I can’t say for certain, of course, that every possible universe must run on math, but I feel safe in claiming that we’ve never imagined a universe, in fiction or through something like religion, which would fail to run on math.
That is a fact about you, not a fact about the universe. Nobody could imagine light being both a particle and a wave, for example, until their study of nature forced them to.
People could imagine such a thing before studying nature showed they needed to; they just didn’t. I think there’s a difference between a concept that people only don’t imagine, and a concept that people can’t imagine. The latter may mean that the concept is incoherent or has an intrinsic flaw, which the former doesn’t.
People could imagine such a thing before studying nature showed they needed to; they just didn’t. I think there’s a difference between a concept that people only don’t imagine, and a concept that people can’t imagine.
In the interest of not having this discussion degenerate into an argument about what “could” means, I would like to point out that your and hen’s only evidence that you couldn’t imagine a world that doesn’t run on math is that you haven’t.
For one thing, “math” trivially happens to run on world, and corresponds to what happens when you have a chain of interactions. Specifically to how one chain of physical interactions (apples being eaten for example) combined with another that looks dissimilar (a binary adder) ends up with conclusion that apples were counted correctly, or how the difference in count between the two processes of counting (none) corresponds to another dissimilar process (the reasoning behind binary arithmetic).
As long as there’s any correspondences at all between different physical processes, you’ll be able to kind of imagine that world runs on world arranged differently, and so it would appear that world “runs on math”.
If we were to discover some new laws of physics that were producing incalculable outcomes, we would just utilize those laws in some sort of computer and co-opt them as part of “math”, substituting processes for equivalent processes. That’s how we came up with math in the first place.
edit: to summarize, I think “the world runs on math” is a really confused way to look at how world relates to the practice of mathematics inside of it. I can perfectly well say that the world doesn’t run on math any more than the radio waves are transmitted by mechanical aether made of gears, springs, and weights, and have exact same expectations about everything.
It seems to me that as long as there’s anything that is describable in the loosest sense, that would be taken to be true.
I mean, look at this, some people believe literally that our universe is a “mathematical object”, what ever that means (tegmarkery), and we haven’t even got a candidate TOE that works.
edit: I think the issue is that Morpheus confuses “made of gears” with “predictable by gears”. Time is not made of gears, and neither are astronomical objects, but a clock is very useful nonetheless.
I don’t see why “describable” would necessarily imply “describable mathematically”. I can imagine a qualia only universe,and I can imagine the ability describe qualia. As things stand, there are a number of things that can’t be described mathematically
What’s your evidence for this? Keep in mind that the history of science is full of people asserting that X has to be the case because they couldn’t imagine the world being otherwise, only for subsequent discoveries to show that X is not in fact the case.
Well, the most famous (or infamous) is Kant’s argument the space must be flat (in the Euclidean sense) because the human mind is incapable of imagining it to be otherwise.
Another example was Lucretius’s argument against the theory that the earth is round: if the earth were round and things fell towards its center than in which direction would an object at the center fall?
Not to mention the standard argument against the universe having a beginning “what happened before it?”
I don’t intend to bicker, I think your point is a good one independently of these examples. In any case, I don’t think at least the first two of these examples of the phenomenon you’re talking about.
Well, the most famous (or infamous) is Kant’s argument the space must be flat (in the Euclidean sense) because the human mind is incapable of imagining it to be otherwise.
I think this comes up in the sequences as an example of the mind-projection fallacy, but that’s not right. Kant did not take himself to be saying anything about the world outside the mind when he said that space was flat. He only took himself to be talking about the world as it appears to us. Space, so far as Kant was concerned, was part of the structure of perception, not the universe. So in the Critique of Pure Reason, he says:
...if we remove our own subject or even only the subjective constitution of the senses in general, then all constitution, all relations of objects in space and time, indeed space and time themselves would disappear, and as appearances they cannot exist in themselves, but only in us. What may be the case with objects in themselves and abstracted from all this receptivity of our sensibility remains entirely unknown to us. (A42/B59–60)
So Kant is pretty explicit that he’s not making a claim about the world, but about the way we percieve it. Kant would very likely poke you in chest and say “No you’re committing the mind-projection fallacy for thinking that space is even in the world, rather than just a form of perception. And don’t tell me about the mind-projection fallacy anyway, I invented that whole move.”
Another example was Lucretius’s argument against the theory that the earth is round: if the earth were round and things fell towards its center than in which direction would an object at the center fall?
This also isn’t an example, because the idea of a spherical world had in fact been imagined in detail by Plato (with whom Lucretius seems to be arguing), Aristotle, and many of Lucretius’ contemporaries and predecessors. Lucretius’ point couldn’t have been that a round earth is unimaginable, but that it was inconsistent with an analysis of the motions of simple bodies in terms of up and down: you can’t say that fire is of a nature to go up if up is entirely relative. Or I suppose, you can say that but you’d have to come up with a more complicated account of natures.
Kant did not take himself to be saying anything about the world outside the mind when he said that space was flat. He only took himself to be talking about the world as it appears to us. Space, so far as Kant was concerned, was part of the structure of perception, not the universe.
And in particular he claimed that this showed it had to be Euclidean because humans couldn’t imagine it otherwise. Well, we now know it’s not Euclidean and people can imagine it that way (I suppose you could dispute this, but that gets into exactly what we mean by “imagine” and attempting to argue about other people’s qualia).
And in particular he claimed that this showed it had to be Euclidean because humans couldn’t imagine it otherwise.
No, he never says that. Feel free to cite something from Kant’s writing, or the SEP or something. I may be wrong, but I just read though the Aesthetic again, and I couldn’t find anything that would support your claim.
EDIT: I did find one passage that mentions imagination:
Space then is a necessary representation a priori, which serves for the foundation of all external intuitions. We never can imagine or make representation to ourselves of the non-existence of space, though we may easily enough think that no objects are found in it.
I’ve edited my post accordingly, but my point remains the same. Notice that Kant does not mention the flatness of space, nor is it at all obvious that he’s inferring anything from our inability to imagine the non-existence of space. END EDIT.
You gave Kant’s views about space as an example of someone saying ‘because we can’t imagine it otherwise, the world must be such and such’. Kant never says this. What he says is that the principles of geometry are not derived simply from the analysis of terms, nor are they empirical. Kant is very, very, explicit...almost annoyingly repetitive, that he is not talking about the world, but about our perceptive faculties. And if indeed we cannot imagine x, that does seem to me to be a good basis from which to draw some conclusions about our perceptive faculties.
I have no idea what Kant would say about whether or not we can imagine non-Euclidian space (I have no idea myself if we can) but the matter is complicated because ‘imagination’ is a technical term in his philosophy. He thought space was an infinite Euclidian magnitude, but Euclidian geometry was the only game in town at the time.
Anyway he’s not a good example. As I said before, I don’t mean to dispute the point the example was meant to illustrate. I just wanted to point out that this is an incorrect view of Kant’s claims about space. It’s not really very important what he thought about space though.
There’s a difference between “can’t imagine” in a colloquial sense, and actual inability to imagine. There’s also a difference between not being able to think of how something fits into our knowledge about the universe (for instance, not being able to come up with a mechanism or not being able to see how the evidence supports it) and not being able to imagine the thing itself.
There also aren’t as many examples of this in the history of science as you probably think. Most of the examples that come to people’s mind involve scientists versus noscientists.
I can’t say for certain, of course, that every possible universe must run on math, but I feel safe in claiming that we’ve never imagined a universe, in fiction or through something like religion, which would fail to run on math.
To which you replied that this is a fact about me, not the universe. But I explicitly say that its not a fact about the universe! My evidence for this is the only evidence that could be relevant: my experience with literature, science fiction, talking to people, etc.
Nor is it relevant that science is full of people that say that something has to be true because they can’t imagine the world otherwise. Again, I’m not making a claim about the world, I’m making a claim about the way we have imagined, or now imagine the world to be. I would be very happy to be pointed toward a hypothetical universe that isn’t subject to mathematical analysis and which contains thinking animals.
So before we go on, please tell me what you think I’m claiming? I don’t wish to defend any opinions but my own.
Hen, I told you how I imagine such a universe, and you told me I couldn’t be imagining it! Maybe you could undertake not to gainsay further hypotheses.
I found your suggestion to be implausible for two reasons: first, I don’t think the idea of epistemically significant qualia is defensible, and second, even on the condition that it is, I don’t think the idea of a universe of nothing but a single quale (one having epistemic significance) is defensible. Both of these points would take some time to work out, and it struck me in our last exchange that you had neither the patience nor the good will to do so, at least not with me. But I’d be happy to discuss the matter if you’re interested in hearing what I have to say.
So before we go on, please tell me what you think I’m claiming?
You said:
I just also think it’s a necessary fact.
I’m not sure what you mean by “necessary”, but the most obvious interpretation is that you think it’s necessarily impossible for the world to not be run by math or at least for humans to understand a world that doesn’t.
it’s [probably] impossible for humans to understand a world that [isn’t subject to mathematical analysis].
This is my claim, and here’s the thought: thinking things are natural, physical objects and they necessarily have some internal complexity. Further, thoughts have some basic complexity: I can’t engage in an inference with a single term.
Any universe which would not in principle be subject to mathematical analysis is a universe in which there is no quantity of anything. So it can’t, for example, involve any space or time, no energy or mass, no plurality of bodies, no forces, nothing like that. It admits of no analysis in terms of propositional logic, so Bayes is right out, as is any understanding of causality. This, it seems to me, would preclude the possibility of thought altogether. It may be that the world we live in is actually like that, and all its multiplicity is merely the contribution of our minds, so I won’t venture a claim about the world as such. So far as I know, the fact that worlds admit of mathematical analysis is a fact about thinking things, not worlds.
thinking things are natural, physical objects and they necessarily have some internal complexity. Further, thoughts have some basic complexity: I can’t engage in an inference with a single term.
What do you mean by “complexity”? I realize you have an intuitive idea, but it could very well be that your idea doesn’t make sense when applied to whatever the real universe is.
Any universe which would not in principle be subject to mathematical analysis is a universe in which there is no quantity of anything.
Um, that seems like a stretch. Just because some aspects of the universe are subject to mathematical analysis doesn’t necessarily mean the whole universe is.
What do you mean by “complexity”? I realize you have an intuitive idea, but it could very well be that your idea doesn’t make sense when applied to whatever the real universe is.
For my purposes, complexity is: involving (in the broadest sense of that word) more than one (in the broadest sense of that word) thing (in the broadest sense of that word). And remember, I’m not talking about the real universe, but about the universe as it appears to creatures capable of thinking.
Um, that seems like a stretch. Just because some aspects of the universe are subject to mathematical analysis doesn’t necessarily mean the whole universe is.
I think it does, if you’re granting me that such a world could be distinguished into parts. It doesn’t mean we could have the rich mathematical understanding of laws we do now, but that’s a higher bar than I’m talking about.
You can always “use” analysis the issue is whether it gives you correct answers. It only gives you the correct answer if the universe obeys certain axioms.
Well, this gets us back to the topic that spawned this whole discussion: I’m not sure we can separate the question ‘can we use it’ from ‘does it give us true results’ with something like math. If I’m right that people always have mostly true beliefs, then when we’re talking about the more basic ways of thinking (not Aristotelian dynamics, but counting, arithmetic, etc.) the fact that we can use them is very good evidence that they mostly return true results. So if you’re right that you can always use, say, arithmetic, then I think we should conclude that a universe is always subject to analysis by arithmetic.
You may be totally wrong that you can always use these things, of course. But I think you’re probably right and I can’t make sense of any suggestion to the contrary that I’ve heard yet.
That is a fact about you, not a fact about the universe. Nobody could imagine light being both a particle and a wave, for example, until their study of nature forced them to.
People could imagine such a thing before studying nature showed they needed to; they just didn’t. I think there’s a difference between a concept that people only don’t imagine, and a concept that people can’t imagine. The latter may mean that the concept is incoherent or has an intrinsic flaw, which the former doesn’t.
In the interest of not having this discussion degenerate into an argument about what “could” means, I would like to point out that your and hen’s only evidence that you couldn’t imagine a world that doesn’t run on math is that you haven’t.
For one thing, “math” trivially happens to run on world, and corresponds to what happens when you have a chain of interactions. Specifically to how one chain of physical interactions (apples being eaten for example) combined with another that looks dissimilar (a binary adder) ends up with conclusion that apples were counted correctly, or how the difference in count between the two processes of counting (none) corresponds to another dissimilar process (the reasoning behind binary arithmetic).
As long as there’s any correspondences at all between different physical processes, you’ll be able to kind of imagine that world runs on world arranged differently, and so it would appear that world “runs on math”.
If we were to discover some new laws of physics that were producing incalculable outcomes, we would just utilize those laws in some sort of computer and co-opt them as part of “math”, substituting processes for equivalent processes. That’s how we came up with math in the first place.
edit: to summarize, I think “the world runs on math” is a really confused way to look at how world relates to the practice of mathematics inside of it. I can perfectly well say that the world doesn’t run on math any more than the radio waves are transmitted by mechanical aether made of gears, springs, and weights, and have exact same expectations about everything.
“There is non trivial subset of maths whish describes physical law” might be better way of stating it
It seems to me that as long as there’s anything that is describable in the loosest sense, that would be taken to be true.
I mean, look at this, some people believe literally that our universe is a “mathematical object”, what ever that means (tegmarkery), and we haven’t even got a candidate TOE that works.
edit: I think the issue is that Morpheus confuses “made of gears” with “predictable by gears”. Time is not made of gears, and neither are astronomical objects, but a clock is very useful nonetheless.
I don’t see why “describable” would necessarily imply “describable mathematically”. I can imagine a qualia only universe,and I can imagine the ability describe qualia. As things stand, there are a number of things that can’t be described mathematically
Example?
Qualia, the passage of time, symbol grounding..
Absolutely, it’s a fact about me, that’s my point. I just also think it’s a necessary fact.
What’s your evidence for this? Keep in mind that the history of science is full of people asserting that X has to be the case because they couldn’t imagine the world being otherwise, only for subsequent discoveries to show that X is not in fact the case.
Name three (as people often say around here).
Well, the most famous (or infamous) is Kant’s argument the space must be flat (in the Euclidean sense) because the human mind is incapable of imagining it to be otherwise.
Another example was Lucretius’s argument against the theory that the earth is round: if the earth were round and things fell towards its center than in which direction would an object at the center fall?
Not to mention the standard argument against the universe having a beginning “what happened before it?”
I don’t intend to bicker, I think your point is a good one independently of these examples. In any case, I don’t think at least the first two of these examples of the phenomenon you’re talking about.
I think this comes up in the sequences as an example of the mind-projection fallacy, but that’s not right. Kant did not take himself to be saying anything about the world outside the mind when he said that space was flat. He only took himself to be talking about the world as it appears to us. Space, so far as Kant was concerned, was part of the structure of perception, not the universe. So in the Critique of Pure Reason, he says:
So Kant is pretty explicit that he’s not making a claim about the world, but about the way we percieve it. Kant would very likely poke you in chest and say “No you’re committing the mind-projection fallacy for thinking that space is even in the world, rather than just a form of perception. And don’t tell me about the mind-projection fallacy anyway, I invented that whole move.”
This also isn’t an example, because the idea of a spherical world had in fact been imagined in detail by Plato (with whom Lucretius seems to be arguing), Aristotle, and many of Lucretius’ contemporaries and predecessors. Lucretius’ point couldn’t have been that a round earth is unimaginable, but that it was inconsistent with an analysis of the motions of simple bodies in terms of up and down: you can’t say that fire is of a nature to go up if up is entirely relative. Or I suppose, you can say that but you’d have to come up with a more complicated account of natures.
And in particular he claimed that this showed it had to be Euclidean because humans couldn’t imagine it otherwise. Well, we now know it’s not Euclidean and people can imagine it that way (I suppose you could dispute this, but that gets into exactly what we mean by “imagine” and attempting to argue about other people’s qualia).
No, he never says that. Feel free to cite something from Kant’s writing, or the SEP or something. I may be wrong, but I just read though the Aesthetic again, and I couldn’t find anything that would support your claim.
EDIT: I did find one passage that mentions imagination:
I’ve edited my post accordingly, but my point remains the same. Notice that Kant does not mention the flatness of space, nor is it at all obvious that he’s inferring anything from our inability to imagine the non-existence of space. END EDIT.
You gave Kant’s views about space as an example of someone saying ‘because we can’t imagine it otherwise, the world must be such and such’. Kant never says this. What he says is that the principles of geometry are not derived simply from the analysis of terms, nor are they empirical. Kant is very, very, explicit...almost annoyingly repetitive, that he is not talking about the world, but about our perceptive faculties. And if indeed we cannot imagine x, that does seem to me to be a good basis from which to draw some conclusions about our perceptive faculties.
I have no idea what Kant would say about whether or not we can imagine non-Euclidian space (I have no idea myself if we can) but the matter is complicated because ‘imagination’ is a technical term in his philosophy. He thought space was an infinite Euclidian magnitude, but Euclidian geometry was the only game in town at the time.
Anyway he’s not a good example. As I said before, I don’t mean to dispute the point the example was meant to illustrate. I just wanted to point out that this is an incorrect view of Kant’s claims about space. It’s not really very important what he thought about space though.
There’s a difference between “can’t imagine” in a colloquial sense, and actual inability to imagine. There’s also a difference between not being able to think of how something fits into our knowledge about the universe (for instance, not being able to come up with a mechanism or not being able to see how the evidence supports it) and not being able to imagine the thing itself.
There also aren’t as many examples of this in the history of science as you probably think. Most of the examples that come to people’s mind involve scientists versus noscientists.
See my reply to army above.
Hold on now, you’re pattern matching me. I said:
To which you replied that this is a fact about me, not the universe. But I explicitly say that its not a fact about the universe! My evidence for this is the only evidence that could be relevant: my experience with literature, science fiction, talking to people, etc.
Nor is it relevant that science is full of people that say that something has to be true because they can’t imagine the world otherwise. Again, I’m not making a claim about the world, I’m making a claim about the way we have imagined, or now imagine the world to be. I would be very happy to be pointed toward a hypothetical universe that isn’t subject to mathematical analysis and which contains thinking animals.
So before we go on, please tell me what you think I’m claiming? I don’t wish to defend any opinions but my own.
Hen, I told you how I imagine such a universe, and you told me I couldn’t be imagining it! Maybe you could undertake not to gainsay further hypotheses.
I found your suggestion to be implausible for two reasons: first, I don’t think the idea of epistemically significant qualia is defensible, and second, even on the condition that it is, I don’t think the idea of a universe of nothing but a single quale (one having epistemic significance) is defensible. Both of these points would take some time to work out, and it struck me in our last exchange that you had neither the patience nor the good will to do so, at least not with me. But I’d be happy to discuss the matter if you’re interested in hearing what I have to say.
You said:
I’m not sure what you mean by “necessary”, but the most obvious interpretation is that you think it’s necessarily impossible for the world to not be run by math or at least for humans to understand a world that doesn’t.
This is my claim, and here’s the thought: thinking things are natural, physical objects and they necessarily have some internal complexity. Further, thoughts have some basic complexity: I can’t engage in an inference with a single term.
Any universe which would not in principle be subject to mathematical analysis is a universe in which there is no quantity of anything. So it can’t, for example, involve any space or time, no energy or mass, no plurality of bodies, no forces, nothing like that. It admits of no analysis in terms of propositional logic, so Bayes is right out, as is any understanding of causality. This, it seems to me, would preclude the possibility of thought altogether. It may be that the world we live in is actually like that, and all its multiplicity is merely the contribution of our minds, so I won’t venture a claim about the world as such. So far as I know, the fact that worlds admit of mathematical analysis is a fact about thinking things, not worlds.
What do you mean by “complexity”? I realize you have an intuitive idea, but it could very well be that your idea doesn’t make sense when applied to whatever the real universe is.
Um, that seems like a stretch. Just because some aspects of the universe are subject to mathematical analysis doesn’t necessarily mean the whole universe is.
For my purposes, complexity is: involving (in the broadest sense of that word) more than one (in the broadest sense of that word) thing (in the broadest sense of that word). And remember, I’m not talking about the real universe, but about the universe as it appears to creatures capable of thinking.
I think it does, if you’re granting me that such a world could be distinguished into parts. It doesn’t mean we could have the rich mathematical understanding of laws we do now, but that’s a higher bar than I’m talking about.
You can always “use” analysis the issue is whether it gives you correct answers. It only gives you the correct answer if the universe obeys certain axioms.
Well, this gets us back to the topic that spawned this whole discussion: I’m not sure we can separate the question ‘can we use it’ from ‘does it give us true results’ with something like math. If I’m right that people always have mostly true beliefs, then when we’re talking about the more basic ways of thinking (not Aristotelian dynamics, but counting, arithmetic, etc.) the fact that we can use them is very good evidence that they mostly return true results. So if you’re right that you can always use, say, arithmetic, then I think we should conclude that a universe is always subject to analysis by arithmetic.
You may be totally wrong that you can always use these things, of course. But I think you’re probably right and I can’t make sense of any suggestion to the contrary that I’ve heard yet.
One could mathematically describe things not analysable by arithmetic, though...
Fair point, arithmetic’s not a good example of a minimum for mathematical description.