What is Mathematics? - an addendum to the comments between Talbert and Maggot

GSTalbert1

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Because the comment section is too limited for me to properly address Maggot's requests I've dumped it here. It's important to note a critical point of philosophy is, especially from Wittgenstein's perspective, "what can we know?" or, put another way: "what questions are valid?"
First portion of the thread, here's Wittgenstein's opening and closing comments on the beginning section of his Lectures on the Foundations of Mathematics:

Witt said:
Witt said:
Obviously.
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*1.) This is an understatement. He was trained as an engineer, and more than managed his work, but was continually distracted by his attempts to get at the foundations of mathematics. There is an obvious parallel to the behavior seen in his work as an architect. He also worked with the top philosophers and mathematicians of the era, including Gottlob Frege who considered him to be the next pioneer of the next major step in mathematical philosophy. He was able to comprehend all there was to know about mathematics at the time within two years of working with Bertrand Russell, no mean feat, and the conversations they had would have only been comprehensible to about half-dozen mathematicians/philosophers/logicians.
 

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GSTalbert1

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As to what I find problematic with axioms, it is essentially that they are a priori. I have no problem with the ad hoc nature of postulates that emerge out of the necessity for their existence. Postulates one establishes as linguistic devices to engage in the social aspect of what we would call the scientific enterprise is one thing entirely, establishing them as fact is another. Newton's physics were in trouble long before Einstein as they were based off of axiomatic systematization. With the arrival of Euler and Gauss, the bottom fell out of not only Newton's physics, but also the whole Enlightenment project.

Think about the issues with the partial/wave objection, that's axiomic logic. This includes not only the whole Negative/Positive Freedom axiom favored so much by libertarians but also the modern liberal conception of the individual. We can get into various conceptions but take this intuition pump for starters: say if we were to take away the force of gravity (I realize the impossibility of even asking this question as we know not fully what gravity actually is but entertain the Cartesian Fallacy of a "clear and distinct ideas" for a moment) everything dissipates, does gravity make everything a "super organism"? If not then why do we demarcate "individuals" the way that we do? Why not postulate our bounds around individual cells?

This may seem silly, but you see this arbitrary and unquestioned axiomatic conception of individuality present in Richard Dawkin's Gaps in the Mind -

Richard Dawkins said:
I can assert, without fear of contradiction, that if somebody succeeded in breeding a chimpanzee/ human hybrid the news would be earth-shattering. Bishops would bleat, lawyers would gloat in anticipation, conservative politicians would thunder, socialists wouldn't know where to put their barricades. The scientist that achieved the feat would be drummed out of politically correct common-rooms; denounced in pulpit and gutter press; condemned, perhaps, by an Ayatollah's fatwah. Politics would never be the same again, nor would theology, sociology, psychology or most branches of philosophy. The world that would be so shaken, by such an incidental event as a hybridisation, is a speciesist world indeed, dominated by the discontinuous mind.


I have argued that the discontinuous gap between humans and ‘apes’ that we erect in our minds is regrettable. I have also argued that, in any case, the present position of the hallowed gap is arbitrary, the result of evolutionary accident. If the contingencies of survival and extinction had been different, the gap would be in a different place. Ethical principles that are based upon accidental caprice should not be respected as if cast in stone.

Nevertheless, it must be conceded that this book's proposal to admit great apes to the charmed circle of human privilege stands square in the discontinuous tradition. Albeit the gap has moved, the fundamental question is still 'Which side of the gap?' Regrettable as this is, as long as our social mores are governed by discontinuously minded lawyers and theologians, it is premature to advocate a quantitative, continuously distributed morality. Accordingly, I support the proposal for which this book stands.
Issues with the Kantian Sythentic A Priori presents themselves within examples from Ludwig von Mises' use:

Mises said:
Its statements and propositions are not derived from experience. They are, like those of logic and mathematics, a priori. They are not subject to verification and falsification on the ground of experience and facts. They are both logically and temporally antecedent to any comprehension of historical facts. They are a necessary requirement of any intellectual grasp of historical events...

The modern natural sciences owe their success to the method of observation and experiment. There is no doubt that empiricism and pragmatism are right as far as they merely describe the procedures of the natural sciences. But it is no less certain that they are entirely wrong in their endeavors to reject any kind of a priori knowledge and to characterize logic, mathematics, and praxeology either as empirical and experimental disciplines or as mere tautologies...

New experience can force us to discard or modify inferences we have drawn from previous experience. But no kind of experience can ever force us to discard or modify a priori theorems. They are not derived from experience; they are logically prior to it and cannot be either proved by corroborative experience or disproved by experience to the contrary...
Murray Rothbard takes the axiom of Individual Natural Rights to rather repulsive extremes -
Rothbard said:
The very concept of “rights” is a “negative” one, demarcating the areas of a person’s action that no man may properly interfere with. No man can therefore have a “right” to compel someone to do a positive act, for in that case the compulsion violates the right of person or property of the individual being coerced.

Applying our theory to parents and children ... (t)he parent ... should have the legal right not to feed the child,i.e., to allow it to die.

This is built into our conceptual discourse, it's not just fringe loons. This sort of axiomatic methodology pops up a lot, especially when it comes to political, i.e. ethical, thought. Take Colbert's friendly discussion with Neil deGrasse. Colbert is not in character so to speak and isn't taking on down for some of the fatal errors deGrasse made:


Note 9:10-10:42, we witness the strange instance where a clown trumps an Astrophysicist, and an exceptionally skilled and knowledgeable on at that, on science.

deGrasse said:
What we should do is come to some understanding of what the prevailing social mores are and know science should not cross those barriers and not and by the way scientists are often ones to try to prevent that.
Here he makes a blatantly baseless assertion that scientists often makes: it's better to know than to not know. He then goes on to state this -
deGrasse said:
So when you're not supported by data you discard the hypothesis that's how science works you don't believe something just because you want to.
Ok... then what about the shift from hunter gatherers to agriculture (articles here, here and here - there's this polemic, but it's wrong as the shift isn't Adam and Eve but Cain and Abel, it's good if you want to try to bother Baya Libertarians and Randroids). Cain, as the story goes, was the creator of agriculture and the founder of the state and from him emerges bronze and iron (metallurgy), the pipe and the lyre (music), not to mention the tent and livestock (dwellings & domestication). This subject is broached on by C.S. Lewis -
C.S. Lewis said:
There neither is nor can be any simple increase of power on Man's side. Each new power won by man is a power over man as well. Each advance leaves him weaker as well as stronger. In every victory, besides being the general who triumphs, he is also the prisoner who follows the triumphal car.
or Heidegger
Heidegger said:
I think that ... there is an idea that technology is in its essence something human beings have under their control. In my opinion, that is not possible. Technology is in its essence something that human beings cannot master of their own accord.
Everything functions. That is exactly what is uncanny. Everything functions and the functioning drives us further and further to more functioning, and technology tears people away and uproots them from the earth more and more.
I wouldn't say I agree with Heidegger's perspective, I prefer Lewis' ambiguity, but it's still part of a larger mosaic. Does technology make our lives "better"? This depends on what you mean by "better" do you mean "happy" or "satisfied"? Yet, science says NOTHING about values, it explicitly shuns meaning. This is problematic when we come to the most important part of all: how we are to run society? How are we to USE technology? Should we use technology? He, and every other scientist, merely assumes some sort of inner goodness and seems to willfully ignore the many many instances in which scientists use technology in ways that are morally offensive to what we would refer to as modern sensibilities. He basically resorts to ad popularum to justify the critical axiom that underpins science in order to brush aside moral or ethical considerations. The reason why modern science can't take into account the the Eden Paradox because to do so would throw out the whole enterprise. Philosophy is the search for the Truth, with a capital T, to understand the universe as it actually is, or as closely as we human beings can come to it. This is nothing less than an act of Faith.

Interestingly, at 43:12-43:45 deGrasse, unwittingly, may as well have sloppily paraphrased Maimonides:

deGrasse said:
And I .. instead of using the word "identity" I'd say: They have an impact on our ego because the more we learn about the universe, the smaller we get in time, and space, in size. I think if you know about what's going on then it's not mysterious and you're a participant in the unfolding cosmos otherwise you are consumed by it and you fear it and you shun it and you say "I don't want to know that I live on a speck called Earth orbiting an undistinguished star, in the corner of an ordinary galaxy in an expanding void of the cosmos There are some happy thoughts in there, like like understanding how that worked recognizing that the human brain figured that out that's kinda cool There's a lot we still don't know but what we do know, I think we can sit proudly and celebrate what we know about the universe.
Though Maimonides phrasing keeps the root of what is being said while pruning deGrasse's obscenities against science & reason.
Maimonides said:
When a man reflects on these things, studies all these created beings, from the angels and spheres down to human beings and so on, and realizes the divine wisdom manifested in them all, his love for God will increase, his soul will thirst, his very flesh will yearn to love God. He will be filled with fear and trembling, as he becomes conscious of his lowly condition, poverty, and insignificance, and compares himself with any of the great and holy bodies; still more when he compares himself with any one of the pure forms that are incorporeal and have never had association with any corporeal substance. He will then realize that he is a vessel full of shame, dishonor, and reproach, empty and deficient.
Looking at the history of ideas we always assume that there is nothing, I mean literally nothing, our ancestors can possibly tell us about ourselves? They are all superstitious, magical thinking, troglodytes that remarkably survived in spite of myths that sunbeams from Jesus teleports demons that make the world every last Thursday. However, they aren't as stupid as one would assume and we aren't as smart as we think. We don't know how the mind works, and just because we know how to drop rocks in amazing ways doesn't mean we know how people work. If we assume that evolution isn't some pipe dream, and that our minds both possess the ability to comprehend and are designed to interact and engage a social environment, then we know just as much about ourselves and knowledge as did our ancient ancestors. Thus it is extraordinary hubris to reject out of hand what they had to say on Man and Man's place in the world, they spent as much (if not a hell of a lot more) time studying and observing human behavior.

Leo Strauss made a striking observation on the differences between the various philosophic sciences in different civilizations -
Strauss" said:
It is true, the Islamic theologians, the Mutakallimun, had asserted the existence of rational laws which were practically identical with what were called natural laws in the Occident; but the Islamic-Jewish philosophers reject this view altogether. The rules of conduct which are called by the Christian scholastics natural laws and by the Mutakallimun rational laws, are called by the Islamic-Jewish philosophers: Generally accepted opinions.
As to the matter of examples of alternative, non-axiomatic, mathematics developments (which by the way organic branches like those of a tree does NOT imply "roots") I'll post in a bit.
 

GSTalbert1

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@CallMeMaggot your request for examples, and links, of the development of mathematics outside the Greek axiomatic paradigm. There's the Rhind Papyrus describing the system of mathematics used to teach students, none of it has axiomatic proposition they present much of this as a mysterious given.

The text I'm drawing from is Victor J. Katz's History of Mathematics, which is a pretty good but does a lousy job if you're actually trying to learn ancient notation, but here's a quote from a quote off of Wiki:

Greek mathematics was much more sophisticated than the mathematics that had been developed by earlier cultures. All surviving records of pre-Greek mathematics show the use of inductive reasoning, that is, repeated observations used to establish rules of thumb. Greek mathematicians, by contrast, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them.

Martin Bernal, "Animadversions on the Origins of Western Science", pp. 72–83 in Michael H. Shank, ed., The Scientific Enterprise in Antiquity and the Middle Ages, (Chicago: University of Chicago Press) 2000, p. 75.
As for more concrete examples, take the Rhind Papyrus:



There is no attempts to explain this, it takes much of this as given.



The Egyptian visual representation of Fractional mathematics via the Eye of Horus -



The world's oldest mathematical text:




Here's from the Zhoubi Saunjing, which dates back to at least several hundred years B.C. describing the use of geometry to solve an algebra problem using the piling of the squares technique:



From A History of Mathematics

Is the argument just given a proof? To meet modern standards, standards it would be necessary to show either that the inscribed figure (the square on c) or the circumscribed figure (the square on a + b) is in fact a square. To the ancients, however, and probably to most students today, this was obvious. The Chinese had no notion of an axiomatic system from which theorems could be derived. "Proof" means where simply a convincing argument. In fact, the earliest Babylonian records of the theorem have no argument for it at all. Nevertheless, the argument given here would certainly have been accessible to the scribes.
I have not moved my God damn field goal once by the way.
 

GSTalbert1

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As to the nature of what is mathematics. That I don't know, but I have speculations. Take Jake Barnett, that little autistic child. Autism specifically is an intense focus on the senses, to the point where they are unable to filter various sensations or cognitive behaviors as most people. The issue with language is not that they lack the capacity to socially and linguistically engage others, but that during critical periods they attention is absorbed by distractions that take up the majority of their neurological formation. The result is that in addition to their already abnormal brain functioning they receive a fundamentally different experience that further removes them from the rest of society. The severity of autism depends on when, and if, one is able to begin some form of semantic communication with a child. There has always been a marked parallel between autism, among other disorders, and mathematics that goes beyond the pop culture. I won't go too deep into details, unless necessary, but I'd say there's a link between the atomic structure of our nervous system and mathematics in that there is a direct parrallel between our sensory input and it's interpretation and mathematical ability and therein may lie the link between autism, with it's overwhelming sensations, and math.



Take the nameless slave boy in Plato’s Meno, whom Socrates demonstrates his theory of math with an exercise in mathematical pedagogy using this square diagram:



Throughout he elaborates his theory through what had transpired.

Meno said:
Soc. Do you observe, Meno, that I am not teaching the boy anything, but only asking him questions; and now he fancies that he knows how long a line is necessary in order to produce a figure of eight square feet; does he not?

Soc. And at present these notions have just been stirred up in him, as in a dream; but if he were frequently asked the same questions, in different forms, he would know as well as any one at last?

Soc. But if he always possessed this knowledge he would always have known; or if he has acquired the knowledge he could not have acquired it in this life, unless he has been taught geometry; for he may be made to do the same with all geometry and every other branch of knowledge. Now, has any one ever taught him all this? You must know about him, if, as you say, he was born and bred in your house.
Men. And I am certain that no one ever did teach him.

Soc. And yet he has the knowledge?

Men. The fact, Socrates, is undeniable.

Soc. But if he did not acquire the knowledge in this life, then he must have had and learned it at some other time?

Men. Clearly he must.

Soc. Which must have been the time when he was not a man?

Men. Yes.

Soc. And if there have been always true thoughts in him, both at the time when he was and was not a man, which only need to be awakened into knowledge by putting questions to him, his soul must have always possessed this knowledge, for he always either was or was not a man?

Men. Obviously.

Soc. At any rate, will you condescend a little, and allow the question "Whether virtue is given by instruction, or in any other way," to be argued upon hypothesis? As the geometrician, when he is asked whether a certain triangle is capable being inscribed in a certain circle, will reply: "I cannot tell you as yet; but I will offer a hypothesis which may assist us in forming a conclusion: If the figure be such that when you have produced a given side of it, the given area of the triangle falls short by an area corresponding to the part produced, then one consequence follows, and if this is impossible then some other; and therefore I wish to assume a hypothesis before I tell you whether this triangle is capable of being inscribed in the circle":-that is a geometrical hypothesis.
This is essentially what I’m stabbing at when I say that axioms are unnecessary for mathematics, even postulates. The reason Jake Barnett or Von Neumann, or various Rain Men etc, learn say calculus within two weeks is because I believe there exists two facets of mathematics, the cognitive and the linguistic. This can be developed further into the philosophy of science but that’s irrelevant for our current discussion. The cognitive aspect seems to be a conscious awareness of the brain’s processing of sensory perceptions.
Hegel speaks of what I’m talking about, the ability of the mind to become aware of its processes:

The Science of Logic said:
To begin with, therefore, it is only the abstract moments that belong to self-consciousness concerning the substance. But since these moments are pure activities and must move forward by their very nature, self-consciousness enriches itself till it has torn from consciousness the entire substance, and absorbed into itself the entire structure of the substance with all its constituent elements. Since this negative attitude towards objectivity is positive as well, establishes and fixes the content, it goes on till it has produced these elements out of itself and thereby reinstated them once more as objects of consciousness. In the notion, knowing itself as notion, the moments thus make their appearance prior to the whole in its complete fulfillment; the movement of these moments is the process by which the whole comes into being. In consciousness, on the other hand, the whole – but not as comprehended conceptually – is prior to the moments.
Now, axioms or even postulates, are not necessary to do mathematics. It’s interesting though that to some this would appear to be the case. This speaks volumes about language, but not mathematics. Language has the capacity to express human experience, but it requires a common pool of experience with which it can relate. The “postulates” and mathematical symbolism, the mathematical language, can only truly speak of the common aspects of a shared reality. The idea that postulates or axioms are extant realities or central to mathematics, and certainly not mathematical process, but they are necessary for mathematical communication as axioms and postulates are necessary for all communicative processes. Now, postulates such as “2” “3” “4” always exist as do concepts as “house” “dog” etc etc, though mathematics is indeed bound to culture as the way in which we perceive and experience numbers greatly influences how we approach them. Take the Pythagorean cult who would sit around in a circle trying to contemplate π, the realization of which would be the achievement of nirvana, and also claimed a man was drowned by the gods for the impious act of divulging the secret of irrational numbers. They would certainly have a very different approach to math, I am certainly not going to make the stupid assessment that such a perspective is inferior and yields inferior results; are you?

Greeks Philosophy is about trying to find Truth, with a capital T. I believe that such a quest is not only a worthy and noble one, but without this science becomes not only impossible but absurd. It is from this search that Axioms were created, that in them lies True Knowledge, this forms the basis of the works of Euclid. This is essentially what Philosophy, and incidentally science, seeks to do to create an irrefutable system of knowledge. Axioms are useful fictions with which we may organize our thoughts and, in the same way that a microscope provides great clarity, allow us to see the world with greater clarity. However, also like a microscope such useful fictions and methodologies are USELESS when you try to view and navigate a wide world through a narrow lens.

Side note:
Maimonides offered a fascinating critique of some of the conclusions derived from Plato's sort of logic, he posits his own version of Plato’s slave boy in the Meno to critique both Plato and Aristotle. Though, he engages Aristotle he doesn’t mention Plato, but that’s all part of the intellectual puzzle of the Guide to the Perplexed. Like the slave boy his character is perfect in intelligence, yet is unable to accept basic facts of life because they seem ridiculously absurd.

EVERYTHING produced comes into existence from non-existence; even when the substance of a thing has been in existence, and has only changed its form, the thing itself, which has gone through the process of genesis and development, and has arrived at its final state, has now different properties from those which it possessed at the commencement of the transition from potentiality to reality, or before that time. Take, e.g., the human ovum as contained in the female's blood when still included in its vessels: its nature is different from what it was in the moment of conception, when it is met by the semen of the male and begins to develop: the properties of the semen in that moment are different from the properties of the living being after its birth when fully developed. It is therefore quite impossible to infer from the nature which a thing possesses after having passed through all stages of its development, what the condition of the thing has been in the moment when this process commenced; nor does the condition of a thing in this moment show what its previous condition has been. If you make this mistake, and attempt to prove the nature of a thing in potential existence by its properties when actually existing, you will fall into great confusion: you win reject evident truths and admit false opinions. Let us assume, in our above instance, that a man born without defect had after his birth been nursed by his mother only a few months; the mother then died, and the father alone brought him up in a lonely island, till he grew up, became wise, and acquired knowledge. Suppose this man has never seen a woman or any female being; he asks some person how man has come into existence, and how he has developed, and receives the following answer: "Man begins his existence in the womb of an individual of his own class, namely, in the womb of a female, which has a certain form. While in the womb he is very small; yet he has life, moves, receives nourishment, and gradually grows, till he arrives at a certain stage of development. He then leaves the womb and continues to grow till he is in the condition in which you see him." The orphan will naturally ask: "Did this person, when he lived, moved, and grew in the womb, eat and drink, and breathe with his mouth and his nostrils? Did he excrete any substance?" The answer will be, "No." Undoubtedly he will then attempt to refute the statements of that person, and to prove their impossibility, by referring to the properties of a fully developed person, in the following manner: "When any one of us is deprived of breath for a short time he dies, and cannot move any longer: how then can we imagine that any one of us has been enclosed in a bag in the midst of a body for several months and remained alive, able to move? If any one of us would swallow a living bird, the bird would die immediately when it reached the stomach, much more so when it came to the lower part of the belly; if we should not take food or drink with our mouth, in a few days we should undoubtedly be dead: how then can man remain alive for months without taking food? If any person would take food and would not be able to excrete it, great pains and death would follow in a short time, and yet I am to believe that man has lived for months without that function! Suppose by accident a hole were formed in the belly of a person, it would prove fatal, and yet we are to believe that the navel of the fetus has been open! Why should the fetus not open the eyes, spread forth the bands and stretch out the legs, if, as you think, the limbs are all whole and perfect." This mode of reasoning would lead to the conclusion that man cannot come into existence and develop in the manner described.
 

CallMeMaggot

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Dude...I really tried, but you really strike me as ADHD ridden

You leap from one theme to another without pause, make pretty weak connections between them, apply conclusions from one to another tenuously related etc etc

It's exhausting.

Bottom line: This post can't be messier. Lol, no surprise you like so much ole Witty

Ok, let's go, briefly:

On the part about Witty, I just see him boasting about how he's gonna deconstruct maths and give symbols new meanings... but just produce a ridiculous example of a lay man mistaking "irrational numbers" with "hysterical numbers"

Groundbreaking.

Also, all this sounds to me like he was in the middle of changing his worldview from "being based around logic, and thus, maths" to "being based on acts, and thus, games"

On the part about Dawkings:
Richie is a retard, all etics are based on accidental chains of events a.k.a history & reality

Axioms aren't really purely a priori, cause no thinking is really a priori.
Raise a child in a sensory privation tank, and you'll see my point. No ideas, no languajes, no axioms, no in ferences...no fucking brain

That some ideas, stupid or not, outside maths are called in fact axioms, doesn't mean they are, nor say anything about their validity. People missusing the lenguaje is a sad erryday fact

Those parts about Cain, Lewis and the lot...you lost me there, no clue about their relevance to the disscussion about maths...but I really didn't try, I must confess.
Next time, perhaps you should try not to cramp a dozen different subjects in the same post

Are u high on meth, or something?

The part about the un-axiomatic maths...I have to say, it looks fucking weak

You are basically saying two things there, that pre-greek axioms certainly existed, just that they were a bit undefined for our actual taste., and that being ancient, we know little about them.

And that the religious and pseudo-mystic organization of egypcians permeated all, even their school system (shocking truth! )

Oh, and the chinks...you surelly realize that in that example you give, those slanted-eyes bastards totally got the concepst (axioms) of square, 90 degree angle, sum, fraction, pitagoras, etc

Another thing entirely different is that they are slick motherfuckers with a penchant for looking mysterious and sage, you know...

But having axioms more loosely defined, and trying to avoid exhaustive demonstrations hardly is any improvement

"Proof" means where simply a convincing argument.
Lol, exactly as us...just that they take in account the lenght of the beard of the master even a bit more than us.

Socrates: motherfucking cheater, lmao. Of course he was directing that child to give the correct answers. Try that with the one raised in the privation tank, and see if "the truth" is in him too-lol

The fact that there is correlation between maths and reality, and so our nervous systems can have a good intuitive grasp of it, doesn't mean that we don't need to start from some basic assuptioms in order to formalize that knowledge.

Anything that has to be formalized, put on paper, criticised (something that chinks avoid to do with their elders...hint, hint!) etc needs to start from somewhere

You can call that starting point axioms or intuitions from ur inner Goddess, and with both tags, you can do a lousy job or a good one. But it's a lot easier if you do it with some method and discipline.

Also, you can do it in two weeks a la Rain Man...if you are a genius savant. And play blackjack, cause I can assure you, Kim Peek never wrote a maths text. In fact, he couldn't explain the moral lesson of any child's book...because, u know, he was a retard

Von Newman and Barnett are entirely different beasts...and I will bet my left nut both of them have axioms and formal logic in high regard, mind you :)
 

GSTalbert1

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Dude...I really tried, but you really strike me as ADHD ridden

You leap from one theme to another without pause, make pretty weak connections between them, apply conclusions from one to another tenuously related etc etc
When talking about quantum mechanics I doubt we should have to establish slope. These are all very basic concepts, I wrote assuming I was speaking to someone who knows what they are talking about. I now realize I'm talking to someone who thinks they know what they are talking about. I'll slow things down for you.

On the part about Witty, I just see him boasting about how he's gonna deconstruct maths and give symbols new meanings... but just produce a ridiculous example of a lay man mistaking "irrational numbers" with "hysterical numbers"
I... don't know what to say. How, how you can not only not understand what he's saying but then posit the exact opposite of what he IS saying is... remarkable.

Groundbreaking.
not really. It's the intro there's nothing really groundbreaking in the lectures. I posted it because his humor is very subtle, most people think he didn't have one but he does, he takes shots at himself the entire time. It's a simple seminar on mathematics for advanced students in logic and the philosophy of mathematics, so I would understand why you'd have trouble with it but... this is just the opening.

Also, all this sounds to me like he was in the middle of changing his worldview from "being based around logic, and thus, maths" to "being based on acts, and thus, games"
Not really, you're regurgitating shit you read on wikis, poorly.

Axioms aren't really purely a priori, cause no thinking is really a priori.
Raise a child in a sensory privation tank, and you'll see my point. No ideas, no languajes, no axioms, no in ferences...no fucking brain
Then you agree with me that axioms are useful fictions, otherwise Axioms are a priori that's why they are axioms and not merely postulates. Mind you the blend of axioms and postulates is essentially what's been going on in the later half of the 20th century.

People missusing the lenguaje is a sad erryday fact
That's Wittgenstein's point.

Those parts about Cain, Lewis and the lot...you lost me there, no clue about their relevance to the disscussion about maths...but I really didn't try, I must confess.
Next time, perhaps you should try not to cramp a dozen different subjects in the same post
I was laying out a series of examples in which the pre-quantum axiomatic model (classical physics) of mathematics has permeated other fields of scientific inquiry - like how science is self-correcting.

Are u high on meth, or something?
:baked: & manning the front desk @ work. Nothing to do for about 6 hours, this all is actually a stitched copypasta of various correspondences.

The part about the un-axiomatic maths...I have to say, it looks fucking weak
well you either don't understand axioms or you're moving the field goal.

You are basically saying two things there, that pre-greek axioms certainly existed, just that they were a bit undefined for our actual taste., and that being ancient, we know little about them.
No, you're moving the field goal. Note in my original comment to you that axioms are useful fictions.

Anything that has to be formalized, put on paper, criticised (something that chinks avoid to do with their elders...hint, hint!) etc needs to start from somewhere
You do realize you're arguing postmodern bullshit. Especially your appeal to historicism and the brain in the vat, seriously that's just a poor man's sloppy version of decartes' demons, not the brain in a vat mind you but what you said. I already pointed out the social and historical aspects are helpful both in directing development and COMMUNICATING experiences, including mathematical ones. My point is that people inherently have spacial intelligence, you don't really have a point unless it's agreeing with what I've already said.
You can call that starting point axioms or intuitions from ur inner Goddess
I didn't bother with either, I certainly don't know what the hell an "inner Goddess" is but it sounds like some delusions you have about the "enemies of science".
, and with both tags, you can do a lousy job or a good one. But it's a lot easier if you do it with some method and discipline.
I'm not arguing against that.

Also, you can do it in two weeks a la Rain Man...if you are a genius savant. And play blackjack, cause I can assure you, Kim Peek never wrote a maths text. In fact, he couldn't explain the moral lesson of any child's book...because, u know, he was a retard
:picard:

The fact that there is correlation between maths and reality, and so our nervous systems can have a good intuitive grasp of it, doesn't mean that we don't need to start from some basic assuptioms in order to formalize that knowledge.
You're saying that our nervous system can have a grasp of math and reality posits that math is external. Moreover you then contradict yourself in the second sentance by claiming that the formalization of math is part of "reality" rather than a social convenience. I'm saying the nervous system's interpretation of sensory input IS math, the formalization that we utilize to communicate with each other is exactly that, a formalization of processes that we naturally do. It is not some sort of external platonic reality but in fact a psychological process, that it is psychological does not negate it's relationship to external reality but is, I think, the mediating process with our external reality. The extent of mathematics is the extent of our sensory systems. This is what makes the human mind so remarkable. Though you're too stupid, ignorant, and high on your own assfumes to understand this, there is a relationship between Barnett and Neumann and the Rain Man.

On the part about Dawkings:
Richie is a retard
Agreed. Doesn't change the fact that his views are very much a standard within academics.
 

CallMeMaggot

Girlvinyl
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see below, in white
I'll slow things down for you.

Good. Do it. I'll try to make you sounds like a coherent debater



I... don't know what to say. How, how you can not only not understand what he's saying but then posit the exact opposite of what he IS saying is... remarkable.

Tell me, in a few and simple words, what he's saying, pls.


not really.

No, certainly not, lol


Not really, you're regurgitating shit you read on wikis, poorly.

True dat. And that makes it utterly valueless...haha, still your old habits.
I remember our first discussion, you didn't refrain either of the old trick of "WK?, lol, loser" back then


Then you agree with me that axioms are useful fictions, otherwise Axioms are a priori that's why they are axioms and not merely postulates. Mind you the blend of axioms and postulates is essentially what's been going on in the later half of the 20th century.

*Sigh... Give me an example of an axiom and and example of a postulate

In modern maths, there's no difference between those terms.

In ancient Greece, there was a slight difference of scope, pretty subtle.

You, again, got excited with some petty point and magnified it to a ridiculous scale. As always.

Proof:

http://wiki.answers.com/Q/What_is_the_difference_between_and_axiom_and_a_postulate?#slide=2

http://mrwadeturner.pbworks.com/w/page/25148928/Postulates, axioms and Theorems

http://en.wikipedia.org/wiki/Axiom

That's Wittgenstein's point.

And to say that obviety he needed years of lectures? What a Gaylord

pre-quantum axiomatic model of mathematics

WTF are you babbling about dude?

Link, pls.

well you either don't understand axioms or you're moving the field goal.

True dat too. I haven't a clue about what u are saying. You seem to be talking about some magical concepts (axioms) which come right out of the blue, or are pure embodiments of...of...I dunno...our nervous systems? Reality?

But anyways, not based in any previous concept nor experience? Is that what u mean with a priori?

As you can see, I don't know what are you tryng to say

Please, state in a few and simple words what do you mean with a priori

No, you're moving the field goal. Note in my original comment to you that axioms are useful fictions.

Yeah, not based in experience, but magically fitting with reality...because they come from our nervous architecture, I guess? Which is "true", but somehow they are still fictions. I get it.

Well, nope.

You do realize you're arguing postmodern bullshit.

No, I don't. I don't give a fuck about if what I'm saying pertains to that movement or another, which probably I don't know shit about anyways because I haven't read about it, and cause I don't have either your anal obsesions with labels.

My point is that people inherently have spacial intelligence, you don't really have a point unless it's agreeing with what I've already said.

Agreed.

But without formalization and elaboration, and to formalize and elaborate anything you need starting points, a commond ground of agreements (AXIOMS)... you can't go too far just with that innate capacity, unless you are an intuitive genius...and if you are, you anyways can't comunicate those intuitions without a code of communication with others...which needs starting points too etc etc


I didn't bother with either, I certainly don't know what the hell an "inner Goddess" is but it sounds like some delusions you have about the "enemies of science".

Lolwut.

So...you don't bother with starting points and reasoning from there...you go right for the conclussion

How bayesque


:picard:


My original assertion was: "Kim Peek never wrote a maths text. In fact, he couldn't explain the moral lesson of any child's book"

Please, explain in a few and simple words what in that sentence is deserving of a facepalm.


You're saying that our nervous system can have a grasp of math and reality posits that math is external.

Not external/internal, that dicotomy is absurd. Reality has a mathematical structure, as demonstrated by the fact that huge chunks of it can be mathematically described with positive results.

Moreover you then contradict yourself in the second sentance

What second sentence, retard? You quoted just one.

See how difficult is to try to have a coherent conversation with you?

by claiming that the formalization of math is part of "reality" rather than a social convenience.

Nope, I didn't said that. Please, quote me saying that.


Fucking cheater :D


I guess you can call the abaility of making thing more complicated than buckets and
I'm saying the nervous system's interpretation of sensory input IS math, the formalization that we utilize to communicate with each other is exactly that, a formalization of processes that we naturally do.

It is. All is maths, in some sense.

Walking is moving. We walk naturally. Saying that Advanced Mechanics 201 is just a formalization of what we do naturally sounds a bit retarded to me, but in some extent I guess is it.

But...who would you hire to buid a bridge,...an ingenieer, or Usain Bolt?

And the ingenieer certainly started his studies with a bunch of your hated axioms, lol


The extent of mathematics is the extent of our sensory systems.

Vat.

So deaf people are worse matemathicians? Or are you saying that we have intuitive and innate grasp of multidimensional geometry, exotic manifolds and the cardinality of infinite sets?

Bwhahaha, ookkkeyyy

No dude, we (except again, some geniuses) have intuitive grasp of thing like 2,+, 1/2, maybe square roots and negative numbers and the like. The most basic mathematical concepts. The 99,99999999999999% remaining it's not intuitive and comes from centuries of elaboration from axioms

Though you're too stupid, ignorant, and high on your own assfumes to understand this

There, there...all is gonna be okay...who's the prettiest? who's the prettiest? Talby is!!!

Better?

:D:D:D
 

Baya Rae 4900

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Thank god I just put Talbert and Baya on Ignore. This thread is even kinda funny that way :D
What did I do?

Stop. You know not what demon you are calling forth. The Eight Psirhc, Keeper of Tribes. Baya Rae, the world of 4900 different and separate realities with no commonalities between them.
*cough*

You're forgetting Patron Saint of Humanity. Oh and I'm not going to contribute. I told Maggot that Tally was a crazy idiot and he didn't believe me. Now he gets to experience it first hand.
 

Twaek

EDF Elite
Joined
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Messages
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I think you both have valid points. Maggot is correct, a lot of this looks like Talbert Wikipedia in a blender. And I'm sure Talbert has a point, because it's statistically impossible for there to not be a point somewhere in there. Are you apporaching this right? Remember, you quoted a segment of a Socratic dialogue, Mister Talbert, so wouldn't that mean that you believe it is a valuable way to come to an understanding, right? Wouldn't it be more beneficial to make a point, post it, let the other guy respond, respond to that, let him respond, blah blah blah?
Don't be a Bayamarchus.
 

Fraud Based Economy

Disinherited Nigerian Prince
Joined
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Messages
2,732
I always saw mathematics as a series of numeric abstractions that often (though not always) are useful in constructing models for various physical phenomena, and is formed using the language of logical rigor.
 

Arcticphoenix95

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Twaek said:
And I'm sure Talbert has a point, because it's statistically impossible for there to not be a point somewhere in there.
His point is that axioms, which are self-evident or universally recognized truths, are unnecessary in mathematics. That's about all I could gather from his text walls.
 
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