It seems a bit like splitting hairs to me. For example, you can model a physical phenomenon using math as an abstract descriptor, but it's just that, an abstract descriptor... and typically of an incomplete system that we use as tool to make reasonably accurate predictions. Each prediction typically at a defined magnification. There is a concrete thing as "two oranges", and counting oranges as discrete objects is a perfectly valid model, but only at one magnification; the model doesn't describe the size/mass of the oranges, or zoom in and describe its constituent parts at a cellular level. I could be wrong, but without looking into this philosophy further, I don't think most mathematicians would argue with most of these tenets.
@@tinkeringtim7999 Thing is math has a crazy strong internal-consistency requirement and is also mapped to actual processes, Harry Potter not so much. Take the two oranges. If you then get another three oranges, that'll make five, same as if you originally had three and then got another two: the order in which you "add" things to your pile doesn't matter, and basic math captures this relation as a property of addition. The internal consistency requirement means you can then use math to figure out consequences of this property which will also hold for orange-counting.
@user-sl6gn1ss8p lol. No it doesn't have such checks. I think you learned the ideology of post Hilbert maths but not much about the reality of mathematics. "crazy strong consistency checks" - tell that to the Banach-Tarski 'paradox' with is ONLY not a proof by contradiction of Hilbert's school because of ideology. It's not a paradox, it's a proof. I could give many more, I just don't think you have any interest in learning or are at a suitable level to learn. Mathamatics and mathamatical formalims are not necessarily consistent with anything other than their own axiomatic basis, if you really believe there is a tree of mathamatics which is consistent and has been checked you should get a refund for whatever maths training you took. Your insights into mathamatics betrays a naivety that's almost cute - only problem is you still think you know what you have barely scratched the surface of.
@@tinkeringtim7999 I hope you do realize that: 1. I said "crazy strong", not "absolute"; 2. The context was a comparison with Harry Potter; 3. Math does, in fact, work for a lot of contexts Harry Potter doesn't; 4. You're way overreaching from a single youtube comment, in an ironically naïve way to boot.
Mathematics is its own entity, you can explore mathematical questions about mathematical objects that are in essence "ideas." I think marh is so useful in science because studying science requires the human mind. Math is like a ethereal hunt for the consequences of our own logical deductions.
I dare anyone to describe Newtonian physics without maths. Forget universal constants like G, I don't think it's even possible to say that gravity diminishes 4 times if you go twice far, without invoking numbers.
Ok, then. Laws of motion: 1. No force, nothing changes. 2. I define force to mean how massive something is by how much it is changing speed. 3. A force acting in one direction has a fellow identical force acting the opposite direction. Law of gravity: Two hypothetical point masses with no actual volume are attracted to one another. Imagine two objects with an imaginary sphere around them of the same arbitrary size. The more mass the proportionally brighter they shine. Then extend their spheres until they precisely intersect with one another. As the imaginary spheres expand they dim proportionally to the area of the sphere. The brightness at the point of contact precisely describes the gravitational attraction for both bodies. There. Done.
@davidmurphy563 Very nice! Point taken! Couple of things though - I'm not sure if concepts like "uniform sphere" and "area" can be well defined. Maybe sphere is all points equidistant from a center, but probably that needs distance, and area still. Maybe area is how many small dots you can fit on the surface, but that's not quite it - maybe somehow state the notion of limits. More difficult would be assigning the values to constants, say to know the ratio of gravitational and electromagnetic forces. But probably numbers and numeric notations (e.g. the decimal system) need not be part of the fiction.
@@jonathandawson3091 Well, this is an exercise of taking reality and grossly simplifying it. It's what physics does because it's useful. So we're in the domain of thought experiments here. So imagine two planets in a void. Now get rid of their dimensions so they have zero volume. It's not supposed to be reality, just a gross over-simplification of it throwing away things you don't need. The spheres are just imaginary and they're of any size you want. They are also of any brightness you want as long as they are proportional to their mass. So, if object A is twice as massive then it's twice as bright. Expand the spheres so the area is twice as big. You'll know this from the brightness. I mean, you can see this so it's surely defined. You could mock this up with basic equipment. When they intersect with each other (the points to the spheres) then they'll be a certain amount bright. This amount will tell you the relative gravitational attraction only, not the absolute amount. They could come together in an instant or over an eternity but the effect will be the same played back at different speeds. Hence the scalar quantity G. The reason for this is the asymmetry of scale. That's quantum. But yeah, if you want the amounts, you need to measure. That's not magic. Btw, did you notice the contradiction between the third law of motion and the law of gravitation? There's no opposite force. That's because in reality there is no force but Newton didn't know that.
@@davidmurphy563 What is speed? What does attraction mean? What does it mean to proportionally dim? I feel like "math" is a way to general term, and so you can always make a case that anything "uses" math. How do I refer to a "space" without invoking math. Does describing a space count as "math"? I'm not a philosopher, but I feel like math would just apply everywhere.
It is fiction in a very concrete way. It is identical to a shared illusion, and there are concrete proofs that it is not a necessary illusion. However, it is of such a nature that if enough people believe in it there is a sense in which it becomes "real". I've spent years researching the historical foundations. Let me know if you're interested to collab on a video.
This type of nonsense is not really helpful. I stopped after the superman reference. Notice how "math is fictional in real world, true in story, but very useful in reality". This statement does not work for any other type of fiction. Flying superman, Frodo, none of these "fictions" are useful in real world. So while symbols might not be "real", the uncanny usefulness in the real world makes math quite special compared to other fiction. Imagine five people throwing 7 rocks across the wall - and then you go and collect them. You will collect 35 rocks every single time. This property of mathematical reasoning coming into the world and building entire modern civilization may require a new word that is divorced from typical usage and typical related terms to fiction. Use of fiction carries connotations. Why don't we just then relegate math to a special corner where it is neither real nor fiction, but is simply...true.
Thanks man nice job this video is so well constructed, clear and structured. I’d be glad to see you further develop on the other mathematical ontological positions in the way you seem suited. Btw if you want subtitles they should probably fit better if they were a bit lower, and on a pure formal standpoint, you voice is good but you could maybe be more lively in the delivery as well as playing around with the image framing. Not an expert tho, just sharing impressions
I'm a mathematician, and this is not even wrong, just from the title alone. If mathematics were an elaborate fiction, first of all, then we wouldn't be able to apply it to numerous technological/generally practical situations. It would have no use. That would mean the world is fiction itself, which is a very rotten philosophical view -- somewhat tantamount to the simulation hypothesis. But this is empty pedantic meandering. What do you mean by "fiction"?
Only a true mathematician would ask to define the word. Math is made up but it also has incredible predictive power, so idk, maybe we aren't meant to understand it.
The easiest way to understand mathematical fictionalism is understanding that math is a human creation (a social construct). Social constructs aren't inherently bad, on a fundamental level social construct make human existence easier through shared definitions. For example, colors are social constructs but if I told you the sky changed colors from blue to black during mid-day it would communicate that there is dangerous weather coming and to go inside. In other words, the cells in your body don't care about exponentials they just divide, planets don't care about their mass they just move. Has understanding these things made human existence easier, YES! If humans didn't eat cooked meat all those years ago would pi exist? Has the idea of pi made human existence easier; OMG YES! However, there is something beautiful about the dedication humans have to explaining why cells divide and planets move. Also, its not that the phrase "There are infinitely many prime numbers" is false its just incoherent to non-homo-sapiens.
"if an assumption is falsified it cannot stand in math". If an assumption is falsified then _your argument is invalid_, the assumption is entirely unaffected; that is the very nature of axioms. Its clear you have studied neither mathamatics nor logic, it would be wise to recognise your current limits and learn rather than throw out misleading opinions in the form of factual claims.
@ no. I think you can have some basic learning first. Axiom is a specific term in logic. Assumption here is a daily concept. You don’t falsify an axiom. But you can falsify assumption about a piece of computation, in some cases by simply executing the computation.
@ Many people make the same kinds of mistakes like yours. When at this philosophical level of discussion, we are not interested in particular “logic systems” or their formalization. We are interested in at the meta level whether math can assert anything or is just a game of meaningless word. If you don’t know lambda calculus (LC) you can look it up. But basically, you can think of math as BOTH meaningless games since the rules (such as LC) are arbitrarily chosen (as long as they are of the same computational power), and meaningful assertions of exactly how these games may play out. It is the latter that makes math not “just fictions”.
@clementdato6328 I didn't make a mistake, you're just in the Dunning-kruger trap. You could've learned something if not enslaved to your ego, enjoy the little bubble.
As a working mathematician, good video! I like that you touched on the "unreasonable effectiveness of mathematics" but about the fictionalism part: the story world of mathematics is indeed constructed by axioms and definitions. The place whereath deviates from other forms of fiction is that it has predictive power and shows emergent patterns that are not obvious from the axioms. In this way math is less like a book and more akin to simulation? If you let your computer run a game does that count as fiction? In all senses, it is making up things but there are also ties to the initial conditions. In the case of mathematics, the initial conditions tie into the real world.
Mathematical objects are real and are probed by mathematical techniques much like subatomic particles are real and can be probed by physics experiments. The question of what that reality implies can differ, but if I can construct an object in front of you, how can you deny its existence?
"Nominalists argue that things like numbers, sets and functions don't exist independently of the human mind; are not part of reality in the way trees, oceans or stars are". Trees, oceans and stars exist independently of the human mind? Then that's at least three things which do. But three does not? Sounds implausible.
It is anti-philosophy. Philosophy is love of knowledge and wisdom. This idea of mathematical fictionalism is love of nonsense and stupidity - fine things to love for sure, but not when trying do do a bit of good science or metaphysics.
That's where anthropology comes in, is philosophy unique to homo-sapiens or is it just a side-effect of advanced reasoning skills due to our large brains?
It seems a bit like splitting hairs to me. For example, you can model a physical phenomenon using math as an abstract descriptor, but it's just that, an abstract descriptor... and typically of an incomplete system that we use as tool to make reasonably accurate predictions. Each prediction typically at a defined magnification. There is a concrete thing as "two oranges", and counting oranges as discrete objects is a perfectly valid model, but only at one magnification; the model doesn't describe the size/mass of the oranges, or zoom in and describe its constituent parts at a cellular level. I could be wrong, but without looking into this philosophy further, I don't think most mathematicians would argue with most of these tenets.
That makes mathamatics exist in the same sense Harry Potter exists (arguably actually HP has a stronger claim to existence).
@@tinkeringtim7999 Thing is math has a crazy strong internal-consistency requirement and is also mapped to actual processes, Harry Potter not so much.
Take the two oranges. If you then get another three oranges, that'll make five, same as if you originally had three and then got another two: the order in which you "add" things to your pile doesn't matter, and basic math captures this relation as a property of addition. The internal consistency requirement means you can then use math to figure out consequences of this property which will also hold for orange-counting.
@user-sl6gn1ss8p lol. No it doesn't have such checks. I think you learned the ideology of post Hilbert maths but not much about the reality of mathematics.
"crazy strong consistency checks" - tell that to the Banach-Tarski 'paradox' with is ONLY not a proof by contradiction of Hilbert's school because of ideology. It's not a paradox, it's a proof. I could give many more, I just don't think you have any interest in learning or are at a suitable level to learn.
Mathamatics and mathamatical formalims are not necessarily consistent with anything other than their own axiomatic basis, if you really believe there is a tree of mathamatics which is consistent and has been checked you should get a refund for whatever maths training you took.
Your insights into mathamatics betrays a naivety that's almost cute - only problem is you still think you know what you have barely scratched the surface of.
@@tinkeringtim7999 I hope you do realize that:
1. I said "crazy strong", not "absolute";
2. The context was a comparison with Harry Potter;
3. Math does, in fact, work for a lot of contexts Harry Potter doesn't;
4. You're way overreaching from a single youtube comment, in an ironically naïve way to boot.
Mathematics is its own entity, you can explore mathematical questions about mathematical objects that are in essence "ideas." I think marh is so useful in science because studying science requires the human mind. Math is like a ethereal hunt for the consequences of our own logical deductions.
I dare anyone to describe Newtonian physics without maths.
Forget universal constants like G, I don't think it's even possible to say that gravity diminishes 4 times if you go twice far, without invoking numbers.
Ok, then.
Laws of motion:
1. No force, nothing changes.
2. I define force to mean how massive something is by how much it is changing speed.
3. A force acting in one direction has a fellow identical force acting the opposite direction.
Law of gravity:
Two hypothetical point masses with no actual volume are attracted to one another. Imagine two objects with an imaginary sphere around them of the same arbitrary size. The more mass the proportionally brighter they shine. Then extend their spheres until they precisely intersect with one another. As the imaginary spheres expand they dim proportionally to the area of the sphere.
The brightness at the point of contact precisely describes the gravitational attraction for both bodies.
There. Done.
@davidmurphy563 Very nice! Point taken!
Couple of things though - I'm not sure if concepts like "uniform sphere" and "area" can be well defined. Maybe sphere is all points equidistant from a center, but probably that needs distance, and area still. Maybe area is how many small dots you can fit on the surface, but that's not quite it - maybe somehow state the notion of limits.
More difficult would be assigning the values to constants, say to know the ratio of gravitational and electromagnetic forces. But probably numbers and numeric notations (e.g. the decimal system) need not be part of the fiction.
@@jonathandawson3091 Well, this is an exercise of taking reality and grossly simplifying it. It's what physics does because it's useful. So we're in the domain of thought experiments here.
So imagine two planets in a void. Now get rid of their dimensions so they have zero volume. It's not supposed to be reality, just a gross over-simplification of it throwing away things you don't need. The spheres are just imaginary and they're of any size you want. They are also of any brightness you want as long as they are proportional to their mass. So, if object A is twice as massive then it's twice as bright.
Expand the spheres so the area is twice as big. You'll know this from the brightness. I mean, you can see this so it's surely defined. You could mock this up with basic equipment.
When they intersect with each other (the points to the spheres) then they'll be a certain amount bright.
This amount will tell you the relative gravitational attraction only, not the absolute amount. They could come together in an instant or over an eternity but the effect will be the same played back at different speeds. Hence the scalar quantity G.
The reason for this is the asymmetry of scale. That's quantum. But yeah, if you want the amounts, you need to measure. That's not magic.
Btw, did you notice the contradiction between the third law of motion and the law of gravitation? There's no opposite force. That's because in reality there is no force but Newton didn't know that.
@@davidmurphy563 What is speed? What does attraction mean? What does it mean to proportionally dim?
I feel like "math" is a way to general term, and so you can always make a case that anything "uses" math. How do I refer to a "space" without invoking math. Does describing a space count as "math"? I'm not a philosopher, but I feel like math would just apply everywhere.
@@davidmurphy563 ok what is speed?
It is fiction in a very concrete way. It is identical to a shared illusion, and there are concrete proofs that it is not a necessary illusion. However, it is of such a nature that if enough people believe in it there is a sense in which it becomes "real".
I've spent years researching the historical foundations.
Let me know if you're interested to collab on a video.
Language is an elaborate fiction.
This type of nonsense is not really helpful. I stopped after the superman reference. Notice how "math is fictional in real world, true in story, but very useful in reality". This statement does not work for any other type of fiction. Flying superman, Frodo, none of these "fictions" are useful in real world. So while symbols might not be "real", the uncanny usefulness in the real world makes math quite special compared to other fiction.
Imagine five people throwing 7 rocks across the wall - and then you go and collect them. You will collect 35 rocks every single time.
This property of mathematical reasoning coming into the world and building entire modern civilization may require a new word that is divorced from typical usage and typical related terms to fiction. Use of fiction carries connotations. Why don't we just then relegate math to a special corner where it is neither real nor fiction, but is simply...true.
Amazing video, very glad I found this channel
I like to think of this often.
Thanks man nice job this video is so well constructed, clear and structured.
I’d be glad to see you further develop on the other mathematical ontological positions in the way you seem suited.
Btw if you want subtitles they should probably fit better if they were a bit lower, and on a pure formal standpoint, you voice is good but you could maybe be more lively in the delivery as well as playing around with the image framing. Not an expert tho, just sharing impressions
Thanks!
Don’t need to watch this to know the premise is nonsense.
If you'd watch the video you'd know the arguments made don't support the title
I'm a mathematician, and this is not even wrong, just from the title alone.
If mathematics were an elaborate fiction, first of all, then we wouldn't be able to apply it to numerous technological/generally practical situations. It would have no use. That would mean the world is fiction itself, which is a very rotten philosophical view -- somewhat tantamount to the simulation hypothesis.
But this is empty pedantic meandering. What do you mean by "fiction"?
Only a true mathematician would ask to define the word.
Math is made up but it also has incredible predictive power, so idk, maybe we aren't meant to understand it.
The easiest way to understand mathematical fictionalism is understanding that math is a human creation (a social construct).
Social constructs aren't inherently bad, on a fundamental level social construct make human existence easier through shared definitions. For example, colors are social constructs but if I told you the sky changed colors from blue to black during mid-day it would communicate that there is dangerous weather coming and to go inside.
In other words, the cells in your body don't care about exponentials they just divide, planets don't care about their mass they just move. Has understanding these things made human existence easier, YES! If humans didn't eat cooked meat all those years ago would pi exist? Has the idea of pi made human existence easier; OMG YES! However, there is something beautiful about the dedication humans have to explaining why cells divide and planets move.
Also, its not that the phrase "There are infinitely many prime numbers" is false its just incoherent to non-homo-sapiens.
No fictionalist is an honest scientist
It is not fiction. It is computation. If an assumption can be decidably falsified, it cannot stand in math.
"if an assumption is falsified it cannot stand in math".
If an assumption is falsified then _your argument is invalid_, the assumption is entirely unaffected; that is the very nature of axioms.
Its clear you have studied neither mathamatics nor logic, it would be wise to recognise your current limits and learn rather than throw out misleading opinions in the form of factual claims.
@ no. I think you can have some basic learning first. Axiom is a specific term in logic. Assumption here is a daily concept.
You don’t falsify an axiom. But you can falsify assumption about a piece of computation, in some cases by simply executing the computation.
@clementdato6328 lol, you trying to school me is hilarious 😂
@ Many people make the same kinds of mistakes like yours. When at this philosophical level of discussion, we are not interested in particular “logic systems” or their formalization. We are interested in at the meta level whether math can assert anything or is just a game of meaningless word.
If you don’t know lambda calculus (LC) you can look it up. But basically, you can think of math as BOTH meaningless games since the rules (such as LC) are arbitrarily chosen (as long as they are of the same computational power), and meaningful assertions of exactly how these games may play out. It is the latter that makes math not “just fictions”.
@clementdato6328 I didn't make a mistake, you're just in the Dunning-kruger trap. You could've learned something if not enslaved to your ego, enjoy the little bubble.
If that were the case then we could give constants like pi or e any value we want
We can still change the base :p
As a working mathematician, good video! I like that you touched on the "unreasonable effectiveness of mathematics" but about the fictionalism part: the story world of mathematics is indeed constructed by axioms and definitions. The place whereath deviates from other forms of fiction is that it has predictive power and shows emergent patterns that are not obvious from the axioms. In this way math is less like a book and more akin to simulation? If you let your computer run a game does that count as fiction? In all senses, it is making up things but there are also ties to the initial conditions. In the case of mathematics, the initial conditions tie into the real world.
It is.
It is
Mathematical objects are real and are probed by mathematical techniques much like subatomic particles are real and can be probed by physics experiments. The question of what that reality implies can differ, but if I can construct an object in front of you, how can you deny its existence?
how does this video only have 50 views
"Nominalists argue that things like numbers, sets and functions don't exist independently of the human mind; are not part of reality in the way trees, oceans or stars are".
Trees, oceans and stars exist independently of the human mind? Then that's at least three things which do. But three does not? Sounds implausible.
Is then logic a fiction?
Yes
It is anti-philosophy. Philosophy is love of knowledge and wisdom. This idea of mathematical fictionalism is love of nonsense and stupidity - fine things to love for sure, but not when trying do do a bit of good science or metaphysics.
What if all of philosophy is just an elaborate fiction?
That's where anthropology comes in, is philosophy unique to homo-sapiens or is it just a side-effect of advanced reasoning skills due to our large brains?