Concepts Of Method Vs Actual Existants

[Spearmint]

I've heard it claimed on several occassions that some of the more bizarre concepts from physics should be treated as 'concepts of methods', rather than as things which actually exist in reality. Examples would include the curvature of space-time, worldlines, and various aspects of the standard model. The same applies to certain mathematical entities (imaginary numbers for example).

By what criteria can we distinguish between physical entities whose existence is predicted by a particular theory, and purely mathematical 'fudges' that are required in order to make the equations work? From my observance of discussions, the only criteria I've noticed is that things which seem to contradict with everyday experience are normally claimed to be only 'concepts of methods', whereas things which make more intuitive sense are readily accepted as describing actual objects. I assume there should be a more objective decision procedure than this, but I'm not sure what it would actually involve.

[stephen_speicher]

I've heard it claimed on several occassions that some of the more bizarre concepts from physics should be treated as 'concepts of methods', rather than as things which actually exist in reality. Examples would include the curvature of space-time, worldlines, and various aspects of the standard model. The same applies to certain mathematical entities (imaginary numbers for example).

The way you set up the issue already skews any response. In fact, there is nothing "bizarre" about the specific concepts that you have noted. If you have knowledge of their nature these concepts are just as normal as any other valid concepts that we form.

By what criteria can we distinguish between physical entities whose existence is predicted  by a particular theory, and purely mathematical 'fudges' that are required in order to make the equations work?

Again this seems to be a somewhat strange formulation. What are "mathematical 'fudges' that are required in order to make the equations work?" In this context I cannot even imagine what is meant by that.

But, as to determining whether or not a particular prediction is correct or not, the obvious way is to look at reality. Afterall, that is exactly what scientific experiments are designed to do. However, there are certain things that we can exclude prior to experiment, on philosophical grounds alone. For instance, any prediction that actually claims existence of a physical singularity is, of necessity, wrong.

From my observance of discussions, the only criteria I've noticed is that things which seem to contradict with everyday experience are normally claimed to be only 'concepts of methods', whereas things which make more intuitive sense are readily accepted as describing actual objects.

There is no reason for concepts of method to "contradict with everyday experience," and our "intuitive sense" is more a function of the extent of our knowledge.

I assume there should be a more objective decision procedure than this, but I'm not sure what it would actually involve.

As Ayn Rand points out in ITOE (pp. 35-36) concepts of method are just a sub-category of concepts that pertain to products of consciousness, and they are formed by the usual rules of concept formation.

"Concepts of method are formed by retaining the distinguishing characteristics of the purposive course of action and of its goal, while omitting the particular measurements of both.For instance, the fundamental concept of method, the one on which all the others depend, is logic. The distinguishing characteristic of logic (the art of non-contradictory identification) indicates the nature of the actions (actions of consciousness required to achieve a correct identification) and their goal knowledge) — while omitting the length, complexity or specific steps of the process of logical inference, as well as the nature of the particular cognitive problem involved in any given instance of using logic."

[stephen_speicher]

Deleted second copy of same post.

[ian]

By what criteria can we distinguish between physical entities whose existence is predicted  by a particular theory, and purely mathematical 'fudges' that are required in order to make the equations work?

Do you mean someone who models reality as e.g. curved space because it gives the best predictions, even though they have no evidence that it is actually curved?

I think the only way to tell which parts of the model really exist is to create

a cause and effect chain to your senses, by using machines such as telescopes or

microscopes etc. If you can't do that you can't say they're real, even though a model that includes them gives perfect predictions.

[stephen_speicher]

Do you mean someone who models reality as e.g. curved space because it gives the best predictions, even though they have no evidence that it is actually curved?

If that is what Spearmint had in mind then it certainly has nothing to do with "purely mathematical 'fudges' that are required in order to make the equations work." Fudging an equation would mean manipulating it to conform with something known, not using the equation to predict that which was not previously known.

I think the only way to tell which parts of the model really exist is to create a cause and effect chain to your senses, by using machines such as telescopes or microscopes etc. If you can't do that you can't say they're real, even though a model that includes them gives perfect predictions.

Would you say then that before atoms were experimentally observed that physicists could not say that the atomic structure of matter was real? I would certainly agree that, ultimately, we need to reduce our knowledge to the perceptual level. But, in our intermediate epistemological states we can still justify being highly probable, or, perhaps, even certain, of the existence of that which we have not yet directly observed.

[Spearmint]

The way you set up the issue already skews any response. In fact, there is nothing "bizarre" about the specific concepts that you have noted. If you have knowledge of their nature these concepts are just as normal as any other valid concepts that we form.

I was obviously colloqualising. However from a quick lookthrough of your previous posts, you have referred to certain things as being concepts of methods rather than actual existants. For instance:

The spacetime manifold of relativity is simply a higher-level mathematical abstraction, with no implication that the manifold itself, and its properties, such as curvature, physically exist in the real world. It is, in effect, a concept of method, and a highly useful one at that.

This is the kind of thing I mean. On what basis can you claim that non-eucildean geometry is simply something 'useful' to suppose as part of a theory rather than something that actually describes reality? How could we determine whether the spacetime manifold here is actually something that exists, or just something that is a useful tool for us to refer to when formulating a description?

Again this seems to be a somewhat strange formulation. What are "mathematical 'fudges' that are required in order to make the equations work?" In this context I cannot even imagine what is meant by that.

By mathematical 'fudges' I mean any mathematical concept that cannot be reduced to any kind of experience, but the existence of which is necessary to allow a certain theory to exist. Imaginary numbers would be the perfect example here, as would anything which has its 'evidence' of existence derived purely from the need to make existing equations work (dark matter for instance)

But, as to determining whether or not a particular prediction is correct or not, the obvious way is to look at reality. Afterall, that is exactly what scientific experiments are designed to do. However, there are certain things that we can exclude prior to experiment, on philosophical grounds alone. For instance, any prediction that actually claims existence of a physical singularity is, of necessity, wrong.

I'm not entirely sure what you mean by a physical singularlity here, but its not that relevant. If the equations derived from a particular theory suggest the existence of a singularity, then I would say that its either necessary to say that said singularity exists, or that the equations themselves are incorrect. Writing the singularity off as being simply a 'concept of method' rather than an actual existent seems intuitively wrong.

[Spearmint]

Do you mean someone who models reality as e.g. curved space because it gives the best predictions, even though they have no evidence that it is actually curved?

Yes basically, however I would say that the fact it gives the best predictions _is_ evidence that space is actually curved. Without conceding this, I'm not sure how you could say that scientific theories could ever predict the existence of anything.

[stephen_speicher]

This is the kind of thing I mean. On what basis can you claim that non-eucildean geometry is simply something 'useful' to suppose as part of a theory rather than something that actually describes reality? How could we determine whether the spacetime manifold here is actually something that exists, or just something that is a useful tool for us to refer to when formulating a description?

If for the standard theory the spacetime manifold is a concept of method, then by definition the spacetime manifold does not have an independent physical existence. On the other hand, it is legitimate to ask if there is an actual physical existent that has some of the same characteristics implied by the use of the concept of method. To answer such a question one needs a separate theory that describes such a physical existent, integrating it with with other physical knowledge that we have, and then we can employ experimental methods to test for its existence.

By mathematical 'fudges' I mean any mathematical concept that cannot be reduced to any kind of experience, but the existence of which is necessary to allow a certain theory to exist. Imaginary numbers would be the perfect example here, as would anything which has its 'evidence' of existence derived purely from the need to make existing equations work (dark matter for instance)

If you read the quote I provided by Ayn Rand, therein she describes logic as a concept of method, as "actions of consciousness required to achieve a correct identification." Likewise imaginary numbers are a concept of method, an action of consciousness whose purpose is to provide a particular kind of mathematical operation. Both logic and imaginary numbers are reducible to the actions of consciousness, each having its own purpose and goal. Consciousness and its actions are just as much a part of reality as are physical existents.

I'm not entirely sure what you mean by a physical singularlity here, but its not that relevant. If the equations derived from a particular theory suggest the existence of a singularity, then I would say that its either necessary to say that said singularity exists, or that the equations themselves are incorrect. Writing the singularity off as being simply a 'concept of method' rather than an actual existent seems intuitively wrong.

You are conflating too many different things. Let me try to separate them out.

There are certain mathematical singularities -- for instance, a function that goes to infinity -- that can be handled with appropriate mathematical methods. But a physical singularity -- for instance, a density that goes to infinity -- cannot exist in physical reality, because infinity is a concept of method, not a physical existent. The law of identity forbids any infinite properties or characteristics of physical existents.

Now, there are several different cases.

(1.) A mathematical formula that uses a concept of method and predicts a valid physical process, one that is verified by experiment.

(2.) A mathematical formula that uses a concept of method and predicts an invalid physical process, such as a physical singularity.

In case (1.) we have a valid use of concept of method, giving rise to a valid prediction. However, in case (2.) there are (at least) two essential possibilities.

(a.) An invalid concept of method was used to give rise to an invalid prediction.

(b.) A valid concept of method was used to give rise to an invalid prediction.

Case (b.) is possible because not all mathematical solutions imply a physical process in reality that must correspond to the solution. For instance, the field equations of general relativity are an extremely complex and difficult to solve set on nonlinear partial differential equations. Certain solutions to these equations have been experimentally confirmed, while other solutions may be philosophically dismissed as not possible in reality. This does not mean that the equations are wrong, but only that certain solutions -- solutions arising from imposing certain conditions on the equations -- are not physically realizable.

As I said before, intuition is really a function of knowledge, and you have to have knowledge of the mathematical and physical processes involved in order to determine what is proper, and what is not.

[JPowersDC]

If the equations derived from a particular theory suggest the existence of a singularity, then I would say that its either necessary to say that said singularity exists, or that the equations themselves are incorrect. Writing the singularity off as being simply a 'concept of method' rather than an actual existent seems intuitively wrong.

Consider the concept of "center of gravity". For the purposes of most calculations, the gravitational pull of an object (such as the Earth) can be considered to be coming from a single point, the object's center of gravity. We know that that isn't the case in reality, but the equations work just fine with that assumption.

[Rojo]

I've heard it claimed on several occassions that some of the more bizarre concepts from physics should be treated as 'concepts of methods', rather than as things which actually exist in reality. Examples would include the curvature of space-time, worldlines, and various aspects of the standard model. The same applies to certain mathematical entities (imaginary numbers for example).

Hmm...lot's of confusion here. First, let's start with mathematics. Math is "Concepts of Methods" pure and simple - even integer counting. Nowhere do numbers exist but within the minds of men as concepts even though the integer counting we learned as children seemed positively concrete.

Now, about Physics. Well...maybe not: I'm to tired tonight to write that much. So, as an excercise, I suggest you ask yourself "What is a mathematically-based Physical Model".

Goodnight.

Rojo