One approach would be to understand beliefs as habits rather than as propositions. Both the belief in gravity and in national borders guide movement. Even aesthetical judgements - what we deem beautiful and ideal in itself - guide massively our orientation in life.
Then the question about the truth isn't purely a relationship between a proposition and some state of things, but a dynamic and fluid relation between a habit and environment.
True beliefs would then be beliefs that are in harmony with the environment. True belief would minimize surprise. For instance, believing in flat earth would lead to surprises when flying in space. This way even things deemed as intersubjective or subjective aren't fully arbitrary. For example, a good society is one which sustains itself with minimal crises.
I don’t buy this. I think there’s something here in this continuum idea, but you’re likely conflating utility with truth.
I think the continuum is better described as the scale of consensus on a given topic, which is itself an objective property of reality. “I like coffee with milk” is an objective fact claim about your personal preferences - it’s either true or not. “Coffee with milk is good” is a subjective value claim, the utility of which increases as a function of its social consensus. As you said, if enough people value something, then that thing becomes more valuable.
None of this impinges on some things being objectively true and other things being false. So I think this intersecting continuum applies to some forms of value beliefs, for sure. Most of what humans are doing - even when they tell themselves it has to do with objective factual reality - is really about values. I agree with that.
But some things still are and aren’t true, and these things include minutiae like your personal preference for X over Y. Again, “X is better than Y” is a value belief, on that continuum of consensus. “I prefer X to Y” is a fact belief that can be inferred from, ie observation. For example, the Pythagorean theorem. Either it is true or it isn’t. Whether or not people disagree on this is irrelevant to the truth, but it can matter for utility. If everyone thinks Pythagoras, as an old white man, is evil and bad, it may be wiser to keep your use of this evil theorem secret. But id still use it.
If everyone in some field agrees that some claim is true, the utility of disbelief in the claim may indeed lower- but it depends on the field and the people! Most financial experts would have told you to stay away from bitcoin 10 years ago. We now know they objectively wrong. If only one person thinks a claim is true, the utility of believing the thing to be true, in general, is much lower. So what I think you are describing in this continuum is not objectivity vs subjectivity, but the scale of value consensus.
There are a couple good points in here I want to address.
First, on the idea of "value consensus"--that's certainly part of the picture. I often hear people refer to Intersubjectivity with the phrase "consensus reality". But there's a lot more consensus on Oslo being the capital of Norway than there is on the Earth being round, and I hope we all agree the latter is far more Objective as facts go. Consensus is _correlated_ with Objectivity, but it's the higher degree of Objectivity that drives consensus, not vice versa (which you seem to get).
More importantly, I want to address your assertion that "some things still are and aren't true". Mostly I agree with this, but the way you describe it suggests you think the pythagorean theorem doesn't belong on the spectrum, or is firmly fixed at some 0 value of subjectivity--that's where I disagree.
To be sure, the pythagorean theorem is very far to the right! This is probably the best steelman for a notion of pure objectivity, so let me try and pick it apart.
First: no one has ever seen a "real" right triangle--right triangles are a human-made abstraction. As you point out, they're quite valuable for doing human things, but there's the notion of "value" poking its head in!
Second: a mathematical statement is only true *given a particular set of axioms*. Pythagoras is only right when you're working within a Euclidean system. Aliens in a non-euclidean universe would wonder why we're so fixated on this little limiting case of geometry.
When doing math, we declare the axioms to be true *by fiat*, and then assume everything we infer from those axioms to be unassailably true. But there's a lot of subjectivity that goes into picking a set of axioms! See e.g. the axiom of choice.
All of mathematics is a language game, with the rules and concepts all chosen by humans. Again, it's a very useful language game! But we always have to remember that *we* made the rules, and *we* determine their value.
This is why I put hard physical facts--like the roundness of Earth--further to the right than mathematics. But even these rely on human categories and distinctions. E.g. you can create a perfectly consistent cosmology where the sun goes round the Earth--the math is just much more complicated, with the planets making jerky (but predictable!) forward and backward motions.
I think this was the hardest point for me to accept, because it involved letting go of a romantic notion of Truth. But I've found it supremely rewarding.
Yes, different assumptions can be made and different assumptions lead to different contingent “truths”. This is like the coffee example: whether or not you like coffee is objectively true, so long as you express your preference as being your own preference (“I like this”) and not a fact (“this is good”).
Likewise, “these axioms, plus these production rules, lead to this conclusion” is not contingent on any axioms, is it?
“In Euclidean geometry (with a given distance metric supplied) the Pythagorean theorem is true” is objectively true. The aliens would happily agree with that assessment, wouldn’t they? They’d see it as tautological. I agree that they might not find it _useful_, but I’d expect any aliens to have also discovered things like, ie Turing completeness.
Agree--we'd probably find a lot of isomorphisms between our mathematical statements and theirs.
There's a sort of game we can play here: you make a very objective sounding statement (e.g. "the pythagorean theorem is true"), then I pick it apart and show how it depends on a heap of context and assumptions. Then you refine your statement to address my criticism (e.g. "the pythagorean theorem is true given the axioms of Euclidean geometry"), and I redouble my efforts finding new cracks. That game can be played ad infinitum.
As one commenter on Twitter observed:
> I think any representation of the objective takes it into the realm of intersubjectivity. You just bang into problems more often the less apt the representation is.
You could say our game is approaching some Objective, Platonic truth. Maybe so. But the "existence" or "realness" of that truth is a metaphysical assertion--not a fact itself!
Can you help me understand how the game goes on forever? Like, what are the cracks in the Pythagorean theorem example that adding in Euclidean geometry doesn’t catch?
With math/logic, the game is trivial. I can always question the consistency of your axioms, claiming that saying "given the axioms of Euclidean geometry" might be as senseless as saying "given that pigs can fly". You adjust your axioms, and we go in a circle.
(You can kind of escape the game by stating a tautology, but tautologies are contentless. They assert nothing.)
The game is more fun with physical-world statements. You say "the earth is spherical", and I point out that no, it has a bulge around the equator. So you say "The earth is approximately spherical, with a bulge", and I say no, there are mountains and valleys and such. So you say "The earth is approximately spherical, +/- 0.1%, with a bulge", and I point out that the Earth is a temporary entity and won't exist forever. So you state that the above is true only for a particular set of times.
My attacks get more and more tiresome and nitpicky, while your statements get more and more precise. So it's an asymmetrical game--I play the pedant, while you play the pragmatic scientist.
I’m not sure I understand. How can you “question the consistency” of a set of axioms? Is that an assertion that the axioms are inconsistent?
How is this game any different from “you could just keep making up nonsense and a person who took you seriously could never convince you it was nonsense.” I dont doubt that’s true, but it doesn’t require any responses more elaborate that putting your fingers in your ears and going “bla bla I don’t hear you.”
Is there some distinction I’m missing between “oh that set of axioms is inconsistent” and “oh, that’s just what THEY want you to think?”
Maybe you can help me understand why a tautology asserts nothing. I’m guessing this is related?
## I am using the term subjective as in mind-dependent and objective as in mind-independent.
So basically the sharing of mutual information between 2 or more subjective viewpoints is intersubjective, between subjective/intersubjective and objective is truth am I getting this correct? So in a sense science could be considered a pursuit to *reduce* the influence of inter-subjective *social value* distortions in the map-territory correspondence from the collective pursuit of knowledge.
I do get your continuum in the sense of social constructs/contracts *feel* harder to change than something like the map-territory correspondence of laws of physics but I think the mutual information is still shared between 2 subjective viewpoints so it's technically changeable. From the POV of a subject inter-subjective discourse is still part of objective reality as you get the (assuming no solipsism,cultural epistemic relativism,lingusitic relativism and other crazy non-sense from humanities). I think large parts of psychology should just embrace that they are mostly just documenting human stereotypes which are *true* but can be potentially changed, this inter-subjectivity is what parts of humanities of the 20th century seems to be obsessing over though. (few parts of psychology seem to be more rigorous like cognitive biases, because it seems the people who say they are unbiased are the most biased people I have ever met lmao, the lack of self-reflection)
So basically what we call as *reality* is *what reality seems like to us or theorized reality* our model is inherently subjective or intersubjective, a true theorized reality would correspond to real reality. We cannot really be infinitely certain that this is the case, but we can be damn sure to land people on the moon with our models. We have over time realized certain epistemic values on mathematical pragmatic and philosophical grounds like occam's razor to prevent conjunction fallacy, predictivism,bayesianism,statistics, logic, probability theory which seem to work reliably now whether you call this truth or empirical adequacy is intellectual masturbation(even though I prefer the former). Like it is totally possible that I am dreaming, but that hypothesis is un-testable since it doesn't make many predictions so I disregard it as not reality or it is possible that earth is flat and all scientists are lying but since that hypothesis is wayy to complex so it's prior is very low.
Now (from what I understand,I may be wrong) the not-so-fond-of-science, humanities people realized along the lines of *wait* doesn't inter-subjectivity also lead to certain objective changes in the world? As in your mutual information between your utility function and the world can also increase when you pursue your goal. Then(given the humanities brained person), doesn't that imply science(as a social institution) can be used as a oppressive and inherently conservative(since it describes the current state of things) social structure when implying causality about socio-biological facts?! Yes it can be! Sure, to an extent, good luck changing the laws of physics though. Hence, the double blinded randomized control trials are popular to imply causation from correlation or a lot of ethically adjacent issues(intersubjective) regarding race and IQ have been withhold for this reason. (although only if people could agree on is-ought distinction but uhh, I guess I am being too idealistic,I guess back to my moral anti-realist pragmatism tranquility)
Another thing being you could philosophically advocate for maths being objective and we are discovering mind-independent objective mathematical facts, as in mathematical realism. (I am not much into philo-math) But that being said I lean more on bayesian empiricism side so I think one could potentially hold 2=3 given enough brain damage or enough evidence to the contrary of 2 apples in 3 apples out of the magic bag.
One approach would be to understand beliefs as habits rather than as propositions. Both the belief in gravity and in national borders guide movement. Even aesthetical judgements - what we deem beautiful and ideal in itself - guide massively our orientation in life.
Then the question about the truth isn't purely a relationship between a proposition and some state of things, but a dynamic and fluid relation between a habit and environment.
True beliefs would then be beliefs that are in harmony with the environment. True belief would minimize surprise. For instance, believing in flat earth would lead to surprises when flying in space. This way even things deemed as intersubjective or subjective aren't fully arbitrary. For example, a good society is one which sustains itself with minimal crises.
I don’t buy this. I think there’s something here in this continuum idea, but you’re likely conflating utility with truth.
I think the continuum is better described as the scale of consensus on a given topic, which is itself an objective property of reality. “I like coffee with milk” is an objective fact claim about your personal preferences - it’s either true or not. “Coffee with milk is good” is a subjective value claim, the utility of which increases as a function of its social consensus. As you said, if enough people value something, then that thing becomes more valuable.
None of this impinges on some things being objectively true and other things being false. So I think this intersecting continuum applies to some forms of value beliefs, for sure. Most of what humans are doing - even when they tell themselves it has to do with objective factual reality - is really about values. I agree with that.
But some things still are and aren’t true, and these things include minutiae like your personal preference for X over Y. Again, “X is better than Y” is a value belief, on that continuum of consensus. “I prefer X to Y” is a fact belief that can be inferred from, ie observation. For example, the Pythagorean theorem. Either it is true or it isn’t. Whether or not people disagree on this is irrelevant to the truth, but it can matter for utility. If everyone thinks Pythagoras, as an old white man, is evil and bad, it may be wiser to keep your use of this evil theorem secret. But id still use it.
If everyone in some field agrees that some claim is true, the utility of disbelief in the claim may indeed lower- but it depends on the field and the people! Most financial experts would have told you to stay away from bitcoin 10 years ago. We now know they objectively wrong. If only one person thinks a claim is true, the utility of believing the thing to be true, in general, is much lower. So what I think you are describing in this continuum is not objectivity vs subjectivity, but the scale of value consensus.
There are a couple good points in here I want to address.
First, on the idea of "value consensus"--that's certainly part of the picture. I often hear people refer to Intersubjectivity with the phrase "consensus reality". But there's a lot more consensus on Oslo being the capital of Norway than there is on the Earth being round, and I hope we all agree the latter is far more Objective as facts go. Consensus is _correlated_ with Objectivity, but it's the higher degree of Objectivity that drives consensus, not vice versa (which you seem to get).
More importantly, I want to address your assertion that "some things still are and aren't true". Mostly I agree with this, but the way you describe it suggests you think the pythagorean theorem doesn't belong on the spectrum, or is firmly fixed at some 0 value of subjectivity--that's where I disagree.
To be sure, the pythagorean theorem is very far to the right! This is probably the best steelman for a notion of pure objectivity, so let me try and pick it apart.
First: no one has ever seen a "real" right triangle--right triangles are a human-made abstraction. As you point out, they're quite valuable for doing human things, but there's the notion of "value" poking its head in!
Second: a mathematical statement is only true *given a particular set of axioms*. Pythagoras is only right when you're working within a Euclidean system. Aliens in a non-euclidean universe would wonder why we're so fixated on this little limiting case of geometry.
When doing math, we declare the axioms to be true *by fiat*, and then assume everything we infer from those axioms to be unassailably true. But there's a lot of subjectivity that goes into picking a set of axioms! See e.g. the axiom of choice.
All of mathematics is a language game, with the rules and concepts all chosen by humans. Again, it's a very useful language game! But we always have to remember that *we* made the rules, and *we* determine their value.
This is why I put hard physical facts--like the roundness of Earth--further to the right than mathematics. But even these rely on human categories and distinctions. E.g. you can create a perfectly consistent cosmology where the sun goes round the Earth--the math is just much more complicated, with the planets making jerky (but predictable!) forward and backward motions.
I think this was the hardest point for me to accept, because it involved letting go of a romantic notion of Truth. But I've found it supremely rewarding.
Yes, different assumptions can be made and different assumptions lead to different contingent “truths”. This is like the coffee example: whether or not you like coffee is objectively true, so long as you express your preference as being your own preference (“I like this”) and not a fact (“this is good”).
Likewise, “these axioms, plus these production rules, lead to this conclusion” is not contingent on any axioms, is it?
“In Euclidean geometry (with a given distance metric supplied) the Pythagorean theorem is true” is objectively true. The aliens would happily agree with that assessment, wouldn’t they? They’d see it as tautological. I agree that they might not find it _useful_, but I’d expect any aliens to have also discovered things like, ie Turing completeness.
Agree--we'd probably find a lot of isomorphisms between our mathematical statements and theirs.
There's a sort of game we can play here: you make a very objective sounding statement (e.g. "the pythagorean theorem is true"), then I pick it apart and show how it depends on a heap of context and assumptions. Then you refine your statement to address my criticism (e.g. "the pythagorean theorem is true given the axioms of Euclidean geometry"), and I redouble my efforts finding new cracks. That game can be played ad infinitum.
As one commenter on Twitter observed:
> I think any representation of the objective takes it into the realm of intersubjectivity. You just bang into problems more often the less apt the representation is.
https://twitter.com/willmatheson/status/1763323941660279082
You could say our game is approaching some Objective, Platonic truth. Maybe so. But the "existence" or "realness" of that truth is a metaphysical assertion--not a fact itself!
Can you help me understand how the game goes on forever? Like, what are the cracks in the Pythagorean theorem example that adding in Euclidean geometry doesn’t catch?
With math/logic, the game is trivial. I can always question the consistency of your axioms, claiming that saying "given the axioms of Euclidean geometry" might be as senseless as saying "given that pigs can fly". You adjust your axioms, and we go in a circle.
(You can kind of escape the game by stating a tautology, but tautologies are contentless. They assert nothing.)
The game is more fun with physical-world statements. You say "the earth is spherical", and I point out that no, it has a bulge around the equator. So you say "The earth is approximately spherical, with a bulge", and I say no, there are mountains and valleys and such. So you say "The earth is approximately spherical, +/- 0.1%, with a bulge", and I point out that the Earth is a temporary entity and won't exist forever. So you state that the above is true only for a particular set of times.
My attacks get more and more tiresome and nitpicky, while your statements get more and more precise. So it's an asymmetrical game--I play the pedant, while you play the pragmatic scientist.
I’m not sure I understand. How can you “question the consistency” of a set of axioms? Is that an assertion that the axioms are inconsistent?
How is this game any different from “you could just keep making up nonsense and a person who took you seriously could never convince you it was nonsense.” I dont doubt that’s true, but it doesn’t require any responses more elaborate that putting your fingers in your ears and going “bla bla I don’t hear you.”
Is there some distinction I’m missing between “oh that set of axioms is inconsistent” and “oh, that’s just what THEY want you to think?”
Maybe you can help me understand why a tautology asserts nothing. I’m guessing this is related?
## I am using the term subjective as in mind-dependent and objective as in mind-independent.
So basically the sharing of mutual information between 2 or more subjective viewpoints is intersubjective, between subjective/intersubjective and objective is truth am I getting this correct? So in a sense science could be considered a pursuit to *reduce* the influence of inter-subjective *social value* distortions in the map-territory correspondence from the collective pursuit of knowledge.
I do get your continuum in the sense of social constructs/contracts *feel* harder to change than something like the map-territory correspondence of laws of physics but I think the mutual information is still shared between 2 subjective viewpoints so it's technically changeable. From the POV of a subject inter-subjective discourse is still part of objective reality as you get the (assuming no solipsism,cultural epistemic relativism,lingusitic relativism and other crazy non-sense from humanities). I think large parts of psychology should just embrace that they are mostly just documenting human stereotypes which are *true* but can be potentially changed, this inter-subjectivity is what parts of humanities of the 20th century seems to be obsessing over though. (few parts of psychology seem to be more rigorous like cognitive biases, because it seems the people who say they are unbiased are the most biased people I have ever met lmao, the lack of self-reflection)
So basically what we call as *reality* is *what reality seems like to us or theorized reality* our model is inherently subjective or intersubjective, a true theorized reality would correspond to real reality. We cannot really be infinitely certain that this is the case, but we can be damn sure to land people on the moon with our models. We have over time realized certain epistemic values on mathematical pragmatic and philosophical grounds like occam's razor to prevent conjunction fallacy, predictivism,bayesianism,statistics, logic, probability theory which seem to work reliably now whether you call this truth or empirical adequacy is intellectual masturbation(even though I prefer the former). Like it is totally possible that I am dreaming, but that hypothesis is un-testable since it doesn't make many predictions so I disregard it as not reality or it is possible that earth is flat and all scientists are lying but since that hypothesis is wayy to complex so it's prior is very low.
Now (from what I understand,I may be wrong) the not-so-fond-of-science, humanities people realized along the lines of *wait* doesn't inter-subjectivity also lead to certain objective changes in the world? As in your mutual information between your utility function and the world can also increase when you pursue your goal. Then(given the humanities brained person), doesn't that imply science(as a social institution) can be used as a oppressive and inherently conservative(since it describes the current state of things) social structure when implying causality about socio-biological facts?! Yes it can be! Sure, to an extent, good luck changing the laws of physics though. Hence, the double blinded randomized control trials are popular to imply causation from correlation or a lot of ethically adjacent issues(intersubjective) regarding race and IQ have been withhold for this reason. (although only if people could agree on is-ought distinction but uhh, I guess I am being too idealistic,I guess back to my moral anti-realist pragmatism tranquility)
Another thing being you could philosophically advocate for maths being objective and we are discovering mind-independent objective mathematical facts, as in mathematical realism. (I am not much into philo-math) But that being said I lean more on bayesian empiricism side so I think one could potentially hold 2=3 given enough brain damage or enough evidence to the contrary of 2 apples in 3 apples out of the magic bag.