scientific community is deeply committed

Andrew Wiles had a proof of Fermat's Last Theorem that had a hole, but then he corrected the hole and got a legitimate proof. This would mean, according to Popper's "falsifiability" theory, that mathematics is a pseudo-science.

The scientific community is deeply committed to a view of its own destiny which is well articulated by theoretical physicists. Historically, science is a series of commitments to mathematical apparatuses which, once they are established, are endlessly elaborated, but never discarded. One builds on Newton, Maxwell, etc., by recycling them; one never repudiates them.

In pure mathematics, the equivalent to this stance is that nobody wants to change the decision for the infinity of primes or the irrationality of [root]2 which was made at the outset of rational mathematics. These tenets are held to be valid by the latest, "Left-wing" standards--and to be the source and guiding light for all that followed them in mathematical history. The profession does not want the Greeks--who adopted the elementary theorems on the basis of elementary proofs--to have taken any other course.

Just as liberal feminists are frequently content with a minimal agenda of legal and social equality for women and ``pro-choice'', so liberal (and even some socialist) mathematicians are often content to work within the hegemonic Zermelo-Fraenkel framework (which, reflecting its nineteenth-century liberal origins, already incorporates the axiom of equality) supplemented only by the axiom of choice. But this framework is grossly insufficient for a liberatory mathematics, as was proven long ago by Cohen (1966).

>>2
you've butthurt.

>>1
Einstein made Newton his bitch.

the hegemonic Zermelo-Fraenkel framework (which, reflecting its nineteenth-century liberal origins, already incorporates the axiom of equality) supplemented only by the axiom of choice.

lol sokal

the irrationality of [root]2
But there's a proof for that.

>>6
...that uses infinity to prove infinity

>>7
also, it uses Law of Excluded Middle (yet another religious postulate).

you can work within frameworks which don't exclude the middle like in synthetic diffgeo

>>9
synthetic
From what is it synthesized? From "infinitesimals"?!! Please, dont be such a jew, nyasha!

Whats the definition of ``pseudo-science'' ?

Look at it this way.

On most browsers, you can bring up your browsing history by pressing Control-H. (No, this is not going to become a discussion of werecows.) On Firefox, this brings up a sidebar that shows up on the left side of the window. If you put your mouse over the edge of the sidebar, the cursor will turn into a different kind of arrow. By clicking and dragging it, you can move the edge of the sidebar back and forth. You are, to put it another way, manipulating the border between the normal window and the history window. By moving the mouse, you can increase the portion of the window devoted to either part. In a more extreme view of this situation, you're increasing or decreasing the amount of existence the sidebar has.

Now, let's apply this idea to something more abstract. Look out your window. If you don't live in a highly urbanized area, you should be able to see the horizon. Think of this as the border between the land and the sky. The land and sky are obviously distinguishable thanks to this boundary. Now, if you were to "drag" the sash between the sky and the land, or to manipulate the border between land and sky, you would end up causing the sky to become larger and the land to become smaller, or vice versa. An effect of this might be to cause something that was just on the ground to suddenly be hundreds of feet in the air. Truly a frightening situation to be in. So, look at it this way - manipulating the border between two physical things shifts whatever balance there is in the interaction between those things. Alternatively, by manipulating the border between two things, you can change the manner in which they exist.

Still, this isn't *that* abstract, since it's still dealing with real things in the real world. Many believe that in this world, there are those things that are true, and those that obviously aren't. This divides reality into two extremes: truth and falsehood. But, since we have two extremes, logically one can imagine a boundary between those two extremes - the border between truth and lies. If one were to manipulate this border, suddenly things that were pure fantasy (flying pigs, for the sake of argument) have become reality - or things from reality have ceased to exist. This is how Yukari is said to have invaded the moon - by manipulating the border between truth and lies, as applied to the reflection of the moon on a pond, she was able to make the reflection of the moon into a manifestation of the actual moon, and so send her youkai army onto it. This is what's truly amazing about Yukari's power - the ability to manipulate the border between completely abstract concepts allows her to fundamentally change reality as we know it (at least in terms of two abstract concepts).

>>10
smooth topos are pretty awesome man

>>11
Pseudo-science is a "science" invented by jews for the sole purpose of tricking people off their money. For example, that you can save your "soul" by giving all your money to the church, or that you can make money by investing into Ponzi-schemes.

Actually, current world economy is the one big ponzi scheme, that has no physical foundations for its claims.

An example of a pseudo-scientist:
http://en.wikipedia.org/wiki/Bernard_Madoff
Bernard Madoff is the admitted operator of what has been described as the largest Ponzi scheme in history.

Madoff was born into a Jewish home in the New York City borough of Queens, on April 29, 1938, and is the son of Ralph and Sylvia (née Muntner) Madoff.

Are you hoping to eventually troll someone with this, or did you just arbitrarily decide that this would be a good place to put your spastic syphilitic delusions into something resembling writing?

This reads like they kicked you out of /sci/, poor boy. Wanna have a doughnut?

>>16
Yeah! I'm trolling, Universe is infinite, you can divide matter into infinitesimal particles, von Neumanm didn't said that "In mathematics you don't understand things", wikipedia lies, jews are honest people, that don't create ponzi-schemes, and you will burn in hell.

>>17
Math is a useless pseudo-science and you cant disprove me. Go! Cry to moderators.

>>17
^{RG9uJ3QgaW5jaXRlIGhpbSwganVzdCB3YWl0IHRpbGwgaGUgZ2V0cyBib3JlZCBhbmQgZ29lcyBhd2F5LiAK}

Mathematicians like to reassure themselves that foundational questions are resolved by some mumbo-jumbo about "Axioms" but in reality successful mathematics requires familiarity with a large collection of "elementary" concepts and underlying linguistic and notational conventions. These are often unwritten, but are part of the training of young people in the subject. For example, an entire essay could be written on the use, implicit and explicit, of ordering and brackets in mathematical statements and equations. -- Norman J Wildberger, Associate Professor in Mathematics.

http://shawnslayton.com/open/books/Book%20%20Michael-Shermer-Why-People-Believe-Weird-Things.pdf

>>1
'Controversial, outlandish claims related to mathematics'
>>2-9000
'NONCONSTRUCTIVE ARGUMENT!'

/thread

>>23
/THREAD MY ANUS

Theory and practice sometimes clash. And when that happens, theory loses. Every single time. -- Linus Torvalds

Thread thread = new Thread(Thread.DefaultThread);

>>1

His particular proof was what was falsifiable. His proof wasn't "mathematically correct" until it wasn't falsifiable (as far as we know). In other words, it didn't belong to the world of mathematically correct ideas until he fixed it. I don't see how that invalidates mathematics under Popper's definition.

I also fail to see the relevance of the political spectrum in your one-man tirade against mankind's entire intellectual history. I think questioning the very nature of science is something that's necessary and long-overdue, but it seems to me that you just deteriorate into angry babble.

If I've misunderstood you, I apologize. Please correct me.

>>22
btw shermer is the biggest retard there is. He would write a hit-piece on how midgets are leprechauns if that would be the 'consensus'.

>shermer is the biggest retard there is.
But he has courage to criticize Ayn Rand fanatics.

In other words, it didn't belong to the world of mathematically correct ideas until he fixed it.
And who decides, what "belongs" and what doesnt? Consensus? You should apologize to Shermer.

>I also fail to see the relevance of the political spectrum in your one-man tirade against mankind's entire intellectual history.
Do you? But that is pretty simple: there always was struggle between objectivists and subjectivists on all levels of society. You can even see it in programming, where some advocate objects, while others say that there is no such things as "objects" only recursive functional relations. Basically, objectivists advocate top-down approach, while subjectivists say that top-down is secondary to bottom-up.

For example, communists are objectivists, as they think that society can be organized top-down by centralized authority, that acts like God, without taking in consideration feedback from individuals.

>>29

And who decides, what "belongs" and what doesnt? Consensus? You should apologize to Shermer.

Why should I apologize to Shermer? Is there something relevant in that PDF or are you confusing me with another poster? >>27 was my only post, >>28 is not me.

Mathematical correctness is decided when the given proof is logically valid based on the given assumptions and ideas that create the system the proof is "working in." If you're going to question any part of that process, it makes more sense to question the underlying foundations of the argument, not the argument itself. As such, you can change *any* basic property of mathematics you want to anything you like, but it has to follow from what you've outlined as properties or axioms. In that sense, everything we've "decided" about mathematics is really a deduction from a hierarchy of simple ideas. If you wish to create a mathematical world where different things are true, nobody is stopping you from picking different properties and going nuts. In fact, for an example of where this has already happened, look at non-Euclidean geometry.

That's the Platonic ideal of mathematics, at least. If you want to argue that our mathematical community is a circlejerk that churns garbage, and that correctness "in the real world" is decided up by people, go right ahead (I'm going to need some evidence to support it, but that's irrelevant). But don't mix up the two, because when you do it makes your argument at best hard to follow and at worst invalid.

Mathematics is just a very large game. As such, I still don't object to you claiming it's not a science, because in a sense it isn't. However, I really don't think Popper's classification is the best tool for refuting its status as a science, at least not in the way you used it above.

Now, what *is* interesting, is the idea that you could create any axiomatic system to support any proposition. That might almost fit the definition Popper used, but there's still another point to be considered: while I can create any arbitrary system to support my ideas, in order to fit within that system things still have to be proven, so there are still ideas that either will or will not work within * that * system.

Also coming in on your side, I think, are Gödel's incompleteness theorems. You can decide if "undecidable" propositions break math's status as a science.

It seems to me that it just comes down to semantic wordplay, and this whole mess assumes you accept Popper's definition anyway. The cold hard fact is that while some science comes down to an incestuous relationship with mathematics, the imperfect, arbitrary models we come up with *do* work well enough to provide usable predictions. It's a long way off from being a deity, but science *does* give us at least some control over nature, and the math *does* back that up at least a little.

tl;dr - I don't think it matters a whole hell of a lot, as long as you remain sensible about math and don't claim to find proof of God's existence in a Calculus book.

>>30
>Mathematical correctness is decided when the given proof is logically valid
And who decides "logical validity"? Because mathematics is a social construction, it is driven a social consensus.

>don't claim to find proof of God's existence in a Calculus book.
I cant claim, that found proof of Infinity's existence in a Calculus book, ether. Just as cant claim that after reading Bible or Quran.

>it is driven by a social consensus.
self fix

>>31

And who decides "logical validity"? Because mathematics is a social construction, it is driven a social consensus.

Mathematics is made by man. Logic is made by man. Who cares? The framework they provide allows constructions that model phenomenon as well as anything else. When something better comes along, we'll use it. No one decides logical validity or anything else, they're attached to the systems in which they were built. If anything is a "social construction", it's the basic principles from which we derive these systems. But really, what does it matter? If you have a systematic way of thinking that's better, present it. I don't understand what you're hoping to arrive at through all of this.

I cant claim, that found proof of Infinity's existence in a Calculus book, ether. Just as cant claim that after reading Bible or Quran.

I was making a joke.

These meanderings through amateur Philosophy of Science topics are starting to bore me.

>>33
He's just an idiot that's been posting these silly threads these past few weeks. I've already explained the error in his understanding a few times, and even gave exact examples that he can use to better recognize his misconceptions, but all he does is either:
1) Ignore most of the posts/comments
2) Post out-of-context quotes he mined from other places
3) If he ever responds to anything, it will be to irrelevant parts, while ignoring the main parts of the arguments presented.

Thus, I've concluded that it's pointless to argue with him as he does not use reason, it would be better if we all collectively ignore him if he refuses to use his own mind. It's probably even worse than arguing from a creationist.

s/from a/with a/

>>34

>If he ever responds to anything, it will be to irrelevant parts, while ignoring the main parts of the arguments presented.

I was starting to get that impression.

>Thus, I've concluded that it's pointless to argue with him as he does not use reason, it would be better if we all collectively ignore him if he refuses to use his own mind. It's probably even worse than arguing from a creationist.

Good point.

>>34
It's probably even worse than arguing from a creationist.
Xarn detected.

>>36
l2quote faggot

>>37
This is not the first time someone incorrectly thinks I'm Xarn, but I don't really care as we're all Anonymous... and there's only 3 people on /prog/, so some of us will have to be Xarn.

/prog/ will be spammed continuously until further notice. we apologize for any inconvenience this may cause.