pseudonous

No, each axiom was assigned its own unknown probability of being correct as follows:
The probability the axioms are true is unknown. The probability of axiom A is 1/x, the probablity of axiom B is 1/y and the probability of axiom C is 1/z.

The probability that two of the three axioms are true is greater than the probability that all three axioms are true.

As Romansh pointed out there may be other unknown axioms which could make the conclusions true even if axioms A, B and C are false. This additional complexity can be taken into account, if the conclusion of the argument based on two of the three axioms is included in the conclusion of the arguement based on all three axioms. On the other hand, if the conclusions of each argument are significantly different there is no way I know of to determine which is more likely.

__________________
"One is most dishonest to one's god: he is not allowed to sin." - Nietzsche

Remster

Pseudonous
No problem – take your time. And sorry for not making my intentions clearer.

Remster

pseudonous

Remster,

I have a question about the wording you used for theory 2.


When you say a powerful being makes it seem that objects behave in an anti-Newtonian way, what exactly are you trying to say? I'm having a hard time imagining this. If, for instance, the anti-Newtonian theory says that lead can be turned into gold, how would a being make lead only appear to be gold? After all, if the metal was shiny like gold had the density, the conductivity, melting point, etc.. of gold then it would be gold. Or, if the anti-Newtonian theory suggested we could build some dark matter engine to send spaceships to other solar systems how could this merely be an illusion? Wouldn't this being have to, in fact, be causing objects to behave in an anti-Newtonian way rather than just giving the illusion that they behave in an anti-Newtonian way?

__________________
"One is most dishonest to one's god: he is not allowed to sin." - Nietzsche

shadowind

ok, i think i see now. it doesn't make sense to have decimals in the denominator for probabilitys right?

__________________
remember "for mere impulse of appetite is slavery, while obedience to a law which we prescirbe to oursleves is liberty"-rousseau: the concept of the general will "if we can not reconcile all opions, then let us endeavour to unite all hearts."-?"to be is to be perceived"-? "‘We can be as honest as we are ignorant. If we are, when asked what is beyond the horizon of the known, we must say that we do not know’-Robert G. Ingersoll

pseudonous

No, the probability would be some number between 0 and 1. So the x in 1/x would have to be 1 or greater.

__________________
"One is most dishonest to one's god: he is not allowed to sin." - Nietzsche

romansh

Rem If I listen for the ringing it's there, sometimes it "imposes itself". Is it there otherwise??? Is my hand there when I put my arm behind my back? I can only suppose.

For x = x, I would treat it as a definition or a bloody good assumption, not necessarily provable ... because I would have to use x = x to prove it. An axiom. For me, x = x is 'more' self evident than god exists is self evident. For example some of the evidence for god existing can have other explanations. Whereas other evidence for x <> x is meaningless?

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There is a theory which states that if ever anybody discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened. ........... Douglas Adams

romansh

Nous,

I'm not sure ... a little out of my depth here
But it would seem to me we should be able to say

1/O(AB) > 1/O(ABC)

Because O(ABCDEF..........) should approach 1?

__________________
There is a theory which states that if ever anybody discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened. ........... Douglas Adams

Remster

Pseudonous

I can't see why. I don't know enough about physics to give a concrete example, but consider whatever observations have led physicists to conclude that Newton was wrong. These observations could all be illusory or otherwise misleading. For example, the being might manipulate our sense organs or the laboratory environment, or he might tamper with our equipment so it produces inaccurate images or readings. Is that hard to imagine?

Remster

Remster

Rom

I'm failing to get the point across. The question I'm raising isn't whether sounds, arms, etc. continue to exist when they're not being perceived, i.e. whether they're objective. Rather, the question I'm raising is whether it's possible to have false beliefs about the subjective, i.e. things that exist only while you're experiencing them.

Pain is often taken as the paradigm subjective thing (presumably because it's often vivid and there's no objective analogue with which it might be confused). Hence my original question: 'Do you know whether you're in pain right now?' You replied (in part): 'I gather some amputees can still feel (including pain from) the missing limb'. I should have stopped you there, because the relevant question isn't whether amputees can be mistaken that they're feeling pain from a missing limb, which evidently they can, but whether they can be mistaken that they're in pain. Can you see the distinction?

First up, the fact that some of the evidence for God's existence can be explained in other ways is kind of irrelevant, since we're talking specifically about the putative self-evidence of God's existence. Can that be explained away in a manner in which the putative self-evidence of 'x=x' can't?

Either way, the main issue here is whether you know that x=x, and the alternative you've given to its being an assumption (which is where I want to end up) is that it's a definition. A definition of what? And is a definition the sort of thing that can be true or false? If so, how do you know whether it's true or false that x=x?

Rem

pseudonous

Romansh

I see what you are saying now. I totally misunderstood and misused your sysmbolism. I agree that O(ABCDEF..........) should approach 1 and that 1/O(AB) > = 1/O(ABC)

Still, if the simpler conclusion is contained in the more complex conclusion
then we can say that the argument with the simpler conclusion is more likely to be true than the argument with the more complex conclusion.

In this case if we had additional axioms that came into play, they would either lead to both conclusions or just the simpler conclusion.

For instance, say that axiom D (prob. 1/s) and axiom E (prob. 1/t) also implied that the conclusion based on axioms A and B. Then the probability that the conclusion is true would become 1/xy + 1/st.

And if any axioms F (prob. 1/n) and G (prob. 1/m) increased the conclusion based on axioms A, B and C to 1/xyz + 1/nm, it would also increase the probability of the simpler conclusion to 1/xy + 1/st + 1/nm.

So the probability of the simpler argument would always remain higher than the more complex argument no matter how many unknown axioms may come into play.

An rough example of two arguments with this relationship would be;

1. Objects in moving in a straight line continue to do so unless acted on by an external force.
2. The planets orbit around the sun.
3. Therefore a force is exerted on the planets.

1. God is the cause of all things.
2. Objects in moving in a straight line continue to do so unless acted on by an external force.
3. The planets orbit around the sun.
4. Therefore the god causes a force to be exerted on the planets.

I'm sure there is a better example but I am getting lazy.


What do think? Are there any flaws?

__________________
"One is most dishonest to one's god: he is not allowed to sin." - Nietzsche