I think object identification is important if we want to analyze beliefs instead of sentences. For beliefs we can’t take a third person perspective and say “it’s clear from context what is meant”. Only the agent knows what he means when he has a belief (or she). So the agent has to have a subjective ability to identify things. For “I” this is unproblematic, because the agent is presumably internal and accessible to himself and therefore can be subjectively referred to directly. But for “this” (and arguably also for terms like “tomorrow”) the referred object depends partly on facts external to the agent. Those external facts might be different even if the internal state of the agent is the same. For example, “this” might not exist, so it can’t be a primitive term (constant) in standard predicate logic.
I’m not exactly sure what you’re saying here, but in case the following helps:
Indicators like “here”/”tomorrow”/”the object I’m pointing to” don’t get stored directly in beliefs. They are pointers used for efficiently identifying some location/time/object from context, but what get’s saved in the world model is the statement where those pointers were substituted for the referent they were pointing to.
One approach would be to analyze the belief that this apple is green as “There is an x such that x is an apple and x is green and x causes e.” Here “e” is a primitive term (similar to “I” in “I’m hungry”) that refers to the current visual experience of a green apple.
So e is subjective experience and therefore internal to the agent. So it can be directly referred to, while this (the green apple he is seeing) is only indirectly referred to (as explained above), similar to “the biggest tree”, “the prime minister of Japan”, “the contents of this box”.
Note the important role of the term “causes” here. The belief is representing a hypothetical physical object (the green apple) causing an internal object (the experience of a green apple). Though maybe it would be better to use “because” (which relates propositions) instead of “causes”, which relates objects or at least noun phrases. But I’m not sure how this would be formalized.
I think I still don’t understand what you’re trying to say, but some notes:
In my system, experiences aren’t objects, they are facts. E.g. the fact “cubefox sees an apple”.
CAUSES relates facts, not objects.
You can say “{(the fact that) there’s an apple on the table} causes {(the fact that) I see an apple}”
Even though we don’t have an explicit separate name in language for every apple we see, our minds still tracks every apple as a separate object which can be identified.
Btw, it’s very likely not what you’re talking about, but you actually need to be careful sometimes when substituting referent objects from indicators, in particular in cases where you talk about the world model of other people. E.g. if you have the beliefs:
Mia believes Superman can fly.
Superman is Clark Kent.
This doesn’t imply that “Mia believes Clark Kent can fly”, because Mia might not know (2). But essentially you just have a separate world model “Mia’s beliefs” in which Superman and Clark Kent are separate objects, and you just need to be careful to choose the referent of names (or likewise with indicators) relative to who’s belief scope you are in.
What I was saying was that we can, from our subjective perspective, only “point” to or “refer” to objects in a certain way. In terms of predicate logic the two ways of referring are via a) individual constants and b) variable quantification. The first corresponds to direct reference, where the reference always points to exactly one object. Mental objects can presumably be referred to directly. For other objects, like physical ones, quantifiers have to be used. Like “at least one” or “the” (the latter only presupposes there is exactly one object satisfying some predicate). E.g. “the cat in the garden”. Perhaps there is no cat in the garden or there are several. So it (the cat) cannot be logically represented with a constant. “I” can be, but “this” again cannot. Even ordinary proper names of people cannot, because they aren’t guaranteed to refer to exactly one object. Maybe “Superman” is actually two people with the same dress, or he doesn’t exist, being the result of a hallucination. This case can be easily solved by treating those names as predicates. Compare:
The woman believes the superhero can fly.
The superhero is the colleague.
The above only has quantifiers and predicates, no constants. The original can be handled analogously:
(The) Mia believes (the) Superman can fly.
(The) Superman is (the) Clark Kent.
The names are also logical predicates here. In English you wouldn’t pronounce the definitive articles for the proper nouns here, but in other languages you would.
Indicators like “here”/”tomorrow”/”the object I’m pointing to” don’t get stored directly in beliefs. They are pointers used for efficiently identifying some location/time/object from context, but what get’s saved in the world model is the statement where those pointers were substituted for the referent they were pointing to.
As I argued above, “pointing” (referring) is a matter of logic, so I would say assuming the existence of separate “pointers” is mistake.
You can say “{(the fact that) there’s an apple on the table} causes {(the fact that) I see an apple}”
But that’s not primitive in terms of predicate logic, because here “the” in “the table” means “this” which is not a primitive constant. You don’t mean any table in the world, but a specific one, which you can identify in the way I explained in my previous comment. I don’t know how it would work with fact causation rather than objects, though there might be an appropriate logical analysis.
I’m still not quite understanding what you’re thinking though.
For other objects, like physical ones, quantifiers have to be used. Like “at least one” or “the” (the latter only presupposes there is exactly one object satisfying some predicate). E.g. “the cat in the garden”. Perhaps there is no cat in the garden or there are several. So it (the cat) cannot be logically represented with a constant.
“the” supposes there’s exactly one canonical choice for what object in the context is indicated by the predicate. When you say “the cat” there’s basically always a specific cat from context you’re talking about. “The cat is in the garden” is different from “There’s exactly one cat in the garden”.
Maybe “Superman” is actually two people with the same dress, or he doesn’t exist, being the result of a hallucination. This case can be easily solved by treating those names as predicates.
The woman believes the superhero can fly.
The superhero is the colleague.
I mean there has to be some possibility for revising your world model if you notice that there are actually 2 objects for something where you previously thought there’s only one.
I agree that “Superman” and “the superhero” denote the same object(assuming you’re in the right context for “the superhero”).
(And yeah to some extent names also depend a bit on context. E.g. if you have 2 friends with the same name.)
You can say “{(the fact that) there’s an apple on the table} causes {(the fact that) I see an apple}”
But that’s not primitive in terms of predicate logic, because here “the” in “the table” means “this” which is not a primitive constant. You don’t mean any table in the world, but a specific one, which you can identify in the way I explained in my previous comment.
Yeah I didn’t mean this as formal statement. formal would be:
{exists x: apple(x) AND location(x, on=Table342)} CAUSES {exists x: apple(x) AND see(SelfPerson, x)}
“the” supposes there’s exactly one canonical choice for what object in the context is indicated by the predicate. When you say “the cat” there’s basically always a specific cat from context you’re talking about. “The cat is in the garden” is different from “There’s exactly one cat in the garden”.
Yes, we have a presupposition that there is exactly one cat. But that presupposition is the same regardless of the actual number of cats (regardless of the context), because the “context” here is a feature of the external world (“territory”), while the belief is a part of the “map”/world model/mind. So when we want to formalize the meaning of “The cat is in the garden”, that formalization has to be independent of the territory, that is, the same for any possible way the world is. So we can’t use individual constants. Because those can’t be used for cases where there is no cat or more than one. The mental content of a belief (the semantic content of a statement) is internal, so it doesn’t depend on what the external world is like.
I mean there has to be some possibility for revising your world model if you notice that there are actually 2 objects for something where you previously thought there’s only one.
The important part is that your world model doesn’t need to depend on what the world is like. If you believe that the cat is in the garden, that belief is the same independently of whether the presuppositions it makes are true. Therefore we cannot inject parts of the territory into the map. Or rather: there is no such injection, and if our formalization of beliefs (map/world model) assumes otherwise, that formalization is wrong.
Yeah I didn’t mean this as formal statement. formal would be: formal would be:
{exists x: apple(x) AND location(x, on=Table342)} CAUSES {exists x: apple(x) AND see(SelfPerson, x)}
Here you use two individual constants: Table342 and SelfPerson. Individual constants can only be used for direct reference, where unique reference can’t fail. So it can only be used for internal (mental) objects. So “SelfPerson” is okay, because you know a priori that you exist uniquly. If you didn’t have a body, you could still refer to yourself, and it’s not possible that you accidentally refer to more than one person, like a copy of you. You are part of your mind, your internal state. But “Table342″ is an external object. It might not exist, or multiple such tables might exist even though you presupposed it was only one. “Table342” is an individual constant, which are incompatible with presupposition failure. So it can’t be used. That formalization is incompatible with possible worlds where the table doesn’t exist uniquely. But you have the same belief whether or not your presupposition is satisfied. So the formalization is faulty. We have to use one where no constants are used for reference to external things like tables.
I mean I do think it can happen in my system that you allocate an object for something that’s actually 0 or >1 objects, and I don’t have a procedure for resolving such map-territory mismatches yet, though I think it’s imaginable to have a procedure that defines new objects and tries to edit all the beliefs associated with the old object.
I definitely haven’t described how we determine when to create a new object to add to our world model, but one could imagine an algorithm checking when there’s some useful latent for explaining some observations, and then constructing a model for that object, and then creating a new object in the abstract reasoning engine. Yeah there’s still open work to do for how a correspondences between the constant symbol for our object and our (e.g. visual) model of the object can be formalized and used, but I don’t see why it wouldn’t be feasible.
I agree that we end up with a map that doesn’t actually fit the territory, but I think it’s fine if there’s a unresolveable mismatch somewhere. There’s still a useful correspondence in most places. (Sure logic would collapse from a contradiction but actually it’s all probabilistic somehow anyways.) Although of course we don’t have anything to describe that the territory is different from the map in our system yet. This is related to embedded agency, and further work on how to model your map as possibly not fitting the territory and how that can be used is still necessary.
I’m not exactly sure what you’re saying here, but in case the following helps:
Indicators like “here”/”tomorrow”/”the object I’m pointing to” don’t get stored directly in beliefs. They are pointers used for efficiently identifying some location/time/object from context, but what get’s saved in the world model is the statement where those pointers were substituted for the referent they were pointing to.
I think I still don’t understand what you’re trying to say, but some notes:
In my system, experiences aren’t objects, they are facts. E.g. the fact “cubefox sees an apple”.
CAUSES relates facts, not objects.
You can say “{(the fact that) there’s an apple on the table} causes {(the fact that) I see an apple}”
Even though we don’t have an explicit separate name in language for every apple we see, our minds still tracks every apple as a separate object which can be identified.
Btw, it’s very likely not what you’re talking about, but you actually need to be careful sometimes when substituting referent objects from indicators, in particular in cases where you talk about the world model of other people. E.g. if you have the beliefs:
Mia believes Superman can fly.
Superman is Clark Kent.
This doesn’t imply that “Mia believes Clark Kent can fly”, because Mia might not know (2). But essentially you just have a separate world model “Mia’s beliefs” in which Superman and Clark Kent are separate objects, and you just need to be careful to choose the referent of names (or likewise with indicators) relative to who’s belief scope you are in.
What I was saying was that we can, from our subjective perspective, only “point” to or “refer” to objects in a certain way. In terms of predicate logic the two ways of referring are via a) individual constants and b) variable quantification. The first corresponds to direct reference, where the reference always points to exactly one object. Mental objects can presumably be referred to directly. For other objects, like physical ones, quantifiers have to be used. Like “at least one” or “the” (the latter only presupposes there is exactly one object satisfying some predicate). E.g. “the cat in the garden”. Perhaps there is no cat in the garden or there are several. So it (the cat) cannot be logically represented with a constant. “I” can be, but “this” again cannot. Even ordinary proper names of people cannot, because they aren’t guaranteed to refer to exactly one object. Maybe “Superman” is actually two people with the same dress, or he doesn’t exist, being the result of a hallucination. This case can be easily solved by treating those names as predicates. Compare:
The woman believes the superhero can fly.
The superhero is the colleague.
The above only has quantifiers and predicates, no constants. The original can be handled analogously:
(The) Mia believes (the) Superman can fly.
(The) Superman is (the) Clark Kent.
The names are also logical predicates here. In English you wouldn’t pronounce the definitive articles for the proper nouns here, but in other languages you would.
As I argued above, “pointing” (referring) is a matter of logic, so I would say assuming the existence of separate “pointers” is mistake.
But that’s not primitive in terms of predicate logic, because here “the” in “the table” means “this” which is not a primitive constant. You don’t mean any table in the world, but a specific one, which you can identify in the way I explained in my previous comment. I don’t know how it would work with fact causation rather than objects, though there might be an appropriate logical analysis.
Thanks.
I’m still not quite understanding what you’re thinking though.
“the” supposes there’s exactly one canonical choice for what object in the context is indicated by the predicate. When you say “the cat” there’s basically always a specific cat from context you’re talking about. “The cat is in the garden” is different from “There’s exactly one cat in the garden”.
I mean there has to be some possibility for revising your world model if you notice that there are actually 2 objects for something where you previously thought there’s only one.
I agree that “Superman” and “the superhero” denote the same object(assuming you’re in the right context for “the superhero”).
(And yeah to some extent names also depend a bit on context. E.g. if you have 2 friends with the same name.)
Yeah I didn’t mean this as formal statement. formal would be:
{exists x: apple(x) AND location(x, on=Table342)} CAUSES {exists x: apple(x) AND see(SelfPerson, x)}
Yes, we have a presupposition that there is exactly one cat. But that presupposition is the same regardless of the actual number of cats (regardless of the context), because the “context” here is a feature of the external world (“territory”), while the belief is a part of the “map”/world model/mind. So when we want to formalize the meaning of “The cat is in the garden”, that formalization has to be independent of the territory, that is, the same for any possible way the world is. So we can’t use individual constants. Because those can’t be used for cases where there is no cat or more than one. The mental content of a belief (the semantic content of a statement) is internal, so it doesn’t depend on what the external world is like.
The important part is that your world model doesn’t need to depend on what the world is like. If you believe that the cat is in the garden, that belief is the same independently of whether the presuppositions it makes are true. Therefore we cannot inject parts of the territory into the map. Or rather: there is no such injection, and if our formalization of beliefs (map/world model) assumes otherwise, that formalization is wrong.
Here you use two individual constants: Table342 and SelfPerson. Individual constants can only be used for direct reference, where unique reference can’t fail. So it can only be used for internal (mental) objects. So “SelfPerson” is okay, because you know a priori that you exist uniquly. If you didn’t have a body, you could still refer to yourself, and it’s not possible that you accidentally refer to more than one person, like a copy of you. You are part of your mind, your internal state. But “Table342″ is an external object. It might not exist, or multiple such tables might exist even though you presupposed it was only one. “Table342” is an individual constant, which are incompatible with presupposition failure. So it can’t be used. That formalization is incompatible with possible worlds where the table doesn’t exist uniquely. But you have the same belief whether or not your presupposition is satisfied. So the formalization is faulty. We have to use one where no constants are used for reference to external things like tables.
Thanks for clarifying.
I mean I do think it can happen in my system that you allocate an object for something that’s actually 0 or >1 objects, and I don’t have a procedure for resolving such map-territory mismatches yet, though I think it’s imaginable to have a procedure that defines new objects and tries to edit all the beliefs associated with the old object.
I definitely haven’t described how we determine when to create a new object to add to our world model, but one could imagine an algorithm checking when there’s some useful latent for explaining some observations, and then constructing a model for that object, and then creating a new object in the abstract reasoning engine. Yeah there’s still open work to do for how a correspondences between the constant symbol for our object and our (e.g. visual) model of the object can be formalized and used, but I don’t see why it wouldn’t be feasible.
I agree that we end up with a map that doesn’t actually fit the territory, but I think it’s fine if there’s a unresolveable mismatch somewhere. There’s still a useful correspondence in most places. (Sure logic would collapse from a contradiction but actually it’s all probabilistic somehow anyways.) Although of course we don’t have anything to describe that the territory is different from the map in our system yet. This is related to embedded agency, and further work on how to model your map as possibly not fitting the territory and how that can be used is still necessary.