@@michaeldraiden9603 questions such as "what is the purpose of pure mathematics?", or "what problem mathematics is trying to solve?", "what are the problems of mathematics?". To me the meaning of "deeper questions" is obvious.
I am glad there are philosophers who are interested in maths. However, I hope that in the future we can understand philosophy from a mathematical context. I would like to see more mathematicians interested in philosophy. I doubt there are many philosophers who have the time to understand the maths deeply to make any philosophical claims of the limits of math.
Philosophers were the original mathematicians. In fact it was Pythagoras who coined the word philosophy. They recognized that math was just the application of logic and approached it from a philosophical standpoint rather than simply regarding its utility
There is actually mathematical philosophy--- using mathematics to solve philosophical problems like the foundations of mathematics itself or what is set and its classes? Then there's philosophy of mathematics obviously still technical but with great emphasis on abstraction and uncovering underlying assumptions being overlooked.
What Silvia notes is that in the biggest scheme of things, mathematical knowledge is very simplistic in the bigger picture. A mathematical analysis is hard, but an ethical analysis is harder. What makes the mathematical analysis sometimes seem harder is that it presumably has a single answer, and hence if you can't put the peg into the circle, you lose. The fact that an ethical analysis does not necessarily have a single answer makes it, in a sense, much harder, if done right. That's why philosophical problems, when tackled by competent folks, bring you to places of epistemological difficulty for which mathematical problems pale in comparison. As she says, an ethical problem may not have a universal solution as might be found in a typical math problem. Kind of makes math sound rather simplistic in comparison, doesn't it?
@Tracchofyre math is invented for our reality but will eventually fails as there might be a reality out there that doesnt persue thinking,or logic nor. You might say we would be able to change math. But the problem is that math would keep changing but we would thn invent an relative derrivative. But that will fail when we end up with 6=0. So what im trying to prove is that philosophy especially on ethics is fugazi
@@kingfarouk4876 The idea that mathematics is "invented for our reality" is a claim that I've never seen a convincing substantiation for. Indeed, even if you take an intuitionistic standpoint, that mathematical knowledge is a priori is still accepted.
I think an interview like this should basically present as a no-op. Mathematics and philosophy are (IMO) topologically identical. I have no proof of this of course, but if it's true, it should become pretty apparent that something like ethics and mathematics are 1:1 and just be totally uninteresting of a statement. It should be as unsurprising as a boulder rolling down a hill.
@@ironmagma I see it as an applied philosophy and a means of knowledge that instead is comprised of letters but of numbers to get as clear an approach as possible rather than through words. But yet math is a language itself, which I also find weird.
In a way, mathematics is often nothing more than a kind of game, and depending on the choice of rules mathematicians start off with, strange phenomena can occur. For example, if they want, mathematicians can choose to start with axioms that permit different kinds of infinity -- not just the infinity of counting 1, 2, 3, ... nor just the infinity of all the decimal expansions 0.abcdefg... (for example, 0.31415...) but other infinities too. But those extra infinities aren't at all necessary. Mathematicians can elect not to work with them or any other initial set of rules if they don't want -- perhaps for philosophical reasons or for greater tractability or on a whim. The pluralistic tenor of math that Dr. Jonas mentions in the video comes from the freedom mathematicians have to play around with math's foundational rules.
That is so kool. Connecting abstract mathematics to the metaphysics. Mathematics and the empirical world mmm mmm. I’ve been in the metaphysics with my abstract mathematical ideas. 🥰
Someone explain how philosophy is related to higher mathematics? This seems like reaching because we already know we can't have proofs for everything in math.
We don't know that. We know that for any consistent formal system that interprets a bit of arithmetic, there are questions unanswerable in that system. But as Gödel himself emphasised, this doesn't mean that we do not have good reasons for accepting new axioms that decide such questions. Gödel himself believed that every mathematical problem should be solvable (read his paper "What is Cantor's Continuum hypothesis?" and his 1951 Gibbs lecture). For example, Hugh Woodin is working on a project that, if successful, would decide the continuum hypothesis, even though CH is formally independent from ZFC (if ZFC is consistent).
Maths aka mathematics is just a language. With it you can neglect, diminuize, exaggerate as well as make up things just like with any other language. Therefore there is no philosophy of maths. Maths is the most synonymous/the least homonymous language. This is what makes it different from the other languages/terminologies we use. We can only use the language mathematics (and by mathematics I mean the most basic form) to practice philosophy...asJudith Grabiner did in her lecture series "mathematics, philosophy and the 'real world'".
Even if one takes the supposition that "mathematics is just a language" seriously, this does not imply the conclusion "there is no philosophy of mathematics", unless you agree that the only philosophy there is is philosophy of language.
yes idealism not materialism. pythagoras, leibniz. and countless others haves said that reality must be interlinked if not one and the same. reality is as it is because of mathmatics. 0 isnt nothing it is pure potential in a infinte sea of 0s
Hi Silvia,,, this is a briliant endeavour, and i really respect that. And i may i kindly ask you, if you can please...I want to write my Dissertation on Mathematics and Metaphysics of God....something like...(Mathematical hypotheses as an axiomatic principle to attain God) and may you you help me around this area if pissible. Thanks so much!
Before you do any philosophy, try changing the typo in your comment from "pissible" to "possible." If not, your philosophy thesis paper is just "pissible" material. :) :).
Muslim philosophy values praxis more than ideas, so engineering is better than science and maths. Biomedical engineering may be the most ethical form of praxis. Applied mathematicians may be saints. Quantum mathematics and compatibilism also cohere with Islamic worldview
Set theory is a field of mathematics that attempts to define or describe all mathematical concepts in terms of groups of other "more primitive" concepts. For example, one way to think of the number 0 is to consider it a group of nothing, and one way to think of the number 1 is to consider it a group of just one thing, that thing being a group of nothing. From a set-theoretical perspective, all of math and logic end up being long, convoluted chains and structures of groups of groups of groups..., any level of which might hold random objects representing arbitrary mathematical ideas.
In my view, it's doomed to failure in the same sense that the attempt to "logicize mathematics" (i.e., Whitehead's Principia) was: it nevertheless lead to innumerable profound developments (contributing to the modern conception of logic as we know it, in fact).
@Calum Tatum Right, it was the "not yet" that AG responded to, which indicates what you articulate now in "moving towards". You then concede that philosophizing does not always is "moving towards" formalism. Well, so a possible differenc between your opinions could be: AG thinks it can nevertheless be reasoning although it can not be formalized. Your statement leaves that question open. What ever we conceive a formalism to be I'd consider it pretty safe to say there has to be non formal reasoning. .... However, I don't know what this has to do with the initial remark an "people slapping philosophy"
she mean old philosophers like plato want ethics and people and all the world to be as order as mathematics so they old philosophers make the divine commend theory etc..
I would not hasten to make so harsh a statement, given that the relationship of mathematics with all of philosophy in general has been a consideration of philosophers since the ancients.
![[Sub Thai] APT. - ROSÉ & Bruno Mars](http://i.ytimg.com/vi/bYjhzP8x_uc/mqdefault.jpg)
I wish the questions were a bit deeper as Silvia can articulate so well! Beautiful idea!
What do you mean by "deeper"?
@@michaeldraiden9603 questions such as "what is the purpose of pure mathematics?", or "what problem mathematics is trying to solve?", "what are the problems of mathematics?". To me the meaning of "deeper questions" is obvious.
I am glad there are philosophers who are interested in maths. However, I hope that in the future we can understand philosophy from a mathematical context. I would like to see more mathematicians interested in philosophy. I doubt there are many philosophers who have the time to understand the maths deeply to make any philosophical claims of the limits of math.
Philosophers were the original mathematicians. In fact it was Pythagoras who coined the word philosophy. They recognized that math was just the application of logic and approached it from a philosophical standpoint rather than simply regarding its utility
An absolutely brilliant acknowledgement!@@lancemannly
There is actually mathematical philosophy--- using mathematics to solve philosophical problems like the foundations of mathematics itself or what is set and its classes? Then there's philosophy of mathematics obviously still technical but with great emphasis on abstraction and uncovering underlying assumptions being overlooked.
' reasearching the evidential forest of using mathematics as a conceptual model' - great phrasing!
What Silvia notes is that in the biggest scheme of things, mathematical knowledge is very simplistic in the bigger picture. A mathematical analysis is hard, but an ethical analysis is harder. What makes the mathematical analysis sometimes seem harder is that it presumably has a single answer, and hence if you can't put the peg into the circle, you lose. The fact that an ethical analysis does not necessarily have a single answer makes it, in a sense, much harder, if done right. That's why philosophical problems, when tackled by competent folks, bring you to places of epistemological difficulty for which mathematical problems pale in comparison. As she says, an ethical problem may not have a universal solution as might be found in a typical math problem. Kind of makes math sound rather simplistic in comparison, doesn't it?
@Tracchofyre math is invented for our reality but will eventually fails as there might be a reality out there that doesnt persue thinking,or logic nor. You might say we would be able to change math. But the problem is that math would keep changing but we would thn invent an relative derrivative. But that will fail when we end up with 6=0. So what im trying to prove is that philosophy especially on ethics is fugazi
@@kingfarouk4876 The idea that mathematics is "invented for our reality" is a claim that I've never seen a convincing substantiation for. Indeed, even if you take an intuitionistic standpoint, that mathematical knowledge is a priori is still accepted.
Unfortunately the questions were not good enough to make this interview very informative.
the interviewer is simply trying to get this woman to ground her answers in language that a general audience might hear and understand.
I think an interview like this should basically present as a no-op. Mathematics and philosophy are (IMO) topologically identical. I have no proof of this of course, but if it's true, it should become pretty apparent that something like ethics and mathematics are 1:1 and just be totally uninteresting of a statement. It should be as unsurprising as a boulder rolling down a hill.
@@ironmagma I see it as an applied philosophy and a means of knowledge that instead is comprised of letters but of numbers to get as clear an approach as possible rather than through words. But yet math is a language itself, which I also find weird.
I wish the interviewer had asked her to expound a bit on her last point: for example, what does she mean by "higher order" questions.
Does anyone know of a better interview with her on the subject?
Kurt Gödel proved the incompleteness theorem of mathematics long ago. Is that what she is referring to?
In a way, mathematics is often nothing more than a kind of game, and depending on the choice of rules mathematicians start off with, strange phenomena can occur. For example, if they want, mathematicians can choose to start with axioms that permit different kinds of infinity -- not just the infinity of counting 1, 2, 3, ... nor just the infinity of all the decimal expansions 0.abcdefg... (for example, 0.31415...) but other infinities too. But those extra infinities aren't at all necessary. Mathematicians can elect not to work with them or any other initial set of rules if they don't want -- perhaps for philosophical reasons or for greater tractability or on a whim. The pluralistic tenor of math that Dr. Jonas mentions in the video comes from the freedom mathematicians have to play around with math's foundational rules.
Interesting, sounds something like the Curry-Howard isomorphism applied to philosophy or category theory of philosophy.
I agree that a better chosen set of questions would have resulted in an interview with more depth.
That is so kool. Connecting abstract mathematics to the metaphysics. Mathematics and the empirical world mmm mmm. I’ve been in the metaphysics with my abstract mathematical ideas. 🥰
Someone explain how philosophy is related to higher mathematics?
This seems like reaching because we already know we can't have proofs for everything in math.
We don't know that. We know that for any consistent formal system that interprets a bit of arithmetic, there are questions unanswerable in that system. But as Gödel himself emphasised, this doesn't mean that we do not have good reasons for accepting new axioms that decide such questions. Gödel himself believed that every mathematical problem should be solvable (read his paper "What is Cantor's Continuum hypothesis?" and his 1951 Gibbs lecture). For example, Hugh Woodin is working on a project that, if successful, would decide the continuum hypothesis, even though CH is formally independent from ZFC (if ZFC is consistent).
Thank you!
Yes, only recently.
Maths aka mathematics is just a language. With it you can neglect, diminuize, exaggerate as well as make up things just like with any other language.
Therefore there is no philosophy of maths. Maths is the most synonymous/the least homonymous language. This is what makes it different from the other languages/terminologies we use.
We can only use the language mathematics (and by mathematics I mean the most basic form) to practice philosophy...asJudith Grabiner did in her lecture series "mathematics, philosophy and the 'real world'".
Even if one takes the supposition that "mathematics is just a language" seriously, this does not imply the conclusion "there is no philosophy of mathematics", unless you agree that the only philosophy there is is philosophy of language.
she's very wise
Yay Silvia!
yes idealism not materialism. pythagoras, leibniz. and countless others haves said that reality must be interlinked if not one and the same. reality is as it is because of mathmatics. 0 isnt nothing it is pure potential in a infinte sea of 0s
Hi Silvia,,, this is a briliant endeavour, and i really respect that. And i may i kindly ask you, if you can please...I want to write my Dissertation on Mathematics and Metaphysics of God....something like...(Mathematical hypotheses as an axiomatic principle to attain God) and may you you help me around this area if pissible. Thanks so much!
Before you do any philosophy, try changing the typo in your comment from "pissible" to "possible." If not, your philosophy thesis paper is just "pissible" material. :) :).
You know a language is truly a language when it has to bow to pluralism and relativism, just a chip off the family block
🙏❤🙏❤🙏❤🙏❤🙏❤
Yeah, like studying Sonic Art with no prospects.
So, if you catch do ‘math’, you can always do ‘philosophy of math’
0:01 Dr.Kleiner.. Left's down..
Muslim philosophy values praxis more than ideas, so engineering is better than science and maths. Biomedical engineering may be the most ethical form of praxis. Applied mathematicians may be saints. Quantum mathematics and compatibilism also cohere with Islamic worldview
Good in Georgia Bad in UK
What is set mathematics?
Set theory is a field of mathematics that attempts to define or describe all mathematical concepts in terms of groups of other "more primitive" concepts. For example, one way to think of the number 0 is to consider it a group of nothing, and one way to think of the number 1 is to consider it a group of just one thing, that thing being a group of nothing. From a set-theoretical perspective, all of math and logic end up being long, convoluted chains and structures of groups of groups of groups..., any level of which might hold random objects representing arbitrary mathematical ideas.
@@declup Many thanks indeed for this explanation!
Villanelle, this is not a good disguise !
Some of these answers are total nonsense.
Max Trump U waterboy and professor of covfefe
The project to mathematize ethics and morals in a strict sense, is doomed to fail, just like the attempts to mathematize aesthetics.
In my view, it's doomed to failure in the same sense that the attempt to "logicize mathematics" (i.e., Whitehead's Principia) was: it nevertheless lead to innumerable profound developments (contributing to the modern conception of logic as we know it, in fact).
People slap philosophy onto any subject
@Calum Tatum not everything that can be reasoned can be formalized...
@Calum Tatum Right, it was the "not yet" that AG responded to, which indicates what you articulate now in "moving towards". You then concede that philosophizing does not always is "moving towards" formalism. Well, so a possible differenc between your opinions could be: AG thinks it can nevertheless be reasoning although it can not be formalized. Your statement leaves that question open. What ever we conceive a formalism to be I'd consider it pretty safe to say there has to be non formal reasoning. .... However, I don't know what this has to do with the initial remark an "people slapping philosophy"
stop dragging to ethics zz
What is she babbling about? How ethics is inspired by mathematics?
she mean old philosophers like plato want ethics and people and all the world to be as order as mathematics so they old philosophers make the divine commend theory etc..
I would not hasten to make so harsh a statement, given that the relationship of mathematics with all of philosophy in general has been a consideration of philosophers since the ancients.
@TheInstituteOfArtAndIdeas