Thanks. Can you describe a bit more about #2 “Abstract objects are real”? I don’t see how this could be believed. There are elements of reality that correspond pretty well to abstract objects, but never (AFAIK) precisely—there are always variants or finer-grained measurements that don’t match the abstraction.
”All models are wrong, some models are useful” seems so completely valid for every abstraction I can think of that I really think I’m missing something basic that someone could claim otherwise.
The concepts of mathematics exist of themselves, independent of the relationships that some of them have to physical reality. They are not anywhere to be found in space-time. They exist separately from that, and are discoverable by reason.
Given these two separate realms of real things, the physical and the mathematical, we may wonder (inspired by the 0-1-infinity rule) whether there are others, and how many. Three candidates are consciousness, morality, and aesthetics. I do not believe that anyone has given a satisfactory account of the existence of subjective experience, the subjective existence of oughtness, or the subjective existence of beauty.
That makes five, which is an even more arbitrary-sounding number than two. How many more are there?
That’s interesting. I’d argue that the concept of “realm” is itself a modeling choice, and non-real, but let’s leave that aside.
So, do those who claim that morals are a “real” thing, similar to mathematics, ALSO claim that esthetics and the others are just as real? And for those other domains, including morality, what are the equivalent fundamental assumptions (like the various definitions of equality to choose from in math)?
Feels weird to me to include this on the list as an additional candidate beyond consciousness. If/when subjective consciousness is “solved”/mechanistically understood, it would also be clear what it means to feel like something is beautiful.
And the reason why things are seen as beautiful in the modern world is because our evolutionarily-trained algorithms (“designed”[1] to make us seek out potentially healthy mates, to explore potentially resource-filled areas, to appreciate cleanliness and the sun, etc) are misfiring in our modern environments that differ so strongly from the EEA.
If/when subjective consciousness is “solved”/mechanistically understood, it would also be clear what it means to feel like something is beautiful.
Not necessarily. Even if the Standard Model is the true theory of physics, there are plenty of physical phenomena that we do not know how to calculate from it. There are still things to discover. Even in mathematics, where, for example, the group axioms in principle settle every question about groups that can be settled, answering such questions can be arbitrarily difficult.
And the reason why things are seen as beautiful in the modern world is because our evolutionarily-trained algorithms (“designed”[1] to make us seek out potentially healthy mates, to explore potentially resource-filled areas, to appreciate cleanliness and the sun, etc) are misfiring in our modern environments that differ so strongly from the EEA.
That could be so, but it is a speculation, and it would be circular reasoning to take the speculation for its own proof. Could the perception of beauty have been predicted from evolutionary theory without knowing there was such a thing? Observing it, does your explanation constrain subsequent possible observations?
Here is my speculation about a long-standing question about music: music produces a subjective sensation of meaning, yet none can say what it means — why? Perhaps, I speculate, it is an accident of our development of language, that uses vocal sounds to communicate meanings, which spills over to other sounds. Perhaps indeed, but I do not know.
I think for many philosophers, the claim “abstract objects are real” doesn’t depend on the use of mathematics to model physical reality. I think considering pure math is more illustrative of this point of view.
Andrew Wiles once described the experience of doing math research as:
“Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it’s dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it’s all illuminated and you can see exactly where you were. Then you enter the next dark room...”
Since this is also what it feels like to study an unfamiliar part of physical reality, it’s intuitive to think that the mathematics you’re studying constitutes some reality that exists independently of human minds. Whether this intuition is actually correct is a rather different question…
Thanks. Can you describe a bit more about #2 “Abstract objects are real”? I don’t see how this could be believed. There are elements of reality that correspond pretty well to abstract objects, but never (AFAIK) precisely—there are always variants or finer-grained measurements that don’t match the abstraction.
”All models are wrong, some models are useful” seems so completely valid for every abstraction I can think of that I really think I’m missing something basic that someone could claim otherwise.
The concepts of mathematics exist of themselves, independent of the relationships that some of them have to physical reality. They are not anywhere to be found in space-time. They exist separately from that, and are discoverable by reason.
Given these two separate realms of real things, the physical and the mathematical, we may wonder (inspired by the 0-1-infinity rule) whether there are others, and how many. Three candidates are consciousness, morality, and aesthetics. I do not believe that anyone has given a satisfactory account of the existence of subjective experience, the subjective existence of oughtness, or the subjective existence of beauty.
That makes five, which is an even more arbitrary-sounding number than two. How many more are there?
That’s interesting. I’d argue that the concept of “realm” is itself a modeling choice, and non-real, but let’s leave that aside.
So, do those who claim that morals are a “real” thing, similar to mathematics, ALSO claim that esthetics and the others are just as real? And for those other domains, including morality, what are the equivalent fundamental assumptions (like the various definitions of equality to choose from in math)?
Feels weird to me to include this on the list as an additional candidate beyond consciousness. If/when subjective consciousness is “solved”/mechanistically understood, it would also be clear what it means to feel like something is beautiful.
And the reason why things are seen as beautiful in the modern world is because our evolutionarily-trained algorithms (“designed”[1] to make us seek out potentially healthy mates, to explore potentially resource-filled areas, to appreciate cleanliness and the sun, etc) are misfiring in our modern environments that differ so strongly from the EEA.
By natural selection
Not necessarily. Even if the Standard Model is the true theory of physics, there are plenty of physical phenomena that we do not know how to calculate from it. There are still things to discover. Even in mathematics, where, for example, the group axioms in principle settle every question about groups that can be settled, answering such questions can be arbitrarily difficult.
That could be so, but it is a speculation, and it would be circular reasoning to take the speculation for its own proof. Could the perception of beauty have been predicted from evolutionary theory without knowing there was such a thing? Observing it, does your explanation constrain subsequent possible observations?
Here is my speculation about a long-standing question about music: music produces a subjective sensation of meaning, yet none can say what it means — why? Perhaps, I speculate, it is an accident of our development of language, that uses vocal sounds to communicate meanings, which spills over to other sounds. Perhaps indeed, but I do not know.
I think for many philosophers, the claim “abstract objects are real” doesn’t depend on the use of mathematics to model physical reality. I think considering pure math is more illustrative of this point of view.
Andrew Wiles once described the experience of doing math research as:
“Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it’s dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it’s all illuminated and you can see exactly where you were. Then you enter the next dark room...”
Since this is also what it feels like to study an unfamiliar part of physical reality, it’s intuitive to think that the mathematics you’re studying constitutes some reality that exists independently of human minds. Whether this intuition is actually correct is a rather different question…