The unsupportability of realism about abstract objects

@jeeprs,

jeeprs wrote:

your objection only addresses the symbol, not the measure.

No it doesn't, it addresses the matter of number. One and the same thing can be described such that two aspects have the same numerical measure or can equally be described such that the two aspects have differing numerical measure. If numbers exist, then I assume they aren't self contradictory, in which case only one of the ways of assigning units of measurement can be correct. How can anyone know which one is correct?

1 Reply

@ughaibu,

ughaibu wrote:

jeeprs wrote:
your objection only addresses the symbol, not the measure.
No it doesn't, it addresses the matter of number. One and the same thing can be described such that two aspects have the same numerical measure or can equally be described such that the two aspects have differing numerical measure.

So, a question then. Take for example Pi. Are you saying we might have completely different number schemes which notate this value in two completely different ways? Or are you saying that the value Pi does not exist apart from the way that it is notated?

1 Reply

@jeeprs,

jeeprs wrote:

Take for example Pi.

Pi isn't a measure, it's a relationship, it has no bearing on my example.

1 Reply

@ughaibu,

Quote:

There is nothing here that supports realism, any more than the fact that I can look at a map and make a prediction about how long it will take me to walk somewhere.

Except for in the case of mathematical physics, the map shows places where nobody has ever been. To press the analogy further, an equation has generated a map of some place where nobody has ever set foot. On this map, there is an X, which says, 'look here for a Y'. You go to this place, and sure enough, in the spot marked X, there is indeed a Y.

So - who drew the map?

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@ughaibu,

Quote:

Pi isn't a measure, it's a relationship, it has no bearing on my example.

But it is represented by a number.

1 Reply

@jeeprs,

jeeprs wrote:

So - who drew the map?

Petrochemists draw such maps.

1 Reply

@jeeprs,

jeeprs wrote:

Quote:
Pi isn't a measure, it's a relationship, it has no bearing on my example.
But it is represented by a number.

So what?

0 Replies

@ughaibu,

ughaibu wrote:

TuringEquivalent wrote:
Any physical model in physics are mathematical in nature. It describes an abstract object.
Only if abstract objects exist, which is what you still haven't given any argument for.
TuringEquivalent wrote:
When the physical theory is good, the abstract object in question is a good model for the real world.
If abstract objects can be false of the actual world, how can they be essential for physics? How can they be true of the phenomenal world other than by coincidence? And, again, how do they make statements true?

You are confused..

Any physical theory postulate the existence of a abstract object that is a 'model' of the real world. Obvious, it is not easy to figure out which model in the "right" model. We started from Newtonian mechanics to General relativity, because the abstract object postulate by GR is a better model of the real world then the AO postulate by Newtonain mechanics.

I did give you an argument. Perhaps, it is better to:

1. I show that abstract objects are presupposed in physical theories.
2. If we good justification for believe in our physical theories.
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3. We ought to commit to the presupposition of our theories, abstract objects.

1 is what i show.
2 is obviously right.

1 Reply

@TuringEquivalent,

TuringEquivalent wrote:

1. I show that abstract objects are presupposed in physical theories.
2. If we good justification for believe in our physical theories.
-------------------------------------------------------------------------------
3. We ought to commit to the presupposition of our theories, abstract objects.

I dont think you've shown this at all, you've assumed it. But in any case, this would only put you at the beginning of the thread, because this is a standard argument addressed in the opening post.

1 Reply

@ughaibu,

ughaibu wrote:

jeeprs wrote:
So - who drew the map?
Petrochemists draw such maps.

Indeed they do, and if weren't for the effectiveness of applied mathematics in these cases, I'm sure we'd all be freezing in the dark.

I think we have discussed Eugene Wigner before. One of the examples he gives of the unreasonable effectiveness of mathematics, in his famous essay of that name,

Quote:

is that of ordinary, elementary quantum mechanics. This originated when Max Born noticed that some rules of computation, given by Heisenberg, were formally identical with the rules of computation with matrices, established a long time before by mathematicians. Born, Jordan, and Heisenberg then proposed to replace by matrices the position and momentum variables of the equations of classical mechanics. They applied the rules of matrix mechanics to a few highly idealized problems and the results were quite satisfactory. However, there was, at that time, no rational evidence that their matrix mechanics would prove correct under more realistic conditions. Indeed, they say "if the mechanics as here proposed should already be correct in its essential traits." As a matter of fact, the first application of their mechanics to a realistic problem, that of the hydrogen atom, was given several months later, by Pauli. This application gave results in agreement with experience. This was satisfactory but still understandable because Heisenberg's rules of calculation were abstracted from problems which included the old theory of the hydrogen atom. The miracle occurred only when matrix mechanics, or a mathematically equivalent theory, was applied to problems for which Heisenberg's calculating rules were meaningless. Heisenberg's rules presupposed that the classical equations of motion had solutions with certain periodicity properties; and the equations of motion of the two electrons of the helium atom, or of the even greater number of electrons of heavier atoms, simply do not have these properties, so that Heisenberg's rules cannot be applied to these cases. Nevertheless, the calculation of the lowest energy level of helium, as carried out a few months ago by Kinoshita at Cornell and by Bazley at the Bureau of Standards, agrees with the experimental data within the accuracy of the observations, which is one part in ten million. Surely in this case we "got something out" of the equations that we did not put in.

2 Replies

@jeeprs,

jeeprs wrote:

I think we have discussed Eugene Wigner before.

And your argument for realism is what? How does the fact that we can use mathematics, sometimes described as the science of measurement, to measure physical things, suggest the reality of neither physical nor mental things?

1 Reply

@ughaibu,

In the example I provided, Eugene Wigner, who won the Physics Nobel not long after this essay was published, said 'we get out of the equations more than what we put in'. So are you saying 'no, we don't'? Why would he say that, and you deny it? Do you know something about it that he doesn't?

1 Reply

@jeeprs,

jeeprs wrote:

'we get out of the equations more than what we put in'. So are you saying 'no, we don't'? Why would he say that, and you deny it? Do you know something about it that he doesn't?

Provide a link that explains non-tautological mathematics.

1 Reply

@jeeprs,

I'm just re-iterating a point I made earlier as a possible solution to the term "realism". A concept is/remains "real" if by consensus it affects the course of subsequent action. Such "action" can be intellectual or otherwise. I avoid the word "object" because that by definition already implies a different view of "reality".

1 Reply

@ughaibu,

you deflect many questions.

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@fresco,

I think that is a pragmatist approach, is it not?

1 Reply

@jeeprs,

Pragmatist and non-dualist.

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@jeeprs,

jeeprs wrote:

you deflect many questions.

As far as I can tell, on this thread so far, nobody has attempted to deal with the arguments presented in the opening post. Instead, I've been faced with a string of questions of doubtful relevance. It is a matter of mathematical proof, that the world can not be exactly modeled mathematically, it's a matter of proof that given any finite data string, no exact prediction is possible. In any case, even if the world were exactly mathematically modelable, you would still need an argument to get from the modelability of the physical world to the suggestion of an abstract realm. On top of which, you would need to meet all the objections. Do you have an argument?

1 Reply

@ughaibu,

ughaibu wrote:

TuringEquivalent wrote:
1. I show that abstract objects are presupposed in physical theories.
2. If we good justification for believe in our physical theories.
-------------------------------------------------------------------------------
3. We ought to commit to the presupposition of our theories, abstract objects.
I dont think you've shown this at all, you've assumed it. But in any case, this would only put you at the beginning of the thread, because this is a standard argument addressed in the opening post.

Do you mean i assume "physical theories are abstract objects"?

1 Reply

@ughaibu,

I don't think we understand each other. I feel that I have raised some objections to your OP, which you haven't understood, and I don't understand many of the things you say, either. But let's keep trying. It is actually a pretty difficult area of philosophy.

I would be interested in a direct response to the example I provided by Wigner. I thought it challenged your position pretty effectively, really. I also fail to see why all the arguments that are put forward, showing that mathematical reasoning has consequences in reality which could not have been discovered by other means, are ignored or downplayed by you. The 'map' analogy you gave does not amount to a rebuttal, in my view.

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The unsupportability of realism about abstract objects

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