On the Success of Scientific Theories

[FallentoReason]

Hello all, here's a little food for thought:

One philosophical theory that attempts to explain the success of science is called the No Miracles Argument, and goes as follows:

P1) Our best scientific theories are successful. (note: a theory is successful when the predictions it makes are true).
P2) The best explanation for the success of science is that our best scientific theories are true.
C) Our best scientific theories are true.

It is called the No Miracles Argument because the thought is that it would be a miracle if our scientific theories were successful, yet entirely wrong. Thus, the need to explain why this intuitive thought is correct.
Now, in order to make the argument fly, we need to wipe out competing explanations that could replace P2. One such competing explanation is this:

*P2) The best explanation for the success of science is that our best scientific theories are empirically adequate. (that is to say, the observations are accounted for by the theory).

The problem here is that a theory can be empirically adequate (EA), yet false. An example is that we could explain the pyramids by saying aliens built them. This theory accounts for the observations, yet is not true.
Another issue is that EA is in fact a mere restatement of what it is that we're trying to prove:

"The predictions of our theories are true (i.e. scientific theories are successful) because (*P2: ) it accounts for the observations."

But this is precisely what it means for a theory to be successful, that it's predictions are true i.e. they have been observed. Therefore, it seems like we've shown *P2 isn't a good premise to have, but our worries don't end there. Our original premise, P2, in fact has the same problem; it is a restatement of what we're trying to explain:

"The predictions of our theories are true (i.e. scientific theories are successful) because (P2: ) they are true."

But what it means, in part, for a scientific theory to be true is that it's predictions are true. Therefore, truth isn't any better an explanation than empirical adequacy is. That means there doesn't seem to be a meaningful explanation that isn't simply the reiteration of what it means for scientific theories to be successful. So, why are they successful?

[Alex K]

As a physicist, this sounds too simplistic to me. No good physicist would say: Theory XY is true. That's just not part of the vocabulary...

To give you a tired standard example: Newtonian theory vs. Special relativity. Newton was once the best theory, but obviously never yields 100% precise results. We know relativity and can roughly quantify the error. The same is true for relativity.

How does this situation fit in your scheme of things?

[FallentoReason]

As a physicist, this sounds too simplistic to me. No good physicist would say: Theory XY is true. That's just not part of the vocabulary...

To give you a tired standard example: Newtonian theory vs. Special relativity. Newton was once the best theory, but obviously never yields 100% precise results. We know relativity and can roughly quantify the error. The same is true for relativity.

How does this situation fit in your scheme of things?

When I speak of the "truth" of a scientific theory, what I really mean is the approximate truth. I think it's important to maintain a certain level of modesty since we don't know everything.

What do I mean by "approximate"? Simply that if T is the set of all true claims about the world, then a theory B will be approximately more true than A if (i) B implies more of the claims in T than does A and (ii) B implies fewer of the claims that are not in T than does A.

I still think the question remains of why it is that science is successful, and if we can give a meaningful explanation.

[Alex K]

I absolutely agree that it is a very interesting question, I just wasn't ok with the wording.

What is the meaning of "approximate truth" as pertaining to theories?

[watchamadoodle]

I wonder if this stuff would help?

Solomonoff's theory of universal inductive inference is a theory of prediction based on logical observations, such as predicting the next symbol based upon a given series of symbols. The only assumption that the theory makes is that the environment follows some unknown but computable probability distribution. It is a mathematical formalization of Occam's razor and the Principle of Multiple Explanations

http://en.wikipedia.org/wiki/Solomonoff%..._inference

[FallentoReason]

I absolutely agree that it is a very interesting question, I just wasn't ok with the wording.

You're right. I should have been more careful with that!

What is the meaning of "approximate truth" as pertaining to theories?

Well, imagine that if we assumed the universe had a set of ultimate truths, T, then the approximate truth of a particular theory would look something like this:

Assume these sets

T: a red ball, blue ball and yellow ball
theory A: a red ball, dog and blue ball
theory B: a blue ball and yellow ball

Then B would be more approximately true than A with respect to the ultimate truths T because A assumes something that isn't true whereas B only fails by not mentioning one other truth, and also according to Occam's Razor, is a better explanation.

Likewise with QM and relativity, it seems they get some things right, but they're not quite there yet, hence what can only be their "approximation" of truth.

---

I wonder if this stuff would help?

Solomonoff's theory of universal inductive inference is a theory of prediction based on logical observations, such as predicting the next symbol based upon a given series of symbols. The only assumption that the theory makes is that the environment follows some unknown but computable probability distribution. It is a mathematical formalization of Occam's razor and the Principle of Multiple Explanations

http://en.wikipedia.org/wiki/Solomonoff%..._inference

Umm, maybe? It depends on what you think this is addressing in the OP. Or were you responding to the notion of approximate truth only?

I'm not quite sure how this fits in.

[Joods]

I am so confused by this. No wonder I did poorly in science class. I was lost with the first post, but kept reading in the hopes that I would understand. I am even more lost now.

[Alex K]

I am so confused by this. No wonder I did poorly in science class. I was lost with the first post, but kept reading in the hopes that I would understand. I am even more lost now.

So, imagine a thought experiment where you let a ball drop (in a vacuum to get rid of complications like air resistance). With Newton's formulas, you can now calculate how long it takes to fall and what its velocity will be etc. You get some numbers out.

It'll be very accurate, but we already know that the theory is not perfect - if you use Einstein's formulas, you'll get a slightly different, more precise result (not noticeable in practise when dropping balls, but let's not get distracted by that technicality). So a question you might ask is now - in which sense do the Newton theory, and the things it talks about (such as Forces) exist in nature, or at least be reflections of aspects of nature. Can one say that relativity, which talks about somewhat different things such as curved spacetime, to achieve similar results, somehow gives us more truth about Nature?

I think the point is that we would like to use these theories for more than just calculating numbers such as how long does the ball take to drop, but would like to use them as explanations for what happens in the world, such as "earth attracts this ball with gravitational force" (Newton), or "earth curves spacetime, and thus the ball gets moving" (Einstein). In which sense are these explanations a true reflection of what happens in nature, and in which sense do the explanations of newer more precise theories come closer to that goal of explaining what is "really going on in nature".

Is this clearer?

[Exian]

This is going to be some clunky wording, but would it be better, maybe more honest, to say "...our best scientific theories are truer than anything else we have." Or "... our best scientific theories have come true more often than other methods used." I may not be getting this. What's the objective? To be able to say that our scientific theories are absolutely true, or just the most accurate method we have to explain reality?

[Alex K]

The second, the first thing, absolutely true, is not something one can ever sensibly claim about a theory.

To me that's the thing: what does explaining reality still mean if different successive best theories use apparently very different words to explain and describe what's going on.

Like this: I'm writing a chapter right now on the physics of the LHC for laypeople, and I'm talking about the effects of virtual particles on measurements. And I wonder, is it philosophically sound to say: such and such is the outcome of this particles collision, *because* if virtual particles being exchanged by the electrons or whatever. Now, virtual particles are a staple of quantum field theory, and *in that theory* they are the things that make other particles do stuff. But can one say: in Nature, the two electrons act like this and that *because* of virtual particles? I don't know, but it sounds wrong. As if each sentence needed a disclaimer: "I actually mean, that's the explanation when nature is interpreted in terms of this theory here. Might be subject to radical reinterpretation in future theories". And that confounds me a bit bc I don't want to lie to readers, nor aggravate the philosophers of science, or seem philosophically naive.