Intro to the Philosophy of Mathematics (Ray Monk)
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- เผยแพร่เมื่อ 5 มิ.ย. 2021
- A good introduction to the philosophy of mathematics by Ray Monk. He considers the issue of the nature of mathematical truth - what mathematics is actually about - and discusses the views of Plato, Aristotle, Kant, Frege and Russell. What is mathematics about? Is mathematics something discovered or is it something invented or constructed by us? If numbers and mathematical objects are mere mental constructs, something invented by us, then why does mathematics work so well and seem to describe the world? On the other hand, if mathematical entities are "out there" in some sense waiting to be discovered, then what is their status and how do we get knowledge of them? After all, you can't see or touch numbers and other mathematical objects. And unlike ordinary empirical truths, mathematical truths seem to have a quite different and special status: they are a priori, necessary, eternal, universal, and absolutely certain. And this is why from the time of Plato onward, people have regarded mathematical truths as an ideal. In this talk, some of the ways in which philosophers have tried to account for the special nature of mathematical truth. (My Summary)
This is a re-upload from the other channel. Note, audio has been improved.
Another good introduction to the philosophy of mathematics: • What Are Numbers? Phil...
More advanced talk on philosophy of mathematics: • Philosophy of Mathemat...
#Philosophy #Epistemology #Mathematics
This lecture heavily influenced my decision to major in pure math at UC Berkeley. Thank you for such a captivating talk.
Wow, same here! Just declared last semester! I revisit this lecture on the regular haha
@@nataliekemper9193 What a small world haha I’ve been coming back to this for a few years now. Just transferred this semester!
best of luck to you! such a captivating concept.
@@sk_4142 so cool! Perhaps we’ll cross paths in class sometime (unless we already have lol)
Career choices after graduating or are you gonna be poor?
This lecture changed my view about what four cows are.
I think a cow is a four-legged animal...
What are four cows?
Is it four cows, or two pairs of cows? :)
@samueldeandrade8535 I think four cows are less than five and more than three, sandwiched in between; symbolically you could write the equation like this:
🐄 +🐄 + 🐄 + 🐄
How many legs do 4 Cows have?, And how many Gods?
Keep up the good work, you have beautiful content. Glad to see you back!
This is the best talk I've listened to on philosophy I've heard in a long long while. Clear, concise, a real gem. Thank you.
Great lecture. Thank you.
All objects are abstractions (including electrons, apples and planets. Existence and any "issness" is also an abstraction. It's about what those abstractions do, or what we can do with them. Actuality is a process. The problem is much bigger than just mathematical objects. Anything that can be meaningfuly spoken about in natural language is abstraction.
Yes, thank you! One of my loved lecture!
Had listened to this about 6 years ago and saved in my favourites playlist. Today I felt like listening to again, but did not find it in my playlist. Means it was deleted.
Thanks for reuploading this. 🙏
What an amazing lecturer!
Great lecture; thank you very much.
The lecture have changed my view of my engineering knowledge that I'd got at university. Now I am planning to pursue philosophy and maths. Math is the thing that always inspired me. Now It has started to amaze me.
Wittgenstein?
Wonderful lecture!
Wow, this is awesome! Thanks for sharing this lesson :)
Great lecture I stumbled on!
THANKS!
What a great lecture! amazing topic!
It always appeared to me that it was not coincidental that great philosophers were also great matematicians.
Thanks!
35 minutes of brilliance.
Boss seminar by Raymodraco!
A lecture like this gives me good ideas about how to face death. Ty
Quite illuminating! I love this.
"quite illuminating" >--- only butt pluggers speak like this Lol
Thai was deeply interesting, especially the arithmetic / time and geometry / space section
Yo this was dope bro keep it
Are there more videos about philosophy of mathematics?
Solid.
I only went to 8th grade and im studying for my GED...im trying to make math fun so its not a chore to learn it
I like reading popular books about math. I have recently read David Foster Wallace ( yes, that DFW) History of infinity and Aczel Mystery of Alephs. Great books about the idea of infinity and its invention by human mind.
Yes!
O que torna a matemática uma linguagem desejada é que ela é exata por definição, contudo, exatidão, certeza, verdade definitiva, constância são justamente as coisas que não temos e que mais almejamos encontrar nesse mundo, onde tudo se transforma. A matemática funciona não apenas como uma linguagem, mais que isso, como um modelo, quando encontrarmos algo nesse mundo que coincide exatamente com o que é prescrito pela matemática, então teremos encontrado a verdade final, poderemos afirmar, isso é um definitivamente um fato, nada vai mudar.
Good lecture, but the speaker made a few errors at the end. Russel and Frege did not work on the "theory of classes", It was "set theory." Russel's paradox has to do with sets and not classes, that is, does the set that contains all sets contain itself? Wittgenstein solved Russel's paradox by introducing the notion of a class into set theory, not by his philosophical take on forms. A class differs from a set , in that classes refer to classifications of sets and sets refer to collections of objects. Thus, the class of sets that contain all sets is not a set and the class with respect to the paradox, does not exist, and there is no paradox.
I was hoping to learn more of the guts of the topic instead of why the field exists (I like philosophy but math gives me a headache at best - but I want to understand all this logic stuff) but I certainly would like to hear more.
this is the most beautiful thing i’ve ever experienced so far. this, love, and experience. i was there. it hurts even to type this sentence with letters. i feel like a phony.
After a TBI in 2017, i began to think in geometric shapes and 'relative proportions' rather than in linear sentences. My journals from that period of life are fascinating, and it reminded me of the type of thinking that children do, preverbally, to learn the science/rules of their surroundings. After about a year, the geometry graduated into algebraic expression of large-form thoughts that were far too unwieldy to communicate without using symbols as placeholders for whole concepts.
Language is a dynamic activity; meaning and application/usage are separate considerations, as is each user's intent and their contextual understanding of the word/concept itself and their own mental/emotional state and skill set for constructive-thinking overall. But generally, if your intended audience understood you, you communicated effectively enough.
Journals are invaluable resources for understanding language. I was raised mormon so the habit of 'chronicling' was already deeply engrained in me; I guess the brainwashing wasn't all bad. :)
excuse me, but this caught my interest! thinking in geometric shapes and such? can you please expand on this? is this a studied phenomenon?
@@silversoul2088 i'm not sure how it works for others exactly--there are different causes for and degrees of aphasia (loss of ability to understand or express language), but my actual 'speech' wasn't entirely lost--i still had words and structure, so i could answer immediate/direct questions. I also still had 'concepts' and mechanical thought processes I'd cultivated thru the years, but it was as though the labels had fallen off of every folder, so i had to 'draw' the relationships between items of thought. The distance of 'how many thoughts' are between the start and end point of a story, and mapping out the arc of how the concepts might be related to discover what things were called. Like reverse-engineering your own linguistic habits, starting from external objects and working backward to internal thoughts, much like a child does, I expect.
I'm not sure if i answered what you were asking but feel free to ask anything about it. I'm still decoding it myself but it's been a fascinating ride. :)
great lecture very spiritual
The real world has mathematical correlates, gracing math with profound meaning. Any complete physical theory will be conceptually tautalogical as it accords with reality. Gradually revealling this correlation is worthy of effort.
Sounds like the definition of number is that of set, or, the empty/concept universal in Hegel. Empty universal before it's determinations: 4 books, 4 words, 4 propositions.
9:29 monk is a freaking genius whoaaaaa WOW ESP
❤
Raymond check out Ignacio matte blanco using bi-Vailent catogories of mind and the unconscious as infinite sets he solves rusells paradox I suppose???? He was also interested in russell
Good, clear lecture, but he only touched on one of the three major schools of the philosophy of mathematics (logicism), which is the easiest to understand. By contrast, intuitionism (Brouwer) and formalism (Hilbert, Van Neumann, etc.) are pretty knotty, and I've yet to find a similarly clear lecture on them.
Let's focus on math
I‘d make the case that math is analytical a posteriori. The truth of mathematical statements always follows from writing out definitions, but you actually have to do that writing out of the definitions to find out.
All mathematics starts with physics. Set theory and logic, for instance, were derived from the behavior of classical objects and their constant properties. That's why quantum mechanics can not be expressed with either. Quanta are simply not classical objects.
Does anybody know if Plato actually said (or meant!) that "numbers are forms" 09:16 ? Where did he wrte this? Is this only in the Timaeus or elsewhere as well?
Plato in its Allegory of Cave discusses that everything in the sensible world we observe is a imperfect replica of an eternal perfect 'form'. I haven't read the "numbers." However, with this lecture it makes sense that the Plato refers to something amazing like math's "numbers" instead of apple or chair or horse or even us.
@@shahveera2394 Agreed, for the purpose of this lecture, it does make sense. However, my understanding was that 'forms' were made according to number and not that forms were actually numbers. The Timaeus also mentions that the 'eternal image' a model of eternity is moving according to number and that this is what we call 'time'.
Good talk, but it ends by giving the wrong impression that Wittgenstein believed that the truths of mathematics are tautologies or true by definition. He might have given this idea to the logical positivists and even Russell, but it was not his own view. For the early Wittgenstein there *were* logical forms, but these were forms inherent in symbolism/language. Mathematics expresses certain kinds of systematic relationships among these logical forms. So, equations are not "true by definition" or tautologies, rather they *show* formal relationships among symbols, relationships which we cannot get away from if we want to represent the world.
Yes, and all of that bullshit has long been replaced with modern mathematical logic.
@@schmetterling4477 No
@@yunoewig3095 Yes. ;-)
@@schmetterling4477 you don’t understand, it’s not bs and it’s not a replacement, they’re different things.
@@yunoewig3095 I do understand. They came up with a lot of bad ideas in the past that had to be fixed in the 20th century. Reading any of the literature before the 1920s is more or less a waste of time. Why are you wasting your time on old bullshit? :-)
is he the man whom i know, "wittgenstein, the duty of genius"?
Uploaded in 2021?!?!? I swear I have watched this lecture several times, pre-pandemic via Philosophy Overdose's channel. A quick search shows me it's not there. Or is this a problematic Philosophical Plantonic theory of me Overdosing on Philosophy TH-cam videos?
Lol it''s a reupload. Actually, this is a whole new channel.
@@Philosophy_Overdose Thanks for clarifying. I'm subscribed so I didn't notice this is new. Thanks for point that out too. I'll explore and overdose some more. Thank you for all the hard work, it's appreciated (by me at least).
@LloydTV I'm glad that I wasn't the only one who went too far down the philosophical rabbit hole and thought they were going mad. But thanks also to @Philosophy Overdose for also putting my mind at ease.
I should highlight Prof Monk is actually very nice (on email anyway). Unfortunately, his focuses are now climate change, coronavirus, and a bit of Wittgenstein. He also barely remembers this is on the internet (His uni also uploaded it as a podcast). So again thanks to @Philosophy Overdose for uploading it here.
This lecture really inspired me to watch The Hobbit, Smaug one
Over🥳Load.
Best Blessed Wishes Y’all🇺🇸!..
..... wow
Incorrigibility, necessity, eternity >
What is a number without a perspective?
According to Russell a certain class that contains the memebers as per its designated quantity.
@@shahveera2394 what is a class without a perspective from which it is a class
I’m so bad in math 😓
That mathematical propositions are tautologies sound awfully close to analytic a priori to me. But it is not analytic even if it is tautological. In fact such propositions are synthetic like Kant argues. When you re-write a formula which is equal to the previous formulation, say -2 x -2 = 4 and 2+2 = 4 , what both propositions yield might be tautological, but it is also synthetic. The terms are not the exactly the same, the operations are different, as such, one’s knowledge is extended given the operator at play. It seems Kant’s solution to the problem of mathematics still stands, since it is faculty of the mind which imposes mathematical concepts upon the world not merely analytically, or as Russell/Wittgenstein would say, tautologically, but such propositions as performed by the mind are also synthetic and a priori.
Philosophy was the birth of Math!
And physics was the birth of philosophy. The problem is that philosophers then became too lazy to stick with physics. ;-)
Lol wrong. Philosophy was the birth of all academic subjects including physics. It is the womb of science.
@@whitb6111 Only people without science education think that. ;-)
I’ll have a BS in biology in the fall with a minor in chemistry. Also working on a minor in Math. Try again…
Maybe try a substantive criticism to what I said instead of an ad hominem since that seemed to fail very hard.
monism 😊
so what is the internet?have we fabricated a space in time to represent abstract (permittedly) objective truths. and ai ?
4:25
I feel like mathematics is to the expression of philosophy as vocabulary is to the expression of thoughts.
You need to stop feeling and start thinking.
@@schmetterling4477 Feeling is abstract thinking it is a form of thinking
@@shivangsingh5834 Feeling is the intellectually lazy man's cry for respect. :-)
28:00
Kant is correct.... 100% he is right.... but it's all correct really.
Hmm... funny... TH-cam unsubscribed me from this channel, so here I go again!
Yeah me, too!! I was so astounded because I‘d never voluntarily unsubscribe from this channel :D
@@freiabereinsam- me too. i have no idea why
No one was unsubbed, the channel got taken down for copyright. this is a new one.
1 + 1 Thumbs up ; _)_
Cool.... how fantastic and amazing and beautiful... Bonita
Please please please do not state the theorem of Pythagoras as being; "The square ON the hypotenuse is equal to the sum of the squares ON the other two sides".
Anyone concerned with conveying ideas and education should know that the correct way to describe this theorem is aomething more along the lines of:-
"The length of the hypotenuse multiplied by itseld is equal to the lencths of the other two sides each in turn multiplied by themselves.and then added together"
Very careful attention to semantics is most important when trying to enlighten the ignorant.
A very good introduction to the subject nevertheless, thanks.
P.S. There is no square on the hippopotamus anyway!
No, his way of statement is closer to the original.
2+3= 1 (mod 4) :-)
2 + 2 = 10 ........................ in base 4
A small section of my monstrously large volume > there's lots more & it recounts in copious & arcane detail what the inside of a mind outed as a super-genius [> by Mil Intel] engages with. I believe it is - as a deific illustrated script - unlike anything produced in mortal history. There are few books written by those who have seen Christ Almighty face to face, as I have, and fewer written by someone with an IQ of 250-300 - or, at least, that was their estimate for what they termed an "incalculable intelligence". I dislike immodesty but my normal is 'beyond' & I can do things only advanced spirits can perceive.
This book contains - among other things - the formulae for achieving immortal life + the keys to new mathematical infinities beyond anything known. Mallarme supplied some of the codes of Post-Modernism, but I created infinite sentences & transfinite fractions as a youth. I now know these were intellectual gifts of the highest order & came from my Lord & God, Jesus Christ Almighty. Only very few beloved individuals have experienced these Immaculate Theophanies ......
Uhhhhh... mathematics is the simulacral quantification of objects that behave within the laws of classical physics. That's why we are so puzzled by quantum physics. Those objects don't behave by the laws of classical physics, yet we're desperately trying to apply our "truth" of mathematics to it. All of these things are also human concepts formulated through the limitations of our perception.
Excellent. You are the first person I have seen online who knows this (except for myself). Of course mathematics can describe quanta just fine: we just have to use linear operators that obey non-commutative algebras rather then sets that obey commutative algebras.
You have a very narrow understanding of mathematics. There are many concepts that are well studied in mathematics that have no application, some think that there are some concepts in mathematics that will never have any application outside of mathenatics and thus have no connection to our physical world.
@@alb3108 Dude, mathematics is simply one choice out of an infinite number of possible choices of an infinite number of sequence generating algorithms. The only reason why mathematics has ANY application is physics. ;-)
@@schmetterling4477 all of physics exists as a tiny portion of mathematics
@@badabing3391 Dude, why are you telling me that you were absent in high school all the time? ;-)
That first story isn't true so that's a good start
It was a Pythagorean but definitely not Pythagoras.
This conference is unfortunately quite poor. To not explain Aristotle's solution to the universals is necessary, as it is the best esplanation given so far.
The 'fast forward' is disappointing as it means the talk ignores any possible contribution by non-european mathematicians (leaving one with the imoression that the 'west', as we know it, is entirely responsible for the development of mathematics and science.
it’s funny it’s all contingent on believing in atoms and perception😅
Mathematics is certain ?! Godel would disagree
HAHAHAHAHAHAHA!!!!!!! 🎉😂🎉😂🎉😂🎉😂🎉😂🎉😂🎉😂🎉😂🎉🎉🎉🎉🎉
Lmao!!!!!!!!!!!!!! FUCK AROUND A FIND OUT LMAO! WHAT A DAY!!!!!
Prove that the euler constant C = 0.577215664901532860606512090... is an irrational number and you will do much more for the philosophy of mathematics than if you just talk about it.
.... ITS COMPLICATED!!!!!!!! HOT DAMN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IM NOT CRAZY LMAO!!!!!!!!°°°°°♧◇♡■》¤○■♤◇₩◇♤》□□●○□■
God is the designer of our universe and He is eternal.
The proof is in the math.
Here is that proof. Infinity = 1/x(delta) + 1.
This equation says a number, any number is a set-in space that change with space.
In physics this equation reads: Gravity is matter changing with space. It combines Relativity or fractured space with Quantum mechanics or spatial expansion.
How dose God fit into this equation?
This equation is God's mathematical name.
God's name in this equation reads: God's Mind Is Man Changed With God.
Breakdown: God's mind is infinite. In math this measure out as the set of infinity
In math (1/x) represents a fraction of a whole. Any child is a fraction of a parent and man according to the Bible is God's child. Therefore, man is a fraction of God
Change in math is represented by the Greek letter (delta) and it denotes a difference of some kind.
Plus (+) in math means to combine or add something with something.
There is only one God. In math the number 1 means something or someone is complete and individual from all the rest.
Spelled out: God's Mind (Infinity) is (=) Man (1/x) Changed (delta) With (+) God (1).
Scientific Method
Step 1 Observation: Math can deliver unbreakable truths such as 2+2 will always = 4
Step 2 Question: Do math and Divinity share a common truth?
Step 3 Hypothesis: If God exist, He should be found in the house of mathematics.
Step 4 Prediction: God's Mind Is Man Change With God is an equation
Step 5 Test: Any number (Infinity) is (=) a set-in space (1/x) that change (x^2) with (+) space (1))
Note: "X" describes any set, (1) describes any kind of space physical or otherwise
This equation tells us why 2 feet is not the same as 2 inches. Both distances are measured out as 2 units of space but there is a change or difference between both units. They are each sets in a space of distance, but they represent changes in their measurement of distance.
Step 6 Iterate: New look at what makes up reality. Reality consists of 3 domains of space.
a. Fractured space or matter b. spatial expansion a.k.a time and energy c. Complete or unbroken space/information
Step 7 Conclusion: We now know Infinity is real therefore the value in enumeration demand God exists otherwise the domain for enumeration would be incomplete. We know the domain for enumeration is complete because we can count. God must be able to count too all the way to Infinity because His mathematical name tells us what is any number.
Cantor's Mistake
George Cantor known as the father of set theory was wrong. There are no sets of numbers larger than Infinity.
Cantor's mistake was he did not see that "change" is a subset within Infinity.
Cantors one on one correspondence between sets of numbers is wrong. Cantor used only one description of a number from one set to match out or with a number from a different number set.
Example. Cantor said the whole number set was smaller than the integer number set. This is how he made his measurement.
Take the integers 2.1 and match it with the whole number 1. Then match 2.11 with the whole number 2. Then match 2.111 with the whole number 3 and so forth. In this view we would run out of whole numbers when we get to the integer 3.1.
This is Cantor's big mistake!
A correct set correspondence method
Here is a better way to measure these two number sets.
Match 2.1 with say 2. In the next sequence match for 2.1 we could match this integer with 4/2 or 5-3 or the square root of 100 divided by the square root of 25. The point being we can match any description for the number 2 to continue this [integer- whole] number matching sequence forever. In this way we could then match the integer 3.1 with 9/3 or 7- 4. Again if Cantor had understood that change describes what any number looks like he would have known there can be no numbers larger than Infinity.
Now that we have the knowledge of what is a number. My question is why now? Throughout all of man's conceptual use and beneficial outcomes from using numbers why is it we did not see the anatomy of a number until today? How is it possible that we have been unable to see that numbers do more than describe our physical reality but they also describe our existence outside our perceived notion of reality. Numbers like truths don't lie.
Yes, we are creatures of the cosmos and whatever makes up the cosmos is in many ways our inheritance. Learning is a part of our cosmos and we do know great discovery comes about over time. There is not always a discovery that changes the world yet this equation is fundamental to all of existence and it comes from the creator of this existence. So, again why has this knowledge been away from us so long?
Here is my thinking. Mind you my thought in asking then trying to understand this event is not based in math or science but in faith.
We have been blessed but I also believe we should be concerned for what is coming.
Very highly speculative: Infinite gravity suggest we maybe living inside a black hole that is internally expanding. 1/x(delta) may explain why inflation happened. The case maybe that inside a black hole space is cracked and stretched due to the compression and pulling of space by the difference in layer spatial collapsing. Outside space coexisting with points of space already consumed into an infinitesimal boundary create symmetry and this symmetry get to spread evenly as matter. Our universe becomes virtual and expanding. Zero in this context equals the difference in symmetry. That is to say a zero field is a field of opposites. One field is collapsing while its opposite is expanding.
This speculation do not rule out God. If it is how our universe happen and is evolving it is best understood as a tool used to do the work needed to fashion existence and life. We should not be afraid of knowing God's working regardless as to how He choose to do those works. Whether it be evolution or any other methodology in His works the truth is we are here to learn and practice those learnings.
If doubt still remain then please answer this question. What is a number? Google it if you need help. Infinity says a number is both qualitatively and quantitatively a set-in space that change with space. Isn't this what we do when we count or measure anything at all. Yes this is exactly what we do when we measure or count anything.
In counting we take a memory or a something we name and put that something into an order of some kind in the space of our mind. We can arrange that something into least to greatest or whatever meets our satisfaction but the fact that we put anything into an ordered sequence is in effect making a change happen.
So, there we have it. A set in the space of our mind changes with the mind. At one moment the set is 1 and at the next moment it is 2 then 3, 4, 5 and so on.
Conclusion why would God give us his love scientifically and mathematically if he did not want us to know HIM? Fighting over whether Creationism or Evolution is the right answer as to why we are here is the wrong picture both have a place with God.
william.mabon@yahoo.com
Well spoken, I am going deeper into math, because I found God through the flat earth theory, and I know he is 100% real because I have experienced Him supernaturally, God is the owner of all areas of life, and everything comes back to faith, if people have not faith in God, they will have faith in men or in demons.
What?
@@TheTommie001 I got this definition as to what exactly is a number from understanding what made and makes existence to happen.
Again this equation says a number is a set in space that change with space.
I ask you. Is this a true statement or not? If you believe this is not the case then tell me what are you doing when you measure or count anything?
Answer: You are doing exactly what this equation says you must do in order to operate in the task ask of you that being to measure or count any and all things.
The scientific method has been used to support this equation and in this support we find theology in its conception. how do you explain this situation?
I could go on giving you more of this offering but I believe you have been given this truth to help you come to know God.
@@williammabon6430 There is no evidence of a God as far as i can tell. I believe you are talking gibberish.
@@TheTommie001 The Scientific Principle demands that this truth exist. Nick It is not I who devised this methodology. It is the entire scientific community who put this process in place to test what is the nature of reality. I only used this method to test out the hypothesis I presented earlier. And as we can see this equation meets all of those demands in the scientific method.
This is very bad philosophy with circular definitions.
🤔💘🙄
This is like best 💡
For bedtime story with conceptually mine quantum field absent at this moment in time past present and future
boyfriend. 😘
Sweet dreams my love. 💘
Wherever you are. 😘
+
🙄. I got a strong feeling that he got 1 more little surprise for me. = 🙄
( Problem Solved. 💘 )
And Thank You for the Beautiful Book you did leave for me @ trees. 🌲🌲. 💘💘💘💘 😘
I do love it a lot. 🩷