But why do some of these stories give correct predictions and others don't? — litewave

But they don't!

They give approximately correct predictions, to the limits of our experimental apparatus.

Newton wasn't correct, nor is Einstein. They get closer and closer to something that may or may not be there.

Back in the day we looked up at the stars and said, "Oh, there's Orion the hunter with his mighty bow." And they took those stories every bit as seriously as we do our stories.

There is no question that science and rational inquiry have been very handy, creating bridges and cellphones and all this wonderful stuff we have around us. The question of why science is so useful is the proper inquiry of the philosophy of science. That's a good question, to which nobody has a conclusive answer.

Another point is that the laws of physics that we've been able to come up with so far are due to the very limited perspective of where we are in time and space. If we lived a long time ago. or farther out in the universe we might find new laws. The uniformity of physical law throughout the universe is an assumption, not a proven fact.

In other words, contradiction is not something that could even in principle apply - or not - to things in the world; you 'can't imagine that reality would be absurd' because absurdity is a function of thought, not being. To say that reality can or can't be 'contradictory' is to project onto the world a category that applies only to our thinking about the world. — StreetlightX

If you think there may be balls that are not balls, fine. I will stick with thinking that there are only balls that are balls; for some reason it seems to be a much better strategy in life too.

They give approximately correct predictions, to the limits of our experimental apparatus. — fishfry

And why do some stories give more correct predictions than others?

Newton wasn't correct, nor is Einstein. They get closer and closer to something that may or may not be there. — fishfry

Well, it better be there. Not sure how they could get closer and closer to something that is not there.

You misunderstand. I do not think that there may be balls that are not balls. I think that this is a non-issue. To say that contradictions do not apply to reality is not to say that there are contradictions in reality. It is to say that there neither are nor are not contradictions in reality. This is what non-application means. It's like asking how much an idea weighs: it neither weighs nor does not weigh anything - the very notion is a category mistake, an error of grammar.

I think non-contradiction applies to reality very well because only non-contradictory statements can correspond to reality. In this sense, reality is non-contradictory too.

I think non-contradiction applies to reality very well because only non-contradictory statements can correspond to reality — litewave

Granting that one can make any sense of the murky and loaded idea of 'correspondence', you've just made a claim about 'statements' - about what we can say of the world. And this is just where contradiction is applicable. And your 'because' does not have a minor premise attached to it: it is an incomplete chain of reasoning. As it stands, it does not qualify as a coherent argument at the level of sheer form, let alone content.

Granting that one can make any sense of the murky and loaded idea of 'correspondence' — StreetlightX

Correspondence means that if we agree to call some kind of object a square then we will call it a square and not a circle. It is also known as correct naming and correct description.

you've just made a claim about 'statements' - about what we can say of the world. And this is just where contradiction is applicable. — StreetlightX

If you agree that only non-contradictory statements correspond to reality then that's all that matters. But among such correct statements is that every thing is what it is and is not what it is not, and so the thing does not contradict itself or any other thing. In other words, every thing - and therefore reality - is non-contradictory.

But among such correct statements is that every thing is what it is and is not what it is not, and so the thing does not contradict itself or any other thing. In other words, every thing - and therefore reality - is non-contradictory. — litewave

Your 'in other words' does not follow. Again, a lack of argument, and a missing minor premise.

One thing to note here is that contradiction is not inconsistency. Or, as a matter of terminological precision: inconsistency is a function of contradiction within a formal system: a system is said to be inconsistent if it contains contradictions. The claimed inconsistencies between relativity and QM are not of this kind: the entire point is that there are inconsistencies between two systems.

Note also just how strict the criteria are to meet the standard of contradiction: X and its opposite must be 'true' in order for contradiction to hold: a proposition must say that X AND ¬X is true. But of course there is no theory that claims any such thing. As it stands, the operator between the apparently 'contradictory' statements between QM and relativity is - I think assumed to be - a XOR operator (exclusive or): X ⊻ ¬X , not X ∧ ¬X. There is no 'contradiction' here, in the logical, intra-systemic sense. Things might be confusing because science writers are not logicians, and they are apt to use terms in ways that are not the technical terms of logic. This is to be expected, but it is also to be watched out for when trying to draw conclusions.

Your 'in other words' does not follow. Again, a lack of argument, and a missing minor premise. — StreetlightX

Actually, it was a simple equivalence. "Thing does not contradict itself or any other thing" = "thing is non-contradictory".

You are still sticking to a formalistic approach which, while, again formally, correct, is rather sterile.
@litewave has a more concrete approach in mind, and your discussion will I am afraid go nowhere.

And why do some stories give more correct predictions than others? — litewave

It would be a mistake to distinguish between "true" and "untrue" or "false" theories. Theories that permit correct predictions are not necessarily true. They can be said to be consistent with reality, but that is really all we can say about them, however long they remain the sole alternative.

In the time of the Ancient Greeks, angels were thought to push the planets around, and Ptolemy had no trouble incorporating this belief in his theory... which by the way allowed astronomers to make many correct predictions.

In the time of the Ancient Greeks, angels were thought to push the planets around, and Ptolemy had no trouble incorporating this belief in his theory... which by the way allowed astronomers to make many correct predictions. — Hachem

The correctness of the predictions of the Ptolemaic geocentric theory followed from the correspondence between the mathematical properties of the theory and the mathematical structure of the universe, not from the assumption of angels. The assumption of angels was not necessary. The correctness of the predictions of Kepler's heliocentric theory, too, followed from the correspondence between the mathematical properties of the theory and the mathematical structure of the universe, but its virtue was that it was much more parsimonious than the geocentric theory - it identified larger regularities in the motion of planets and thus simplified the description.

So two different theories can be correct, within certain limits, but one can be simpler than the other. And then there are theories that are not correct even within those limits.

The correctness of the predictions of the Ptolemaic geocentric theory followed from the correspondence between the mathematical properties of the theory and the mathematical structure of the universe, not from the assumption of angels. — litewave

This is a very modern reading of Ptolemy that does not do justice to the (metaphysical) beliefs that held all theories together. Correct calculations were of course a prerequisite for any astronomical theory. But these calculations had to be embedded in a view of the universe that cost Giordano Bruno his life at the staple, and compelled Galileo to recant.

Nowadays Physics is still embedded in a view of the universe, and we are still trying to figure out the correct view. There are still people who think that God does not play dice, while others vote for a more probabilistic/random approach.

It would be therefore a mistake to approach Physics as a clinical endeavor whose propositions are only dictated by logic and observable facts.

In fact, at a certain level, "facts" are almost entirely theoretical constructs.

Nowadays Physics is still embedded in a view of the universe, and we are still trying to figure out the correct view. There are still people who think that God does not play dice, while others vote for a more probabilistic/random approach. — Hachem

Still, contemporary theories are much more parsimonious than Ptolemy's and they can predict much more than Ptolemy could even imagine. They correctly describe a much larger portion of reality than Ptolemy's theory did.

Still, contemporary theories are much more parsimonious than Ptolemy's and they can predict much more than Ptolemy could even imagine.
. — litewave

I have no problem with that. Except that you should be careful about the second part.

They correctly describe a much larger portion of reality than Ptolemy's theory did. — litewave

Correct is always a judgment carried by a scientific community at a certain period. We have no idea what the science community will say over 1000 years or more.

or less.

Correct is always a judgment carried by a scientific community at a certain period. We have no idea what the science community will say over 1000 years or more. — Hachem

By correct I mean that the theory fits with observation.

I agree

There is an implicit caveat. Observations are theory guided for a large part. And that is in fact one of the reasons why scientific ideas and convictions change with time. A theory can therefore never be said to be absolutely correct on the basis of observations. It does mean that it should be considered superior to theories which have no apparent empirical basis.

I would like to go a step further and consider theories that not only predict correct observations but also allow practical implementation.

The temptation is great in thinking that these kind of theories somehow should be considered as "true".

I would like to point out that the difference between theories which can be put in practice and those that allow passive observations and predictions only is more a difference of level than nature.

It might be hard to see, but practical implementations are no more a proof of "truth" than mere observations. They are certainly a very serious indication of the usefulness of the theory.

Suppose that for Angie, events A and B occur at the same time; But for Beth, A occurs before B. The transformation formulas in special relativity allow both Angie and Beth to agree with these two statements:

From Angie's frame of reference, events A and B occur at the same time.
From Beth's frame of reference, A occurs before B.

That is, both Angie and Beth, and anyone else that cares to do the calculations, will agree that for Angie, events A and B are simultaneous. — Banno

So Angie believes that A and B are simultaneous. Beth believes that A and B are not simultaneous. The transformation formulas allow that what Angie believes is true, and what Beth believes is true. How is this not a violation of the law of non-contradiction, when what Beth believes is clearly contradictory to what Angie believes?

How is this not a violation of the law of non-contradiction, when what Beth believes is clearly contradictory to what Angie believes? — Metaphysician Undercover

Wait, that's not right. X believes P, and Y believes not-P. That's not a contradiction.

A contradiction would be, X believes P and X believes not-P. Actually I'm not sure that's a contradiction. A contradiction would be, X believes P and X does NOT believe P. It's possible that X may have no beliefs about P at all one way or the other.

The issue is not one of contradiction since, indeed, two different persons from two different frames of reference have two different beliefs.

As I see it the issue is: how come we know that? Where is the knowing subject standing? What is his own frame of reference?

It looks very much like a god-like perspective to me.

One thing to note here is that contradiction is not inconsistency. Or, as a matter of terminological precision: inconsistency is a function of contradiction within a formal system: a system is said to be inconsistent if it contains contradictions. The claimed inconsistencies between relativity and QM are not of this kind: the entire point is that there are inconsistencies between two systems. — StreetlightX

Point well taken. I'm aware of what inconsistency means in the context of the study of formal systems, ie axiomatics. Of course you and @Banno are correct that I'm using the word inconsistency when I should be saying incompatibility.

There's no axiomatic basis for physics in the first place, so we can't be meaning inconsistency in the technical sense. But I can see that I've been confused myself on this point. The right word is incompatibility.

The nature of the incompatibility between QM and Relativity is in their predictions. There are situations where in a given situation, they predict different outcomes. If we wanted to express this formally it would be "Theory X predicts P and theory Y predicts not-P". Does this relate to modal logic?

Note also just how strict the criteria are to meet the standard of contradiction: X and its opposite must be 'true' in order for contradiction to hold: a proposition must say that X AND ¬X is true. — StreetlightX

Picky picky, you mean provable, not true. An axiomatic system is inconsistent if it allows a formal proof of both X and ¬X for some proposition X. It's purely syntactic. The idea of truth belongs to semantics, where we put an interpretation on the symbols.

But of course there is no theory that claims any such thing. As it stands, the operator between the apparently 'contradictory' statements between QM and relativity is - I think assumed to be - a XOR operator (exclusive or): X ⊻ ¬X , not X ∧ ¬X. — StreetlightX

I'm trying to understand this. In the first place, neither QM nor R are axiomatic theories. They're not formal systems at all. They're a collection of heuristics and differential equations. In other words when a QM or R theorist wants to calculate the expected output of an experiment, they don't apply axioms or theorems. Rather, they plug their numbers into models, which are essentially differential equations [I'm way over my depth here physics-wise]. In other words there are no "propositions" in the sense of logic.

That's my understanding, anyway. That the conclusions of both QM and R are not deductions, they're approximations to some theory that's not axiomatized. So the entire field of logic doesn't really apply the way we're trying to apply it.

Ok now I see your point. There's some experiment for which QM and R predict different results. So it's an XOR. Yes I see that!! Ok got it. Yes, good point.

There is no 'contradiction' here, in the logical, intra-systemic sense. Things might be confusing because science writers are not logicians, and they are apt to use terms in ways that are not the technical terms of logic. This is to be expected, but it is also to be watched out for when trying to draw conclusions. — StreetlightX

Yes I think you're right.

Wait, that's not right. X believes P, and Y believes not-P. That's not a contradiction. — fishfry

Yes, that itself is not a contradiction. But as Banno stated, the transformation equations make what X believes, and what Y believes both true, so that's where the contradiction enters, in saying that these, P and not-P, are both true. That is, unless you allow that we can say P is true, and not-P is true, without contradiction. You can do this by contriving your definition of "true", such that truth is relative to the observer, or in the case of SR, relative to the frame of reference.

You can do this by contriving your definition of "true", such that truth is relative to the observer, — Metaphysician Undercover

That's not how sentential logic works. A proposition P is true or false. There are no observers.

I am not aware of any effort within physics to rewrite the rules of logic to account for this.

For this reason I don't quite understand what you're saying here.

Thank you, @fishfry. It is apparent I had misunderstood you. My apologies.

One is a principle of classical logic; and the other is a principle of modern physics. — fishfry

Going back to the start, I had taken this to be along the lines of Gould's non-overlapping magisteria. I see now that your view is more nuanced than that.

I'm pretty sure we have hd this discussion before.

@Fishfry is right in that your introduction of belief radically changes the argument. It's what it true that counts.

Contemplate this:
From Angie's frame of reference, events A and B occur at the same time.
From Beth's frame of reference, A occurs before B.

These two statements are both true for both Angie and Beth.

There is no contradiction.