You mean back when they were sperm? lol
Sorry, couldn’t resist.
Sure, I don’t believe in coincidences. Look, Bush was so atrociously bad that it allowed everyone to swing anti-Bush, and Obama could be Chinese or Canadian and he would still be the front runner.
But there is a difference between not believing in coincidences and seeing everything as a conspiracy.
Baldwin is alright, better than that red faced idiot Barr.
Why isn’t Cynthia McKinney in the news when she’s a woman and she’s an African American? They can’t Use her thats why! They have no political use for her!
If it’s not a coincidence then what is it? I don’t believe it’s one big conspiracy 100%, I’m actually open minded about it. One of the reasons that I keep an open mind about this one big conspiracy is because I read in a few places that the NWO was born hundreds maybe thousands? of years ago. Everyone I know is anti-bush and anti-republican. Like I said before it’s just part of the pie or puzzle , not the whole thing.
I remember where I read about that now. I read it in the paper titled Sinister instructions by the same author of vatican assassins http://www.vaticanassassins.org/. That paper and the book is rich in history.
from The Economist:
Oct 23rd 2008
From The Economist print edition
Illustration by KAL
IN “W.”, his biopic about his Yale classmate, Oliver Stone details Colin Powell’s agonies during George Bush’s first term. Throughout the film Mr Powell repeatedly raises doubts about the invasion of Iraq—and is repeatedly overruled by the ghoulish trio of Dick Cheney, Donald Rumsfeld and Karl Rove. In one of the final scenes, with his direst warnings proving correct, Mr Powell turns to Mr Cheney and delivers a heartfelt “Fuck you”.
The real Colin Powell used more diplomatic language in endorsing Barack Obama on October 19th, but the impact was much the same. Mr Obama is a “transformational figure”, he mildly said, and his old friend John McCain had erred in choosing a neophyte as a running-mate. But you would have to be naive not to see the endorsement as a verdict on the Bush years.
Mr Powell is now a four-star general in America’s most surprising new army: the Obamacons. The army includes other big names such as Susan Eisenhower, Dwight’s granddaughter, who introduced Mr Obama at the Democratic National Convention and Christopher Buckley, the son of the conservative icon William Buckley, who complains that he has not left the Republican Party: the Republican Party has left him. Chuck Hagel, a Republican senator from Nebraska and one-time bosom buddy of Mr McCain has also flirted heavily with the movement, though he has refrained from issuing an official endorsement.
The biggest brigade in the Obamacon army consists of libertarians, furious with Mr Bush’s big-government conservatism, worried about his commitment to an open-ended “war on terror”, and disgusted by his cavalier way with civil rights. There are two competing “libertarians for Obama” web sites. CaféPress is even offering a “libertarian for Obama” lawn sign for $19.95. Larry Hunter, who helped to devise Newt Gingrich’s Contract with America in 1994, thinks that Mr Obama can free America from the grip of the “zombies” who now run the Republican Party.
But the army has many other brigades, too: repentant neocons such as Francis Fukuyama, legal scholars such as Douglas Kmiec, and conservative talk-show hosts such as Michael Smerconish. And it is picking up unexpected new recruits as the campaign approaches its denouement. Many disillusioned Republicans hoped that Mr McCain would provide a compass for a party that has lost its way, but now feel that the compass has gone haywire. Kenneth Adelman, who once described the invasion of Iraq as a “cakewalk”, decided this week to vote for Mr Obama mainly because he regards Sarah Palin as “not close to being acceptable in high office”.
The rise of the Obamacons is more than a reaction against Mr Bush’s remodelling of the Republican Party and Mr McCain’s desperation: there were plenty of disillusioned Republicans in 2004 who did not warm to John Kerry. It is also a positive verdict on Mr Obama. For many conservatives, Mr Obama embodies qualities that their party has abandoned: pragmatism, competence and respect for the head rather than the heart. Mr Obama’s calm and collected response to the turmoil on Wall Street contrasted sharply with Mr McCain’s grandstanding.
Much of Mr Obama’s rhetoric is strikingly conservative, even Reaganesque. He preaches the virtues of personal responsibility and family values, and practises them too. He talks in uplifting terms about the promise of American life. His story also appeals to conservatives: it holds the possibility of freeing America from its racial demons, proving that the country is a race-blind meritocracy and, in the process, bankrupting a race-grievance industry that has produced the likes of Jesse Jackson and Al Sharpton.
How much do these Obamacons matter? More than Mr McCain would like to think. The Obamacons are manifestations of a deeper turmoil in the Republican rank-and-file, as the old coalition of small-government activists, social conservatives and business Republicans falls apart. They also influence opinion. This is obvious in the case of Mr Powell: Mr Obama is making liberal use of his endorsement to refute the latest Republican criticism that he is a “socialist”. But it is also true of lesser-known scribblers. At least 27 newspapers that backed Mr Bush in 2004 have endorsed Mr Obama.
Moreover, the revolt of the intellectuals is coinciding with a migration of culturally conservative voters—particularly white working-class voters—into Obamaland. Mr Obama is now level-pegging or leading among swing-groups such as Catholics and working-class whites. A recent Washington Post-ABC poll shows him winning 22% of self-described conservatives, a higher proportion than any Democratic nominee since 1980.
The more tantalising question is whether the rise of the Obamacons signals a lasting political realignment. In 1980 the rise of the neocons—liberal intellectuals who abandoned a spineless Democratic Party—was reinforced by the birth of working class “Reagan Democrats”. Is the Reagan revolution now going into reverse? There are reasons for scepticism. Will libertarians really stick with “Senator Government”, as Mr McCain labelled Mr Obama in the best slip of the tongue of the campaign? Will economic conservatives cleave to a president who believes in “spreading the wealth around”?
Much depends on how Mr Obama governs if he wins, and how the Republicans behave if they lose. Mr Obama talks about creating an administration of all the talents. He promises to take the cultural anxieties of Reagan Democrats seriously. For their part, hard-core Republicans are handling their party’s travails abysmally, retreating into elite-bashing populism and denouncing the Obamacons as “rats” who are deserting a sinking ship. If the Republican Party continues to think that the problem lies with the rats, rather than the seaworthiness of the ship, then the Obamacons are here to stay.
Chávez actually has expressed an interest in restoring relations with the next U.S. President, whoever he happens to be. I still believe dialogue is the best option. They could sort out things and reverse the escalation of conflicts should they little by little find points of common ground of interest for the people of both countries.
Beacause the U.S. is still the “Empire”, the world’s superpower, even though its relative importance for the sake of humanity’s stability is slowly diminishing.
Oct 23rd 2008
From The Economist print edition
IN “W.”, his biopic about his Yale classmate, Oliver Stone details Colin Powell’s agonies during George Bush’s first term. Throughout the film Mr Powell repeatedly raises doubts about the invasion of Iraq—and is repeatedly overruled by the ghoulish trio of Dick Cheney, Donald Rumsfeld and Karl Rove. In one of the final scenes, with his direst warnings proving correct, Mr Powell turns to Mr Cheney and delivers a heartfelt “Fuck you”.
The real Colin Powell used more diplomatic language in endorsing Barack Obama on October 19th, but the impact was much the same. Mr Obama is a “transformational figure”, he mildly said, and his old friend John McCain had erred in choosing a neophyte as a running-mate. But you would have to be naive not to see the endorsement as a verdict on the Bush years.
Mr Powell is now a four-star general in America’s most surprising new army: the Obamacons. The army includes other big names such as Susan Eisenhower, Dwight’s granddaughter, who introduced Mr Obama at the Democratic National Convention and Christopher Buckley, the son of the conservative icon William Buckley, who complains that he has not left the Republican Party: the Republican Party has left him. Chuck Hagel, a Republican senator from Nebraska and one-time bosom buddy of Mr McCain has also flirted heavily with the movement, though he has refrained from issuing an official endorsement.
The biggest brigade in the Obamacon army consists of libertarians, furious with Mr Bush’s big-government conservatism, worried about his commitment to an open-ended “war on terror”, and disgusted by his cavalier way with civil rights. There are two competing “libertarians for Obama” web sites. CaféPress is even offering a “libertarian for Obama” lawn sign for $19.95. Larry Hunter, who helped to devise Newt Gingrich’s Contract with America in 1994, thinks that Mr Obama can free America from the grip of the “zombies” who now run the Republican Party.
But the army has many other brigades, too: repentant neocons such as Francis Fukuyama, legal scholars such as Douglas Kmiec, and conservative talk-show hosts such as Michael Smerconish. And it is picking up unexpected new recruits as the campaign approaches its denouement. Many disillusioned Republicans hoped that Mr McCain would provide a compass for a party that has lost its way, but now feel that the compass has gone haywire. Kenneth Adelman, who once described the invasion of Iraq as a “cakewalk”, decided this week to vote for Mr Obama mainly because he regards Sarah Palin as “not close to being acceptable in high office”.
The rise of the Obamacons is more than a reaction against Mr Bush’s remodelling of the Republican Party and Mr McCain’s desperation: there were plenty of disillusioned Republicans in 2004 who did not warm to John Kerry. It is also a positive verdict on Mr Obama. For many conservatives, Mr Obama embodies qualities that their party has abandoned: pragmatism, competence and respect for the head rather than the heart. Mr Obama’s calm and collected response to the turmoil on Wall Street contrasted sharply with Mr McCain’s grandstanding.
Much of Mr Obama’s rhetoric is strikingly conservative, even Reaganesque. He preaches the virtues of personal responsibility and family values, and practises them too. He talks in uplifting terms about the promise of American life. His story also appeals to conservatives: it holds the possibility of freeing America from its racial demons, proving that the country is a race-blind meritocracy and, in the process, bankrupting a race-grievance industry that has produced the likes of Jesse Jackson and Al Sharpton.
How much do these Obamacons matter? More than Mr McCain would like to think. The Obamacons are manifestations of a deeper turmoil in the Republican rank-and-file, as the old coalition of small-government activists, social conservatives and business Republicans falls apart. They also influence opinion. This is obvious in the case of Mr Powell: Mr Obama is making liberal use of his endorsement to refute the latest Republican criticism that he is a “socialist”. But it is also true of lesser-known scribblers. At least 27 newspapers that backed Mr Bush in 2004 have endorsed Mr Obama.
Moreover, the revolt of the intellectuals is coinciding with a migration of culturally conservative voters—particularly white working-class voters—into Obamaland. Mr Obama is now level-pegging or leading among swing-groups such as Catholics and working-class whites. A recent Washington Post-ABC poll shows him winning 22% of self-described conservatives, a higher proportion than any Democratic nominee since 1980.
The more tantalising question is whether the rise of the Obamacons signals a lasting political realignment. In 1980 the rise of the neocons—liberal intellectuals who abandoned a spineless Democratic Party—was reinforced by the birth of working class “Reagan Democrats”. Is the Reagan revolution now going into reverse? There are reasons for scepticism. Will libertarians really stick with “Senator Government”, as Mr McCain labelled Mr Obama in the best slip of the tongue of the campaign? Will economic conservatives cleave to a president who believes in “spreading the wealth around”?
Much depends on how Mr Obama governs if he wins, and how the Republicans behave if they lose. Mr Obama talks about creating an administration of all the talents. He promises to take the cultural anxieties of Reagan Democrats seriously. For their part, hard-core Republicans are handling their party’s travails abysmally, retreating into elite-bashing populism and denouncing the Obamacons as “rats” who are deserting a sinking ship. If the Republican Party continues to think that the problem lies with the rats, rather than the seaworthiness of the ship, then the Obamacons are here to stay.
Completely wrong!
Actually peer pressure in the hypothetical case that Venezuelans could vote in U.S. elections would certainly benefit McCain. Please refer to an interesting poll by the Economist where it show a world map showing how each country would vote on the U.S. election. The whole planet wants to vote for Obama, except for about 10 exceptions, including Venezuela. Here McCain has a lot of support because many Venezuelans fear that Obama will impress upon American citizens the same sociualist disgrace Chávez has inflicted to us over the past decade. McCain is more popular in Venezuela than in the United States.
You use a liberal magazine to explain how conservatives are going to vote for liberals…biased?
“You use a liberal magazine to explain how conservatives are going to vote for liberals…biased?”
Jonathan, you are labeling The Economist as a liberal magazine. Readers of The Economist label themselves as conservatives. Therefore I’d rather omit the use of any labels whatsoever.
In any case, any single piece of writing is biased. Even an argument could be made that Mathematics has a certain philosophical bias.
quite vague about the bias inherent in math. do you mean someone could make such an argument, but that they would be wrong, or are you trying to say that you make such arguments. do you mean a bias towards reason logic truth when there are other things that may be of value, aesthetics etc… this sounds silly.
The Economist is liberal? Neo-liberal maybe…
-Jon
I do not want to go off topic. But in Mathematics, a proof by contradiction is sometimes considered not even like a proof because you are not proving anything, but rather proving that its opposite is not possible. So you must use the help of logic and philosophy to accept the validity of such mathematical proofs.
is it you who ‘sometimes consider it not to be a proof’ ?
for myself at least, reductio ad absurdum is as good valid a proof as any other, always, no exceptions
I suggest you to go into writings of philosophy of Mathematics. Reductio ad absurdum is not universally considered as a strict proof in the most theoretical sense. In any case, my original point is that all written statement always imply a certain degree of hidden or explicit bias.
can you suggest any credible author in particular?
Intuitionists and constructivists and their ilk only disallow the law of the excluded middle (and hence reductio ad absurdum) when dealing with the infinite, as one commonly does in mathematics. It’s perfectly legitimate when dealing with finite reality.
Realists, the most mainstream school, permit the law of the excluded middle in all cases.
Reductio ad absurdum (Latin for “reduction to the absurd”), also known as an apagogical argument, reductio ad impossibile, or proof by contradiction, is a type of logical argument where one assumes a claim for the sake of argument and derives an absurd or ridiculous outcome, and then concludes that the original claim must have been wrong as it led to an absurd result.
It makes use of the law of non-contradiction — a statement cannot be both true and false. In some cases it may also make use of the law of excluded middle — a statement must be either true or false. The phrase is traceable back to the Greek ἡ εἰς ἄτοπον ἀπαγωγή (hē eis átopon apagōgḗ), meaning “reduction to the absurd”, often used by Aristotle.
In mathematics and formal logic, this refers specifically to an argument where a contradiction is derived from some assumption (thus showing that the assumption must be false). However, Reductio ad absurdum is also often used to describe any argument where a conclusion is derived in the belief that everyone (or at least those being argued against) will accept that it is false or absurd. This is a comparatively weak form of reductio, as the decision to reject the premise requires that the conclusion is accepted as being absurd. Although a formal contradiction is by definition absurd (unacceptable), a weak reductio ad absurdum argument can be rejected simply by accepting the purportedly absurd conclusion. Such arguments also risk degenerating into strawman arguments, an informal fallacy caused when an argument or theory is twisted by the opposing side to appear ridiculous.
## Contents[hide] - 1 Explanation - 2 Examples - 2.1 Cubing-the-cube puzzle - 2.2 In mathematics - 2.3 In mathematical logic - 2.4 Humour - 3 Notation - 4 Quotations - 5 References - 6 Further reading |
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In formal logic, reductio ad absurdum is used when a formal contradiction can be derived from a premise, allowing one to conclude that the premise is false. If a contradiction is derived from a set of premises, this shows that at least one of the premises is false; if there are several, other means must be used to determine which ones. Mathematical proofs are sometimes constructed using reductio ad absurdum, by first assuming the opposite of the theorem the presenter wishes to prove, then reasoning logically from that assumption until presented with a contradiction. Upon reaching the contradiction, the assumption is disproved and therefore its opposite, due to the law of excluded middle, must be true.
There is a fairly common misconception that reductio ad absurdum simply denotes “a silly argument” and is itself a formal fallacy. However, this is not correct; a properly constructed reductio constitutes a correct argument. When reductio ad absurdum is in error, it is because of a fallacy in the reasoning used to arrive at the contradiction, not the act of reduction itself.
A classic reductio proof from Greek mathematics is the proof that the square root of 2 is irrational. If it were rational, it could be expressed as a fraction a/b in lowest terms, where a and b are integers. But if a/b = √2, then a2 = 2b2. That implies a2 is even. Since the square of an odd number is odd, that in turn implies that a is even. If a is even, then a2 is a multiple of 4. If a2 is a multiple of 4 and a2 = 2b2, then 2b2 is a multiple of 4, and therefore b2 is even. If b2 is even then b is even. But now a and b are both even. Therefore the fraction a/b is not in lowest terms. That is a contradiction. Therefore the initial assumption—that √2 is rational—must be false.
A more recent use of a reductio argument is the proof that a cube cannot be cut into a finite number of smaller cubes with no two the same size. Consider the smallest cube on the bottom face; on each of its four sides, either a neighbouring cube or the border of the main cube is rising above it. This means that any larger cube will not fit on top of it (the “footprint” of such a cube is too large). Since different cubes aren’t permitted to have the same sizes, only smaller cubes can be placed directly on top of it. But then the smallest of these would likewise be surrounded by larger cubes, so could only have smaller cubes directly on top of it… and so on, in an infinite regress, requiring an infinite number of cubes, which violates our conditions. (This gives rise to a proof by induction that the cubing-the-cube puzzle is also unsolvable in dimensions higher than three.)
Say we wish to disprove proposition p. The procedure is to show that assuming p leads to a logical contradiction. Thus, according to the law of non-contradiction, p must be false.
Say instead we wish to prove proposition p. We can proceed by assuming “not p” (i.e. that p is false), and show that it leads to a logical contradiction. Thus, according to the law of non-contradiction, “not p” must be false, and so, according to the law of the excluded middle, p is true.
In symbols:
To disprove p: one uses the tautology (p → (R ∧ ¬R)) → ¬p, where R is any proposition and the ∧ symbol is taken to mean “and”. Assuming p, one proves R and ¬R, and concludes from this that p → (R ∧ ¬R). This and the tautology together imply ¬p.
To prove p: one uses the tautology (¬p → (R ∧ ¬R)) → p where R is any proposition. Assuming ¬p, one proves R and ¬R, and concludes from this that ¬p → (R ∧ ¬R). This and the tautology together imply p.
For a simple example of the first kind, consider the proposition “there is no smallest rational number greater than 0”. In a reductio ad absurdum argument, we would start by assuming the opposite: that there is a smallest rational number, say, r0.
Now let 
. Then x is a rational number, and it’s greater than 0; and x is smaller than r0. (In the above symbolic argument, “x is the smallest rational number” would be R and “r (which is different from x) is the smallest rational number” would be ¬R.) But that contradicts our initial assumption that r0 was the smallest rational number. So we can conclude that the original proposition must be true — “there is no smallest rational number greater than 0”.
It is not uncommon to use this first type of argument with propositions such as the one above, concerning the non-existence of some mathematical object. One assumes that such an object exists, and then proves that this would lead to a contradiction; thus, such an object does not exist. For other examples, see proof that the square root of 2 is not rational and Cantor’s diagonal argument.
On the other hand, it is also common to use arguments of the second type concerning the existence of some mathematical object. One assumes that the object doesn’t exist, and then proves that this would lead to a contradiction; thus, such an object must exist. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of argument as universally valid. See further Nonconstructive proof.
In mathematical logic, the reductio ad absurdum is represented as:
or
In the above, p is the proposition we wish to prove or disprove; and S is a set of statements which are given as true — these could be, for example, the axioms of the theory we are working in, or earlier theorems we can build upon. We consider p, or the negation of p, in addition to S; if this leads to a logical contradiction F, then we can conclude that the statements in S lead to the negation of p, or p itself, respectively.
Note that the set-theoretic union, in some contexts closely related to logical disjunction (or), is used here for sets of statements in such a way that it is more related to logical conjunction (and).
The often humorous outcome of extending the simplification of a flawed statement to ridiculous proportions with the aim of criticising the result is frequently utilised in forms of humour. In fiction, seemingly simple and innocuous actions that are extended beyond reasonable circumstance to chaotic outcomes, typically by use of stereotype and literal interpretation, can also be categorised as reductio ad absurdum[1]. See farce.
Proofs by reductio ad absurdum often end “Contradiction!” or “Which is a contradiction.” Isaac Barrow and Baermann used the notation Q.E.A., for “quod est absurdum” (“which is absurd”), along the lines of Q.E.D., but this notation is rarely used today[2]. A graphical symbol sometimes used for contradictions is a downwards zigzag arrow “lightning” symbol (U+21AF: ↯), for example in Davey and Priestley[3]. Others sometimes used include a pair of opposing arrows (as 
or 
), struck-out arrows (
), a stylized form of hash (such as U+2A33: ⨳), or the “reference mark” (U+203B: ※).[4][5] The “up tack” symbol (U+22A5: ⊥) used by philosophers and logicians (see contradiction) also appears, but is often avoided due to its usage for orthogonality.
In the words of G. H. Hardy (A Mathematician’s Apology), “Reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.”
In the first paragraph of the Quentin Section (Part 2: June Second, 1910) of William Faulkner’s The Sound and the Fury, Quentin’s Father, Mr. Compson, gives his son a watch that has been in the family for many generations. His father explains, “It [The Watch] was Grandfather’s and when Father gave it to me he said I give you the mausoleum of all hope and desire; it’s rather excruciating-ly apt that you will use it to gain the reducto absurdum of all human experience which can fit your individual needs no better that it fitted his or his father’s”. This example represents a corruption of the Latin phrase Reductio ad absurdum.
Categories: Rules of inference | Proofs | Mathematical terminology | Latin logical phrases | Latin philosophical phrases
The mathematical school of so-called intuitionism has taken a definite line regarding the limitation of reductio argumentation for the purposes of existence proofs. The only valid way to establish existence, so they maintain, is by providing a concrete instance or example: general-principle argumentation is not acceptable here. This means, in specific, that one cannot establish (x)Fx by deducing an absurdity from (x)~Fx. Accordingly, intuitionists would not let us infer the existence of invertebrate ancestors of homo sapiens from the patent absurdity of the supposition that humans are vertebrates all the way back. They would maintain that in such cases where we are totally in the dark as to the individuals involved we are not in a position to maintain their existence.
from
What do you mean? Is it true? Is it not turtles all the way down?
It is absurd to believe that this forum topic was always way off topic. Therefore, once upon a time, it might have actually been about “Libertarians for Obama”, and not some frankly absurd foray into mathematical theology.
A libertarian is free to vote for Obama. They might have a hard time being taken seriously by either libertarians or liberals afterwards, however…
Ruben, a conservative is a very different thing from a libertarian. There are a lot of conservatives I know who plan to vote for Obama, for all the difference it will make in this bought-and-paid-for election.