you are interested in finding the best explanation for.your observations—that’s metaphysics. Shminux seems.sure that certain negative metaphysical claims are true—there are No Platonic numbers, objective laws,.nor real probabilities
I really don’t understand what “best explanation”, “true”, or “exist” mean, as stand-alone words divorced from predictions about observations we might ultimately make about them.
This isn’t just a semantic point, I think. If there are no observations we can make that ultimately reflect whether something exists in this (seems to me to be) free-floating sense, I don’t understand what it can mean to have evidence for or against such a proposition. So I don’t understand how I am even supposed to ever justifiably change my mind on this topic, even if I were to accept it as something worth discussing on the object-level.
A: “I am interested in knowing whether Platonic mathematical entities exist.”
B: “What does it mean for something to ‘exist’?”
A: “Well, it seems to be an irreducible metaphysical claim; something can exist, or not exist.”
B: “Um… I’m not sure about this whole notion of ‘metaphysics’. But anyway, trying a different track, do these Platonic mathematical entities interact with observable physical reality in any discernible way?”
A: “I mean, as a practical descriptor, we use those particular mathematical entities because they are useful to us when we model reality; but at their core, they are supposed to be Platonic. They are forms, not concrete entities. Nevertheless, we can reason about them; we can define them, relate them to one another, prove theorems about them. We can even develop better intuitions about them over time as we work with them more and more. Is that what do you mean by ‘discernible’?”
“Information theory 101,” the boy said in a lecturing tone. “Observing variable X conveys information about variable Y, if and only if the possible values of X have different probabilities given different states of Y.
B (continuing): “So let’s think of the existence/non-existence status of Platonic math as the variable Y. Now, look, I am fine with accepting a broad perspective on the ‘variable’ X. Let it be an ocular observation, or the running of a scientific experiment, or a bunch of internal reasoning, or other stuff you might propose. I just want to know whether, given that these Platonic entities seem to live in an entirely separate magisterium, how is it that any observation/thought/conclusion we reach about the supposed existence of Platonic math (i.e., any particular value of Y) can result in different probabilities for the possible values of X?”
A: “You’re implicitly adopting a strong Bayesian perspective that you have neither argued for nor properly applied-”
B: “Fine! Drop the explicit probability stuff, then. I exist as a being embedded in the physical world. These mathematical entities are defined to exist (if they exist, which seems to be the question) in a Platonic realm that does not intersect this reality. After all, they are ideal forms, not concrete instances. So where is the entanglement between the two realms?”
A: “What do you mean by entanglement? I hope you’re not sneakily trying to assume a correspondence theory of truth yet again without justifying it.”
B: “What I mean is that I don’t understand how anything I do in this physical world that I belong to-”
A: “What makes you so sure you really live in a physical world? That’s the territory, not the map. All you have access to is the information given by your sense data and by your internal state of mind, including your memory. Maybe there is no outside world after all; maybe solipsism is true; maybe you live in an infinite-layer-deep simulation. Or maybe all of that is wrong and you actually are correct about living in some universe that runs on rough modifications of General Relativity and QFT, but even in that case, at the present moment you are totally not justified in assigning such confidence to this. You are merely assuming it instead, and this is precisely the type of metaphysical assumption you were pretending to be unable to wrap your head around at the start of the conversation.”
B: “Good Lord, fine! I’ll drop the physical universe assumption as well, for purposes of this conversation, even though I think I actually do have great justifications for being confident in it. But I won’t let the discussion get derailed any further in that direction. But I can still say that I am a concrete entity, precisely the type of being that shminux was contrasting the nature of when they mentioned Platonic mathematics. So I am concrete, and everything that goes on in my brain runs on the concrete me-stuff (I am intentionally avoiding the word ‘matter’), and yet I am supposed to have an opinion about the existence/non-existence of something that is entirely not concrete.”
A: “Isn’t that something you already conceded you were willing to try to do when you entered this dialogue? You could have walked away at the beginning or anytime after giving your whole spiel about beliefs paying rent in anticipated experiences.”
B: “Yes, I am willing to try to do that. But I don’t understand how I am supposed to ever change my mind on this topic, as I have already mentioned. What can possibly sway me one way or another when all variables X that I appear to be able to observe (or think about, etc.) are in the concrete realm, which is defined to be entirely non-intersecting with the Platonic realm? Does anything in this concrete realm have different values, or likelihoods, or entanglements, given different possible versions of whether the Platonic realm and its inhabitants exist? If math exists, is there anything that distinguishes this possibility? If math doesn’t exist, is there anything that distinguishes that possibility? What can count as epistemically justifiable updating (or, if you dislike the Bayesian connotations around that word, think ‘mind-changing’ instead) on this topic? As a general matter, I usually change my mind if I see new evidence or hear new good arguments, but I think of ‘good arguments’ as lines of logic and reasoning, whose validity and soundness implies we are more likely to be in a world where certain possibilities are true rather than others (when mulling over multiple hypotheses). What can that possibly mean in this context?”
A: [I’m not sure I can simulate A’s perspective after this point]
I really don’t understand what “best explanation”, “true”, or “exist” mean, as stand-alone words divorced from predictions about observations we might ultimately make about them.
Nobody is saying that anything has to be divorced from prediction , in the sense that emperical evidence is ignored: the realist claim is that empirical evidence should be supplemented by other epistemic considerations.
Best explanation:-
I already pointed out that EY is not an instrumentalist. For instance, he supports the MWI over the CI, although they make identical predictions. Why does he do that? For reasons of explanatory simplicity , consilience with the rest of physics, etc
.as he says. That gives you a clue as to what “best explanation” is. (Your bafflement is baffling...it sometimes sounds like you have read the sequences, it sometimes sounds like you haven’t. Of course abduction, parsimony, etc are widely discussed in the mainstream literature as well ).
True:- mental concept corresponds to reality.
Exists:- You can take yourself as existing , and you can regard other putative entieties as existing if they gave some ability to causally interact with you. That’s another baffling one, because you actually use something like that definition in your argument against mathematical realism below.
This isn’t just a semantic point, I think. If there are no observations we can make that ultimately reflect whether something exists in this (seems to me to be) free-floating sense, I don’t understand what it can mean to have evidence for or against such a proposition.
Empirical evidence doesn’t exhaust justification. But you kind of know that, because you mention “good argument” below.
So I don’t understand how I am even supposed to ever justifiably change my mind on this topic, even if I were to accept it as something worth discussing on the object-level.
Apriori necessary truths can be novel and surprising to an agent, in practice, even though they are apriori and necessary in principle… because a realistic agent can’t instantaneously and perfectly correlate their mental contents, and don’t have an oracular list of every theory in their head. You are not a perfect Bayesian. You can notice a contradiction that you haven’t noticed before. You can be informed of a simpler explanation that you hadn’t formulated yourself.
What can possibly sway me one way or another when all variables X that I appear to be able to observe (or think about, etc.) are in the concrete realm, which is defined to be entirely non-intersecting with the Platonic realm?
Huh? I was debating nomic realism. Mathematical realism is another thing. Objectively existing natural laws obviously intersect with concrete observations , because if Gravity worked on an inverse cube law (etc), everything looked very different.
You don’t have to buy into realism about all things, or anti realism about all things. You can pick and choose. I don’t personally believe in Platonic realism about mathematics, for the same reasons you don’t. I believe Nomic realism is another question...its logically possible for physical laws to have been different.
@shminux defined the the thing he is arguing against as “Platonic” .. I don’t have to completely agree with that, nor do you. Maybe it’s just a mistake to think of nomic realism as Platonism. Platonism marries the idea of non-mental existence and the idea of non causality...But they can be treated separately.
What can that possibly mean in this context?”
what context? You’re talking about mathematical realism, I’m talking about nomic realism.
as lines of logic and reasoning, whose validity and soundness implies we are more likely to be in a world where certain possibilities are true rather than others (when mulling over multiple hypotheses
What have I said that makes you think I have departed from that?
@Shminux
If push comes to shove, I would even dispute that “real” is a useful category once we start examining deep ontological claims
Useful for what? If you terminally value uncovering the true nature of reality, as most scientists and philosophers do, you can hardly manage without some concept of “real”. If you only value making predictions, perhaps you don’t need the concept....But then the instrumentalist/realist divide is a difference in values, as I previously said, not a case of one side being wrong and the other side being right.
“Exist” is another emergent concept that is not even close to being binary, but more of a multidimensional spectrum (numbers, fairies and historical figures lie on some of the axes).
“Not a binary” is a different take from “not useful”.
The critical point is that we have no direct access to the underlying reality, so we, as tiny embedded agents, are stuck dealing with the models regardless.
“No direct access to reality” is a different claim to “no access to reality” is a different claim to “there is no reality” is a different to “the concept of reality is not useful”.l
I can provisionally accept that there is something like a universe that “exists”, but, as I said many years ago in another thread, I am much more comfortable with the ontology where it is models all thea way down (and up and sideways and every which way).
It’s incoherent. What are these models, models of?
Thanks, I think you are doing a much better job voicing my objections than I would.
If push comes to shove, I would even dispute that “real” is a useful category once we start examining deep ontological claims. “Exist” is another emergent concept that is not even close to being binary, but more of a multidimensional spectrum (numbers, fairies and historical figures lie on some of the axes). I can provisionally accept that there is something like a universe that “exists”, but, as I said many years ago in another thread, I am much more comfortable with the ontology where it is models all the way down (and up and sideways and every which way). This is not really a critical point though. The critical point is that we have no direct access to the underlying reality, so we, as tiny embedded agents, are stuck dealing with the models regardless.
I really don’t understand what “best explanation”, “true”, or “exist” mean, as stand-alone words divorced from predictions about observations we might ultimately make about them.
This isn’t just a semantic point, I think. If there are no observations we can make that ultimately reflect whether something exists in this (seems to me to be) free-floating sense, I don’t understand what it can mean to have evidence for or against such a proposition. So I don’t understand how I am even supposed to ever justifiably change my mind on this topic, even if I were to accept it as something worth discussing on the object-level.
A: “I am interested in knowing whether Platonic mathematical entities exist.”
B: “What does it mean for something to ‘exist’?”
A: “Well, it seems to be an irreducible metaphysical claim; something can exist, or not exist.”
B: “Um… I’m not sure about this whole notion of ‘metaphysics’. But anyway, trying a different track, do these Platonic mathematical entities interact with observable physical reality in any discernible way?”
A: “I mean, as a practical descriptor, we use those particular mathematical entities because they are useful to us when we model reality; but at their core, they are supposed to be Platonic. They are forms, not concrete entities. Nevertheless, we can reason about them; we can define them, relate them to one another, prove theorems about them. We can even develop better intuitions about them over time as we work with them more and more. Is that what do you mean by ‘discernible’?”
B: “Not exactly… Look, as Eliezer has said:
B (continuing): “So let’s think of the existence/non-existence status of Platonic math as the variable Y. Now, look, I am fine with accepting a broad perspective on the ‘variable’ X. Let it be an ocular observation, or the running of a scientific experiment, or a bunch of internal reasoning, or other stuff you might propose. I just want to know whether, given that these Platonic entities seem to live in an entirely separate magisterium, how is it that any observation/thought/conclusion we reach about the supposed existence of Platonic math (i.e., any particular value of Y) can result in different probabilities for the possible values of X?”
A: “You’re implicitly adopting a strong Bayesian perspective that you have neither argued for nor properly applied-”
B: “Fine! Drop the explicit probability stuff, then. I exist as a being embedded in the physical world. These mathematical entities are defined to exist (if they exist, which seems to be the question) in a Platonic realm that does not intersect this reality. After all, they are ideal forms, not concrete instances. So where is the entanglement between the two realms?”
A: “What do you mean by entanglement? I hope you’re not sneakily trying to assume a correspondence theory of truth yet again without justifying it.”
B: “What I mean is that I don’t understand how anything I do in this physical world that I belong to-”
A: “What makes you so sure you really live in a physical world? That’s the territory, not the map. All you have access to is the information given by your sense data and by your internal state of mind, including your memory. Maybe there is no outside world after all; maybe solipsism is true; maybe you live in an infinite-layer-deep simulation. Or maybe all of that is wrong and you actually are correct about living in some universe that runs on rough modifications of General Relativity and QFT, but even in that case, at the present moment you are totally not justified in assigning such confidence to this. You are merely assuming it instead, and this is precisely the type of metaphysical assumption you were pretending to be unable to wrap your head around at the start of the conversation.”
B: “Good Lord, fine! I’ll drop the physical universe assumption as well, for purposes of this conversation, even though I think I actually do have great justifications for being confident in it. But I won’t let the discussion get derailed any further in that direction. But I can still say that I am a concrete entity, precisely the type of being that shminux was contrasting the nature of when they mentioned Platonic mathematics. So I am concrete, and everything that goes on in my brain runs on the concrete me-stuff (I am intentionally avoiding the word ‘matter’), and yet I am supposed to have an opinion about the existence/non-existence of something that is entirely not concrete.”
A: “Isn’t that something you already conceded you were willing to try to do when you entered this dialogue? You could have walked away at the beginning or anytime after giving your whole spiel about beliefs paying rent in anticipated experiences.”
B: “Yes, I am willing to try to do that. But I don’t understand how I am supposed to ever change my mind on this topic, as I have already mentioned. What can possibly sway me one way or another when all variables X that I appear to be able to observe (or think about, etc.) are in the concrete realm, which is defined to be entirely non-intersecting with the Platonic realm? Does anything in this concrete realm have different values, or likelihoods, or entanglements, given different possible versions of whether the Platonic realm and its inhabitants exist? If math exists, is there anything that distinguishes this possibility? If math doesn’t exist, is there anything that distinguishes that possibility? What can count as epistemically justifiable updating (or, if you dislike the Bayesian connotations around that word, think ‘mind-changing’ instead) on this topic? As a general matter, I usually change my mind if I see new evidence or hear new good arguments, but I think of ‘good arguments’ as lines of logic and reasoning, whose validity and soundness implies we are more likely to be in a world where certain possibilities are true rather than others (when mulling over multiple hypotheses). What can that possibly mean in this context?”
A: [I’m not sure I can simulate A’s perspective after this point]
Nobody is saying that anything has to be divorced from prediction , in the sense that emperical evidence is ignored: the realist claim is that empirical evidence should be supplemented by other epistemic considerations.
Best explanation:- I already pointed out that EY is not an instrumentalist. For instance, he supports the MWI over the CI, although they make identical predictions. Why does he do that? For reasons of explanatory simplicity , consilience with the rest of physics, etc .as he says. That gives you a clue as to what “best explanation” is. (Your bafflement is baffling...it sometimes sounds like you have read the sequences, it sometimes sounds like you haven’t. Of course abduction, parsimony, etc are widely discussed in the mainstream literature as well ).
True:- mental concept corresponds to reality.
Exists:- You can take yourself as existing , and you can regard other putative entieties as existing if they gave some ability to causally interact with you. That’s another baffling one, because you actually use something like that definition in your argument against mathematical realism below.
Empirical evidence doesn’t exhaust justification. But you kind of know that, because you mention “good argument” below.
Apriori necessary truths can be novel and surprising to an agent, in practice, even though they are apriori and necessary in principle… because a realistic agent can’t instantaneously and perfectly correlate their mental contents, and don’t have an oracular list of every theory in their head. You are not a perfect Bayesian. You can notice a contradiction that you haven’t noticed before. You can be informed of a simpler explanation that you hadn’t formulated yourself.
Huh? I was debating nomic realism. Mathematical realism is another thing. Objectively existing natural laws obviously intersect with concrete observations , because if Gravity worked on an inverse cube law (etc), everything looked very different.
You don’t have to buy into realism about all things, or anti realism about all things. You can pick and choose. I don’t personally believe in Platonic realism about mathematics, for the same reasons you don’t. I believe Nomic realism is another question...its logically possible for physical laws to have been different.
@shminux defined the the thing he is arguing against as “Platonic” .. I don’t have to completely agree with that, nor do you. Maybe it’s just a mistake to think of nomic realism as Platonism. Platonism marries the idea of non-mental existence and the idea of non causality...But they can be treated separately.
what context? You’re talking about mathematical realism, I’m talking about nomic realism.
What have I said that makes you think I have departed from that?
@Shminux
Useful for what? If you terminally value uncovering the true nature of reality, as most scientists and philosophers do, you can hardly manage without some concept of “real”. If you only value making predictions, perhaps you don’t need the concept....But then the instrumentalist/realist divide is a difference in values, as I previously said, not a case of one side being wrong and the other side being right.
“Not a binary” is a different take from “not useful”.
“No direct access to reality” is a different claim to “no access to reality” is a different claim to “there is no reality” is a different to “the concept of reality is not useful”.l
It’s incoherent. What are these models, models of?
Thanks, I think you are doing a much better job voicing my objections than I would.
If push comes to shove, I would even dispute that “real” is a useful category once we start examining deep ontological claims. “Exist” is another emergent concept that is not even close to being binary, but more of a multidimensional spectrum (numbers, fairies and historical figures lie on some of the axes). I can provisionally accept that there is something like a universe that “exists”, but, as I said many years ago in another thread, I am much more comfortable with the ontology where it is models all the way down (and up and sideways and every which way). This is not really a critical point though. The critical point is that we have no direct access to the underlying reality, so we, as tiny embedded agents, are stuck dealing with the models regardless.