Theoretical Concepts and Empirical Equivalence: Will the Real Concept Please Stand Up

Although I might wear out my welcome, (which I suspect to some extent I may already have :slight_smile:) I’ve decided to try a different approach to see if it helps to move forward the conversation I’ve brought up in one of my last posts, and other related posts, and give a better and hopefully clearer picture of what I’m getting at.

First I think there are two different questions that need to be recognized that are being addressed by a theory in physics in regards to theoretical concepts.

  1. From empirical verification, which concepts as frameworks are best for formulating generalized equations that provide the most accurate methods for calculating measurements to describe how matter moves through space?
  2. From objective observation and shared common experience, which concepts best explain what hidden reality is like?

In the first question, from the mathematical equations deductive inferences, generally agreed upon as providing the highest degree of certainty, are generated, and from empirical verification inductive inferences (as used in the narrow sense in physics), generally agreed upon as providing the next highest degree of certainty, are generated. In the second question, from observable evidence abductive inferences, generally agreed upon as at the least not having as high a degree of certainty as the first two types of inferences, are generated.

Both realists and antirealists generally acknowledge the first question. However, in general the antirealists disregard the second question as either useless, or unanswerable. The first question, when empirically verified, is usually without any significant dispute. However on the realist view, the second question, depending on the strength of the evidence, generally leaves much more room for debate.

Next I want to bring up the subject of empirical equivalence. The question I have is, doesn’t empirical equivalence demonstrate that it’s possible to have more than one conceptual framework, e.g., Lorentzian vs Minkowskian SRT, that yield the same outcome? If so, in regards to the first question, wouldn’t that suggest that concepts as frameworks, being compatible in a mathematical sense, only serve a utilitarian role and play no role epistemically unlike, in regards to the second question, concepts as explanations that it seems are intended to play an entirely epistemic role?

If that’s the case, from a realist perspective, wouldn’t it suggest that being a useful concept doesn’t necessarily correspond with being a true concept, i.e., corresponding to what reality is really like. If that’s the case, wouldn’t it be unjustified to claim that the concept in a theory that answers the first question necessarily has to be the concept in that theory for the second question? And if that’s the case, wouldn’t it suggest that both questions are independent of each other, and in any particular theory one isn’t necessarily committed to use the same concept for both the first and the second question?

If so, empirical equivalence seems to suggest that there is no inherent conflict between the utilitarian use of different conceptual frameworks in empirically equivalent theories, and that thence there is no direct relationship between the first question and the second question, which would seem to suggest that the answers to both questions are not necessarily one and the same.

If that’s the case it seems the option is available in a theory to use one concept for the first question while holding to a different concept for the second question. However, though in the first question there can be more than one concept that turns out to be useful, in the second question only one concept can be the true concept for what reality is like, unless the claim is held that more than one reality exists simultaneously, which I would argue seems extremely unlikely.

If what I’m arguing for is warranted it opens up a whole new dimension in the discussion of the problem of the “theory of everything.” However, I will wait before delving into that discussion to see what kind of response I get from what I’ve posted so far.

I thought it might be helpful to lay out what I perceive as the general view regarding theoretical concepts in physics so if I’m off on that someone can set me straight. As far as I can tell, I think the general way they’re looked upon is that, as a framework, their function is to guide the physicist in formulating equations for making measurements that most accurately describe the motion of matter through space.

On an antirealist view a theoretical concept simply represent a useful fiction which has no correspondence to reality, or it might correspond to reality, but there’s just no way to know if that’s the case. This avoids a lot of the issues that the realist has to deal with.

On a realist view, it represents the fundamental hidden structure of matter itself, or an approximation thereof. In other words, for a realist, who unlike the antirealist has the added aspect of theoretical concepts as explanations of reality, both questions of which is the best concept as a framework and what actual reality is really like are inextricably linked.

On realism, for example, take Newton’s theory of gravity vs general relativity. As I understand it, the fact that the equations in GR are the most accurate somehow vindicates the claim that the explanation that space as an entity exists in a relative or relational fashion, since relativity as a conceptual framework formulates the most accurate equations.

So those realists who want to argue for the existence of space as an absolute entity, as I understand it, would need to come up with equations based on absoluteness as a conceptual framework that resolve the issues with classical mechanics in such a way that produces either more accurate equations than relativistic mechanics, or at least obtains equivalent results.

With regards to empirical equivalency, I think the way a realist reconciles this is to say that even though the outcomes are the same, only one of the theories can represent actual reality, and the way to discern which of those theories is true is by a sort of inference to the best explanation where the main criteria, in this case, seems to be simplicity and maybe elegance as well, although I’m not sure if, as criteria, those two are one and the same thing.

Is that generally what’s going on?

So I think in general I have a reasonable understanding of what’s going on with theoretical concepts in physics. And since there are no contrary comments offered, I’m just going to assume for now that’s the case until it has been shown otherwise.

So what I’m questioning is the apparent assumption on a realist view that both questions are inextricably linked, i.e., the success of a theory entails that the concept it’s based upon is a true representation of actual unobserved fundamental layers of reality.

Here’s what I think the argument looks like:

  1. In physical theories theoretical concepts are used as frameworks for formulating equations to devise methods to measure and track matter as it moves through space.
  2. The equations are confirmed as accurate by empirical verification.
  3. Therefor as accurate descriptions of how matter behaves those theories must accurately reflect what unobserved fundamental levels of reality are like.

This is the argument I’m challenging. How can it be that a concept used for the purpose of describing how matter behaves entails what unobserved fundamental levels of reality are like? I just don’t see how such a conclusion would follow from those premises.

I think the best that can be said is that empirical verification of a physical theory doesn’t entail, but can be considered as an indication that the concept it’s based upon represents what unobserved fundamental layers of reality are like, kind of like how establishing a motive in an investigation supports a claim that a certain suspect committed the crime. It isn’t proof, but just a piece of evidence in a cumulative case in support of a particular claim.

So it would be incorrect to say, for example, that the success of the theory of relativity entails that space must be relative. The success of the theory would at best only be a piece of evidence to support that claim. But all of the relevant types of evidence either for or against it would have to be examined to establish the truth of that claim as the best explanation for the available relevant evidence.

I haven’t previously replied in this thread, because it has been unclear what you were looking for. But at least this gives a better picture:

Speaking only for myself, I do not go with your step 3. I take a scientific theory to be followed on pragmatic grounds. I do not assert that the theory is true.

I tend to think of a scientific theory as neither true nor false. And that’s because we do not have criteria by which we can evaluate the truth of theories. We can only assess a theory on pragmatic criteria, or on how useful the theory is to us.

This is somewhat analogous to an axiom system in mathematics. While working with a particular axiom system, we assume those axioms. That is to say, we do our mathematics as if those axioms are true. But we can then switch to a different axiom system.

We do something similar in science. We often go along with geocentrism as assumed axioms, such as when we talk about sunrise, or the sun going from east to west. But if we want to discuss astronomy, we switch to a heliocentric axiom system.

You seem interested in “what unobserved fundamental levels of reality are like.” But why should they be like anything at all? To say “X is like Y” is to make a statement about how we perceive them. So why should we make such a statement about that which we cannot perceive (about unobserved reality)? We could, of course, take science to extend our perception. And maybe that’s the best we can do.

1 Like

So from what I gather you are an anti-realist, i.e., we can only make meaningful statements about what we can observe, and either there is no existence beyond that, or if there is an underlying level of reality we cannot “know” anything about it, and therefore have to take an agnostic position. Is that correct?


I have been told that I am an anti-realist. But I do not recognize that.

As a mathematician, I make meaningful statements about mathematical entities. But we do not observe those. As a mathematical fictionalist, I usually say that mathematical entities don’t actually exist though it is useful and meaningful to talk of them as if they exist.

Yes, I disagree with a lot of what metaphysical realists say. That’s probably why they say that I am an anti-realist.

The anti-realist wants to say that electrons don’t actually exist; they are just part of the descriptive system used by science. If we want to look at it that way, then we should say that cats don’t actually exist; they are just part of the descriptive system used in ordinary language. Similarly, we should say that food doesn’t actually exist; it is just part of the descriptive system used in ordinary language. However, if I feel hungry, I am going to eat some food.

Perhaps we cannot have justified true belief about it. But we can know about it, much as I can know that eating that food will alleviate my hunger.

Interesting. So let me see if I understand correctly. So you seem to say that, at least in regards to physics, theory has pragmatic implications but doesn’t necessarily have implications as to the question of what unobserved layers of reality are like. But you don’t deny that there are unobserved layers of reality that, though can’t be observed, can still to a certain degree be known. Is that somewhat in the ballpark of what your position is?

When you talk of “layers of reality”, you are assuming a layered structure. I don’t know of any basis for that.

We interact with reality via our sensory modalities. And then we invent useful ways of talking about that reality. Science isn’t much different. Science just gives us new ways of interacting with reality, and allows us to further extend how we talk about.

I’m suggesting that this all depends on pragmatics. There isn’t any true or false about how we go about it. Once we have invented ways of talking about reality, we can discuss whether our descriptions follow those invented rules. But there isn’t any true or false about how we invent rules of description – the are only pragmatic requirements.

I’m suggesting that “the question of what unobserved layers of reality are like” is a meaningless question.

OK. I’m assuming from what you’ve mentioned that you hold to a form of metaphysical antirealism called pragmatism.
Edit: It seems from further reading that there seems to be another use of pragmatism that refers to a third alternative to metaphysical realism and antirealism. I think that is what the link is about. However, I think there may be a form of pragmatism within the category of metaphysical antirealism, but I’m not sure that’s the case. Maybe you know?

If what you suggest is that at the least questions about unobserved reality, whether layered or not, are meaningless then scientific antirealism seems to be the category you fit into, which is a separate distinction from metaphysical antirealism.

If so, my next question would be, what is your view on abductive reasoning? My guess is that you would also view it as meaningless. Is that correct?

I would not call it meaningless. But I tend to be skeptical of the way that the term is used.

I would define it as reasoning from incomplete information. And I would say it’s the type of reasoning used in, for example, historical studies, criminal investigations, and science regarding past events and unobservable foundations of reality. Would that be something you would agree with?

I’m more inclined to say that “abduction” is the name people use to describe the case where they don’t know how the conclusion was reached, but it seemed reasonable enough.

How about deduction is where there is only one option, i.e., it has to be. Induction, at least with regards to mechanics in physics, there are only two options, i.e., either it is or it isn’t. And with abduction possible options can be narrowed down to what is plausible, and from those more than one plausible options using generally agreed upon criteria it can be narrowed down to the best option? Would that be in line with how you see it?

I’m doubtful that science ever uses induction, except in the sense of statistical inference. Philosophers just have this wrong, in my opinion.

What they do use, is model construction. And some people confuse that with abduction or induction. Yes, there is an element of art in model construction, which is why it might seem that there are several possible choices.

Let me see if I’m tracking with what you’re saying. As I understand it, when a prediction from a mechanical theory is empirically verified, it is said that it inductively infers the theory is accurate in predicting how matter behaves inasmuch as it reconfirms what has yet to be shown to be inaccurate.

However, since all of the possibilities of whether or not it is accurate have not yet been explored, it is said to be tentatively confirmed until such a time when something might happen to show that it isn’t accurate. Are you saying you don’t agree with this?

As I understand it, a model is just a visualization of a theoretical concept. For example, a model of the big bang would be a visualization of what the theoretical concept of a singularity expanding into the universe would look like. Is that correct?

Yes, that’s what I am saying.

That could be called a model. But it is not what I meant.

OK. I think I’m getting an idea of where you’re coming from. So for you, asking questions that aren’t useful in some practical way like, do concepts in physics represent what reality is like, is a meaningless endeavor. Is that sort of the gist of it?

No, that’s not it at all.

I’m a mathematician. And that has to do with pure mathematics, rather than applied mathematics. I’m very much a theorist.

I see the question “What is reality like?” as meaningless, because nobody can explain the meaning.

If you ask “What is reality like to me?” then I at least know what you are asking. I might not be able to fully answer, because we don’t have the words for some of it.

If you ask “What is reality like to God?” I might wonder which God. If you ask that about the Christian God, it seems it would have to be very different from what it is like to us. Omniscience requires that it be different.

When you just ask “What is reality like?” you are not asking anything meaningful at all.

I’m not tracking with you at all. Sorry. :slight_smile: Since we seem to be starting from different philosophical positions, pragmatism and realism, we’re obviously going to come to different conclusions. And since your objection was to premise 3, which I also don’t accept, maybe I’ll just go ahead and continue on with the topic of the op and see what kind of objections are raised with what I think is the way premise 3 should read, and take it from there.

So the way I see it, in physics the purpose of a theoretical concept practically speaking is solely to act as a framework. The question of whether or not the concept equates with reality isn’t really addressed by the theory. So from a realist perspective, I would argue that the success of the theory can possibly be counted as evidence that the concept might equate with reality, but it doesn’t entail that it does.

So premise 3 should be reformulated to say:
3. Therefor as accurate descriptions of how matter behaves those theories are evidence that the concept may reflect what unobserved fundamental reality is like.

From there what needs to happen, as I see it, to arrive at the best explanation for what reality is actually like is to weigh all the available relevant evidence and decide on what the plausible options for explaining the evidence are, and arrive at the best of those options through a criteria based method such as IBE.

So even though there may be those who disagree with that based on differing philosophical starting points, what I want to know is if there are any objections that would possibly refute or rebut my position so that I would be unwarranted to hold to such a position. If so, I’ll try to address them. If not, I’ll move on to what kind of implications I think what I’m suggesting might have.

So in case it wasn’t clear from my last post on this topic here, assuming the change to premise 3 holds water, what could happen is that a concept from a successful theory could in principle not be the best explanation for what fundamental reality is really like if all of the relevant evidence was best explained by another concept.

So assuming the issue is that no one can follow my train of thought, I think what I’ll do is make one last attempt and elaborate a bit more to see if that works to get through to anyone. And if that doesn’t work, then I’ll start a new thread that gets into what I think the implications are if the position I’m taking is warranted.

So it seems from what I’ve argued so far that a successful physical theory doesn’t entail that it represents the fundamental nature of reality, but is only an indication of what it could possibly be like. I guess this is where things get a bit fuzzy for me. If something doesn’t entail a conclusion, but is only evidence to support a particular conclusion, isn’t it possible, even in the case of what might appear to be a good piece of evidence, to override the conclusion it supports if there is sufficient evidence to the contrary?

For example, couldn’t it be argued something to the effect that relativity as a successful theory is based on the reality of human limitation concerning measurement of motion, i.e., as a human we can’t be aware of everything all at once, and since we can only be in one place at one time we are generally limited to measure motion relative to the locations of different entities.

But it seems to me that relativity theory is directed at the question of how matter behaves, not at the question of what the fundamental nature of reality that underlies observation is. So despite it being successful, it isn’t necessarily representative of that reality, only a possible indication of what it might be, right?

And assuming our senses can be relied upon, based on the evidence that our shared human perception is of space, time, and simultaneity as absolutes, and also the fact that for the most part we never really see or experience any of the weirdness that relativity would suggest if accepted as representative of underlying reality, wouldn’t it seem to suggest that there’s good reason to be skeptical of relativity as an explanation of that reality even if it’s acknowledged as a successful theory and its formulas were able to be confirmed to be correct in every aspect?

I think for the last point about correct results there is also support that can be drawn from empirically equivalent theories. If having the same outcome from different concepts is possible, that seems to suggest that getting the right results isn’t necessarily a sign of correspondence to an underlying fundamental reality since it seems most likely that there can’t be more than one concept that represents that reality in actuality.