I think that representation is best explained as both correspondence and the outcome of optimization—specifically, representation is some sort of correspondence (which can be loose) that is caused by some sort of optimization process.
I’ll speak primarily in defense of correspondence since I think that is where we disagree.
“All models are wrong, but some are useful” is a common aphorism in statistics, and I think it is helpful here too. You seem to treat mistaken representations as a separate sort of representation. However, even an ordinarily correct representation can contain some mistaken elements. For example:
A child might correctly identify a horse, but not know that horses are made out of atoms.
A man in 1970 might correctly identify a campfire, but mistakenly believe that the fire is a release of phlogiston.
Likewise ordinarily mistaken representations can contain correct elements:
If I think I’ve seen a horse when I’ve actually seen a cow at night, I’ve still correctly identified a thing-which-looks-like-a-horse. I may still correctly predict that others will see it as a horse too.
A child who believes in Santa Claus will be likely to correctly predict the behavior of a “mall Santa” i.e. an actor pretending to be Santa in a public place.
There are also edge cases where a representation mixes correct and incorrect elements, such that it isn’t clear whether we should call it a mistaken representation or not:
Methyl methacrylate adhesive is often sold under the name “plastic epoxy.” Chemically speaking, it’s not an epoxy at all—but practically speaking it is a binary adhesive that is used just like an epoxy. If you think that it is epoxy, you will only be wrong in ways that (almost) never matter.
If you think that a tomato is a vegetable, then you are conventionally considered correct in a culinary context. However, by the botanical definition, a tomato is actually a fruit.
This suggests that it is useful to stop thinking about mistaken and correct representations as separate types, but rather to think about representations having mistaken and correct elements.
Having made this shift, I think that the correspondence theory of representation becomes viable again. Even a representation that is conventionally classified as mistaken may contain many correct elements—enough correct elements to make it about whatever it is about. A child’s representation of Santa Claus contains many correct elements (often wears red, jolly, brings presents) and one very prominent incorrect element (the child thinks that Santa physically exists rather than being a well-known fiction). It may very well be the case that most of the bits in the child’s representation are correct; we just pay more attention to the few that are wrong. For another example: if I think that I see a horse, but I actually see a cow at night, the correct elements include “it looks like a horse to me,” and “it’s that thing over there that I’m looking at right now.” There’s a lot of specificity in that last correct element! I think that’s enough to make my representation be about the cow.
On the other hand, we can consider examples where an optimization process exists but where it fails to create correspondence:
A child tells you that Santa lives in deserts, has a venomous stinger, and is a close relative of spiders. You’d probably say that they aren’t actually talking about Santa at all. They’re describing a scorpion and getting the name wrong.
Once in high school, when assigned to write an essay about a historical figure, I accidentally wrote my first draft about a different figure with the same name. If my teacher was mean, they could have interpreted this first draft as being about the first figure and docked me many points becasue I had nearly every fact about them wrong. Instead, they noticed the real mistake (which was in a sense their mistake; the assignment was ambiguous) and marked accordingly.
With that being said, I do agree with you that optimization is an important piece of the puzzle—but not becasue it can explain how something can be about something else even if it is mistaken. Rather, I think that optimization is the answer to the problem of coincidences. For example:
A novelist writes a murder-mystery which, by coincidence, is a correct description of a real murder. The naive correspondence theory of representation says that the novel is about the real murder; common sense says that it is not.
Adding the second criteria—that the correspondence must be caused by an optimization process—prevents a definition of representation from identifying coincidences as representations.
I think that representation is best explained as both correspondence and the outcome of optimization—specifically, representation is some sort of correspondence (which can be loose) that is caused by some sort of optimization process.
I’ll speak primarily in defense of correspondence since I think that is where we disagree.
“All models are wrong, but some are useful” is a common aphorism in statistics, and I think it is helpful here too. You seem to treat mistaken representations as a separate sort of representation. However, even an ordinarily correct representation can contain some mistaken elements. For example:
A child might correctly identify a horse, but not know that horses are made out of atoms.
A man in 1970 might correctly identify a campfire, but mistakenly believe that the fire is a release of phlogiston.
Likewise ordinarily mistaken representations can contain correct elements:
If I think I’ve seen a horse when I’ve actually seen a cow at night, I’ve still correctly identified a thing-which-looks-like-a-horse. I may still correctly predict that others will see it as a horse too.
A child who believes in Santa Claus will be likely to correctly predict the behavior of a “mall Santa” i.e. an actor pretending to be Santa in a public place.
There are also edge cases where a representation mixes correct and incorrect elements, such that it isn’t clear whether we should call it a mistaken representation or not:
Methyl methacrylate adhesive is often sold under the name “plastic epoxy.” Chemically speaking, it’s not an epoxy at all—but practically speaking it is a binary adhesive that is used just like an epoxy. If you think that it is epoxy, you will only be wrong in ways that (almost) never matter.
If you think that a tomato is a vegetable, then you are conventionally considered correct in a culinary context. However, by the botanical definition, a tomato is actually a fruit.
This suggests that it is useful to stop thinking about mistaken and correct representations as separate types, but rather to think about representations having mistaken and correct elements.
Having made this shift, I think that the correspondence theory of representation becomes viable again. Even a representation that is conventionally classified as mistaken may contain many correct elements—enough correct elements to make it about whatever it is about. A child’s representation of Santa Claus contains many correct elements (often wears red, jolly, brings presents) and one very prominent incorrect element (the child thinks that Santa physically exists rather than being a well-known fiction). It may very well be the case that most of the bits in the child’s representation are correct; we just pay more attention to the few that are wrong. For another example: if I think that I see a horse, but I actually see a cow at night, the correct elements include “it looks like a horse to me,” and “it’s that thing over there that I’m looking at right now.” There’s a lot of specificity in that last correct element! I think that’s enough to make my representation be about the cow.
On the other hand, we can consider examples where an optimization process exists but where it fails to create correspondence:
A child tells you that Santa lives in deserts, has a venomous stinger, and is a close relative of spiders. You’d probably say that they aren’t actually talking about Santa at all. They’re describing a scorpion and getting the name wrong.
Once in high school, when assigned to write an essay about a historical figure, I accidentally wrote my first draft about a different figure with the same name. If my teacher was mean, they could have interpreted this first draft as being about the first figure and docked me many points becasue I had nearly every fact about them wrong. Instead, they noticed the real mistake (which was in a sense their mistake; the assignment was ambiguous) and marked accordingly.
With that being said, I do agree with you that optimization is an important piece of the puzzle—but not becasue it can explain how something can be about something else even if it is mistaken. Rather, I think that optimization is the answer to the problem of coincidences. For example:
A novelist writes a murder-mystery which, by coincidence, is a correct description of a real murder. The naive correspondence theory of representation says that the novel is about the real murder; common sense says that it is not.
Adding the second criteria—that the correspondence must be caused by an optimization process—prevents a definition of representation from identifying coincidences as representations.