This is only correct if we presuppose that the concept of mathematically true is a meaningful thing separate from physics.
That’s not an extraordinary claim: Mathematics uses a different notion of proof to physics, so at the very least it has a different set of truths, and quite possibly a different concept of proof. I would say that the reverse claim is extraordinary, since it means that physicists are wasting huge sums on particle accelerators, when they only need pencil and paper.
Since not presupposing this is strictly simpler,
A theory needs to be as simple as possible, under the constraint that it still explains the facts. The facts are that physics is empirical, maths is apriori, and most mathematical truth isn’t physical truth.
If we take as assumption that everything humans have observed has been made up of smaller physical parts (except possibly for the current elementary particles du jour, but that doesn’t matter for the sake of this argument) and that the macro state is entirely determined by the micro state (regardless of if it’s easy to compute for humans), there is a simple conclusion that follows logically from that.
This conclusion is that nothing extraphysical can have any predictive power above what we can predict from knowledge about physics. This follows because for something to have predictive power, it needs to have some influence on what happens. If it doesn’t have any influence on what happens, its existence and non-existence cannot allow us to make any conclusions about the world.
This argument applies to mathematics: if the existence of mathematics separately from physics allowed us to make any conclusions about the world, it would have to have a causal effect on what happens, which would contradict the fact that all macro state we’ve ever observed has been determined by just the micro state.
Since the original assumption is one with very strong evidence backing it, it’s safe to conclude that, in general, whenever we think something extraphysical is required to explain the known facts, we have to be making a mistake somewhere.
In the specific instance of your comment, I think the mistake is that the difference between “a priori” truths and other truths is artificial. When you’re doing math you have be doing work inside your brain and getting information from that. This is not fundamentally different from observing particle accelerators and getting information from them.
Thats just a long winded way of saying that the subset of mathematical truth which does the same job as physics—predicting things about the world—is the same as physical truth. Which is a tautology.
The problem is that mathematical truth is larger than the set of physical truths and a lot of it is physically useless.… and the set of mathematical truths is larger than the set of physical truths because a lot of it is physically useless.
If you accept that the existence of mathematical truths beyond physical truths cannot have any predictive power, then how do you reconcile that with this previous statement of yours:
Presupposing things without evidence
As you can see, I am not doing that.
I will say again that I don’t reject any mathematics. Even ‘useless’ mathematics is encoded inside physical human brains.
If you accept that the existence of mathematical truths beyond physical truths cannot have any predictive power,
If they did have predictive power, they would be physical truths.
I will say again that I don’t reject any mathematics. Even ‘useless’ mathematics is encoded inside physical human brains.
And wrong mathematics, and stuff that isn’t mathematics at all. The observation you keep making doesn’t explain anything … it doesn’t tell you what maths is, and it doesn’t telly you what makes true maths true … so it’s not an explanatory reduction … so it’s not a reduction at all, as most people use the term.
That’s not an extraordinary claim: Mathematics uses a different notion of proof to physics, so at the very least it has a different set of truths, and quite possibly a different concept of proof. I would say that the reverse claim is extraordinary, since it means that physicists are wasting huge sums on particle accelerators, when they only need pencil and paper.
A theory needs to be as simple as possible, under the constraint that it still explains the facts. The facts are that physics is empirical, maths is apriori, and most mathematical truth isn’t physical truth.
As you can see, I am not doing that.
If we take as assumption that everything humans have observed has been made up of smaller physical parts (except possibly for the current elementary particles du jour, but that doesn’t matter for the sake of this argument) and that the macro state is entirely determined by the micro state (regardless of if it’s easy to compute for humans), there is a simple conclusion that follows logically from that.
This conclusion is that nothing extraphysical can have any predictive power above what we can predict from knowledge about physics. This follows because for something to have predictive power, it needs to have some influence on what happens. If it doesn’t have any influence on what happens, its existence and non-existence cannot allow us to make any conclusions about the world.
This argument applies to mathematics: if the existence of mathematics separately from physics allowed us to make any conclusions about the world, it would have to have a causal effect on what happens, which would contradict the fact that all macro state we’ve ever observed has been determined by just the micro state.
Since the original assumption is one with very strong evidence backing it, it’s safe to conclude that, in general, whenever we think something extraphysical is required to explain the known facts, we have to be making a mistake somewhere.
In the specific instance of your comment, I think the mistake is that the difference between “a priori” truths and other truths is artificial. When you’re doing math you have be doing work inside your brain and getting information from that. This is not fundamentally different from observing particle accelerators and getting information from them.
Thats just a long winded way of saying that the subset of mathematical truth which does the same job as physics—predicting things about the world—is the same as physical truth. Which is a tautology.
The problem is that mathematical truth is larger than the set of physical truths and a lot of it is physically useless.… and the set of mathematical truths is larger than the set of physical truths because a lot of it is physically useless.
If you accept that the existence of mathematical truths beyond physical truths cannot have any predictive power, then how do you reconcile that with this previous statement of yours:
I will say again that I don’t reject any mathematics. Even ‘useless’ mathematics is encoded inside physical human brains.
If they did have predictive power, they would be physical truths.
And wrong mathematics, and stuff that isn’t mathematics at all. The observation you keep making doesn’t explain anything … it doesn’t tell you what maths is, and it doesn’t telly you what makes true maths true … so it’s not an explanatory reduction … so it’s not a reduction at all, as most people use the term.