Concepts are concepts, and equations are equations, and never the twain shall meet; abduction and realism vs anti-realism

[Jim]

I’ve changed the term theoretical in the op to theoretical concepts to be more inline with what the author of Science and Its Limits claims is a relatively popular definition of theory. However, I noticed that a central point that needs to be addressed in the op isn’t as clear as I would like it to be, so I’m going to add it here.

That is that mechanical equations can only inductively infer how matter behaves. But that seems to me to be the extent of what they can infer. To suggest that they can be used to infer what underlies observable physical reality has no logical justification at all that I can see.

The only logical means that I’m aware of to infer such things is through abductive reasoning, and the relevant evidence from which to infer such things would be physical observation, not abstract mechanical equations.

[Rumraket (Mikkel R.)]

@Jim

That is that mechanical equations can only inductively infer how matter behaves.

Perhaps you meant to say that the mechanical equations which scientists posit as representations of the ways in which matter behaves, ultimately rest on inductive reasoning from limited sets of observations?

[Jim]

@Rumraket

Perhaps you meant to say that the mechanical equations which scientists posit as representations of the ways in which matter behaves, ultimately rest on inductive reasoning from limited sets of observations?

Oh, right. Would this be correct? The equations deduce what should be observed if the generalization of the behavior is correct. The observations inductively infer that what the equations describe is correct and tentatively confirms that the general behavior is such.

[Jim]

Actually this might be more accurate. Mechanical equations deduce what should be observed if the generalization of the behavior they represent is correct. The observations empirically verify that the equations are correct and tentatively confirm by inductive inference that the general behavior is such.

[Rumraket (Mikkel R.)]

I think I know what you’re trying to say with that, and I don’t disagree with it, I just think the grammar leaves something to be desired.

Mechanical equations, and observations, do not take actions. They do not deduce things, and they don’t verify. They can’t think or reach conclusions. It is people who do that by using the equations of course. What I think you should be saying is for example that “Deductions from mechanical equations, implied that… something”. Or “It was verified empirically that the equations were correct…”

[Jim]

@Jim

Mechanical equations deduce what should be observed if the generalization of the behavior they represent is correct. The observations empirically verify that the equations are correct and tentatively confirm by inductive inference that the general behavior is such.

Oh, OK. Good point. How’s this? From mechanical equations we can deduce what should be observed if the generalization of the behavior they represent is correct. From observations we can empirically verify that the equations are correct and tentatively confirm by inductive inference that the general behavior is such.

[Rumraket (Mikkel R.)]

Much better, and thus easier to understand.

[nwrickert (Neil Rickert)]

@Jim

Would this be correct? The equations deduce what should be observed if the generalization of the behavior is correct. The observations inductively infer that what the equations describe is correct and tentatively confirms that the general behavior is such

Sigh!

Equations don’t deduce. Humans deduce, and possibly use equation as part of that deduction.

Likewise, observations don’t inductively infer. Humans infer, with observations playing a role in that inference.

[Jim]

@nwrickert this was already mentioned by @Rumraket and corrected if you read a few more comments down.

OK, one more try. From mechanical equations we can deduce what should be observed if the generalization of the behavior they represent is correct. From observations we can empirically verify that the equations are correct and tentatively confirm by inductive inference that the general behavior is such.

But to suggest that mechanical equations can be used to infer what underlies observable physical reality has no logical justification that I can see. The only logical means that I’m aware of to infer such things is through abductive reasoning, and the relevant evidence from which to infer such things would be physical observation, not abstract mechanical equations.

Assuming the above is correct, the antirealist would only be correct about theoretical concepts having no correspondence to reality by denying that abductive inference has no epistemological value, which is pretty much what seems to be the antirealist stance.

On the other hand, the realist would be wrong if he were to base his claim that they do correspond to reality if he were basing it on the assumption that its use as a conceptual framework for particular mechanical equations provides some epistemological value in some strange way. But it seems obvious, at least to me, that to justifiably claim correspondence with reality one would have to rely on abductive reasoning, i.e., following the relevant evidence where it leads.

So with that in mind, I again conclude that it seems to me that to be consistent one would have to take a position to either accept or reject the efficacy of abductive reasoning. And going back and forth when convenient would seem to be a completely arbitrary and logically unjustified move.

So for example, if one holds to the Copenhagen interpretation, it seems it would mean holding to anitrealism since its interpretation, as far as I can tell, is not attached to any observable reality and in that sense only instrumentally there to provide a conceptual framwork for the formulas. In other words, though a visualization that could in principle be real, it’s not a reality driven abductive inference from real and relevant observations.

But if one is committed to antirealism on theorectical concepts in QM, to be consistent it seems one would also be committed to antirealism on all theoretical concepts in science, including abiogenesis, relativity, big bang cosmology, evolution, etc.

[dga471 (Daniel)]

@Jim

But to suggest that mechanical equations can be used to infer what underlies observable physical reality has no logical justification that I can see. The only logical means that I’m aware of to infer such things is through abductive reasoning, and the relevant evidence from which to infer such things would be physical observation, not abstract mechanical equations.

I’m confused about this constant invoking of abductive reasoning. You drop a ball from a certain distance 100 times, and it always comes down to the ground within, say, 1.0-1.2 seconds. On the 101th time, do you have justification that it will repeat the same behavior?

[Jim]

@dga471

I’m confused about this constant invoking of abductive reasoning. You drop a ball from a certain distance 100 times, and it always comes down to the ground within, say, 1.0-1.2 seconds. On the 101th time, do you have justification that it will repeat the same behavior?

OK. It’s an inductive inference, and yes, from what I understand it’s a justifiable inference. But that only answers the question of how matter behaves. But I’m curious to know how is an inductive inference about observable behavior relevant to an abductive inference about past events, or hidden existence that underlies what we observe? Or in what way is the observation of dropping a ball 100 times and measuring the time it takes to hit the ground relevant to understanding past events or how or in what form hidden reality exists?

[dga471 (Daniel)]

@Jim

But that only answers the question of how matter behaves. But I’m curious to know how is an inductive inference about observable behavior relevant to an abductive inference about past events, or hidden existence that underlies what we observe?

OK, so you agree that what I described is a valid instance of induction. From that, we can infer an equation to describe the behavior of the ball:
h = 1/2 g t ^2,
where h = height from which the ball is dropped, g = Earth’s gravitational acceleration, and t = time for the ball to drop.

This would then be an example of induction being used to support validity of a “mechanical equation” without resolving to “abductive reasoning” (which I’m still not 100% sure what you mean by that). It would disprove your earlier statement:

@Jim

But to suggest that mechanical equations can be used to infer what underlies observable physical reality has no logical justification that I can see. The only logical means that I’m aware of to infer such things is through abductive reasoning, and the relevant evidence from which to infer such things would be physical observation, not abstract mechanical equations.

[Jim]

Now I’m confused. How did you get from

@Jim

But to suggest that mechanical equations can be used to infer what underlies observable physical reality has no logical justification that I can see

to

@dga471

This would then be an example of induction being used to support validity of a “mechanical equation” without resolving to “abductive reasoning” (which I’m still not 100% sure what you mean by that). It would disprove your earlier statement:

Somehow I don’t quite follow what you seem to imply here? Can you clarify?

[dga471 (Daniel)]

I took your statement to say that the idea that certain mechanical equations reflect behavior of matter in nature and thus can be used to predict their future behavior can only be justified by abductive reasoning. I showed a case where it came about by inductive reasoning.

[Jim]

Oh, OK. That’s not what I meant. It’s not about using abduction as a means to justify mechanical equations as accurate descriptions. Those are inductive inference which I’ve said several times now. But the issue I’m raising is about when theoretical concepts as explanations are somehow seemingly justified by being associated with successful mechanical equations. The issue is about how the concepts, which cannot be empirically verified, are justified, which I’m arguing can only be justified by abductive reasoning. As I’ve said before, I have no problems with accepting successfully verified mechanics.

[dga471 (Daniel)]

@Jim

But the issue I’m raising is about when theoretical concepts as explanations are somehow seemingly justified by being associated with successful mechanical equations.

I think you should give a specific example of theis claimed “association with a successful equation” gives rise to a theoretical concept which you think is unjustified.

[Jim]

@dga471

I think you should give a specific example of theis claimed “association with a successful equation” gives rise to a theoretical concept which you think is unjustified.

That’s not exactly what I’m saying. The theoretical concepts are visualizations that are used as frameworks for formulating the equations. They don’t necessarily have to represent reality. They just need to provide a framework.

The problem is when these visualizations start being used as representations of reality. Just because of the fact that they are used as conceptual frameworks for consensus interpretations with empirically verified equations doesn’t justify them as explanations for reality.

If that’s what is happening, which I believe it is, I just don’t see how that could be a logically justifiable move. If they are going to be claims to reality there needs to be some logical premise on which to base that claim. That’s where I see abductive reasoning would need to come into the picture.

So let’s use the Copenhagen interpretation as an example. One of the explanations is that at the quantum level, entities exist as “wave functions” until being measured. How is that explanation arrived at abductively? That’s just a head scratcher for me. Maybe you could explain that to me.

But just because the Copenhagen interpretation has enjoyed the most support among scientists over the years, it seems to me without any justification the concept gets a free ride as to how or in what form reality does actually exists.

[dga471 (Daniel)]

@Jim

So let’s use the Copenhagen interpretation as an example. One of the explanations is that at the quantum level, entities exist as “wave functions” until being measured. How is that explanation arrived at abductively? That’s just a head scratcher for me. Maybe you could explain that to me.

But just because the Copenhagen interpretation has enjoyed the most support among scientists over the years, it seems to me without any justification the concept gets a free ride as to how or in what form reality does actually exists.

@Jim, I agree with you that the Copenhagen interpretation is not demanded by the scientific evidence. It is incomplete. I suspect that many physicists assume this interpretation because it is in line with the naive “shut up and calculate” approach and has been casually included in many quantum mechanics textbooks. But I don’t think most people would say that it is the only acceptable interpretation, even if everyone agrees that QM “works”. It is more of a philosophical position rather than a scientific one. For example, Sean Carroll highlights this informal poll at a conference which shows that Copenhagen is the preferred interpretation of only 42% of physicists.

[Jim]

I’m not sure you’re following my train of thought. What I’m saying would apply just as much to relativity when applying its theoretical concepts to reality.

[dga471 (Daniel)]

Well, can you elaborate more on how it applies to relativity?