phildonnia
Master Poster
- Joined
- Oct 20, 2001
- Messages
- 2,439
The technique of "perfect induction" can be used to prove a negative. If you were somehow able to observe every blue whale in the universe, and none of them were in your room, then you'd have the proof.
This technique is quite useful for proving things about finite sets, but it doesn't have much application for finite sets, let alone vague philosophy.
The real problem here is that the existence of God is not falsifiable: that is, there is no imaginable phenomenon that would disprove the God hypothesis. This doesn't amount to a proof that God doesn't exist, but it does mean that logic and science are unable to test the matter.
This technique is quite useful for proving things about finite sets, but it doesn't have much application for finite sets, let alone vague philosophy.
The real problem here is that the existence of God is not falsifiable: that is, there is no imaginable phenomenon that would disprove the God hypothesis. This doesn't amount to a proof that God doesn't exist, but it does mean that logic and science are unable to test the matter.
Abdul, I did not introduce mathematics, Cecil did. You explain to me what you mean, and then I'll respond. I'm talking about logic and critical thinking. I'm not ducking and weaving, I'm just trying to get a handle on this aspect of the discussion.
I think we're both approaching the same thing from different disciplines. I'm afraid we may be dancing right past one another here...
Now, about my idea as to why "you can't prove a negative" is an acceptable thing to say, even though it cannot be proven? "You can't prove a negative" is a conclusion based upon a preponderance of evidence that only positives can be proven.
I think we're both approaching the same thing from different disciplines. I'm afraid we may be dancing right past one another here...
Now, about my idea as to why "you can't prove a negative" is an acceptable thing to say, even though it cannot be proven? "You can't prove a negative" is a conclusion based upon a preponderance of evidence that only positives can be proven.
Abdul Alhazred
Philosopher
- Joined
- Sep 4, 2003
- Messages
- 6,023
mistake. see next.
Abdul Alhazred
Philosopher
- Joined
- Sep 4, 2003
- Messages
- 6,023
Well gee whiz. I can't be here all the time, but I'm back. 
To me, logic and mathematics are inseparable. And only in that realm is it reasonable to speak of absolute proof.
But what of non-absolute proof?
To my way of thinking, critical thinking means plausible inference, not proof.
For example, I believe King David was a real person even though I don't believe everything the Bible says about him.
A bit of archaeological evidence combined with what the Bible says leads me to the conclusion that most likely King David actually existed.
The non-Biblical evidence, though fragmentary, is the determining factor. But only in light of the Bible.
This is different from the Biblical "evidence" that Noah existed. In King David's case we have slight corroboration from other sources and no scientific evidence against the nasty dynastic struggles.
Just as the story of George Washington and the cherry tree, though false, is still evidence that George Washington existed. But not proof.
This is much weaker than "proof", but it's good enough for most purposes.
There is also the legal definition of proof "beyond a reasonable doubt". That's stronger than plausible inference as explained above, but weaker than mathemetical proof.
To me, logic and mathematics are inseparable. And only in that realm is it reasonable to speak of absolute proof.
But what of non-absolute proof?
To my way of thinking, critical thinking means plausible inference, not proof.
For example, I believe King David was a real person even though I don't believe everything the Bible says about him.
A bit of archaeological evidence combined with what the Bible says leads me to the conclusion that most likely King David actually existed.
The non-Biblical evidence, though fragmentary, is the determining factor. But only in light of the Bible.
This is different from the Biblical "evidence" that Noah existed. In King David's case we have slight corroboration from other sources and no scientific evidence against the nasty dynastic struggles.
Just as the story of George Washington and the cherry tree, though false, is still evidence that George Washington existed. But not proof.
This is much weaker than "proof", but it's good enough for most purposes.
There is also the legal definition of proof "beyond a reasonable doubt". That's stronger than plausible inference as explained above, but weaker than mathemetical proof.
Abdul, you're bringing up some other stuff here. Coming close to straw man, but not quite.
Here's the thing about your mathematical example. Stating that no three consecutive integers add up to 100 is a statement of conclusion. You're working backwards from knowledge you already possess.
Somewhere, a loooong time ago, some mathematician, probably Greek, decided to find out if three consecutive integers could add up to 100. He added them up and checked the totals again and again. He could find no evidence that any three consecutive integers would add up to 100. Based upon those findings, he concluded that no three consecutive integers add up to 100.
Thousands of years later, you now present his conclusion, and the calculation as proof. That is wrong.
Here's the thing about your mathematical example. Stating that no three consecutive integers add up to 100 is a statement of conclusion. You're working backwards from knowledge you already possess.
Somewhere, a loooong time ago, some mathematician, probably Greek, decided to find out if three consecutive integers could add up to 100. He added them up and checked the totals again and again. He could find no evidence that any three consecutive integers would add up to 100. Based upon those findings, he concluded that no three consecutive integers add up to 100.
Thousands of years later, you now present his conclusion, and the calculation as proof. That is wrong.