Knowledge - a priori and a posteriori, Math - not an exact science

[Antiprosynthesis]

We have two kinds of knowledge, we speak about a priori propositions and a posteriori propositions.

A posteriori propositions (afterwards knowledge) are formed after the processing of sensory input, all a posteriori propositions are synthetic: this means the proposition makes a synthesis of sensory input and An object (OR subject) for example; this ball is red.

A priori propositions (before hand knowledge) are formed using analysis of the subject. A priori propositions can be Both synthetic as analytic; analytic would be that ball is round, cause there is no synthesis, the term ball implies that IT is round; synthetic would be every change has a cause, cause we can still figure this out using analysis but since change does not implie a cause, IT is still synthesis.

Mathematica would be a priori synthetic knowledge and the first to state this was Immanuel Kant, he did this in his critic on pure reason. Kant wrote 3 critiques, each asking one big question and each in a different field of philosophy, in this case IT asks what can we know, and this concerns knowledge theory. The other two ask the questions what may we believe, concerning metaphysics and what should we do, concerning morals...

Math is often seen as our most exact science, but this is not the case, and IT all started with Russell; he stumbled upon a contradictio in set theory - he said suppose you have two groups, one containing all recursive groups and one containing all non recursive groups, where would you place the non recursive groups?

Not in the group of recursive groups cause they are non recursive, but also not in the group of non recursive groups as this would make Them recursive...

Russell could not accept that math was not exact so he wrote, together with Whitehead, two huge books called the 'Principia Mathematica'; he constructs a symbolic language called mathematical logic and only in this language one is allowed to speak about math - he hoped this would rule out any recursiveness ergo self reference and so avoid the possibility of contradictions...

However, along came Gödel, and he said the Principia Mathematica was so recursive that IT was a book that was consious about itself (its generally accepted that consiousness would be highly recursive) and he proved, using mathematical logic, the proposition phi, that States from itself IT can't be Proven...

Also interesting is that exact sciences originally were philosophy, Newton wrote down his 3 equations concerning Gravity (the only 3 equations NASA needed to land on the moon) in what he titled the Principia mathematica Philosophiae Naturalis, OR the mathematical principles of nature philosophy... Today this is considered to be physics, not philosophy.

An example of how philosophical thinking can enrich exact science is how the theories of relativity of Einstein came to be; he was riding on a train and saw himself moving away from a clocktower and he said what if I would be moving faster than light, then I would see the clock go backwards...

According to Einstein, time travel is allowed by the laws of nature but there is a problem, the speed of light would be the fastests anything could travel, cause the faster you travel, the more mass you gain, the more energy is needed to travel that fast - traveling at the speed of light would need almost An infinite amounts of energy...

However, they did An experiment with the LHC which suggests particles, called Tachyons, exchanging information faster than light.

Time is also a fluid concept, according to Einstein time moves slower when Gravity is higher OR the faster we travel (which makes sense, the faster you travel, the bigger the mass, the higher Gravity) and this was proved by An experiment using two atom clocks - this are clocks that keep exact time using a Pulse being bounced between two plates...

One of the clocks was kept on earth, the other cirkeled the earth a while in a fast jet, when the clocks were afterwards compared to each other the clock from the jet was behind on the clock that stayed on earth, explanation: as the one clock travels fast, the Pulse inside the clock started moving diagonally instead of horizontally meaning IT had to travel a larger distance ergo time slowed down...

I tried my best to explain IT in English, im not sure how well I succeeded, anyone interested?

 

[Jabberwocky]

Frege's formulation of set theory not being sound (i.e. what Russell showed) does not mean maths is not exact. Further, Russell reformulated set theory to remove the contradiction. The question was in which set do we put the set of all sets that do not contain themselves.

Kant was wrong. He claimed that Euclidean geometry being the only type of geometry was a priori, and then hyperbolic and elliptical geometry put paid to that. I liked his categorical imperative but he's not my go to for logic.

Godel did not prove that maths inherently contains contradictions. In fact his PhD thesis was the proof of the soundness and completelness of Propositional Logic. He then proved that predicate calculus was incomplete (his 1st incompleteness theorem), and that there was no axiom you could add that would make it complete (2nd incompleteness theorem).

I am extremely interested in this, I love this stuff so I got a masters in mathematical logic. I think you are misunderstanding a lot of things and could benefit from wider reading in the philosophy of maths and doing some basic set theory (we used Hamilton's numbers, sets, and axioms but it was a while back so maybe something new is better). None of the work you mention suggests maths is not exact. There are branches of logic that even deal with things that are inexact (non-standard logics) such as modal and real valued logics.

Godel went nuts, he starved himself to death because he thought everyone was trying to poison him and apparently couldn't cook. He was a truly great mathematician but his stuff about Godelian intuition is not widely accepted.

I'd really recommend you read Hoftstader's Godel, Escher, Bach: An eternal golden braid, for some insights into the relationship between this type of maths and consciousness. Its a beautiful, beautiful book.

this entire post is very iirc. i used to live and breathe this stuff but not for a long time, and a lot has happened in the interim.

 

[Antiprosynthesis]

Frege's formulation of set theory not being sound (i.e. what Russell showed) does not mean maths is not exact. Further, Russell reformulated set theory to remove the contradiction. The question was in which set do we put the set of all sets that do not contain themselves.

Kant was wrong. He claimed that Euclidean geometry being the only type of geometry was a priori, and then hyperbolic and elliptical geometry put paid to that. I liked his categorical imperative but he's not my go to for logic.

Godel did not prove that maths inherently contains contradictions. In fact his PhD thesis was the proof of the soundness and completelness of Propositional Logic. He then proved that predicate calculus was incomplete (his 1st incompleteness theorem), and that there was no axiom you could add that would make it complete (2nd incompleteness theorem).

I am extremely interested in this, I love this stuff so I got a masters in mathematical logic. I think you are misunderstanding a lot of things and could benefit from wider reading in the philosophy of maths and doing some basic set theory (we used Hamilton's numbers, sets, and axioms but it was a while back so maybe something new is better). None of the work you mention suggests maths is not exact. There are branches of logic that even deal with things that are inexact (non-standard logics) such as modal and real valued logics.

Godel went nuts, he starved himself to death because he thought everyone was trying to poison him and apparently couldn't cook. He was a truly great mathematician but his stuff about Godelian intuition is not widely accepted.

I'd really recommend you read Hoftstader's Godel, Escher, Bach: An eternal golden braid, for some insights into the relationship between this type of maths and consciousness. Its a beautiful, beautiful book.

this entire post is very iirc. i used to live and breathe this stuff but not for a long time, and a lot has happened in the interim.

Thx a lot for your reply, Im very interested and exploring these things, but I studied Art so I got very little science in my education...

I took a few coarses at the university tho, among Them mathematical logic in the study philosophy but this was very shallow and over 20 yrs ago, so in no way can I say anything of interest to a master in mathematical logic and I can easily accept that my knowledge on this matter is flawed and limited...

However, I really enjoy stuff like this and (popular) science...

I actually own a copy of Gödel Escher Bach, but I go deeper into the art and music than the math, since I studied graphic arts and later on classical music, piano and composition, at the conservatory...

I do my best to learn as much as possible, but I get bored easily so I jump rather quick from one thing to another...

Lately I experience difficulties in such things, probably due to damage due to extensive drug use...

Also, communicating such things in any language other than my own makes IT more difficult for me to say the things I want to say the way I would like to say Them, which means some things are not meant the way I put IT...

Also, I never said Kant was right, I do find his philosophies quite interesting and IT is known that Einstein Read Kant at a Young age but also later in life still referred to him...

Anyway, the professor at the university made IT quite clear that IT meant that math was anything but exact, however, this were introductury coarses so Im sure I got a simplified version of what is actually going on...

Can you maybe elaborate a bit more on philosophy of math?

 

[Jabberwocky]

i can definitely see how communicating in a different language makes this difficult. you are doing a good job.

also, i've fucked my brains with drugs so am definitely not a master. but i did study this area and was quite consumed by it for a while so hopefully i haven't forgotten everything.

read GEB, honestly its fucking brilliant. don't get too bogged down in his explanation of hte proof of godel's theorem, i don't think its a good way to explain it personally.

the philosophy of maths is what got me interested in logic. it covers questions like 'what is maths?' and related things like 'what is the status of mathematical objects,' 'do mathematical objects exist outside of our consciousness.' the main ones i remember off the top of my head are constructivism, which iirc claims that mathematical objects are constructed by us and have no external reality. related is intuitionism, which i forgot everything about other than i think they don't even allow you the law of excluded middle.

i was really interested in the relationship between maths and physics. the so called unreasonable effectiveness of mathematics in the physical sciences. beyond the obvious, and easily explainable based on the fact we devised maths to explain things in our surroundings, i.e. for the same reason we devised physics, so of course they kinda fit together. there are some mind blowing discovered of really esoteric bits of maths being applicable to physics. like the reimann zeta function (used in number theory) being applicable to quantum chaos and fucking undecidability in the spectral gap.

i'm still confused as to how anyone could ever claim that maths is not exact? like what is the argument? are the claiming that 2+2~4? it may be worth looking into the definitons of soundness and completeness as i think these may be closer to what you mean. its not clear to me at all what maths not being exact means.

i'm sorry for how vague most of the info in this post is, i'm more trying to signpost and give words that might help you google stuff you'd find interesting. but let me know if you do cos i still love this stuff even if i'm shit at it now.

 

[Antiprosynthesis]

i can definitely see how communicating in a different language makes this difficult. you are doing a good job.

also, i've fucked my brains with drugs so am definitely not a master. but i did study this area and was quite consumed by it for a while so hopefully i haven't forgotten everything.

read GEB, honestly its fucking brilliant. don't get too bogged down in his explanation of hte proof of godel's theorem, i don't think its a good way to explain it personally.

the philosophy of maths is what got me interested in logic. it covers questions like 'what is maths?' and related things like 'what is the status of mathematical objects,' 'do mathematical objects exist outside of our consciousness.' the main ones i remember off the top of my head are constructivism, which iirc claims that mathematical objects are constructed by us and have no external reality. related is intuitionism, which i forgot everything about other than i think they don't even allow you the law of excluded middle.

i was really interested in the relationship between maths and physics. the so called unreasonable effectiveness of mathematics in the physical sciences. beyond the obvious, and easily explainable based on the fact we devised maths to explain things in our surroundings, i.e. for the same reason we devised physics, so of course they kinda fit together. there are some mind blowing discovered of really esoteric bits of maths being applicable to physics. like the reimann zeta function (used in number theory) being applicable to quantum chaos and fucking undecidability in the spectral gap.

i'm still confused as to how anyone could ever claim that maths is not exact? like what is the argument? are the claiming that 2+2~4? it may be worth looking into the definitons of soundness and completeness as i think these may be closer to what you mean. its not clear to me at all what maths not being exact means.

i'm sorry for how vague most of the info in this post is, i'm more trying to signpost and give words that might help you google stuff you'd find interesting. but let me know if you do cos i still love this stuff even if i'm shit at it now.

You dont have to be sorry, i enjoy your replies very much and I indeed AM planning to use specific terms and so on that you use for further research, but I cant really say when i Will do so as i constantly do so many different things...

Thx for the compliment about my english, cause i actually care a great deal about language, I even studied some years of literary Creation at the academy, i really AM very good with my own language, i have a huge vocabulary and im able to create long scentences that are very clear to Read and my Friends tell me i can explain complex stuff in a really good way, but the difference with the other languages I speak (i also know some french, german, spanish and Italian) is so huge that i Am really ashamed about my abilities and I feel this limits me extremely...

One thing about philosophy of math, i understand what you mean with the question if mathematical objects exist out of our head, does this in any way can be linked to the world of ideas from Plato?

I always liked thinking that what math describes is like the DNA of inanimate matter, but i have no idea if this has any reality to IT...

 

[Jabberwocky]

One thing about philosophy of math, i understand what you mean with the question if mathematical objects exist out of our head, does this in any way can be linked to the world of ideas from Plato?

yes!!! this stuff goes back to the greeks and platonic ideals are one of the first concepts taught in the philosophy of maths. the philosophical issue there is that if numbers are these 'ideal' things that exist eternally, unchanging, independently from us, then how do we access them? how can we come to know about things we are causally separated from?

I always liked thinking that what math describes is like the DNA of inanimate matter, but i have no idea if this has any reality to IT...

there is actually a philosophy of science called ontic structural realism that could be roughly translated into that analogy. 'DNA of inanimate matter' is a really nice analogy. ontic structural realism claims that only structure exists, so the relationships between things, not the things themselves. it actually makes a lot more sense than i'm making it sound in the context of modern theoretical physics, but i'm too tired to do the reading i'd need to to try and explain further right now.

 

[Antiprosynthesis]

yes!!! this stuff goes back to the greeks and platonic ideals are one of the first concepts taught in the philosophy of maths. the philosophical issue there is that if numbers are these 'ideal' things that exist eternally, unchanging, independently from us, then how do we access them? how can we come to know about things we are causally separated from?


there is actually a philosophy of science called ontic structural realism that could be roughly translated into that analogy. 'DNA of inanimate matter' is a really nice analogy. ontic structural realism claims that only structure exists, so the relationships between things, not the things themselves. it actually makes a lot more sense than i'm making it sound in the context of modern theoretical physics, but i'm too tired to do the reading i'd need to to try and explain further right now.

Very interesting, I have a special interest in these things, because a friend of mine - who is way more into philosophy than me and never did Any drugs, and he claims math is not a priori but a posteriori, but i strongly believe otherwise, not only due to psychedelics but many psychedelics make me see, especially with cev, a range of mathematical objects, from simply rectangles and triangles to very complex structures like fractals and (other) recursive structures (in this regard I really like Changa), and I believe these are not Just a posteriori memories OR so but i (want to) believe these structures are a priori inherent to the brain and nature...

When i was very Young and ignorant I made the mistake of saying that math was the language of nature, but of course math is nothing more than symbols invented by ppl and only describes reality in a limited way, in a sense math can, i think, be seen as An idealistic way of describing reality, im not sure if this in any way makes clear what i mean, for example, a cirkle seems perfectly round to us, but (correct me if im wrong) i think a circle is not round but only aproximated by infinite triangles ( im not sure IT were triangles) that create the illusion of a cirkle...

But i believe that what math describes is inherent to nature and make up building blocks, in art these math principles are often used, like the nautilus OR fibonacci sequence, and that what follows these principles is seen as beautiful and answers to the laws of esthetica (like always use dark colors at the Bottom and light colors on top, of course you can choose to not follow these principles but then you still need to know these laws to know in which way to violate Them, in art this is often very conceptual, in music a good example is that jazz mucisions know very well how to violate the classical rules to create specific rythms, and rythm (and music in general) is math...

In my post graduate at the conservatory we also had to write a scription theoritical and I titled mine the math of music, but this work was highly derivative and contained very little original input, but i did really good cause i didn't study music theory, which every student gets but IT was not my main subject, so creating a highly original thesis was not the purpose, however my paper was published and generally produced positive comments...

Back to math, i Also find math terapeuthic, i am able to solve equations with some ease, and in the past when i suffered tension and OR anxiety, i solved equations and this calmed me down - my shrink said that this was because I was so insecure and that i worried so much that exact science gave me such certainty that this helped me being insecure and calmed me down and had An anxiolytic effect on me...

Also An idea I have, but cant figure out if this Idea is of Any interest to others and I dont talk about very often, is that i Am by all means An atheist (well actually I feel close to the contradictory atheïst theism, which culminated in Spinoza and the pantheism, which States the divine is in everything and everything is divine, so even tho i dont like religion, i AM no stranger to the religious experience, and to get to the point, i like the idea of God being some sort of ultimate, creating force of nature, and we already know the god particle, but i like the idea to quantify god in An ultimate equation and make metaphysics into physics expressed by math, but like i said I dont know if anyone besides me find this interesting since at the end this is nothing more than terminoligy and I doubt the reality value of this Idea, but its my (poor) personal attempt to unify my interest in logic, reason and facts with my feelings that can be described as religious...

 

[Antiprosynthesis]

yes!!! this stuff goes back to the greeks and platonic ideals are one of the first concepts taught in the philosophy of maths. the philosophical issue there is that if numbers are these 'ideal' things that exist eternally, unchanging, independently from us, then how do we access them? how can we come to know about things we are causally separated from?


there is actually a philosophy of science called ontic structural realism that could be roughly translated into that analogy. 'DNA of inanimate matter' is a really nice analogy. ontic structural realism claims that only structure exists, so the relationships between things, not the things themselves. it actually makes a lot more sense than i'm making it sound in the context of modern theoretical physics, but i'm too tired to do the reading i'd need to to try and explain further right now.

What you say about ontic structural realism makes me hop to something more psychological, that often something does only exist because of some structures that create (i dont want to say illusion but i want to mention IT) certain things without these things actually exist, OR that some qualities of something only get shaped by other information OR sensory input that determines the other thing its qualities, and that these qualities are variables, like how colors can change due to the color of the background, Just tell me if im not making sense, im Just thinking out loud, but i feel like with enough information about these things this could be translated into math and that this could maybe result in the description of structures, like that certain structures create in a way specific structures that only make sense when seen in relation to these other structures, i dont know if this makes Any sense at all, but i say IT cause even if you say im totally wrong, this falsification makes me gain more new knowledge than if you would agree with me, but to be honest I know too little about math to actually say stuff like this...

Also interesting in this regard are holistic principles, things that you can bring about that because of this create An extra value to these things, without that Any of the things that create this extra value on its own in any way even implie that this extra value can come from this... I believe this is the case with our brain and consiousness,.but if im making Any sense, can you give some examples and information about the holistic principles in math?

Also something that fascinates me is infinity, cause we are so bound by time and everything to us is finite, we Just cant in any way understand infinity, but its cool that math quantifies this, could you maybe share something about infinity and math? I think Russell also was interested in this and if im not mistaken this also has relevance regarding the history of mathematical logic.

Maybe you know this comic book, like IT lot and I doubt IT could teach you something you dont already know, but to me this teached me some things, its called logicomix and describes the history of mathematicalogic, with pleasant romantic moments such as Wittgenstein getting totally mad and very agressively ripping apart papers containing work that Russell did, of course this is more something like a gadget than actually a source of information (at least for ppl that know about this stuff, i know many newbies that find the theories in that comic book too difficult to understand), but i really like IT... This Just as a fun addendum...

Do you find anything interesting in the things i say OR is this Just testing your patience and philantropy?

 

[Antiprosynthesis]

Also, i was talking physics with someone who seemed to know a lot more about science than me, but he said IT was impossible to create a theory of everything, cause a certain system, like math, would only explain what IT describes, but can not describe OR explain that system via that system itself, IT would need a different system to explain itself, leasing to An infinite regression of every time we explain everything, this does not include this explanation itself and we always need a new system to explain the former explanation, he gave as example that genealogy explains things like genes etc, but that genealogy can not explain itself and we need physics to do so...

I really dont know ything about this but find IT interesting, can you tell something more about this, and could maybe a system explain itself if IT would be highly recursive? Maybe you find this An idiotic question, i Just know too little about recursive structures to know if this has any relevance?

And please forgive me some crucial language errors like me saying if a system could explain itself, i realize the system explains nothing and is Just a tool for ppl to explain things, i Also sometimes make the mistake of saying a system cant understand itself, while of course something like understanding had no meaning in this context, but to me this way of stating things sais something more about this but something I dont understand and cant explain in any other way, definitely not if im not using my native language, however I editted this post to add this cause i give a lot value to describing things accurately, a talent I sometimes dont seem to be able to control that much, but i try to be aware of the dangers that come with language and its complex nature, i like language philosophy like the Tractatus Logico Philosophicus from Wittgenstein, which the Wiener kreiss assumed this ended metaphysics, but Wittgenstein got mad and said that metaphysics is about the most important stuff...

I also Read speach acts by searle and I enjoyed this, this is a very logical way of analysing language and how language can be An act on its own and by itself...

My grandfather, the father of my father, is actually one of the most famous writers of my country, and he was even named several yrs as a possible winner of the noble price for literature, and from a very Young age he introduced me to world literature and expected me to write papers about the books he made me Read and he teached me how to do this succesfully, so language was almost my entire life quite important to me, for example when i was about 7 he introduced me to books such as heart of darkness by Conrad, Lolita by nabokov, 1984 by Orwell OR which I also enjoyed the catcher in the rye, i cant remember atm who wrote that... Edit I believe the author was salinger...

When i pay attention to what i write, which I dont right now cause im on my phone and I Just try to be fast, i use logic and mathematical principles to construct a text, i use certain structures to build structures within structures and my writing is often recursive...

IT has been said to me that my style sounds not modern and that i use a lot of words to explain something, which I fully agree with but are things i like about my style...

Of course what i type here is not in any way a reflection of how my dutch and carefully constructed writings are...

 

[Antiprosynthesis]

And of course math is quite exact, there are ppl that claim that believing in science is the same thing as believing in religion - i can not in any way agree with this, cause science had practical applications constructed by technology and the machines that we create seem to work quite well, which proves that science can explain lots of things for a large part in such a way that we can assume that at least in our universe, with our laws of physics, for so far as our mind is wired to understand things science is able to come up with information that can be applied in such a way that this proves IT is correct for how we experience reality...

I often have problems discussing certain things with religious ppl cause they assume they know the absolute and apodictic truth and not in any way are open to doubt themselves and dont even consider other theories, while these other theories can consist of logical arguments while they cant seem to give even one solid logical argument, this can really frustrate me...

 

[Antiprosynthesis]

(I have a very broad spectrum of things i say but my mind constructs so many links between so many different things that IT all seems relevant to me and makes up a consistent Unity in my head...)

 

[Jabberwocky]

What you say about ontic structural realism makes me hop to something more psychological, that often something does only exist because of some structures that create (i dont want to say illusion but i want to mention IT) certain things without these things actually exist, OR that some qualities of something only get shaped by other information OR sensory input that determines the other thing its qualities, and that these qualities are variables, like how colors can change due to the color of the background, Just tell me if im not making sense, im Just thinking out loud, but i feel like with enough information about these things this could be translated into math and that this could maybe result in the description of structures, like that certain structures create in a way specific structures that only make sense when seen in relation to these other structures, i dont know if this makes Any sense at all, but i say IT cause even if you say im totally wrong, this falsification makes me gain more new knowledge than if you would agree with me, but to be honest I know too little about math to actually say stuff like this...

Also interesting in this regard are holistic principles, things that you can bring about that because of this create An extra value to these things, without that Any of the things that create this extra value on its own in any way even implie that this extra value can come from this... I believe this is the case with our brain and consiousness,.but if im making Any sense, can you give some examples and information about the holistic principles in math?

Also something that fascinates me is infinity, cause we are so bound by time and everything to us is finite, we Just cant in any way understand infinity, but its cool that math quantifies this, could you maybe share something about infinity and math? I think Russell also was interested in this and if im not mistaken this also has relevance regarding the history of mathematical logic.

Maybe you know this comic book, like IT lot and I doubt IT could teach you something you dont already know, but to me this teached me some things, its called logicomix and describes the history of mathematicalogic, with pleasant romantic moments such as Wittgenstein getting totally mad and very agressively ripping apart papers containing work that Russell did, of course this is more something like a gadget than actually a source of information (at least for ppl that know about this stuff, i know many newbies that find the theories in that comic book too difficult to understand), but i really like IT... This Just as a fun addendum...

Do you find anything interesting in the things i say OR is this Just testing your patience and philantropy?

that comic sounds super cool!! i will have to check it out.

i think the analogy to psychology works. so we both see the same object, but cos of our different brain states, we perceive it differently. but the structure remains the same. and no matter how many people will see it, it will always be the same fundamental structure (though it may evolve over time, as physical objects are wont to do).

OSR was, i think, developed as a response to Kuhn's theories put forward in his book the Structure of Scientific Revolutions. In that, he states that scientific revolutions are brought about by paradigm shifts. When the current paradigm gets to the end of its useful life, because we are finding more and more questions that it can't answer, we need a scientific revolution to bring about an entirely new paradigm. Usually you'll get a few competing but one will win out. OSR points out that the new paradigm has to explain all the things the old paradigm did, and make new predictions. So even though the old paradigm may look nothing like the new one, consider quantum vs classical mechanics, the structure (in a mathematical sense) is preserved.

Also, i was talking physics with someone who seemed to know a lot more about science than me, but he said IT was impossible to create a theory of everything, cause a certain system, like math, would only explain what IT describes, but can not describe OR explain that system via that system itself, IT would need a different system to explain itself, leasing to An infinite regression of every time we explain everything, this does not include this explanation itself and we always need a new system to explain the former explanation, he gave as example that genealogy explains things like genes etc, but that genealogy can not explain itself and we need physics to do so...

i think the person you were talking to may not have been thinking completely clearly. i would bet that they explain things about themselves every day, so its clearly not impossible for things to explain themselves. this is discussed quite extensively in Hoftstadters follow up to GEB, called 'i am a strange loop.'

the types of logic that are strong enough for Godel's theorems to apply are able to describe themselves, and its exactly that power that makes them susceptible to incompleteness. if you think about it, the incompleteness theorems talk about themselves.

i do agree that we probably will never create a theory of everything though. if we got to what we consider right now would amount to a theory of everything, i strongly suspect it would bring up more questions than it would answer.

regarding infinities. i like them too. but i'm afraid i became totally unstuck when trying to study them in set theory, my brain just couldn't cope. if you're not familiar with the paradoxes infinity brings out then look into Hilbert's hotel. to understand how one infinity can be bigger than another, look into Cantor's diagonal argument. once we discovered that the infinity of the natural number was smaller than the infinity of the real numbers, the next obvious question was 'is there an infinity between these?' this is called the continuum hypothesis. it turns out that the continuum hypothesis is independent of ZFC (the most common formulation of set theory), meaning that you can add either it or its negation to your set of axioms and still have a consistent system.

And of course math is quite exact, there are ppl that claim that believing in science is the same thing as believing in religion - i can not in any way agree with this, cause science had practical applications constructed by technology and the machines that we create seem to work quite well, which proves that science can explain lots of things for a large part in such a way that we can assume that at least in our universe, with our laws of physics, for so far as our mind is wired to understand things science is able to come up with information that can be applied in such a way that this proves IT is correct for how we experience reality...

yeah. the 'science is religion' crowd bug the hell out of me. i am a research scientist, i spend my entire fucking life trying to work out why i'm wrong, why the paper i'm reading is wrong, etc. that is pretty much the opposite of dogmatic. unfortunately the people who put forward that argument seem to have so little comprehension of what science actually is that i find it impossible to correct them.

also, you are by no means testing my patience. i love this stuff, i get bored and frustrated discussing it with people who are obviously idiots but you are clearly intelligent and thoughtful. its also nice to see that even if i think my memory and cognitive abilities are fucked, once i jog my memory quite a lot is coming back. or i'm just making it up and not realising, i haven't fact checked any of the above..... but i'm pretty sure its mostly roughly correct.

 

[Antiprosynthesis]

that comic sounds super cool!! i will have to check it out.

i think the analogy to psychology works. so we both see the same object, but cos of our different brain states, we perceive it differently. but the structure remains the same. and no matter how many people will see it, it will always be the same fundamental structure (though it may evolve over time, as physical objects are wont to do).

OSR was, i think, developed as a response to Kuhn's theories put forward in his book the Structure of Scientific Revolutions. In that, he states that scientific revolutions are brought about by paradigm shifts. When the current paradigm gets to the end of its useful life, because we are finding more and more questions that it can't answer, we need a scientific revolution to bring about an entirely new paradigm. Usually you'll get a few competing but one will win out. OSR points out that the new paradigm has to explain all the things the old paradigm did, and make new predictions. So even though the old paradigm may look nothing like the new one, consider quantum vs classical mechanics, the structure (in a mathematical sense) is preserved.



i think the person you were talking to may not have been thinking completely clearly. i would bet that they explain things about themselves every day, so its clearly not impossible for things to explain themselves. this is discussed quite extensively in Hoftstadters follow up to GEB, called 'i am a strange loop.'

the types of logic that are strong enough for Godel's theorems to apply are able to describe themselves, and its exactly that power that makes them susceptible to incompleteness. if you think about it, the incompleteness theorems talk about themselves.

i do agree that we probably will never create a theory of everything though. if we got to what we consider right now would amount to a theory of everything, i strongly suspect it would bring up more questions than it would answer.

regarding infinities. i like them too. but i'm afraid i became totally unstuck when trying to study them in set theory, my brain just couldn't cope. if you're not familiar with the paradoxes infinity brings out then look into Hilbert's hotel. to understand how one infinity can be bigger than another, look into Cantor's diagonal argument. once we discovered that the infinity of the natural number was smaller than the infinity of the real numbers, the next obvious question was 'is there an infinity between these?' this is called the continuum hypothesis. it turns out that the continuum hypothesis is independent of ZFC (the most common formulation of set theory), meaning that you can add either it or its negation to your set of axioms and still have a consistent system.



yeah. the 'science is religion' crowd bug the hell out of me. i am a research scientist, i spend my entire fucking life trying to work out why i'm wrong, why the paper i'm reading is wrong, etc. that is pretty much the opposite of dogmatic. unfortunately the people who put forward that argument seem to have so little comprehension of what science actually is that i find it impossible to correct them.

also, you are by no means testing my patience. i love this stuff, i get bored and frustrated discussing it with people who are obviously idiots but you are clearly intelligent and thoughtful. its also nice to see that even if i think my memory and cognitive abilities are fucked, once i jog my memory quite a lot is coming back. or i'm just making it up and not realising, i haven't fact checked any of the above..... but i'm pretty sure its mostly roughly correct.

Im glad you also like the idea of that comic book,.if you are in to such things.especially if you are a master in math logic, i suspect you could enjoy IT quite a bit...

I have a copy of Kuhn the structure of scientific revolutions, as well as i have popper in my collection BTW, but i remember very little of IT, this could very well trigger me to Read IT again...

I like the idea of systems explaining themself, AM i right to say this is in a way a simple form of recursiveness OR is that Just wrong? Could you maybe also give me a jump start into recursiveness? This fascinates me and I know way too little about IT...

Its not to be comprehended, not by me at least, how one infinity can be bigger OR smaller than another infinity, i heard about this before but know nothing more about this, its illusive character of course makes IT Just more interesting, something I definitely explore a bit more...

Im glad you also dont care for dogmas which I already expected, however you never know, i know a priest that really has interesting philosophical ideas but he really isnt that dogmatic, but IT surprises me when i hear his.views.on some things that hè is a priest...

Thx for the compliment and im very happy you are also enyoing this, otherwise i wouldnt be able to really enjoy this...

And thx for your extensive reply, i notice that you know way more about this stuff than me and im happy you enjoy sharing some of this luxury with me.

Im sorry that i didn't really had anything to add this time, but by.now i suffer a bit sleep deprivation and stimulant comedown which affects my reasoning skills...

But i do hope, if you would like to do this as well, that we can still continue this information exchange...

 

[Antiprosynthesis]

BTW the way, you seem to be up rather early, OR isnt IT morning atm where you live? Most like not, i Just feel like its morning over there too cause You didn't reply a big part of the night over here, which creates the illusion in my head that you were sleeping...

 

[Antiprosynthesis]

Something I can add, is that probably every answer brings about new questions,.this would complicate finding a theory that explains everything - i said this to someone once, that probably every answer brings about more questions and we did a simple experiment, i asked what is the nature of reality, and he said that what consiousness percieves, so i asked what is it that consiousness percieves, and.so on... This continued for a while, of course you cant keep this going and such An experiment is more Just a way to kill time than anything else since you can already reasonably assume, at least imo, that IT is probabel that every answer brings about new questions, would this be in any way a hint of the holistic principle?

Just tell me if you feel like sleep deprivation and stim comedown has overpowered my brain and if you feel like im not able to continue with Any reasonable level of me being able to make some sense...

I can go a long time on and on about even a.very simple thing, cause everything has so many aspects...

About math, An idea I also like is that, if.math actually is a priori knowledge and perhaps is the DNA of inamite matter and is intrinsicly embedded in the brain and nature and so on, is that in a way this abstract way of viewing reality is more real to me than the world I see, as das ding An sich ist ein unbekantenes, which if im not mistaken belongs to Hegel (i like dialectic philosophy cause of its structure, thesis, anti thesis and synthesis, tho i Am antiprosynthesis which is a concept I AM currently developing but its too soon To already tell anyone about IT), which mean that things themselves are not able to be known, in german...

For example, everything we see is simple reflection of light, the colors we see are the short middle OR long waves of the electromagnetic.spectrum (i AM aware you already know this stuff) being absorbed and OR reflected,...

So we can not know what color something has OR even If IT has any color, maybe without light reflection colors.dont exist, but what would something without color look like? Black? Is it even possible to view something at all when IT has no color?

OR I also only know the things as my very limited brain and how its wired is able to percieve things, with a different brain things would simply be different... When on a psychedelic like LSD reality changes, but this is among other things due to signals in the brain getting send to another location in the brain than usually, in a way this is equally real imo, its Just a different way of processing that information, leading to different results, of course functioning on LSD brings about some practical issues due to processing information differently, but I still feel this sais something about the nature of reality...

Okay, so we cant know reality as.it exists apart from us and our brain, back to math, this makes the abstract way of understanding reality via math in a way very real to me, cause i (want to) believe that math describes the Essential structure of things and that this could be a higher level of reality that is maybe is more consistent in how IT presents itself to various ways of processing information, but i fear I must consider that with a different brain maybe our math would not make Any sense and perhaps this other brain uses other logic to understand things, maybe in a way that IT would not seem as logic to us, but brings about the same results...

However, there is a positive correlation between the logical principles in how the world works and the logical principles in how our brain works, logic and also math still seem to me as if Both are simply the way everything works, but what about QM? This seems to play with logic in ways that IT bends and stretches the laws of logic...


Im Just thinking out loud,.this are in no way certain ideas I developed OR anything, im Just letting myself go in things i find interesting...

There could very well be many universes in the multiverse with completely different laws of nature, physics, in a black hole OR An Einstein Rosen bridge, OR wormhole as i assume you know, the laws of nature as we know IT are completely different, as a kid i once Read that if you enter An Einstein Rosen bridge and enter IT again, you would meet yourself...

So probably math as we know IT is not able to describe all possible sets of laws of nature and so on... Maybe there exists a system that is able to function equally well in different brains and universes, but i feel like this is getting a bit too metaphysical and I feel like im not able to produce anything that actually matters out of this thinking out loud ...

At least i was able to figure out that math is not in any way A more or less absolute way to understand and describe reality... But these must be things you already figured out so long ago and some of the things i say must either sound so obvious to you OR else so ridicoulous that i hope you dont lose all interest in communicating with me anymore... Like i said, a bit of sleep deprivation and stim comedown affects my mind seriously...

Something that Just popped in my head and i want to ask cause i simply dont know: i assume math is not dead at all but instead Alive and kicking, so my conclusion is that there constantly must be developed new math, so i wonder are there Areas,.like for example QM since IT is often not logical to us, in which math is not fully able to do its job anymore? And i also wonder; are there Essential OR in anyway remarkable differences as math evolves?

I feel like this is all quite some BS and i AM not happy at all with the thinking i did OR even the questions i asked, and i dont even know why i feel the need to hit post reply and not Just delete this...

Maybe its not that bad, i dont really know, my brain is no longer able to figure this out, which probably sais enough about the content of this post...

 

[Jabberwocky]

I have a copy of Kuhn the structure of scientific revolutions, as well as i have popper in my collection BTW, but i remember very little of IT, this could very well trigger me to Read IT again...

I like the idea of systems explaining themself, AM i right to say this is in a way a simple form of recursiveness OR is that Just wrong? Could you maybe also give me a jump start into recursiveness? This fascinates me and I know way too little about IT...

you have a lot of good books on our shelf!! i don't think i've got SSR (i forget, most of my books are in boxes until i sort out shelving). i had to read some of it while i was at uni though.

the word 'recursive' can have a couple of meanings depending on the context. in computing a recursive function is a function that calls itself. this captures the essence of the meaning to me, its a function that is able to make reference to itself. in maths the word 'recursive' denotes a function containing a predicate (so it differentiates propositional logic from predicate logic, the former is complete, the latter incomplete). the way that such functions talk about themselves isn't obvious and the beauty of godel's theorem is his encoding, which he used to make predicate calculus talk about itself. so he literally used the building blocks of the formalism to make a 'language' then used that language to talk about the system. but in terms of logic, recursive functions are, iirc, fully equivalent to the predicate calculus, meaning there is a defined way to map one to the other and back.

BTW the way, you seem to be up rather early, OR isnt IT morning atm where you live? Most like not, i Just feel like its morning over there too cause You didn't reply a big part of the night over here, which creates the illusion in my head that you were sleeping...

i'm in the UK so just an hour different from you i think. and i work a 9-5, sometimes about in the day but i've been working hard today.

About math, An idea I also like is that, if.math actually is a priori knowledge and perhaps is the DNA of inamite matter and is intrinsicly embedded in the brain and nature and so on, is that in a way this abstract way of viewing reality is more real to me than the world I see, as das ding An sich ist ein unbekantenes, which if im not mistaken belongs to Hegel (i like dialectic philosophy cause of its structure, thesis, anti thesis and synthesis, tho i Am antiprosynthesis which is a concept I AM currently developing but its too soon To already tell anyone about IT), which mean that things themselves are not able to be known, in german...

ahhhhhhh i have not studied hegel. i was strictly within the analytical tradition. i tried to learn some continental philosophy in my free time and just couldn't understand what was going on. i think translations from german are also very difficult, its part of why a lot of native english speakers find Kant hard too.

So we can not know what color something has OR even If IT has any color, maybe without light reflection colors.dont exist, but what would something without color look like? Black? Is it even possible to view something at all when IT has no color?

colour is the way that the electrons surrounding an object interact with light. so i think the only things really without colour are black holes because they truly reflect no light. though i don't think something that doesn't interact with electromagnetic waves would have a colour.

OR I also only know the things as my very limited brain and how its wired is able to percieve things, with a different brain things would simply be different... When on a psychedelic like LSD reality changes, but this is among other things due to signals in the brain getting send to another location in the brain than usually, in a way this is equally real imo, its Just a different way of processing that information, leading to different results, of course functioning on LSD brings about some practical issues due to processing information differently, but I still feel this sais something about the nature of reality...

completely agree that psychedelics just make our brain process information in a different way. i'm not sure they say anything about reality. not anything more than crack psychosis (which sadly 've experienced a lot and its contributed to me destroying my brain), and i really hope that doesn't reflect the nature of reality!! i think they say something about our brains though. which are part of reality. so the snake always eats its tail.....

Okay, so we cant know reality as.it exists apart from us and our brain, back to math, this makes the abstract way of understanding reality via math in a way very real to me, cause i (want to) believe that math describes the Essential structure of things and that this could be a higher level of reality that is maybe is more consistent in how IT presents itself to various ways of processing information, but i fear I must consider that with a different brain maybe our math would not make Any sense and perhaps this other brain uses other logic to understand things, maybe in a way that IT would not seem as logic to us, but brings about the same results...

However, there is a positive correlation between the logical principles in how the world works and the logical principles in how our brain works, logic and also math still seem to me as if Both are simply the way everything works, but what about QM? This seems to play with logic in ways that IT bends and stretches the laws of logic...

QM is formulated within our standard mathematical frameworks. the maths of it actually makes a lot of sense and is relatively simple (my PhD was in quantum information so i've studied it a lot, all my maths friends were quite dismissive of the maths involved in QM). the logic defying bit is when we try and interpret its predictions in the context of the way we experience reality.

There could very well be many universes in the multiverse with completely different laws of nature, physics, in a black hole OR An Einstein Rosen bridge, OR wormhole as i assume you know, the laws of nature as we know IT are completely different, as a kid i once Read that if you enter An Einstein Rosen bridge and enter IT again, you would meet yourself...

So probably math as we know IT is not able to describe all possible sets of laws of nature and so on... Maybe there exists a system that is able to function equally well in different brains and universes, but i feel like this is getting a bit too metaphysical and I feel like im not able to produce anything that actually matters out of this thinking out loud ...

you might be interested in looking into the church-turing thesis. that basically says that the laws of nature are computable. we might not have developed the tools to describe them yet though. and, it might be false, its not really testable because its an equation but one side is a mathematical principle and the other side is an empirical claim.

i am actually a many worlds theorist when it comes to quantum mechanics. according to this formulation we accept the wave function at face value, and instead of thinking there is something mysterious called wave function collapse, we say that in a larger reference frame the wave function never collapses. we just perceive it as so because the universe has 'splt.' so basically at every moment the universe is splitting into more and more parallel copies, each of which containing a possible course of events. but the laws of nature are the same in each.

there is no reason for it not to be possible for there to be universes with different laws of nature but i'm not sure that it's possible for us to be causally related to them. if we travelled to them what would happen to our bodies? like how would we know we were there if they didn't produce heat, or light, or anything that our bodies can interact with? i suspect we'd probably die. but i am possibly lacking creativity. its an interesting question. though we can't survive even slight changes to the magnitude of the force of gravity, so maybe i'm not being too pessimistic.

 

[Antiprosynthesis]

Im not saying this to show off, tho i admit i AM quite proud of that, but when i was about 20 I did An iq test cause my shrink at the time pushed me to, tho i was rather curious and quite sure i would do well, but i was a bit afraid the score might turn out to be disapointing and i feared this might work counter productive as i was in essence a concert pianist,.i Also got two first prizes at the two only piano contests i ever entered, the diminduendo competition at age 14, which is the max age you can enter this contest as It is for Young pianists, but the level is already really professional, to give you An idea you had to play one work with orchestra and i played the first piano concert of Liszt, i dont know if this means anything to you, but i was only 14 and this is a piece that most pianists that are not professionals and who studied 9 yrs at the academy not even come.close to even being able to try play a piece of such level, Liszt belongs to some of the most difficult, complex, technical, virtuose and demanding music ever written, and the yahama competition at age 21 during my master at the conservatory, BTW i specialized in the romantic era and my favorite composer is Chopin, which is the only composer of who I master the complete works, IT is not for Any pianist, not even the greatest pianists, possible to fully master the complete works of two composers if they Both have An extensive repertoir... This is very demanding and extremely difficult, especially at a professional level, a few hundred students from different countries try out for the demanding admission exams and only 6 get in,.if you do not constantly perform at the highest level they Simply kick you out and take in the next in Line and many studente got kicked out, so you can Imagine this is something that requires a high intellect, but also demands a huge confidence, especily to perform concerts attended by lots of professionals and producers and such that are going to make OR break your career... So to get back to where i started, i feared a disappointment in the score of this IQ test might damage my confidence since i always concidered myself to at least in music having a really high intellect and lots of talent and these were very important notions to me...

I scored 145 and was very happy with this,.but i would have liked IT if i could have beat Einstein, who had An IQ of 154 which is actually quite low for a genius, Bohr had An IQ of 220...

But i can honestly say that As a pianist i was very good in what i did, but you must realize I sacrificied almost my entire life as a kid and the years before, during and some yrs after the conservatory to be able to perform at this level, i played 8 hrs a day literally every day, if i didn't play one Day, i needed two days To Just get back at the level i was, so IT was Simply not possible to not play even 1 Day, and besides playing for 8 hrs I mostly at night did analysis of my scores, and focus on composing, which is not done behind the piano, if you want to study at the conservatory.you need absolute pitch, this makes you able to Just sit behind a desk behind An empty score and you Just write down the notes that you construct in your head, so anyway i slept very little, and in this world IT was quite common to use coke to keep performimg at that level, even the director of the conservatory at that time was addicted to coke and he i would say had some qualities I carefully would consider as being genius, hè was the only belgian to ever win the belgian piano contest Queen Elisabeth competition which is regarding contests that dont focus on Just one composer by far the most prestigieus and demanding competition in the world, i was preparing myself to enter the only Chopin competition in the world, which is even more demanding, but IT never came to that, but ill tell more about IT later on... So i got into coke and this even elevated my performances to An even higher level, as you probably know coke is the ultimate ego drug and gives you a really megalomaniac feeling, so when i entered the stage i often was a bit nervlous and i worried about some things, but man on coke, woohoow, i simply felt like the best, i was going to show everyone hoe its really done,.i felt like God, and this attitude actually helped, but i played so much and difficult works that i developed chronic tendinitis in my wrists and problems with nerves in my fingers, which slowly but surely made IT impossible to me to play piano well and not at all on a professional, this really broke me, IT was the uttermost important thing in my life for which I sacrificied so much and IT was a lifelong dream of mine to become a concert pianist and i was on the way to a great Carreer, i often already daydreamed about playing great concert Halls all over the world, publishing cd's and compositions and give masterclasses to Young talents, maybe one Day slow down and take it a bit more easy teaching as a professor at a conservatory and i prefereer IT to be in another country, so my entire world crashes, and this prompted almost instantly my first real bad drug period, i since then used my entire life a couple of years real bad and i partied and endulged in anything that could give pleasure, switched with yrs of using nothing at all in which I did productive things, of course after a while music money started to run out and I needed money, but there was Just no way i would consider a.normal job,.so i figured out clever ways to in An interesting way in a short time enough money so i could afterwards live well and do nothing a few years but do drugs and so on... Over the years i did many things, for example i set up fake businesses and would score money of other businisses tru ways of investment and such, i manufactured drugs and sold large amounts, i spent two yrs in South America where i trafficked hundred of kilo's.coke,.well actually not more than 220 kilo cause i could not stash more,.by.boat, that's how i lived...

By.now i suffer brain damage and such,.i once.ended up in a coma in which I suffered oxygen deprivation which instantly damaged me a lot,.i dont have the same intellectual capacities anymore as before,.and after losing piano now also this,.these are things i struggle with a lot in life, but im still able to in general be a quite happy person, that's Just my nature...

 

[Antiprosynthesis]

You dont have to Read my previous post if you dont want to, i felt like going off topic and share something personal, only realizing after posting this that such things might Just not interest you...

Okay, you are from the uk, im originally from antwerp, belgium, but already live quite some time in Amsterdam, NL...

How are drugs in the uk?

I actually got with moments quite interested in metaphysics and Continental philosophy, i try to Read as much as i can in the original language as i feel lots get lost in translation, actually translations from german can have their own problems, especially with such difficult texts as Continental philosophy, cause germans have the tendency to create highly complex texts and they do some things like for example they postpone the subject of a sentence till the end, which is complex.but works in german, but this.creates difficulties for translators, making german translations more difficult to Read...

But Lets assume An every day object would not interact with electromagnetic waves, what would IT look like without color? I can not Imagine this...

Im surprised that you say you dont think psychedelics say something about the nature of reality, since if i see things in a different way ergo when i exepierence a.different reality and all that's changed is the way i process information while i believe we agree this other perception of reality is equally real, doesn't this say that the nature of reality is not a fixed thing.but variabel to how we process information meaning that reality is not real in An absolute sense and differs as States of mind differ,.wouldnt you agree this means IT sais something about the nature of reality? If you still dont agree and you feel like IT, argue your point of view, maybe im mistaken about this, and if so i want to find out...

 

[Antiprosynthesis]

Im binging on very strong levo dextro amfetamine BTW, lab tested 69%, are you on anything?

 

[Brendan12]

Knowledge is the source of our intuitions in my opinion..

You feel things because of knowledge..

But where does the knowledge come from?

An anthropomorphism?

Or the collective unconscious perhaps?

Archetypes like the heroes journey.. the fool and the star..

Tarot is an attempt to work with these archetypes.