I think many people’s default philosophical assumption (mine, certainly) is that mathematics are a discourse about the truth, a way to describe it, but they are not, fundamentally, the truth. Thus, in the vulgarisation efforts of professional quantum physicists (those who care to vulgarize), it is relatively common to find the admission that while they understand the maths of it well enough (I mean… hopefully, being professionals) they couldn’t say with any confidence that they understood the truth of it, that they understood, at an intimate level, the nature of what is going on. And I don’t think it’s simply playing cute or false modesty (although of course there will always be a bit of that, also) either. Now of course you could say, which would solve many problems, that there is no such thing as the “truth of it”, no “nature of what is going on”, that the mathematical formalism is really the alpha and omega, the totality of the knoweable and the meaningful as it relates to it. That position can certainly be argued with some semblance of reason, but it does feel like a defeat for the human mind.
Math referes to both a formalised language and a formalised mode of thought that are continuous with common language and mode of thought. What else could there be to learn about the truth of the matter for humans? Or even for other hypothetical minds (with their analogous ‘math’)? It seems like reifying the idea of “truth” to something that you don’t even know what it looks like or even if it’s a coherent or real idea, and you have very good reasons to think it’s not.
Math is what we use to create the best mental models of reality (any mental model will be formalised in the way of something we can reasonably call ‘math’), there’s nothing to comprehend outside of our models.
I’m using ‘math’ here to mean the mode of thought, not the representation of mathematical objects or the act of doing calculations.
But what is there to comprehend other than math? math is not a special way of thinking limited by ‘made-up’ mathy concepts, it’s just our thinking formalised. You can have a better or worse intuition about the meaning of mathematical objects, but the intuition is math.
Sure, math is limited, but the limitations of it are our limitations. There are no limitations inherent to math.
I mean: I just look at the world as it is, right, without preconceived notions, and it seems relatively evident to me that no: it cannot be fully explained and understood through math. Please describe to me, in mathematical terms, the differences between Spanish and Italian culture? Please explain to me, in mathematical terms, the role and function of sheriffs in medieval England. I could go on and on and on…
I mean, I was always referring to the point that you presented in your first comment. Your first comment was explicitly about how physicists are not “playing cute” when they say they don’t know if they understand “the truth of it, the nature of what is going on”. My point was that there’s nothing to understand outside of the math because there’s nothing to understand outside of your model of reality (which is math). And understanding the math is understanding what the math means (how reality appears to work to us) not just how to manipulate the mathematical objects.
About what you are saying now, how do you distinguish what is math or what isn’t for this:
Please describe to me, in mathematical terms, the differences between Spanish and Italian culture? Please explain to me, in mathematical terms, the role and function of sheriffs in medieval England
Philosophically : no. When you look at the planet Jupiter you don’t say : “Hum, oh: - there’s nothing to understand about this physical object beyond math, because my model of it, which is sufficient for a full understanding of its reality, is mathematic.” Or mabye you do—but then I think our differences might too deep to bridge. If you don’t—why don’t you with Jupiter, but would with an electron or a photon?
mmm, but the deepest intuition about the reasons behind the phenomenological properties of Jupiter (like its retrograde movement in the sky, or its colors) comes from intuition about the extrinsic meaning and intrinsic properties of mathematical models about Jupiter. How else?
Sure, it’s the perspective of observers, not reality in-and-of-itself, but that’s a fundamental limitation of any observer (regardless if they use math or don’t), and the model can be epistemically wrong, but that’s not the point (that’s not exclusively a property of math).
Just to be clear, I’ve always been speaking epistemically not ontologically.
Yes it does, what you understand (the intuition about how things work) is your model of the world, the model of the world is a representation of reality made based on empirical tests. You don’t have epistemic access to reality itself. That’s what I mean by saying that “understanding is within the map, not within the territory”.
What do you understand about reality outside of your model of reality?
Except that empirical tests don’t allow you to have direct epistemic access to ‘reality itself’ (direct knowledge about reality), because you need to interpret those tests to derive the models (the knowledge), and it’s not always determined wh. ‘Direct epistemic access to reality’ is the idealisation of knowing what reality would be like independently of any model (of course, not anything that is actually possible).
‘Understanding’ is a cognitive process and only exists within your cognition, the way you think your model represents reality is still part of the model itself, it doesn’t mean it’s wrong (although it predictably could be, at least it definitely is a simplification), it still explains what you observe after all, which is the thing you are directly acquainted with. The underlying reality can be completely unlike what it feels like from the inside, imagine that the substrate of ‘a’ reality is the transistors that simulate it or a holograph or ‘physical’ things, and someone inside it can’t tell which it is because the underlying physics can be any of those.
No I haven’t, but this is basic stuff(? Like, this type of skepticism has existed since the Antiquity in some schools of thought, and this is no different from the Cartesian doubt.
Descartes of course summon God as a solution to the problem. He chickened out >->
Forms of scepticism based on the directness of perception as revealed by the scientific world view are modern, in the sense of only going back a few centuries.
I think many people’s default philosophical assumption (mine, certainly) is that mathematics are a discourse about the truth, a way to describe it, but they are not, fundamentally, the truth. Thus, in the vulgarisation efforts of professional quantum physicists (those who care to vulgarize), it is relatively common to find the admission that while they understand the maths of it well enough (I mean… hopefully, being professionals) they couldn’t say with any confidence that they understood the truth of it, that they understood, at an intimate level, the nature of what is going on. And I don’t think it’s simply playing cute or false modesty (although of course there will always be a bit of that, also) either. Now of course you could say, which would solve many problems, that there is no such thing as the “truth of it”, no “nature of what is going on”, that the mathematical formalism is really the alpha and omega, the totality of the knoweable and the meaningful as it relates to it. That position can certainly be argued with some semblance of reason, but it does feel like a defeat for the human mind.
Math referes to both a formalised language and a formalised mode of thought that are continuous with common language and mode of thought. What else could there be to learn about the truth of the matter for humans? Or even for other hypothetical minds (with their analogous ‘math’)? It seems like reifying the idea of “truth” to something that you don’t even know what it looks like or even if it’s a coherent or real idea, and you have very good reasons to think it’s not.
Math is what we use to create the best mental models of reality (any mental model will be formalised in the way of something we can reasonably call ‘math’), there’s nothing to comprehend outside of our models.
Yeah… as they say: there’s often a big gap between smart and wise.
Smart people are usually good at math. Which means they have a strong emotional incentive to believe that math can explain everything.
Wise people are aware of the emotional incentives that fashion their beliefs, and they know to distrust them.
Ideally—one would be both: smart and wise.
I’m using ‘math’ here to mean the mode of thought, not the representation of mathematical objects or the act of doing calculations.
But what is there to comprehend other than math? math is not a special way of thinking limited by ‘made-up’ mathy concepts, it’s just our thinking formalised. You can have a better or worse intuition about the meaning of mathematical objects, but the intuition is math.
Sure, math is limited, but the limitations of it are our limitations. There are no limitations inherent to math.
I mean: I just look at the world as it is, right, without preconceived notions, and it seems relatively evident to me that no: it cannot be fully explained and understood through math. Please describe to me, in mathematical terms, the differences between Spanish and Italian culture? Please explain to me, in mathematical terms, the role and function of sheriffs in medieval England. I could go on and on and on…
I mean, I was always referring to the point that you presented in your first comment. Your first comment was explicitly about how physicists are not “playing cute” when they say they don’t know if they understand “the truth of it, the nature of what is going on”. My point was that there’s nothing to understand outside of the math because there’s nothing to understand outside of your model of reality (which is math). And understanding the math is understanding what the math means (how reality appears to work to us) not just how to manipulate the mathematical objects.
About what you are saying now, how do you distinguish what is math or what isn’t for this:
Philosophically : no. When you look at the planet Jupiter you don’t say : “Hum, oh: - there’s nothing to understand about this physical object beyond math, because my model of it, which is sufficient for a full understanding of its reality, is mathematic.” Or mabye you do—but then I think our differences might too deep to bridge. If you don’t—why don’t you with Jupiter, but would with an electron or a photon?
mmm, but the deepest intuition about the reasons behind the phenomenological properties of Jupiter (like its retrograde movement in the sky, or its colors) comes from intuition about the extrinsic meaning and intrinsic properties of mathematical models about Jupiter. How else?
Sure, it’s the perspective of observers, not reality in-and-of-itself, but that’s a fundamental limitation of any observer (regardless if they use math or don’t), and the model can be epistemically wrong, but that’s not the point (that’s not exclusively a property of math).
Just to be clear, I’ve always been speaking epistemically not ontologically.
What is to be understood outside your model of reality is reality. The model is an attempt to understand it.
Yeah but your intuition of how reality works is within the model that you’ve built from empirical results.
..in an attempt to understand reality.
Of course, but ‘intuition’ and ‘understanding’ are within the map, not within the territory.
Which still doesn’t show “there’s nothing to understand outside of your model of reality”
Yes it does, what you understand (the intuition about how things work) is your model of the world, the model of the world is a representation of reality made based on empirical tests. You don’t have epistemic access to reality itself. That’s what I mean by saying that “understanding is within the map, not within the territory”.
What do you understand about reality outside of your model of reality?
...except via
Except that empirical tests don’t allow you to have direct epistemic access to ‘reality itself’ (direct knowledge about reality), because you need to interpret those tests to derive the models (the knowledge), and it’s not always determined wh. ‘Direct epistemic access to reality’ is the idealisation of knowing what reality would be like independently of any model (of course, not anything that is actually possible).
‘Understanding’ is a cognitive process and only exists within your cognition, the way you think your model represents reality is still part of the model itself, it doesn’t mean it’s wrong (although it predictably could be, at least it definitely is a simplification), it still explains what you observe after all, which is the thing you are directly acquainted with. The underlying reality can be completely unlike what it feels like from the inside, imagine that the substrate of ‘a’ reality is the transistors that simulate it or a holograph or ‘physical’ things, and someone inside it can’t tell which it is because the underlying physics can be any of those.
Yes, but “direct” is the crux… you didn’t mention it before.
I said ‘reality itself’ though, as in ‘reality independently of any observer’. Whatever it’s fine, it’s an understandable confusion between us.
Have you read Kant or are you reinventing him?
No I haven’t, but this is basic stuff(? Like, this type of skepticism has existed since the Antiquity in some schools of thought, and this is no different from the Cartesian doubt.
Descartes of course summon God as a solution to the problem. He chickened out >->
Forms of scepticism based on the directness of perception as revealed by the scientific world view are modern, in the sense of only going back a few centuries.
Ok, I thought that some Buddhist schools and the Pyrrhonists had taught that type of skepticism, but it doesn’t seem to be so.