08 Feb '16 16:01>
Originally posted by moonbusBayesian reasoning tells us that if Julius Caesar did have two heads [a very low probability occurrence
If I may add a small proviso to that: just because a theory or conjectire has't been conclusively refuted, doesn't mean it is advisable to hold it. It hasn't been clusively proven that Julius Ceasar did not have two heads, but it would be silly to believe it.
a-priori] then there should be evidence that this was the case [two headed statues, writings
from contemporaries [especially enemies] etc etc]. Given that this evidence has not been found when
we should have been able to find it, coupled with the very low probability of both this condition occurring
in the first place and then his survival and success as a general and then [essentially] emperor while
having this condition we can conclude that the probability given the information we have that Julius Caesar
had two heads is vanishingly small and improbable beyond reasonable doubt. And as such we can safely
believe that Julius Caesar had but one head.
Such reasoning does in fact refute the idea that Julius Caesar had two heads beyond any reasonable doubt
which is what is required.
Falsification is simply the special case that observed evidence directly and strongly contradicts the proposed
hypothesis. However as an absence of evidence is evidence of absence [albeit typically weak evidence] where
evidence should be expected to exist and is not found [Particularly when dealing with propositions with low
prior probabilities] we can reach the point where the proposition/hypothesis is so improbable [particularly with
respect to alternate propositions/hypotheses] that we can justifiably regard it as being false without having
observed evidence that directly contradicts/falsifies the proposition/hypothesis.
This explains why it is 'silly to believe' that Julius Caesar had two heads, or that [for example] the Christian god exists.
There is no evidence we could possibly observe that would falsify the Christian god claim because it is always
possible that that god could be deliberately hiding it's existence from us. [this does pretty much preclude a morally
good god, but then the proposed Christian god is clearly not morally good]
However, we can still justifiably claim to know that such a god does not exist because the prior probability of such a
god is infinitesimal, and there is NO evidence FOR it's existence, and plenty of evidence FOR the competing hypothesis
that [like all other proposed gods] it was simply invented by primitive peoples looking for psychological comfort in the
face of a bewildering world. [We can track the development and evolution of the ideas that would become the Christian
religion over time].
This shows that just because a claim is unfalsifiable, that doesn't put that claim beyond the reach of rational or scientific
enquiry, nor does it mean we cannot justifiably claim to know the truth value of that claim.
Which is why I am a gnostic atheist with respect to the Christian god.