Christianity: Obstacle to reason?

Originally posted by whodey
The plan fact of the matter is that life seems full of contradictions. For example, why does it seem that you receive the most by giving? Why is it that atheists post in the spirituality forum? Why is it that they insist on shoving that white cotton ball inside the container that hold my vitamins that I take every day when it only becomes an obstacle for w ...[text shortened]... y no even though I may not completely be able to work out this seemingly unworkable equation.

There aren't contradictions, there just seems to be. While that may true in some cases, there are many that aren't. Like I said, the bar is set exceedingly low.

By the way, the cotton balls: They're there to protect the vitamins during shipment. I can only hope that you pitch it after you open it up instead of stuffing it back in the bottle each time you retrieve one.

Originally posted by ThinkOfOne
For many Christians, their core beliefs require them to hold contradictory beliefs. From discussions I've had with many of them, it is apparent that they don't see a problem with this. This sets the bar exceedingly low when it comes to logic and reason. For them, a "belief" is true even though reason dictates otherwise. Does this ultimately make it imposs word of God despite that fact that the Bible is filled with contradictions.

etc.

Many seem to believe that the Bible is the inerrant word of God despite that fact that the Bible is filled with contradictions.

"Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth." ~ Blaise Pascal

A truth may in fact ultimately be amenable to reason, just not always immediately coherent or obvious.

Thus, one may find two contradictory statements in scripture alluding to a deeper truth, itself expressed only in part.

Originally posted by ThinkOfOne

By the way, the cotton balls: They're there to protect the vitamins during shipment. I can only hope that you pitch it after you open it up instead of stuffing it back in the bottle each time you retrieve one.[/b]

😳

Originally posted by epiphinehas


"Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth." ~ Blaise Pascal

Blaise Pascal was wrong.

Do you believe that the square root of 2 is a rational or irrational number? If you believe it is irrational (which it is), can you provide a proof that doesn't rely on the method of proof by contradiction (a mathematically valid technique of inferring the truth of proposition P when a contradiction can be derived by supposing Not-P; i.e. acknowledging that contradiction is in fact a sign of falsity)? I have never seen such a proof, so if you really believe Pascal's claim, you should remain unconvinced by standard proofs that the square root of 2 cannot be expressed as the ratio of two integers (leaving you several centuries behind modern number theory).

Originally posted by DoctorScribbles
Blaise Pascal was wrong.

Do you believe that the square root of 2 is a rational or irrational number? If you believe it is irrational (which it is), can you provide a proof that doesn't rely on the method of proof by contradiction (a mathematically valid technique of inferring the truth of proposition P when a contradiction can be derived by supp ssed as the ratio of two integers (leaving you several centuries behind modern number theory).

What if Pascal's statement was modified to "Contradiction is not always a sign of falsity"? Would that mollify you a bit?

Originally posted by Conrau K
What if Pascal's statement was modified to "Contradiction is not always a sign of falsity"? Would that mollify you a bit?

No, because that claim is also false. If it were true, then in every instance where proof by contradiction is employed, such as in proving the irrationality of the square root of two, a lemma would be required demonstrating that in the case at hand (but not generally), this contradiction indicates that the supposition is false and thus that the desired inference is valid, which would be absurd.

Rather, such lemmas are unnecessary because it is true generally, following from the definitions of the logical operators, that any proposition at all can be derived from a contradiction.

So, your acceptance of even the modified version of Pascal's claim leaves you in the same predicament with regard to keeping pace with modern number theorists regarding obviously true theorems about integers.

Originally posted by DoctorScribbles
Do you deny this?

Pascal does. His example is that the infinite number can be neither even nor not even. Thus, demonstrating that it is not even cannot give a proof that it is uneven. He believes that reductio ad absurdum does fail in some unique cases.

Paraconsistent logics do deny this and perhaps other non-classical logics which purportedly reject the law of excluded middle, such as intuitionist and fuzzy logics. Your lemma would be required in such cases when the contradiction does indeed show that the negation is true.

Originally posted by Conrau K
Pascal does. His example is that the infinite number can be neither even nor not even. Thus, demonstrating that it is not even cannot give a proof that it is uneven. He believes that reductio ad absurdum does fail in some unique cases.

Paraconsistent logics do deny this and perhaps other non-classical logics which purportedly reject the law of excluded middle, such as intuitionist logics.

Then Pascal is a fool along with the rest of them. It is a trivial exercise to construct a valid deduction of P from A AND NOT-A, for any given P and A. I would suggest you try this enlightening exercise if you actually deny that it is always possible.

'The infiinite number' doesn't even exist, even notionally, so I'm not going to entertain proofs based on premises about its properties.

What next? Are you going to suggest that Pascal's Wager is a sound argument?

Originally posted by DoctorScribbles
Then Pascal is a fool along with the rest of them.

'The infiinite number' doesn't even exist, even notionally, so I'm not going to entertain proofs based on premises about its properties.

What next? Are you going to suggest that Pascal's Wager is a sound argument?

So what if the infinite number does not exist? The excluded middle still fails. And anyway, there are major schools of logic which deny that proof by contradiction always succeeds: fuzzy, intuitionist and paraconsistent logics for starters.

And yes, I do believe that Pascal's Wager is sound. I just don't find it very compelling.

Originally posted by DoctorScribbles
It is a trivial exercise to construct a valid deduction of P from A AND NOT-A, for any given P and A.

Wow. Are you trapped in the dark ages or something? This argument does not obtain for any given P and A. This argument would fail if A contained a vague predicate and hence the conjunction of A and not-A had a non-zero truth-value. It would also fail in non-normal modal worlds in which contradictions are allowable.

Originally posted by Conrau K

And yes, I do believe that Pascal's Wager is sound.

You can't be serious. I mean, really, you can't.

OK, what's next? Are you going to tell me that Anselm's argument is also sound?

Originally posted by Conrau K
Are you trapped in the dark ages or something?

One of us sure is. You're the one who thinks Pascal's Wager is sound, so my bet is it's you.

Originally posted by DoctorScribbles
You can't be serious. I mean, really, you can't.

OK, what's next? Are you going to tell me that Anselm's argument is also sound?

Show that the argument is not sound. And perhaps you should resist criticising famous philosophers whom you have never read. Do you remember the last time when you claimed that Aquinas' argument for the existence of God was contradictory? It was quite clear you had not read his work.

Originally posted by DoctorScribbles
One of us sure is. You're the one who thinks Pascal's Wager is sound, so my bet is it's you.

Why are you ignoring the salient point that a number of schools of modern logic (which most universities teach after or along side of first-order logic) deny your argument?

Originally posted by Conrau K
Show that the argument is not sound.

Please. It's been refuted six ways to Sunday. It's quite possible that you're the last remaining person on earth to actually believe that it is sound.

What if I posit the possible existence of an even more powerful God who will send you to eternal torment for believing in the God of the original Wager, but grant you eternal paradise for rejecting the God of the original Wager. Based on your acceptance of the soundness of Pascal's Wager, should you believe in the God of the original Wager?