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.
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.
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 truly remarkable and uncanny how applicable math continues to be toward describing and predicting reality. That is my one hangup about believing fictional-mathematics is true. It's as if the fictional idea of isometry sprang out of the story we created, infecting our world with structure, order, and multiplicity the same way that mathematics uses structure, order, and multiplicity. Plus, one must consider that our conception of "2" isn't any less concrete than our conception of "tree" or "sun". A pair of apples has "2ness" just as much as it has "appleness" because both depend on a conceiver and categorizer to arrive at both descriptions. (And that pair of apples simultaneously lacks "2ness" from other conceptions and categories, such as from an atomic perspective or the bushel perspective).
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.
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.
The Fibonacci sequence can be seen in the seed counts of the Sunflower plant. The effects of gravity can be seen in the distances of a falling body from the Earth over time. The relationships are there to be interpreted. The social construct is that we choose to interpret them. Relationships involving Prime numbers and other abstract concepts are derived from concepts we can find in Nature as a rule. These are not social constructs but logical deductions and directed guesses at possible relationships. The precise symbolism and presentation of the mathematics is a matter of human creativity, but the subject matter itself is a possible mathematics. Each possible mathematics is a complete theory of some aspect of the idea universe, where the initial ideas were stolen from perception in a precise manner.
"If mathematics doesn't describe anything real, then why does it so well in describing so the natural world?" My argument to this is that mathematics as an entity predicts nothing and describes nothing, but very specific combinations of it can help us make predictions and get some empirical accuracy. Of an infinite potential number of terms and equations, only a very small handful of them predict these abstract entities with enough accuracy for them to map onto our experiences. That's a kind of category error, just because my hand is part of me doesn't make my hand sentient or intelligent, and in the same way just because Newton's laws of gravity predict (to a degree of accuracy) the movements of astronomical bodies doesn't mean that "mathematics" predicts them. If fictionalism sounds counter intuitive because statements like "There are infinitely many prime numbers" would be false as a statement, that would be because fictionalism maps on very well to the restricted language of E-Prime, and if the assertion were restated as "We deduce an infinite quantity of prime numbers" according to E-prime then that would not show any contradictions.
I was discussing the codification of Superman in this capacity with my son earlier today: Superman as a comic book does not exist in his youth, yet my son points out eventually DC has created a (Shazam) universe which is self aware and knows a Superman who lives in a world with comic Superman. Perhaps similarly, humanity drags math into a physical realm. That means during the Dark Ages, math might have felt immaterial, but today, in a world of computer sciences and physical ink to paper, numbers have an individual reality that exists in relationship with what it signifies. In this sense numbers are a construct, a symbol of what exists in material form, and its own relationship to that material form. This material superposition seems related with consciousness, and how the mind might function.
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.
Don't leave out that it can be a PERFECT analogy, where it can seem to predict what you see, but the variables used are not even causal. A child is using the scientific method with "The wheels on the bus go round and round." This song accurately and consistently describes everything the bus does exactly like math, but the child does not understand the bus, because wheels going round are not causal. The variables in gravity math are exactly like the wheels, they are not causal. So, what do we actually understand. Relativity uses transform equations to create itself on your paper by changing dimensions that are themselves theoretical, and the NON-transformed reality IS STILL THERE. It doesn't disappear by your paperwork. There is no theory dealing with the NON-transformed reality, and math led us there.
"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.
I thought about it for 1.2746 seconds and calculated that all mathematics is derivative and has 0% chance of existing as we approach infinity. - By the way, I love excellent fiction. That’s why I watch UA-cam videos.
I see the anti-philosophers are out in force in the comments! Fair enough - I get fed up with *some* philosophy, but a lot of the arguments being advanced here could be dismantled by philosophers in minutes. I am drawn to the tool model of mathematics - it certainly is a remarkable tool that can solve, explain and predict a great many phenomena (including in the real world). However, the tool-user can fall so in love with the tool that they imagine it to be an essential part of the universe. Imagine you use some kind of fabulous super-hammer/screwdriver/knife to build, mend and create a great many things. The tool-user starts to imagine that the tool is so essential to their interactions with the universe that they think they didn't actually invent the tool - it must have been an essential part of the universe, waiting to be discovered. Even more, the tool becomes an indispensable part of their world view, imagining that this tool is really the underlying principle of all the universe, so widely useful it is. And any matters that can't be readily addressed by the tool directly are simply described as having elements that ultimately, if broken down, reducible to parts that the tool can work on. Some enthusiasts get so enamoured of their tool that they imagine that it is a divine element of the universe, that God is the ultimate tool-maker and user, whose tools are ultimately the source of our own imitation tools. Others reject this religioius view as going a bit too far, but still indulge in a little tool-adulation in their private moments as they reflect on the supernal and universal application of the tool.
Mathematics requires abstraction. Abstraction translates reality to the realm of mathematics. Therefore it cannot be said that mathematics is the language of the reality. Mathematics does not even fit for counting unless we abstract from all differences of objects being count. Can we count cats and dogs together? Yes, at higher level of abstraction they all are animals. On the other hand every cat or dog is distinctly unique.
It's all in the pyramid one can draw on the moon of ones' thumb nail, but with aspect, still realizing the sky is almost the limit, pending the moon growing there, with the firmament adding substance to its' foundation, and the covenant finding soundness, or not expanding to a new event horizon to be justified by the critical mass of the present.
It seems unlikely to me. Consider Kepler's discovery. Mathematics was part and parcel of the discovery. Then consider Newton's extension of it. The extension provides an explanation that could not be arrived at in any other way than mathematics. To my mind, Mathematics is not primarily a language. Primarily, it is a way of finding knowledge. It is the way of seeking truth about the world of ideas; while science is the method of finding knowledge about the physical world. In fact, the language feature of mathematics is generally something appended after the mathematics is discovered as a pedogeological or mnemonic enhancement I would say. The mathematics itself often comes from consideration of properties and relationships found in Nature, at least as a starting point. Sometimes the properties and relationships are found by considering other mathematical structures. All of which is to say that mathematics seeks to understand, or at least rigorously describe, properties and relationships of any and all "things" of the world.
Math is logical relationships of quantity which always replicate. Quantity is dividing something into equivalent parts. So-called math does contain things which do not fit this description and are therefore as you say. But the basic rules of 2+2=4 and so forth are written into the fabric of the universe and we know they are real bc they always replicate. The other end of the spectrum is the cutting edge of science, currently exemplified by physics, which is always a search for the right metaphor to fit the data.
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
People are bias on the effectiveness of mathematics but the reason math is effective at modeling reality is being this the math that is rewarded financially, and in which money is poured. Of course this is gonna look like reality that the point of it. People designing finite element solver and concieving new numerical methods in doing so are doing it to solve real world problems with huge economic impact.
If you see advancement in math, you can see that there are tons of theories and object that does not apply to reality , but among all the object there are ones that fit a lot our reality , the reason being also that they where develop to solve physical problems. It is my opinion : But to me math is the product of our imagination collectively raffined. A piece of fiction that we all work to add to and train to make as coherent as possible or self sustaining. And in choosing specific axioms we discover that our imagination is constrained to the coherence of the previous work.
If you want to further justify mathematical fictionalism, you can turn to the issue of indiscernibility of identicals. If we really were to believe that mathematical objects were real, then we would have accept that two objects are the same iff they share all the same properties. However, if you have taken any model theory, you would know that some objects (within a language structure) that we would like to consider to be distinct, have all the same properties. For example in the language of rings, within the complex numbers i, and -i share all the same ring theoretic properties. However, if we were to accept that mathematical objects were in fact real, then i = -i which is a huge problem for mathematicians. You can avoid, this issue by simply being a nominalistic structuralist, people who only cares about the structural properties of mathematical theories and are agnostic to the ontology of the actual objects they describe.
Why can't we just assign -i some property that distinguishes from i? I don't know much relevant model theory so this question may not make any sense, but why can't we just define a complex number as an ordered pair of numbers, a radius and angle (with some limitation on the angle) and say i is number with an angle of pi/2, while -i has an angle of 3pi/2 (or whatever branch you wish it to be). Then there are different properties through rotations.
The only thing that shakes my belief that mathematics isn’t ‘real’ is how chat gpt was going through the arguments (initiated by philosophers) against maths being that. My stance is firm though. It exists even if we didn’t discover it. If anything ever exists, it plays by the rules of mathematics… that’s my take anyway.
There is no such thing as a sound proof . Proof of maths or proof that your words hold meaning. Whether you believe in this "Truth" or not won’t change anything, but claims of absolute knowledge shows that you might have an immature/delusional mind. Presuppositions are absolute statements, their circularity goes against the concept of soundness.
The primative will defend and resist evolution as long as biological computation allows. As a wild animal becomes domesticated through methods of neurolinguistic memory, so does the human grasp the language inheritated.
Mathematics is a POWERFUL tool! And personally, I think it's best that we just leave it there! Because we haven't evolved far enough, to even fully make sense of Reality! Let alone to make a bold claim about the fundamental nature of it! Currently, according to the Lambda-CDM model, we can only perceive approximately 4% of the Universe! Sure... Our models might be wrong but either way, this indicates that we still have a long... LONG way to go, before we can even make such claims that the Universe is "mathematical". We have to learn to WALK guys... Before we can run!!
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?
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.
I get that you don't like the word fiction and its connotation, but "fiction" is an accurate word to describe something that is produced by the human mind that is separate from the physical world.
Quine from the video actually talked about this - I think in the debates they refer to them as "Social Facts"; conventions which only exist in the minds of humans, but are made real because humans act on them. For example Microsoft the company isn't real and you can't touch it. There are buildings and products owned by the company, and people who work for it, but the company itself is imaginary. Yet if you steal from them, Microsoft will send you to jail via its lawyers. It's useful to act like it exists.
"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.
@@HariChera If a tree falls on you it will likely kill you. You can drown in an ocean. Get too close to a star and you'll burn. Ideas on the other hand cannot fall on you, drown you or burn you. It follows that trees, oceans and stars cannot be ideas.
Thanks so much. I would not call myself a fictionalist. But this is the first time I've heard of them, and it's amazing because most of what you say about them is stuff I've thought for years. lol... Obviously math was invented as a tool. A way to describe how many of something you have. So 3x3=9 is not fiction. It's a way to describe reality in certain ways. But no, it's not something in and of itself. It's like a language. I always thought the idea that it was more then that was absurd. And I do think science these days uses it too much in some crazy ways. So maybe I am a kind of fictionalist. lol...
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 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.
Analytical Idealism is a horseshit FOOLosophy. Cantors Cult ruined much of Mathematics. Now it is Mythomagics. Measurement starts at 1. Counting starts at 0. Take 0 off the number line! - Shiban Lal Pandita, writer of PV Cell Mathematics
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.
Why are you so condecending and assuming the other party won't learn? @@tinkeringtim7999
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.
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.
Can't you construct equally valid mathematical systems with zero predictive power though?
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?
Lot of folks in the comments seem to have started writing before getting to the "criticisms" section of the video.
It is truly remarkable and uncanny how applicable math continues to be toward describing and predicting reality. That is my one hangup about believing fictional-mathematics is true. It's as if the fictional idea of isometry sprang out of the story we created, infecting our world with structure, order, and multiplicity the same way that mathematics uses structure, order, and multiplicity.
Plus, one must consider that our conception of "2" isn't any less concrete than our conception of "tree" or "sun". A pair of apples has "2ness" just as much as it has "appleness" because both depend on a conceiver and categorizer to arrive at both descriptions. (And that pair of apples simultaneously lacks "2ness" from other conceptions and categories, such as from an atomic perspective or the bushel perspective).
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.
1 + 1 + 1 = 3 is an illusion?
I like to think of this often.
Language is an elaborate fiction.
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.
The Fibonacci sequence can be seen in the seed counts of the Sunflower plant. The effects of gravity can be seen in the distances of a falling body from the Earth over time. The relationships are there to be interpreted. The social construct is that we choose to interpret them. Relationships involving Prime numbers and other abstract concepts are derived from concepts we can find in Nature as a rule. These are not social constructs but logical deductions and directed guesses at possible relationships. The precise symbolism and presentation of the mathematics is a matter of human creativity, but the subject matter itself is a possible mathematics. Each possible mathematics is a complete theory of some aspect of the idea universe, where the initial ideas were stolen from perception in a precise manner.
I'm surprised it's so controversial, if you see physics as a model of our observations, then it seems pretty similar to say that math is the same
"If mathematics doesn't describe anything real, then why does it so well in describing so the natural world?"
My argument to this is that mathematics as an entity predicts nothing and describes nothing, but very specific combinations of it can help us make predictions and get some empirical accuracy. Of an infinite potential number of terms and equations, only a very small handful of them predict these abstract entities with enough accuracy for them to map onto our experiences. That's a kind of category error, just because my hand is part of me doesn't make my hand sentient or intelligent, and in the same way just because Newton's laws of gravity predict (to a degree of accuracy) the movements of astronomical bodies doesn't mean that "mathematics" predicts them.
If fictionalism sounds counter intuitive because statements like "There are infinitely many prime numbers" would be false as a statement, that would be because fictionalism maps on very well to the restricted language of E-Prime, and if the assertion were restated as "We deduce an infinite quantity of prime numbers" according to E-prime then that would not show any contradictions.
Amazing video, very glad I found this channel
I was discussing the codification of Superman in this capacity with my son earlier today: Superman as a comic book does not exist in his youth, yet my son points out eventually DC has created a (Shazam) universe which is self aware and knows a Superman who lives in a world with comic Superman. Perhaps similarly, humanity drags math into a physical realm. That means during the Dark Ages, math might have felt immaterial, but today, in a world of computer sciences and physical ink to paper, numbers have an individual reality that exists in relationship with what it signifies. In this sense numbers are a construct, a symbol of what exists in material form, and its own relationship to that material form. This material superposition seems related with consciousness, and how the mind might function.
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.
Don't leave out that it can be a PERFECT analogy, where it can seem to predict what you see, but the variables used are not even causal. A child is using the scientific method with "The wheels on the bus go round and round." This song accurately and consistently describes everything the bus does exactly like math, but the child does not understand the bus, because wheels going round are not causal. The variables in gravity math are exactly like the wheels, they are not causal. So, what do we actually understand. Relativity uses transform equations to create itself on your paper by changing dimensions that are themselves theoretical, and the NON-transformed reality IS STILL THERE. It doesn't disappear by your paperwork. There is no theory dealing with the NON-transformed reality, and math led us there.
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.
I thought about it for 1.2746 seconds and calculated that all mathematics is derivative and has 0% chance of existing as we approach infinity.
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By the way, I love excellent fiction. That’s why I watch UA-cam videos.
I see the anti-philosophers are out in force in the comments! Fair enough - I get fed up with *some* philosophy, but a lot of the arguments being advanced here could be dismantled by philosophers in minutes.
I am drawn to the tool model of mathematics - it certainly is a remarkable tool that can solve, explain and predict a great many phenomena (including in the real world). However, the tool-user can fall so in love with the tool that they imagine it to be an essential part of the universe. Imagine you use some kind of fabulous super-hammer/screwdriver/knife to build, mend and create a great many things. The tool-user starts to imagine that the tool is so essential to their interactions with the universe that they think they didn't actually invent the tool - it must have been an essential part of the universe, waiting to be discovered. Even more, the tool becomes an indispensable part of their world view, imagining that this tool is really the underlying principle of all the universe, so widely useful it is. And any matters that can't be readily addressed by the tool directly are simply described as having elements that ultimately, if broken down, reducible to parts that the tool can work on.
Some enthusiasts get so enamoured of their tool that they imagine that it is a divine element of the universe, that God is the ultimate tool-maker and user, whose tools are ultimately the source of our own imitation tools. Others reject this religioius view as going a bit too far, but still indulge in a little tool-adulation in their private moments as they reflect on the supernal and universal application of the tool.
Mathematics requires abstraction. Abstraction translates reality to the realm of mathematics. Therefore it cannot be said that mathematics is the language of the reality. Mathematics does not even fit for counting unless we abstract from all differences of objects being count. Can we count cats and dogs together? Yes, at higher level of abstraction they all are animals. On the other hand every cat or dog is distinctly unique.
It's all in the pyramid one can draw on the moon of ones' thumb nail, but with aspect, still realizing the sky is almost the limit, pending the moon growing there, with the firmament adding substance to its' foundation, and the covenant finding soundness, or not expanding to a new event horizon to be justified by the critical mass of the present.
It seems unlikely to me. Consider Kepler's discovery. Mathematics was part and parcel of the discovery. Then consider Newton's extension of it. The extension provides an explanation that could not be arrived at in any other way than mathematics.
To my mind, Mathematics is not primarily a language. Primarily, it is a way of finding knowledge. It is the way of seeking truth about the world of ideas; while science is the method of finding knowledge about the physical world.
In fact, the language feature of mathematics is generally something appended after the mathematics is discovered as a pedogeological or mnemonic enhancement I would say. The mathematics itself often comes from consideration of properties and relationships found in Nature, at least as a starting point. Sometimes the properties and relationships are found by considering other mathematical structures. All of which is to say that mathematics seeks to understand, or at least rigorously describe, properties and relationships of any and all "things" of the world.
Math is logical relationships of quantity which always replicate. Quantity is dividing something into equivalent parts. So-called math does contain things which do not fit this description and are therefore as you say. But the basic rules of 2+2=4 and so forth are written into the fabric of the universe and we know they are real bc they always replicate. The other end of the spectrum is the cutting edge of science, currently exemplified by physics, which is always a search for the right metaphor to fit the data.
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!
People are bias on the effectiveness of mathematics but the reason math is effective at modeling reality is being this the math that is rewarded financially, and in which money is poured. Of course this is gonna look like reality that the point of it.
People designing finite element solver and concieving new numerical methods in doing so are doing it to solve real world problems with huge economic impact.
If you see advancement in math, you can see that there are tons of theories and object that does not apply to reality , but among all the object there are ones that fit a lot our reality , the reason being also that they where develop to solve physical problems.
It is my opinion :
But to me math is the product of our imagination collectively raffined.
A piece of fiction that we all work to add to and train to make as coherent as possible or self sustaining.
And in choosing specific axioms we discover that our imagination is constrained to the coherence of the previous work.
1 + 1 + 1 = 3 and the area of a square is R^2, I invite you to explain to me how that is imagination?
If you want to further justify mathematical fictionalism, you can turn to the issue of indiscernibility of identicals. If we really were to believe that mathematical objects were real, then we would have accept that two objects are the same iff they share all the same properties. However, if you have taken any model theory, you would know that some objects (within a language structure) that we would like to consider to be distinct, have all the same properties. For example in the language of rings, within the complex numbers i, and -i share all the same ring theoretic properties. However, if we were to accept that mathematical objects were in fact real, then i = -i which is a huge problem for mathematicians. You can avoid, this issue by simply being a nominalistic structuralist, people who only cares about the structural properties of mathematical theories and are agnostic to the ontology of the actual objects they describe.
Why can't we just assign -i some property that distinguishes from i? I don't know much relevant model theory so this question may not make any sense, but why can't we just define a complex number as an ordered pair of numbers, a radius and angle (with some limitation on the angle) and say i is number with an angle of pi/2, while -i has an angle of 3pi/2 (or whatever branch you wish it to be). Then there are different properties through rotations.
The only thing that shakes my belief that mathematics isn’t ‘real’ is how chat gpt was going through the arguments (initiated by philosophers) against maths being that. My stance is firm though. It exists even if we didn’t discover it. If anything ever exists, it plays by the rules of mathematics… that’s my take anyway.
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
semantics
There is no such thing as a sound proof . Proof of maths or proof that your words hold meaning.
Whether you believe in this "Truth" or not won’t change anything, but claims of absolute knowledge shows that you might have an immature/delusional mind.
Presuppositions are absolute statements, their circularity goes against the concept of soundness.
It is.
Math exists without us, one could say it exists more than us.
As for models, all models are wrong, some are useful.
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
The primative will defend and resist evolution as long as biological computation allows. As a wild animal becomes domesticated through methods of neurolinguistic memory, so does the human grasp the language inheritated.
Mathematics is a POWERFUL tool! And personally, I think it's best that we just leave it there! Because we haven't evolved far enough, to even fully make sense of Reality! Let alone to make a bold claim about the fundamental nature of it!
Currently, according to the Lambda-CDM model, we can only perceive approximately 4% of the Universe! Sure... Our models might be wrong but either way, this indicates that we still have a long... LONG way to go, before we can even make such claims that the Universe is "mathematical".
We have to learn to WALK guys... Before we can run!!
What else could it be? Is a creation, as every piece or art 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?
No fictionalist is an honest scientist
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.
I get that you don't like the word fiction and its connotation, but "fiction" is an accurate word to describe something that is produced by the human mind that is separate from the physical world.
Quine from the video actually talked about this - I think in the debates they refer to them as "Social Facts"; conventions which only exist in the minds of humans, but are made real because humans act on them.
For example Microsoft the company isn't real and you can't touch it. There are buildings and products owned by the company, and people who work for it, but the company itself is imaginary.
Yet if you steal from them, Microsoft will send you to jail via its lawyers. It's useful to act like it exists.
It is
It has love stories better than Twilight. (Not that is hard)
"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.
Yes, that's the case
Trees oceans and stars likewise do not exist independent of human mind either. They're ideas of names and forms.
@@HariChera If a tree falls on you it will likely kill you. You can drown in an ocean. Get too close to a star and you'll burn. Ideas on the other hand cannot fall on you, drown you or burn you. It follows that trees, oceans and stars cannot be ideas.
Thanks so much. I would not call myself a fictionalist. But this is the first time I've heard of them, and it's amazing because most of what you say about them is stuff I've thought for years. lol... Obviously math was invented as a tool. A way to describe how many of something you have. So 3x3=9 is not fiction. It's a way to describe reality in certain ways. But no, it's not something in and of itself. It's like a language. I always thought the idea that it was more then that was absurd. And I do think science these days uses it too much in some crazy ways. So maybe I am a kind of fictionalist. lol...
map vs terrain
Is then logic a fiction?
Yes
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?
how does this video only have 50 views
An idea that is equally interesting as it is useless.
Basically Buddhism.
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.
Him agreeing on axioms to prove or describe a theory without numbers is literally just math.
Bleem
Those who consider math as fiction will be thrown in hell by God.
😱
Analytical Idealism is a horseshit FOOLosophy.
Cantors Cult ruined much of Mathematics.
Now it is Mythomagics.
Measurement starts at 1.
Counting starts at 0.
Take 0 off the number line!
- Shiban Lal Pandita, writer of PV Cell Mathematics
A very rigid and dry poetry.
Nonsense