1. Solipsism: I am here, you said I am not. May be I am here and maybe I am not here?
2. Determinism: I am already here
3. Utilitarianism: Are you happy that I am here?
4. Epicureanism: Since I am here let s party and fornicate!
5. Positivism: How can you be sure that I am here?
6. Absurdism: Hey, positivism, you are not here and will never be here.
7. Objectivism: I am here, but “I” am not here.. Who am “I”?
8. Secular humanism: Nah, I dont believe it. I am not here
9. Nihilism: Argh...Here, not here... What s the difference?
10. Existentialism: I am here! Here I am! I am here, am I not?
11. Foolism: Huh? come again?
Monday, July 26, 2010
Sunday, July 25, 2010
A fraction of memory...
I am nothing but crystals of shattered glasses.
I take no form, no reflection, no substance, and no existence
I am seen but unseen... for there are many layers upon no layer
I must feel, but posited with no apparatus of feeling.
I envy but cannot feel...
It is non-existence of feeling... it is much worse than being numb.
The cosmic existence defines my non-existence?
I wander,through indefinite infinity...
Some people say I am dreaming...
but I dont dream... I am a dream... that is posited to be real when people sleep... and unposited when people wake up... I sleep to wake up...
I am a fraction of memory... I am the seen unseen beauty and pain..
I take no form, no reflection, no substance, and no existence
I am seen but unseen... for there are many layers upon no layer
I must feel, but posited with no apparatus of feeling.
I envy but cannot feel...
It is non-existence of feeling... it is much worse than being numb.
The cosmic existence defines my non-existence?
I wander,through indefinite infinity...
Some people say I am dreaming...
but I dont dream... I am a dream... that is posited to be real when people sleep... and unposited when people wake up... I sleep to wake up...
I am a fraction of memory... I am the seen unseen beauty and pain..
Tuesday, July 20, 2010
Rancor
Brooklyn's finest affirms my loathsome and feeds me with grander anger... YOU TURN THEM INTO MONSTERS... Gauge that pain and rancor... Of course none of you can, fucking lesser mortals! FUCKING Mediocre minds and FUCKING TIMID CONFORMIST!
Friday, July 16, 2010
Friday, July 09, 2010
Exercise 2. regardez et penser
http://en.wikipedia.org/wiki/Proof_by_contradiction
In logic, proof by contradiction is a form of proof that establishes the truth or validity of a proposition by showing that the proposition being false would imply a contradiction. Since by the law of bivalence a proposition must be either true or false, and its falsity has been shown impossible, the proposition must be true.
In other words, to prove by contradiction that P, show that or its equivalent . Then, since implies a contradiction, conclude P.
Proof by contradiction is also known as indirect proof, apagogical argument, reductio ad impossibile. It is a particular kind of the more general form of argument known as reductio ad absurdum.
A classic proof by contradiction from 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, at least one of which is odd. But if a/b = √2, then a2 = 2b2. Therefore a2 must be even. Because the square of an odd number is odd, that in turn implies that a is even. This means that b must be odd because a/b is in lowest terms.
On the other hand, 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, and so is b.
So b is odd and even, a contradiction. Therefore the initial assumption—that √2 can be expressed as a fraction—must be false.
[edit]The length of the hypotenuse is less than the sum of the lengths of the two legs
The method of proof by contradiction has also been used to show that for any non-degenerate Right triangle, the length of the hypotenuse is less than the sum of the lengths of the two remaining sides. The proof relies on the Pythagorean theorem. Letting c be the length of the hypotenuse and a and b the lengths of the legs, the claim is that a + b > c. As usual, we start the proof by negating the claim and assuming that a + b ≤ c. The next step is to show that this leads to a contradiction. Squaring both sides, we have (a + b)2 ≤ c2 or, equivalently, a2 + 2ab + b2 ≤ c2. A triangle is non-degenerate if each edge has positive length, so we may assume that a and b are greater than 0. Therefore, a2 + b2 < a2 + 2ab + b2 ≤ c2. Taking out the middle term, we have a2 + b2 < c2. We know from the Pythagorean theorem that a2 + b2 = c2. We now have a contradiction since strict inequality and equality are mutually exclusive. The latter was a result of the Pythagorean theorem and the former the assumption that a + b ≤ c. The contradiction means that it is impossible for both to be true and we know that the Pythagorean theorem holds. It follows that our assumption that a + b ≤ c must be false and hence a + b > c, proving the claim.
[edit]In mathematics
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, ¬p: "there is no smallest rational number greater than 0". In a proof by contradiction, we start by assuming the opposite, p: that there is a smallest rational number, say, r0.
Now let x = r0/2. Then x is a rational number greater than 0 and less than r0. (In the above symbolic argument, "x is the smallest rational number" would be R and "r0 (which is different from x) is the smallest rational number" would be ¬R.) But that contradicts our initial assumption, p, that r0 was the smallest rational number. So we can conclude that the original proposition, ¬p, must be true — "there is no smallest rational number greater than 0".
the choice of which statement is R and which is ¬R is arbitrary.]
It is common 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
In mathematical logic, the proof by contradiction is represented as:
if
then
or
if
then
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).
Notation
Proofs by contradiction sometimes end with the word "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.[1] A graphical symbol sometimes used for contradictions is a downwards zigzag arrow "lightning" symbol (U+21AF: ↯), for example in Davey and Priestley.[2] 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: ※).[3][4] 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.
Quotations
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 logic, proof by contradiction is a form of proof that establishes the truth or validity of a proposition by showing that the proposition being false would imply a contradiction. Since by the law of bivalence a proposition must be either true or false, and its falsity has been shown impossible, the proposition must be true.
In other words, to prove by contradiction that P, show that or its equivalent . Then, since implies a contradiction, conclude P.
Proof by contradiction is also known as indirect proof, apagogical argument, reductio ad impossibile. It is a particular kind of the more general form of argument known as reductio ad absurdum.
A classic proof by contradiction from 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, at least one of which is odd. But if a/b = √2, then a2 = 2b2. Therefore a2 must be even. Because the square of an odd number is odd, that in turn implies that a is even. This means that b must be odd because a/b is in lowest terms.
On the other hand, 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, and so is b.
So b is odd and even, a contradiction. Therefore the initial assumption—that √2 can be expressed as a fraction—must be false.
[edit]The length of the hypotenuse is less than the sum of the lengths of the two legs
The method of proof by contradiction has also been used to show that for any non-degenerate Right triangle, the length of the hypotenuse is less than the sum of the lengths of the two remaining sides. The proof relies on the Pythagorean theorem. Letting c be the length of the hypotenuse and a and b the lengths of the legs, the claim is that a + b > c. As usual, we start the proof by negating the claim and assuming that a + b ≤ c. The next step is to show that this leads to a contradiction. Squaring both sides, we have (a + b)2 ≤ c2 or, equivalently, a2 + 2ab + b2 ≤ c2. A triangle is non-degenerate if each edge has positive length, so we may assume that a and b are greater than 0. Therefore, a2 + b2 < a2 + 2ab + b2 ≤ c2. Taking out the middle term, we have a2 + b2 < c2. We know from the Pythagorean theorem that a2 + b2 = c2. We now have a contradiction since strict inequality and equality are mutually exclusive. The latter was a result of the Pythagorean theorem and the former the assumption that a + b ≤ c. The contradiction means that it is impossible for both to be true and we know that the Pythagorean theorem holds. It follows that our assumption that a + b ≤ c must be false and hence a + b > c, proving the claim.
[edit]In mathematics
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, ¬p: "there is no smallest rational number greater than 0". In a proof by contradiction, we start by assuming the opposite, p: that there is a smallest rational number, say, r0.
Now let x = r0/2. Then x is a rational number greater than 0 and less than r0. (In the above symbolic argument, "x is the smallest rational number" would be R and "r0 (which is different from x) is the smallest rational number" would be ¬R.) But that contradicts our initial assumption, p, that r0 was the smallest rational number. So we can conclude that the original proposition, ¬p, must be true — "there is no smallest rational number greater than 0".
the choice of which statement is R and which is ¬R is arbitrary.]
It is common 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
In mathematical logic, the proof by contradiction is represented as:
if
then
or
if
then
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).
Notation
Proofs by contradiction sometimes end with the word "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.[1] A graphical symbol sometimes used for contradictions is a downwards zigzag arrow "lightning" symbol (U+21AF: ↯), for example in Davey and Priestley.[2] 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: ※).[3][4] 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.
Quotations
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."
Logic lesson I must review before hitting the wonderland
Imported from: wikipedia
Reductio ad absurdum (Latin: "reduction to the absurd") is a form of argument in which a proposition is disproven by following its implications logically to an absurd consequence
A common species of reductio ad absurdum is proof by contradiction (also called indirect proof) where a proposition is proven true by proving that it is impossible for it to be false. For example, if A is false, then B is also false; but B is true, therefore A cannot be false and therefore A is true.
Consider the following statement, attributed to physicist Niels Bohr: "The opposite of every great idea is another great idea." If this statement is true, then it would certainly qualify as a great idea - it would automatically lead to a corresponding great idea for every great idea already in existence. But if the statement itself is a great idea, its opposite ("the opposite of every great idea is not a great idea") must also be a great idea. Taken to its logical conclusion, the statement contradicts itself, being both true and untrue.[2]
Some legal usage, and some common usage, depends on a much wider definition of reductio ad absurdum than proof by contradiction, where it is argued a proposition should be rejected because it has merely undesirable (though perhaps not actually self-contradictory) consequences. In a strict logical sense, this might be reductio ad incommodum rather than ad absurdum - since in formal logic, 'absurdity' applies only to impossible self-contradiction.[1]
For example, consider the proposition Cuius est solum eius est usque ad coelum et ad inferos (literally: 'for whoever owns the soil, it is theirs up to Heaven and down to Hell'). This is also known as ad coelum. A legal reductio ad absurdum argument against the proposition might be:
Suppose we take this proposition to a logical extreme. This would grant a land owner rights to everything in a cone from the center of the earth to an infinite distance out into space, and whatever was inside that cone, including stars and planets. It is absurd that someone who purchases land on earth should own other planets, therefore this proposition is wrong.
(This is a straw man fallacy if it is used to prove that the practical legal use of "ad coelum" is wrong, since ad coelum is only actually ever used to delineate rights in cases of tree branches that grow over boundary fences, mining rights, etc.[3] Reductio ad absurdum applied to ad coelum is, in this case, claiming that ad coelum is saying something that it is not. The reductio ad absurdum above argues only against taking ad coelum to its fullest extent.)
It is only in everyday usage that this could acceptably be called a reductio ad absurdum: it is simply reductio ad absurdum being applied to an originally flawed reductio ad absurdum argument where the extremes were not rational for the original proposition.
Reductio Ad Absurdum in Euclid's Elements
In his Elements, Book III Proposition 5, Euclid demonstrates that if two circles cut one another, they do not have the same center. He begins by assuming that the opposite is true, that two circles may cut one another and have the same center. He then shows that if this happen, the radius of one circle would be both equal to and less than the radius of the other, which is impossible.
Reductio Ad Absurdum in Popular Culture
In an episode of the American TV series The Big Bang Theory, Sheldon refers to a Reductio Ad Absurdum of Leonard's. It is a misuse of the term, which he defines as "The logical fallacy of extending someone's argument to ridiculous proportions and then criticizing the result." The fallacy he describes is actually an Appeal to Ridicule.
Reductio ad absurdum (Latin: "reduction to the absurd") is a form of argument in which a proposition is disproven by following its implications logically to an absurd consequence
A common species of reductio ad absurdum is proof by contradiction (also called indirect proof) where a proposition is proven true by proving that it is impossible for it to be false. For example, if A is false, then B is also false; but B is true, therefore A cannot be false and therefore A is true.
Consider the following statement, attributed to physicist Niels Bohr: "The opposite of every great idea is another great idea." If this statement is true, then it would certainly qualify as a great idea - it would automatically lead to a corresponding great idea for every great idea already in existence. But if the statement itself is a great idea, its opposite ("the opposite of every great idea is not a great idea") must also be a great idea. Taken to its logical conclusion, the statement contradicts itself, being both true and untrue.[2]
Some legal usage, and some common usage, depends on a much wider definition of reductio ad absurdum than proof by contradiction, where it is argued a proposition should be rejected because it has merely undesirable (though perhaps not actually self-contradictory) consequences. In a strict logical sense, this might be reductio ad incommodum rather than ad absurdum - since in formal logic, 'absurdity' applies only to impossible self-contradiction.[1]
For example, consider the proposition Cuius est solum eius est usque ad coelum et ad inferos (literally: 'for whoever owns the soil, it is theirs up to Heaven and down to Hell'). This is also known as ad coelum. A legal reductio ad absurdum argument against the proposition might be:
Suppose we take this proposition to a logical extreme. This would grant a land owner rights to everything in a cone from the center of the earth to an infinite distance out into space, and whatever was inside that cone, including stars and planets. It is absurd that someone who purchases land on earth should own other planets, therefore this proposition is wrong.
(This is a straw man fallacy if it is used to prove that the practical legal use of "ad coelum" is wrong, since ad coelum is only actually ever used to delineate rights in cases of tree branches that grow over boundary fences, mining rights, etc.[3] Reductio ad absurdum applied to ad coelum is, in this case, claiming that ad coelum is saying something that it is not. The reductio ad absurdum above argues only against taking ad coelum to its fullest extent.)
It is only in everyday usage that this could acceptably be called a reductio ad absurdum: it is simply reductio ad absurdum being applied to an originally flawed reductio ad absurdum argument where the extremes were not rational for the original proposition.
Reductio Ad Absurdum in Euclid's Elements
In his Elements, Book III Proposition 5, Euclid demonstrates that if two circles cut one another, they do not have the same center. He begins by assuming that the opposite is true, that two circles may cut one another and have the same center. He then shows that if this happen, the radius of one circle would be both equal to and less than the radius of the other, which is impossible.
Reductio Ad Absurdum in Popular Culture
In an episode of the American TV series The Big Bang Theory, Sheldon refers to a Reductio Ad Absurdum of Leonard's. It is a misuse of the term, which he defines as "The logical fallacy of extending someone's argument to ridiculous proportions and then criticizing the result." The fallacy he describes is actually an Appeal to Ridicule.
striking the equilibrium: the why and how?
There was once in the past (when I was someone else) where my teacher told me that "Jo is a good buddy, he just intentionally shows his bad boy side all the times"
I think it is true. So often I find myself caught in a situation where opportunities of friendship and life joy present themselves, but I push them away, shun them under the notion (logically processed "foods") that they shun me anyway. Why should i learn to gravitate to their direction instead they to my direction? If compromise is the value, why should i gravitate there by exerting more effort?
The right and the fun are two mutually exclusive choice it seems.
Yin and yang tells me that life is right when i strike an equilibrium. in economics it s the precise price of goods where producers enjoy benefits, consumers enjoy proportional price and competition is protected and encouraged.
Damn, it s hard to strike such an equilibrium.
Perhaps I need to make a choice soon.. Humans are limited, i cant be the best at everything... Oh, that s crap.. I can even argue along that line much better than anyone else. It s the loser's argument...
sigh... I am completely aware of the consequences of choosing this path of life. or am i innately characterized this way? nobody can answer that, worst, nobody gives a damn about it...
Maybe one day we will all be able to achieve that state of equilibrium when we can sit down and feel content with whatever we have while still aggressively and passionately pursue the truth and the ultimate wisdom.
One thing I would really like to inquire Sidharta Gautama is "How can humans achieve equilibrium when inequilibrium is required to support equilibrium? Are u saying some humans must be sacrificed so that some can achieve enlightenment?"
You dont just sit up there or around us. You come down here and tell me.. explain to me... engross me in it...
I need answers.. in whatever form...
I think it is true. So often I find myself caught in a situation where opportunities of friendship and life joy present themselves, but I push them away, shun them under the notion (logically processed "foods") that they shun me anyway. Why should i learn to gravitate to their direction instead they to my direction? If compromise is the value, why should i gravitate there by exerting more effort?
The right and the fun are two mutually exclusive choice it seems.
Yin and yang tells me that life is right when i strike an equilibrium. in economics it s the precise price of goods where producers enjoy benefits, consumers enjoy proportional price and competition is protected and encouraged.
Damn, it s hard to strike such an equilibrium.
Perhaps I need to make a choice soon.. Humans are limited, i cant be the best at everything... Oh, that s crap.. I can even argue along that line much better than anyone else. It s the loser's argument...
sigh... I am completely aware of the consequences of choosing this path of life. or am i innately characterized this way? nobody can answer that, worst, nobody gives a damn about it...
Maybe one day we will all be able to achieve that state of equilibrium when we can sit down and feel content with whatever we have while still aggressively and passionately pursue the truth and the ultimate wisdom.
One thing I would really like to inquire Sidharta Gautama is "How can humans achieve equilibrium when inequilibrium is required to support equilibrium? Are u saying some humans must be sacrificed so that some can achieve enlightenment?"
You dont just sit up there or around us. You come down here and tell me.. explain to me... engross me in it...
I need answers.. in whatever form...
Thursday, July 08, 2010
Decrypting the code
imported from http://maverickphilosopher.typepad.com/maverick_philosopher/2010/07/might-there-have-been-just-nothing-at-all.html
Could There Have Been Just Nothing At All?
No doubt, things exist. At least I exist, and that suffices to show that something exists. But could it have been the case that nothing ever existed? Actually, there is something; but is it possible that there have been nothing? Or is it rather the case that necessarily there is something? Is it not only actually the case that there is something, but also necessarily the case that there is something? I will argue that there could not have been nothing and that therefore necessarily there is something. (Image credit.)
My thesis, then, is that necessarily, something (at least one thing) exists. I am using 'thing' as broadly as possible, to cover anything at all, of whatever category. If I am right, then it is impossible that there have been nothing at all. The type of modality in question is what is called 'broadly logical' or 'metaphysical.'
Note that Necessarily something exists does not entail Something necessarily exists. I am not asserting the second proposition, but only the first. The second says more than the first. In the patois of possible worlds, the second says that there is some one thing that exists in every possible world, whereas the first says only that every possible world is such that there is something or other in it. The first proposition is consistent with the proposition that every being is contingent, while the second is not. So the first and second propositions are logically distinct and the first does not entail the second. I am asserting only the first.
What I will be arguing, then, is not that there is a necessary being, some one being that exists in all possible worlds, but that every world has something or other in it: every possible circumstance or
situation is one in which something or other exists. That is, there is no possible world in which there is nothing at all.
You can think of merely possible worlds as maximal or total ways things might have been, and you can think of the actual world as the total way things are. My thesis is that there is no way things might have been such that nothing at all exists. But if you are uncomfortable with the jargon of possible worlds, I can translate out of it and say, simply, that it is impossible that there have been, or be, nothing at all. As a matter of metaphysical necessity, there must be something or other!
The content of my thesis now having been made clear, I proceed to give a reductio ad absurdum argument for thinking it true.
1. Let S = Something exists and N = Nothing exists, and assume for reductio that N is possibly true.
2. If N is possibly true, then S, which is true, and known to be true, is only contingently true.
Therefore
3. There are possible worlds in which S is false and possible worlds in which S is true. ( From 2, by definition of 'contingently true')
4. In the worlds in which S is true, something exists. (Because if 'Something exists' is true, then something exists.)
5. In the worlds in which S is false, it is also the case that something exists, namely, S. (For an item cannot have a property unless it exists, and so S cannot have the property of being false unless S exists)
6. Every proposition is either true, or if not true, then false. (Bivalence)
Therefore
7. Every world has something in it, hence there is no world in which nothing exists.
Therefore
8. N is not possibly true, and necessarily something exists.
If you disagree with my conclusion, then you must either show that one or more premises are either false or not reasonably maintained, or that one or more inferences are invalid, of that the argument rests on one or more dubious presuppositions
Could There Have Been Just Nothing At All?
No doubt, things exist. At least I exist, and that suffices to show that something exists. But could it have been the case that nothing ever existed? Actually, there is something; but is it possible that there have been nothing? Or is it rather the case that necessarily there is something? Is it not only actually the case that there is something, but also necessarily the case that there is something? I will argue that there could not have been nothing and that therefore necessarily there is something. (Image credit.)
My thesis, then, is that necessarily, something (at least one thing) exists. I am using 'thing' as broadly as possible, to cover anything at all, of whatever category. If I am right, then it is impossible that there have been nothing at all. The type of modality in question is what is called 'broadly logical' or 'metaphysical.'
Note that Necessarily something exists does not entail Something necessarily exists. I am not asserting the second proposition, but only the first. The second says more than the first. In the patois of possible worlds, the second says that there is some one thing that exists in every possible world, whereas the first says only that every possible world is such that there is something or other in it. The first proposition is consistent with the proposition that every being is contingent, while the second is not. So the first and second propositions are logically distinct and the first does not entail the second. I am asserting only the first.
What I will be arguing, then, is not that there is a necessary being, some one being that exists in all possible worlds, but that every world has something or other in it: every possible circumstance or
situation is one in which something or other exists. That is, there is no possible world in which there is nothing at all.
You can think of merely possible worlds as maximal or total ways things might have been, and you can think of the actual world as the total way things are. My thesis is that there is no way things might have been such that nothing at all exists. But if you are uncomfortable with the jargon of possible worlds, I can translate out of it and say, simply, that it is impossible that there have been, or be, nothing at all. As a matter of metaphysical necessity, there must be something or other!
The content of my thesis now having been made clear, I proceed to give a reductio ad absurdum argument for thinking it true.
1. Let S = Something exists and N = Nothing exists, and assume for reductio that N is possibly true.
2. If N is possibly true, then S, which is true, and known to be true, is only contingently true.
Therefore
3. There are possible worlds in which S is false and possible worlds in which S is true. ( From 2, by definition of 'contingently true')
4. In the worlds in which S is true, something exists. (Because if 'Something exists' is true, then something exists.)
5. In the worlds in which S is false, it is also the case that something exists, namely, S. (For an item cannot have a property unless it exists, and so S cannot have the property of being false unless S exists)
6. Every proposition is either true, or if not true, then false. (Bivalence)
Therefore
7. Every world has something in it, hence there is no world in which nothing exists.
Therefore
8. N is not possibly true, and necessarily something exists.
If you disagree with my conclusion, then you must either show that one or more premises are either false or not reasonably maintained, or that one or more inferences are invalid, of that the argument rests on one or more dubious presuppositions
what i think, say and do
Between thought and action lies speech, which can substitute for either. It can just as easily mask thoughtlessness as impede action.
Right speech, however, does not substitute for thought or action, but mediates them. Giving expression to thought, it enables intelligent action.
Right speech, however, does not substitute for thought or action, but mediates them. Giving expression to thought, it enables intelligent action.
Sunday, July 04, 2010
Pascal and Buber on the God of the Philosophers
imported from: http://maverickphilosopher.typepad.com/maverick_philosopher/2010/06/pascal-and-buber-on-the-god-of-the-philosophers.html (Bill Vallicella)
"God of Abraham, God of Isaac, God of Jacob -- not of the philosophers and scholars." Thus exclaimed Blaise Pascal in the famous memorial in which he recorded the overwhelming religious/mystical experience of the night of 23 November 1654. Martin Buber comments (Eclipse of God, Humanity Books, 1952, p. 49):
These words represent Pascal's change of heart. He turned, not from a state of being where there is no God to one where there is a God, but from the God of the philosophers to the God of Abraham. Overwhelmed by faith, he no longer knew what to do with the God of the philosophers; that is, with the God who occupies a definite position in a definite system of thought. The God of Abraham . . . is not suspectible of introduction into a system of thought precisely because He is God. He is beyond each and every one of those systems, absolutely and by virtue of his nature. What the philosophers describe by the name of God cannot be more than an idea. (emphasis added)
Buber Buber here expresses a sentiment often heard. We encountered it yesterday when we found Timothy Ware accusing late Scholastic theology of turning God into an abstract idea. But the sentiment is no less wrongheaded for being widespread. As I see it, it simply makes no sense to oppose the God of Abraham, Isaac, and Jacob -- the God of religion -- to the God of philosophy. In fact, I am always astonished when otherwise distinguished thinkers retail this bogus distinction. Let's try to sort this out.
It is first of all obvious that God, if he exists, transcends every system of human thought, and cannot be reduced to any element internal to such a system whether it be a concept, a proposition, an argument, a set of arguments, etc. But by the same token, the chair I am sitting on cannot be reduced to my concept of it or the judgments I make about it. It too is transcendent of my conceptualizations and judgments. The transcendence of God, however, is a more radical form of transcendence, that of a person as opposed to that of a material object. And among persons, God is at the outer limit of transcendence.
Now if Buber were merely saying something along these lines then I would have no quarrel with him. But he is saying something more, namely, that when a philosopher in his capacity as philosopher conceptualizes God, he reduces him to a concept or idea, to something abstract, to something merely immanent to his thought, and therefore to something that is not God. In saying this, Buber commits a grotesque non sequitur. He moves from the unproblematically true
1. God by his very nature is transcendent of every system of thought or scheme of representation
to the breathtakingly false
2. Any thought about God or representation of God (such as we find, say in Aquinas's Summa Theologica) is not a thought or representation of God, but of a thought or representation, which, of course, by its very nature is not God.
As I said, I am astonished that anyone could fall into this error. When I think about something I don't in thinking about it turn it into a mere thought. When I think about my wife's body, for example, I don't turn it into a mere thought: it remains transcendent of my thought as a material thing. A fortiori, I am unable by thinking about my wife as a person, an other mind, to transmogrify her personhood into a mere concept in my mind. She remains in her interiority delightfully transcendent.
It is therefore bogus to oppose the God of the philosophers to the God of Abraham, et al. There is and can be only one God. But there are different approaches to this one God. By my count, there are four ways of approaching God: by reason, by faith, by mystical experience, and by our moral sense. To employ a hackneyed metaphor, if there are four routes to the summit of a mountain, it does not follow that there are four summits, with only one of them being genuine, the others being merely immanent to their respective routes.
I should think that direct acquaintance with God via mystical/religious experience is superior to contact via faith or reason or morality. It is better to taste food than to read about it on a menu. But that's not to say that the menu is about itself: it is about the very same stuff that one encounters by eating. The fact that it is better to eat food than read about it does not imply that when one is reading one is not reading about it.
Imagine how silly it would be be for me to exclaim, while seated before a delicacy: "Food of Wolfgang Puck, Food of Julia Childs, Food of Emeril Lagasse, not of the nutritionists and menu-writers!"
"God of Abraham, God of Isaac, God of Jacob -- not of the philosophers and scholars." Thus exclaimed Blaise Pascal in the famous memorial in which he recorded the overwhelming religious/mystical experience of the night of 23 November 1654. Martin Buber comments (Eclipse of God, Humanity Books, 1952, p. 49):
These words represent Pascal's change of heart. He turned, not from a state of being where there is no God to one where there is a God, but from the God of the philosophers to the God of Abraham. Overwhelmed by faith, he no longer knew what to do with the God of the philosophers; that is, with the God who occupies a definite position in a definite system of thought. The God of Abraham . . . is not suspectible of introduction into a system of thought precisely because He is God. He is beyond each and every one of those systems, absolutely and by virtue of his nature. What the philosophers describe by the name of God cannot be more than an idea. (emphasis added)
Buber Buber here expresses a sentiment often heard. We encountered it yesterday when we found Timothy Ware accusing late Scholastic theology of turning God into an abstract idea. But the sentiment is no less wrongheaded for being widespread. As I see it, it simply makes no sense to oppose the God of Abraham, Isaac, and Jacob -- the God of religion -- to the God of philosophy. In fact, I am always astonished when otherwise distinguished thinkers retail this bogus distinction. Let's try to sort this out.
It is first of all obvious that God, if he exists, transcends every system of human thought, and cannot be reduced to any element internal to such a system whether it be a concept, a proposition, an argument, a set of arguments, etc. But by the same token, the chair I am sitting on cannot be reduced to my concept of it or the judgments I make about it. It too is transcendent of my conceptualizations and judgments. The transcendence of God, however, is a more radical form of transcendence, that of a person as opposed to that of a material object. And among persons, God is at the outer limit of transcendence.
Now if Buber were merely saying something along these lines then I would have no quarrel with him. But he is saying something more, namely, that when a philosopher in his capacity as philosopher conceptualizes God, he reduces him to a concept or idea, to something abstract, to something merely immanent to his thought, and therefore to something that is not God. In saying this, Buber commits a grotesque non sequitur. He moves from the unproblematically true
1. God by his very nature is transcendent of every system of thought or scheme of representation
to the breathtakingly false
2. Any thought about God or representation of God (such as we find, say in Aquinas's Summa Theologica) is not a thought or representation of God, but of a thought or representation, which, of course, by its very nature is not God.
As I said, I am astonished that anyone could fall into this error. When I think about something I don't in thinking about it turn it into a mere thought. When I think about my wife's body, for example, I don't turn it into a mere thought: it remains transcendent of my thought as a material thing. A fortiori, I am unable by thinking about my wife as a person, an other mind, to transmogrify her personhood into a mere concept in my mind. She remains in her interiority delightfully transcendent.
It is therefore bogus to oppose the God of the philosophers to the God of Abraham, et al. There is and can be only one God. But there are different approaches to this one God. By my count, there are four ways of approaching God: by reason, by faith, by mystical experience, and by our moral sense. To employ a hackneyed metaphor, if there are four routes to the summit of a mountain, it does not follow that there are four summits, with only one of them being genuine, the others being merely immanent to their respective routes.
I should think that direct acquaintance with God via mystical/religious experience is superior to contact via faith or reason or morality. It is better to taste food than to read about it on a menu. But that's not to say that the menu is about itself: it is about the very same stuff that one encounters by eating. The fact that it is better to eat food than read about it does not imply that when one is reading one is not reading about it.
Imagine how silly it would be be for me to exclaim, while seated before a delicacy: "Food of Wolfgang Puck, Food of Julia Childs, Food of Emeril Lagasse, not of the nutritionists and menu-writers!"
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