, tend to be rejected. However, the task to make a more mathematical and logical foundation of physics, remains. 

Akira   --  If you have to resort to impuning personalities, you don't have an argument. You can look it up in most classical mechanics textbooks or on Wikipedia .

This whole discussion has been rather far removed from actually making a measurement, which, believe it or not, is an essential part of physics. Kuhn's criterion "proving a theory" only seeks to prove that is the only one. In physics we aren't really looking for proof of this sort. All we are looking for is agreement. Of course if there are others that predict the same thing, the theory is less interesting than it might be. But it's still a theory.

In physics, the truth of a model is given only by the combination of formal and logical consistency of the theory and by its experimental predictions.

The purpose of physics is to construct predictive mathematical models of natural phenomena so that we don't have to conduct experiments when the outcome is predictable. For example, although the design for a plutonium bomb was tested at Trinity before being used, Szilard's uranium bomb was never tested before being dropped on Hiroshima because the engineering was trivial. We can prove a model is false (incomplete is a better word) with a counter-example. We may keep the model anyway if counter-examples are rare or occur in limiting cases. But we can never prove a model is true, which is why we call them "theories," because the converse of a true statement isn't necessarily true. In other words, model predicts phenomena doesn't mean phenomena predicts model. This is an example of a theorem from the calculus of propositions, which deals in absolute truth, so the premise of your question is wrong.

Dear Akira,

"Physics seems to be for simple and corrupted minds" I am not certain on this.

But it is the working principle of science to question an established result, not only its validity but the possibility of getting an alternative and better way to reach there. The Pythagorean theorem x²+y²=z² on sides of a right triangle is known since ancient Greeks but more than 367 proofs were established just to justify a single relation. In science facts and scientific truths are authorities to dictate. Individuals receive respect and recognition in some form for the contributions they have made.   

The problem to axiomatize physics has also been put by David Hilbert as the 6.th problem in his problem list. So far there are two axiomatisations: the standard model of particle physics and the general relativity. They are together logically inconsistent. A new theory of quantum gravity is strongly needed. Considering this logical inconsistency of the two existent axiom systems, Akira Kanda is right. And the 6.th Hilbert problem is still unsolved.

Akira  --  Your prejudices are showing. Actually Noether was a mathematician.

@ Manuel Morales

I am curious how does your theory work with reversed time. If you run the film backwards, do you get a consistent sequence of events, or not? I think, you should not get a consistent sequence of events, but I don't know. It is always a good test. It is also a fundamental difficulty that mechanics (both classical and relativist), electrodynamics and quantum mechanics works also in reversed time, but thermodynamics and cosmology do not. Seen so, you should also get a consistent sequence of events also when running a reversed time...

A very general answer comes from Andre Gide (1869-1951):

"Believe those who are seeking the truth. Doubt those who find it."

That's kind of physics.

@ Manuel Morales

I think that I understand something ... It seems that time has a preferential direction in this model, although it is a mechanics. The point, why I have put the question, was tht I tried to imagine that in reversed time, one has other bifurcation points, where choices must be done - so we had not only an undetermined future, with many possibilities, but also an undetermined past, with many possibilities. I don't say, that it was impossible - but just that such an image is unusual. Even in the SF literature, the past is always fix and strongly determined by the present, and only the future has many different possibilities. In fact this is a contradiction. If we accept and theoretize the bifurcation and election for the future, we must do it also for the past. Or we don't, bu then we must accept the purely determinist universe. 

Sorry, Manuel, it was not only for you and your paper. I ' ve just thought loudly.

There is too much of dismissal of conceptual discussion.  I think it got a bad reputation thanks to Bohr and some of his descendants.  Landau and Feynman really pioneered to modern tradition of mathy shortcuts and "shut up and calculate" although Feynman seemed to understand the importance of foundations.  I think the tightness of resources and publication metrics for success have constrained more serious approaches and created a kind of natural selection in favor of physicists who don't get this stuff and really think doing calculations is all there is.  The only test they have for validity is experimental data (if any is available) even though many calculations can be shown to be rubbish from the start based on consistency and thought experiments.  

I think I disagree with the need for axioms in general.  The over mathematization of physics has led to our current crisis.  We don't need arbitrary axioms about what our equations mean.  We need well defined initial data and evolution equations that lead to our observations.  Some in quantum don't believe they exist and this opens the door to all kinds of dead end abstraction.  

Akira, some have argued the people didn't see blue until recently because there was not a distinct word for it from green and that cultures that lack such a distinction verbally cannot distinguish the colors on a chart test.  I haven't dug deeply into this and it is kind of shocking to consider.  I wonder if this related to what you are saying.  http://www.businessinsider.com/what-is-blue-and-how-do-we-see-color-2015-2

I remember reading Max Jammer's book on the philosophy of quantum mechanics and he was talking about Popper there.  Akira, I spent many years trying to forge QFT into a well defined initial value formalism.  I hate to plug my own work here but I would be interested to see if you feel this addresses some of the weakness in the formal approaches and gives a well defined basis for QED calculations.

I did have a strong math background and just got my first acceptance to JMP.  I almost went to math grad school instead and have audited my way through most of a math grad program.  Maybe we can chat sometimes about the shape of a resolution to these problems.  

Article Beyond Quantum Fields: An Operator-Free Covering Theory for QED

Can we say that in Pure Mathematics the following is an absolute truth: "Either truth and false exist together or they do not exist at all"

Akira,

yes I have studied Bohm.  As I recall Einstein really liked his book but Bohr was dead silent about it.  I dislike the pilot wave idea but respect his direction.  The part I don't like is that the idea of a point particle remains instead a fully many dimensional wave function approach.  The real challenge in a such an approach is not arriving at quantum statistics as much as giving a quantum description of "classical" matter and resolving some of the apparent problems with how the universe ever arrived at such a peculiar subset of many body wavefunctions that can describe the universe we perceive as largely three dimensional and classical.  In such a universe, "correlations" are generally the rule so how the universe partitions into pockets of apparently uncorrelated matter (and us!) is a great challenge.  I've spent a long time on this.  Maybe I've got something to say now.  We'll have to wait on the reviewers.  

See my article (with C. Berta)

on the dialectic between

absolute truth and relative truth

(in italian).

I have not seen physicists' statements about "truth".  Sometimes they spoke about a true physical theory (for instance, theory of light) as a goal of their research.  However, there was no obsession about an improved theory one created being TRUE. This kind of talk physicists reserved for after-dinner entertainment but not for publications. There were exceptions, but very few.  For instance, Brewster called the wave theory  not true because it had not explained then all optical phenomena.  When Poisson called Fresnel's theory not true, it was because he didn't like Fresnel's mathematics, but that was not published.

I suspect that I am not answering the original question, but is it not  possible that the question was not properly formulated?  Perhaps he meant only a certain part of physics, and I found myself in a wrong crowd. Sorry.

Manuel's question lacks clarity.  I did not study the subject and may, thus, offer little of value. The common definitions "pseudoscience" are circuitous: this activity is wrong (unscientific) because it has no scientific basis. But this may mean that the basis is not yet found.  There is also a question of accepting something as a scientific fact when no explanation exist, as dowsing for water.  For centuries this technique was proven successful, but we still do not know how it works.  As to repeatability of phenomena, sometimes nature prevents it, while at other times the properties of our brains. Apparently, if we learn something from dowsing and some other phenomena (telepathy) is that the assumption that every human may repeat the phenomenon others had done has no scientific basis. Thus, I would be in no hurry about pronouncing an activity scientific or not.

I have 2 questions for Ellis Cooper.

1. Does the term "mental model of science" implies that one's response to a theory is, to a degree, subjective?

2. Perhaps "falsifiability" is clear in mathematics but not so in physics.  The received view appears to be that a new theory is sinless (conforms to all known facts) like a new baby, and it waits for someone to come to falsify it, that is to offer an experiment incompatible with this theory.  However, the theories I am familiar with have inborn defects, and sometimes the author himself (no offense to women, but I mean particular people) knows this.  Moreover, sometimes the author does not even try to make the theory compatible with ALL known phenomena.

Manuel, no I am not. I have to think about this.  It looks I have to start with defining "cause" and "effect".  Are these concepts always proper?  If  I define "cause" as a complex of conditions necessary to produce an effect, then, say, to produce a diffraction pattern it is necessary to have several causes: light, a material body of a certain range of dimensions,  certain distances between the diffractor, the source of light and the eye, and perhaps others. When Fresnel predicted a light spot in the center of the shadow of a disk, this was achieved mathematically, but the circumstances necessary to actually see the spot remained: light, dimensions, distances, etc.  Are we on the same wavelength or not?

Steve, I completely disagree with what you say: Mathematics is the only place on earth where we can get absolute truths. The World of Mathematics is the only place I feel comfortable in because everything is predictable and can be judged in an absolute manner, since all the rules of inference and writing have been artificially created by us in a planned way. 

Marcia,

Is correct in one sense.  Math is completely correct.  The problem is that we set the rules for math and those rules do not always follow nature.  As a matter of fact they are not even close as all the natural systems have limits and boundaries.  We must add the limits and boundaries to the math systems and we are not good at doing that to match nature.

Nature is not bound by our infallible systems that we call math.  This is the problem we have with and between math and science.

George