I'm an atheist...

[Joe Bloe]

And those who say that are morons (Or simply uneducated or miseducated)

A.C. Grayling, a moron?
http://www.prospectmagazine.co.uk/2008/0...squestion/

[Autumnlicious]

Posted in full for Sae:

Is it impossible to prove a negative?

The claim that negatives cannot be proved is beloved of theists who resist the assaults of sceptics by asserting that the non-existence of God cannot be proved. By this they hope to persuade themselves and others that at least the possibility remains open that a supernatural agency exists; from there they make the inflationary move from alleged mere possibility to not eating meat on Fridays. They are, however, wrong both about not being able to prove a negative, and about not being able to prove supernatural agencies exist and are active in the universe. Seeing why requires a brief refresher on the nature of proof.

Proof in a formal deductive system consists in deriving a conclusion from premises by rules. Formal derivations are literally explications, in the sense that all the information that constitutes the conclusion is already in the premises, so a derivation is in fact merely a rearrangement. There is no logical novelty in the conclusion, though there might be and often is psychological novelty, in the sense that the conclusion can seem unobvious or even surprising because the information constituting it was so dispersed among the premises.

Demonstrative proof, as just explained, is watertight and conclusive. It is a mechanical matter; computers do it best. Change the rules or axioms of a formal system, and you change the results. Such proof is only to be found in mathematics and logic.
Proof in all other spheres of reasoning consists in adducing evidence of the kind and in the quantity that makes it irrational, absurd, irresponsible or even lunatic to reject the conclusion thus being supported. This is proof in the scientific and common-sense meaning. The definitive illustration of what this means, especially for the use that theists would like to make of the myth that you cannot prove a negative, is Carl Sagan’s “dragon in the garage” story, which involves the teller claiming that he has a dragon in his garage—except that it’s invisible, incorporeal and undetectable. In response to which one can only ask— if there’s no way to disprove a contention, and no conceivable experiment that would count against it, what does it mean to say that something exists?

No self-respecting theist would go so far as to claim that “you cannot prove the non-existence of God” entails “God exists.” As mentioned, their point is merely to leave open the possibility that such a being might exist. But Sagan’s dragon dashes even this hope. For one can show that it is absurd, irrational, intellectually irresponsible or even lunatic to believe that fairies, goblins, the Norse gods, the Hindu gods, the gods of early Judaism (yes, there were several: go check), and so endlessly on, “might exist.” It would compound the felony a millionfold to grant this and yet insist that one’s own (Christian or Muslim, say) deity “nevertheless” exists or might exist.

For a simple case of proving a negative, by the way, consider how you prove the absence of pennies in a piggy-bank.

REF: http://www.prospectmagazine.co.uk/2008/0...squestion/

Thoughts:
I like his reasoning and the quick exploration of argumentation and proofs.

[macskeptic]

First of all... welcome, Sudekai!

Now...

Posted in full for Sae:

Is it impossible to prove a negative?

The claim that negatives cannot be proved is beloved of theists who resist the assaults of sceptics by asserting that the non-existence of God cannot be proved. By this they hope to persuade themselves and others that at least the possibility remains open that a supernatural agency exists; from there they make the inflationary move from alleged mere possibility to not eating meat on Fridays. They are, however, wrong both about not being able to prove a negative, and about not being able to prove supernatural agencies exist and are active in the universe. Seeing why requires a brief refresher on the nature of proof.

Proof in a formal deductive system consists in deriving a conclusion from premises by rules. Formal derivations are literally explications, in the sense that all the information that constitutes the conclusion is already in the premises, so a derivation is in fact merely a rearrangement. There is no logical novelty in the conclusion, though there might be and often is psychological novelty, in the sense that the conclusion can seem unobvious or even surprising because the information constituting it was so dispersed among the premises.

Demonstrative proof, as just explained, is watertight and conclusive. It is a mechanical matter; computers do it best. Change the rules or axioms of a formal system, and you change the results. Such proof is only to be found in mathematics and logic.
Proof in all other spheres of reasoning consists in adducing evidence of the kind and in the quantity that makes it irrational, absurd, irresponsible or even lunatic to reject the conclusion thus being supported. This is proof in the scientific and common-sense meaning. The definitive illustration of what this means, especially for the use that theists would like to make of the myth that you cannot prove a negative, is Carl Sagan’s “dragon in the garage” story, which involves the teller claiming that he has a dragon in his garage—except that it’s invisible, incorporeal and undetectable. In response to which one can only ask— if there’s no way to disprove a contention, and no conceivable experiment that would count against it, what does it mean to say that something exists?

No self-respecting theist would go so far as to claim that “you cannot prove the non-existence of God” entails “God exists.” As mentioned, their point is merely to leave open the possibility that such a being might exist. But Sagan’s dragon dashes even this hope. For one can show that it is absurd, irrational, intellectually irresponsible or even lunatic to believe that fairies, goblins, the Norse gods, the Hindu gods, the gods of early Judaism (yes, there were several: go check), and so endlessly on, “might exist.” It would compound the felony a millionfold to grant this and yet insist that one’s own (Christian or Muslim, say) deity “nevertheless” exists or might exist.

For a simple case of proving a negative, by the way, consider how you prove the absence of pennies in a piggy-bank.

Thoughts:
I like his reasoning and the quick exploration of argumentation and proofs.

I fail to understand how does the reasoning in this excerpt proves (or disproves) anything. Sagan's dragon just puts god in the same basket as the other things mentioned: fairies, goblins, etc. If one cannot experiment with the idea (either logically or empirically), there is no concrete and definite way to prove or disprove it.

"For one can show that it is absurd, irrational, intellectually irresponsible or even lunatic to believe that (...)"

Why is it lunatic to believe in fairies? I mean, their existence is quite unlikely due to lack of evidence, but can't someone just be, let's say, "optimistic" about it?

The only adjective that I think that actually counts towards proving something in the phrase I've emphasized above is probably "irrational". Yes, it is irrational to believe something without proof, but so it is to say that since there is no proof of its existence, it's been proven to not exist.

Translating to mathematics (or logic)

P: There is evidence for fairies
Q: We can say that fairies exist for sure

P => Q (P is a sufficient condition for Q, as Q is a necessary condition for P)

We know for sure that P is false, right?
But even then, there is no logical, rational way to get from there to a point when we can say anything about Q.

[Tiberius]

Translating to mathematics (or logic)

P: There is evidence for fairies
Q: We can say that fairies exist for sure

P => Q (P is a sufficient condition for Q, as Q is a necessary condition for P)

We know for sure that P is false, right?
But even then, there is no logical, rational way to get from there to a point when we can say anything about Q.

Bad use of logic.

P => Q means that P is a sufficient condition for Q, but not vice-versa. Just because someone (or all of us) can say "fairies exist for sure" doesn't mean there is evidence for them.

Indeed, if we "know for sure" that P is false, then Q *is* false by definition.

[macskeptic]

Translating to mathematics (or logic)

P: There is evidence for fairies
Q: We can say that fairies exist for sure

P => Q (P is a sufficient condition for Q, as Q is a necessary condition for P)

We know for sure that P is false, right?
But even then, there is no logical, rational way to get from there to a point when we can say anything about Q.

Bad use of logic.

P => Q means that P is a sufficient condition for Q, but not vice-versa. Just because someone (or all of us) can say "fairies exist for sure" doesn't mean there is evidence for them.

Indeed, if we "know for sure" that P is false, then Q *is* false by definition.

Actually I will have to disagree.

To make things easier I will throw a much less complicated example.

P: I threw a lit torch on the forest
Q: The forest caught on fire

P => Q (let's assume that if I do throw the torch, there is NO WAY it won't caught on fire, just for the sake of the argument)

You may say that if Q (the forest caught on fire) that means that certainly P (I threw the lit torch in it) [this is wrong, I will get there in a second]
You may also say that if P is false (I didn't threw the lit torch), then Q is false (the forest didn't caught on fire) [this is also wrong]

Both are wrong because the forest caught of fire because of this:
R => Q

R: A lightning struck a tree on the forest

In other words... in this simplified scenario the jumped conclusion was incorrect due to lack of the total variable involved in the problem.

That was to demonstrate that my logic concept is right =P

Now, for the fairies problem, it is a little more complicated - because the way I constructed it (which might be wrong, but the logic is not) "P => Q" states that there can be fairies (Q) without necessarily being evidence for their existence (~P).

The possible outcomes of a P => Q expression are:

if P is true and Q is true then the expression is true
if P is false and Q is true then the expression can be true*
if P is false and Q is false then the expression can be true*
if P is true and Q is false then the expression is false

* With these two comes that the lack of evidence (~P, or false P) is not enough information for us to affirm that fairies exist or not (Q or ~Q).

Just to clarify...

Yes, I think it is pretty useless to adopt a completely neutral posture with things like fairies, or unicorns, or gods because of these logical deadlocks. After all, it would get in the way of our thought process.

My point is just that the logical construct "lack of evidence" doesn't contribute to proving or disproving anything logically.

[Tiberius]

Yeah, I have no idea where my argument came from. I'm tired

I think I just got distracted by your statement that Q was a neccessary condition for P, when it isn't.

[macskeptic]

Yeah, I have no idea where my argument came from. I'm tired

I think I just got distracted by your statement that Q was a neccessary condition for P, when it isn't.

Actually it is.

If I say that if a throw a ball (P) it will fall (Q) due to gravity.

You can never, ever say that I threw a ball (P) if it didn't fell (Q) - henceforth the fall is a necessary observation for stating that the throw happened.

If you look at it over time, yes Q happens after P, but even so, logically Q is a necessary condition/observation to affirm P.

[Tiberius]

Q isn't a condition for P, it is the result of P. That is the difference.

If P => Q and Q => P you have a circular argument. Either both are true from the outset, or both are false from the outset. You can't have P (false) => Q (true) as you could before, because if Q is true, P is true (since you claim Q is a neccessary condition of P).

Going back to your example, you are confusing things yet again. You said "Q is a neccessary condition to affirm P", yet your example to show this is and example of P => Q, not Q => P. You said you can't say that if you throw the ball, it didn't fall (an example of P => Q).

However, you can easily have a ball falling (Q) without P. For instance, if R is dropping a ball. R => Q.

So, we can demonstrate a logical contradiction:

P = Throwing a ball.
R = Dropping a ball.
Q = The ball falls.

P => Q
Q => P
R => Q

P is false (we're not throwing the ball). If R then Q (this is true since R => Q). If Q then P (taken from Q => P). Yet P is false and Q is true, and true => false isn't a case of Q => P.

Q.E.D

[macskeptic]

Q isn't a condition for P, it is the result of P. That is the difference.

If P => Q and Q => P you have a circular argument. Either both are true from the outset, or both are false from the outset. You can't have P (false) => Q (true) as you could before, because if Q is true, P is true (since you claim Q is a neccessary condition of P).

Going back to your example, you are confusing things yet again. You said "Q is a neccessary condition to affirm P", yet your example to show this is and example of P => Q, not Q => P. You said you can't say that if you throw the ball, it didn't fall (an example of P => Q).

However, you can easily have a ball falling (Q) without P. For instance, if R is dropping a ball. R => Q.

So, we can demonstrate a logical contradiction:

P = Throwing a ball.
R = Dropping a ball.
Q = The ball falls.

P => Q
Q => P
R => Q

P is false (we're not throwing the ball). If R then Q (this is true since R => Q). If Q then P (taken from Q => P). Yet P is false and Q is true, and true => false isn't a case of Q => P.

Q.E.D

Ok, rephrasing your example:

The fact that the ball fell, isn't enough (sufficient) to say that I threw the ball. (so... no Q => P), I think we agreed until here, right?

Ok, so let's take Q => P totally out of the example, since we both agree it is wrong.

But, what I am saying is that, if you say that either P or R happened (be it letting go of the ball or throwing it), you will necessarily have to see/observe that Q happens, otherwise what you are saying with P => Q / R => Q is a lie (or, in other words, an invalid argument).

The mathematical terms are exactly these actually.
P => Q can be read: P is sufficient for Q or Q is necessary for P. (Reference: http://en.wikipedia.org/wiki/Necessary_a..._condition)
It applies in a strict logical sense, this should not be confused with cause and effect - we agree that Q is an effect that can be caused by either P or R.

---------- edit -----------

I believe our disagreement has much more to do with how it is versed in language (english) than the logics itself.

[Tiberius]

I agree with that. My only problem with your argument was your assertion that because P => Q, Q => P, which is a logically invalid statement (as per my proof).