Why can we never be certain of our scientific theories?

[Functor97]

Why can we never be certain of our scientific theories? The reason i love mathematics and physics is that the rigorous knowledge they impart about reality or what lies beneath it. Yet the more physics I study, the more I realizes how very little we know. What is gravity? what is force? What is inertia? What is time? These type of questions continually nag away at the back of my mind. I have read a great deal of scientific philosophy (such as Popper, Quine, Putnam) and realize that we cannot determine what these things "are" without referring to our own perspective or analogy. I realize that science is empirical, but to me it seems that even empiricism has failings.

Assume we have two theories f(x) and g(x) and all our physics observations match both of these theories. Assume furthermore that f(x) and g(x) are mutually exclusive. How do we differentiate between which theory is true? I would assume that the search to differentiate between the two via experimental evidence will continue, but what if there is always two or more theories that may be correct?

This really irritates me, as science is my personal quest for knowledge and truth, but it seems to be providing only more questions. I enjoy answering questions, but, and i feel quite embarrassed to say this, I feel frustration knowing that i will never, can never know why or even how the universe works at the deepest levels. I shall die and fade into obscurity without ever achieving the sense of understanding i desire. Do any of the rest of you harbour similar thoughts or doubts? Is there any philosopher who deals with this issue in depth?

 

[Simon Bridge]

It in Empiricism vs Rationalism and the Problem of Induction.
Go look them up - it's actually quite a deep question.

In a nutshell - we can come up with a general theory about nature which is completely internally consistent and logical and mathematically rigorous but this does not mean that it is true. To find out it is true, we have to go look at nature and test it.

If the test comes out negative then this is definite (barring mistakes - I'm simplifying here) and clear. But if it comes out positive then the theory has been confirmed for the specific circumstances of the test only. Someone cleverer may come up with a better test that checks for something different ... we cannot be sure that this will not happen. It only takes one such test to disprove the theory.

Get the idea?

In practice, all our physical theories are thought of as "models" which are only as good as they have been tested. The strength of a theory is proportional to the cleverness of the attempts to find fault with it.

We hope that, by stripping away the false ideas, we will approach a more and more accurate model for the Truth. We do not ever expect to get there. Though scientists, especially physicists, often appear arrogant, there is a basic humility that goes with this knowledge: the Universe always knows more than we do, and we are probably wrong about a great deal. We can take heart that we are less likely to be wrong in an unhelpful way :)

Science provides a toolbox to search for truth, but it is not the end of the search.

 

[Functor97]

It in Empiricism vs Rationalism and the Problem of Induction.
Go look them up - it's actually quite a deep question.

In a nutshell - we can come up with a general theory about nature which is completely internally consistent and logical and mathematically rigorous but this does not mean that it is true. To find out it is true, we have to go look at nature and test it.

If the test comes out negative then this is definite (barring mistakes - I'm simplifying here) and clear. But if it comes out positive then the theory has been confirmed for the specific circumstances of the test only. Someone cleverer may come up with a better test that checks for something different ... we cannot be sure that this will not happen. It only takes one such test to disprove the theory.

Get the idea?

In practice, all our physical theories are thought of as "models" which are only as good as they have been tested. The strength of a theory is proportional to the cleverness of the attempts to find fault with it.

We hope that, by stripping away the false ideas, we will approach a more and more accurate model for the Truth. We do not ever expect to get there. Though scientists, especially physicists, often appear arrogant, there is a basic humility that goes with this knowledge: the Universe always knows more than we do, and we are probably wrong about a great deal. We can take heart that we are less likely to be wrong in an unhelpful way :)

Science provides a toolbox to search for truth, but it is not the end of the search.

Thanks for the prompt reply Simon.

I understand all of what you have said. I still believe that our science and mathematics is representative of a deeper truth, but i cannot prove this and that is my frustration. How would it be truth if i was basing it upon belief? I have a fear that our vision of reality is somehow a lie, that our mathematics and physics reveals nothing about underlying reality. I am unsure how to remove these doubts.
Thanks, Functor97.

 

[DaveC426913]

I understand all of what you have said. I still believe that our science and mathematics is representative of a deeper truth, but i cannot prove this and that is my frustration. How would it be truth if i was basing it upon belief? I have a fear that our vision of reality is somehow a lie, that our mathematics and physics reveals nothing about underlying reality. I am unsure how to remove these doubts.
Thanks, Functor97.

Science does not attempt to "prove" anything, or find "truth". It only attempts to examine what we see and model it.

Truth is something left for religion. If any scientist ever thought he had "the truth", he would be (rightly) branded a crackpot and ostracized. That is not the scientific way.

 

[Functor97]

Science does not attempt to "prove" anything, or find "truth". It only attempts to examine what we see and model it.

Truth is something left for religion. If any scientist ever thought he had "the truth", he would be (rightly) branded a crackpot and ostracized. That is not the scientific way.

So you would deny that according to experimental data it is true that the speed of light is constant in all intertial frames of reference?

 

[Pythagorean]

We can be certain. We just have to quantify that certainty.

 

[DaveC426913]

So you would deny that according to experimental data it is true that the speed of light is constant in all intertial frames of reference?

It is certainly not true.

The constancy of c is a postulate.

i.e.:

Suppose we take it that c is constant in every inertial frame, what would we see?
(Turns out it describes extremely well what we see.)

 

[Pythagorean]

Science does not attempt to "prove" anything, or find "truth". It only attempts to examine what we see and model it.

Truth is something left for religion. If any scientist ever thought he had "the truth", he would be (rightly) branded a crackpot and ostracized. That is not the scientific way.

I agree with your first statement, but the second statement isn't entirely true. Many scientists do care about a secular version of "truth". Science is exactly one of the tools I use to examine "truth". I use it to understand myself, where I came from, how I can help myself and others through applications (medicine, happiness). I would only ever publish the observations, but my I'm still free, in my spare time, to interpret those observations.

Of course, I recognize that my version of the truth is always going to have errors associated with it, and I'm always willing to change my version of the truth in light of strong evidence. But the pursuit, the motivation for all the energy that I put into my research would not be there for... well, most of us, I believe... if we thought what we were pursuing was in any way the opposite of the truth.

 

[Functor97]

It is certainly not true.

The constancy of c is a postulate.

i.e.:

Suppose we take it that c is constant in every inertial frame, what would we see?
(Turns out it describes extremely well what we see.)

but according to experimental data it is, otherwise we would have postulated something more suitable. It is true as far as we can tell, so why does science not deal with truths?

Religion has nothing to do with truth, science is the best notion of truth we have, and mathematics is the basis for this.

 

[DaveC426913]

but according to experimental data it is,

No. Data doesn't say anything.

It is our models that give meaning to the data that say things.

Religion has nothing to do with truth

The point is not whether religion is truth, the point I'm making is that Religion claims to know truths.

Science does not.

 

[Simon Bridge]

So you would deny that according to experimental data it is true that the speed of light [in a vacuum] is constant in all intertial frames of reference?

I would add: Within the limits of the experiments that have been performed so far.

Some empirical findings have been very strongly verified. Many, like the invariance of c, are so strongly confirmed that they have formed the basis of other theories. It's also the reason when some neutrinos seemed to arrive early in an experiment, the immediate thought was that "something got overlooked" was the more likely reason.

Still, there is no way of knowing if some future scientists may come up with an inertial frame of reference where the speed of light is observed to be different from the others. There is no way to demonstrate that this will never happen.

We don't expect it will happen any time soon and if it did we would expect the variation to be of a kind that still allows all the other physics that depends on it to work with little modification.

Note: while it was introduced as a postulate it is a postulate that has been tested in different reference frames using different kinds of clocks. Note that Einsteins math would still work even had the postulate proved non-physical - it would just mean he had not discovered any physics.

All this is philosophy of science 101.

 

[DaveC426913]

Of course, I recognize that my version of the truth is always going to have errors associated with it, and I'm always willing to change my version of the truth in light of strong evidence. But the pursuit, the motivation for all the energy that I put into my research would not be there for... well, most of us, I believe... if we thought what we were pursuing was in any way the opposite of the truth.

If you know it can have errors and you are willing to change it, then even you know it wasn't truth.

 

[Pythagorean]

but according to experimental data it is, otherwise we would have postulated something more suitable. It is true as far as we can tell, so why does science not deal with truths?

Religion has nothing to do with truth, science is the best notion of truth we have, and mathematics is the basis for this.

Mathematics is only another tool. I think (good) philosophy is the only rational subject to speak directly of truth. In the sciences, we integrate both philosophy and mathematics. Generally, scientists utilize an empirical philosophy (a 'good' philosophy, I think ) mathematics is one of the tools we use to understand how our expectations match observation. But the mathematics can go behind the scenes (and often must, for very complex mathematics... I only use it to program my data so that I can see it as more of a visual representation, because no sense can be made of a bunch of numbers and complicated equations. I know what each term of the equations describes physically, but taken all together, any intuitive exploration of 100+ dimensional systems the mathematics is not enough, you have to possesses the spatial metaphor: geometry.)

 

[Pythagorean]

If you know it can have errors and you are willing to change it, then even you know it wasn't truth.

That's not the argument, though... I've, in fact, already said this exact same thing myself (as you quoted). The argument is about the existence of a truth that doesn't belong to religion, not my possession of it.

 

[Functor97]

If you know it can have errors and you are willing to change it, then even you know it wasn't truth.

It could have errors, but that does not imply that it does.

 

[Pythagorean]

It could have errors, but that does not imply that it does.

...? what kind of argument is this?

 

[DaveC426913]

It could have errors, but that does not imply that it does.

That's OK. The point is, we don't deal with it being The Truth, since we can never know that. Any theory can always be overturned with the next piece of data.

 

[Functor97]

Mathematics is only another tool. I think (good) philosophy is the only rational subject to speak directly of truth. In the sciences, we integrate both philosophy and mathematics. Generally, scientists utilize an empirical philosophy (a 'good' philosophy, I think ) mathematics is one of the tools we use to understand how our expectations match observation. But the mathematics can go behind the scenes (and often must, for very complex mathematics... I only use it to program my data so that I can see it as more of a visual representation, because no sense can be made of a bunch of numbers and complicated equations. I know what each term of the equations describes physically, but taken all together, any intuitive exploration of 100+ dimensional systems the mathematics is not enough, you have to possesses the spatial metaphor: geometry.)

Mathematics is not just a "tool", it is the living breathing heart of the sciences. Without mathematics there would be no theory of relativity, because General Relativity is a mathematical theory. We use our empirical data to match our mathematical theory.

We may one day have a theory which accounts for all observations. We cannot prove that the theory is perfect, because that would contradict our empirical method, it is impossible. That does not mean that the universe does not follow these laws, regardless of our minds or perspectives, making it for all intents and purposes the truth.

 

[Functor97]

That's OK. The point is, we don't deal with it being The Truth, since we can never know that. Any theory can always be overturned with the next piece of data.

Yes I agree, however we aim for the truth!

 

[Pythagorean]

I guess I'm not a 1-0 kind of guy.

I see science as producing "small truths" (truths that hold within a given frame of reference). The statements are true and self-consistent (because it's implicit in the statement that our assumptions could be wrong).

"The Truth" is definitely and ominous, creepy, suspect sounding title for the subject; I would not trust even a scientists showing me evidence if he claimed to have "The Truth". I don't believe in this "1". But I also don't believe "0": that the universe is completely stochastic and without reason.

 

[Functor97]

I guess I'm not a 1-0 kind of guy.

I see science as producing "small truths" (truths that hold within a given frame of reference). The statements are true and self-consistent (because it's implicit in the statement that our assumptions could be wrong).

"The Truth" is definitely and ominous, creepy, suspect sounding title for the subject; I would not trust even a scientists showing me evidence if he claimed to have "The Truth". I don't believe in this "1". But I also don't believe "0": that the universe is completely stochastic and without reason.

I see your point. I acknowledge that our human conception of truth is probably misplaced. However the essence of reality which science provides is far more rationale a process than any other, so i accept it as truth.

 

[Pythagorean]

Mathematics is not just a "tool", it is the living breathing heart of the sciences. Without mathematics there would be no theory of relativity, because General Relativity is a mathematical theory. We use our empirical data to match our mathematical theory.

You realize that sentence 2 is a non-sequitor with respect to sentence 1?
your last sentence does not conflict with my statement about mathematics being a tool.

We may one day have a theory which accounts for all observations. We cannot prove that the theory is perfect, because that would contradict our empirical method, it is impossible. That does not mean that the universe does not follow these laws, regardless of our minds or perspectives, making it for all intents and purposes the truth.[

Mathematics is an even smaller truth than observation. It is almost so self-consistently true as to be irrelevant; we must qualify mathematics to utilize it. At least observation has some direct interaction with reality.

 

[Pythagorean]

I see your point. I acknowledge that our human conception of truth is probably misplaced. However the essence of reality which science provides is far more rationale a process than any other, so i accept it as truth.

Well yes, I agree. I think science is one of the ways we know that our concept of truth is displaced (which is itself, a truth).

 

[Functor97]

You realize that sentence 2 is a non-sequitor with respect to sentence 1?
your last sentence does not conflict with my statement about mathematics being a tool.



Mathematics is an even smaller truth than observation. It is almost so self-consistently true as to be irrelevant; we must qualify mathematics to utilize it. At least observation has some direct interaction with reality.

I apologize for not expressing myself clearly.

I acknowledge that without experiment, physics would never get of the ground. What i mean to say is that mathematics explains the reason for physical theories. We generate our mathematics from empiracism (our logic evolving to match our environment so as to survive). Mathematics is the only to tool we have to explain anything, as mathematics is indicative of reality itself. I acknowledge that mathematics is a very useful tool, but i do not believe it was designed as a tool, but discovered and implemented to explain.

 

[Pythagorean]

I don't know. I see mathematics as a subject at a university. Some elements of it are discovered, some elements of it are invented. Some elements might not fit so nicely into such a simple, two-boxed system as "discovered" or "invented".

 

[Simon Bridge]

It is true as far as we can tell, so why does science not deal with truths?

(my emphasis) That's not the same thing as saying it is "true" true.

In philosophy, "truth" has a more careful definition than it has in real life. Science does not deal with truth but in reality. You don't need absolute knowledge to function in the real world - good old approximate knowledge is fine for sitting down and hitting keys.

Religion has nothing to do with truth, science is the best notion of truth we have,

And the best notion is to sort out what is not true. In a way, the only certain truth we can have is of falsehood.

and mathematics is the basis for this.

... you may notice that not all mathematical constructs have their analog in reality. Even some of the ones that looked promising, like Euclidean geometry, turned out to be flawed. Don't get too cocky about math - it is a human construction.

Learn Humility monkey-sage ;)

Bear in mind that these are philosophical disputes that have been around for millenia right? We are not going to do justice to them in a few forum posts.

I'm going to give you a bunch of primers:

Realism vs Phenominalism (Problem of perception)
http://plato.stanford.edu/entries/perception-problem/
phenominalism: nothing is real - it's all just sense data
realism: there exists a reality behind our sense-data, and our sences give us useful information about it

Empiricism vs Rationalism
http://plato.stanford.edu/entries/rationalism-empiricism/
Rationalism: some synthetic truths can be known a-priori
Empiricism: the rationalist is full of it.

Problem of induction
http://plato.stanford.edu/entries/induction-problem/
... a synthetic truth cannot be known with certainty from repeated observation.
See 4.2 (Popper) for a description of scientific knowledge (deduction) in this context, and section 5 for the application of probability.

There are probably less dry sources but these are pretty short.

 

[Functor97]

I don't know. I see mathematics as a subject at a university. Some elements of it are discovered, some elements of it are invented. Some elements might not fit so nicely into such a simple, two-boxed system as "discovered" or "invented".

We invent the definitions to generate a clear consise understanding of the subject matter. This is no different to our laws of physics, did we invent the laws of physics?

It is quite odd that a pythagorean would claim that mathematics was even slightly invented

 

[Pythagorean]

And the best notion is to sort out what is not true. In a way, the only certain truth we can have is of falsehood.

The goal of science is not to open the door to everlasting wisdom, but to set a limit on everlasting error.
-Galileo

 

[Functor97]

(my emphasis) That's not the same thing as saying it is "true" true.

In philosophy, "truth" has a more careful definition than it has in real life. Science does not deal with truth but in reality. You don't need absolute knowledge to function in the real world - good old approximate knowledge is fine for sitting down and hitting keys.

And the best notion is to sort out what is not true. In a way, the only certain truth we can have is of falsehood.

... you may notice that not all mathematical constructs have their analog in reality. Even some of the ones that looked promising, like Euclidean geometry, turned out to be flawed. Don't get too cocky about math - it is a human construction.

Learn Humility monkey-sage ;)

Bear in mind that these are philosophical disputes that have been around for millenia right? We are not going to do justice to them in a few forum posts.

I'm going to give you a bunch of primers:

Realism vs Phenominalism (Problem of perception)
http://plato.stanford.edu/entries/perception-problem/
phenominalism: nothing is real - it's all just sense data
realism: there exists a reality behind our sense-data, and our sences give us useful information about it

Empiricism vs Rationalism
http://plato.stanford.edu/entries/rationalism-empiricism/
Rationalism: some synthetic truths can be known a-priori
Empiricism: the rationalist is full of it.

Problem of induction
http://plato.stanford.edu/entries/induction-problem/
... a synthetic truth cannot be known with certainty from repeated observation.
See 4.2 (Popper) for a description of scientific knowledge (deduction) in this context, and section 5 for the application of probability.

There are probably less dry sources but these are pretty short.

Thank you for posting those links, i have read the stanford philosophy wiki before, it is a good resource.

I however think you are overstepping the line, claiming that not all mathematical construction correspond to reality. Does this not fit you criterion of falsehood? i.e. It seems that way, but we cannot prove it.
What if string theory or the multiverse is somehow supported by experiment? It is not beyond the realms of possibility. If so, and each "universe" is a homogenous set of physical laws, then it is quite possible that all mathematical "constructions" are embedded in a deeper reality.
I also disagree with your claim that mathematics is man made. This is a ridiculous claim. We can't find an even prime besides two, no matter how much we may want to, nor may we construct one without changing the meaning of a prime.

 

[Functor97]

The goal of science is not to open the door to everlasting wisdom, but to set a limit on everlasting error.
-Galileo

I have never read that quote before, thank you for posting it!