Proving a negative

The crucial question is this:

If I say "Caesar sneezed....", does that imply "I know that Caesar sneezed...."?

If it does, then the statement is false. If, however, it is taken as a bare statement about Caesar, with no implication about my knowledge, then it is merely unjustified (it may be true or false).

Can we all at least agree on that?

I.e.: Prove to me that you never read 'War and Peace'

I was hoping that this debate was over, but here we go.

First, proof is a mathematical term.

The more accurate question would be - do you have evidence that you never read war and peace.

... I will still answer your question.

The only evidence that I have never read war and peace (and I haven't) is that I know that I've never read war and peace, but I hope to in the future.

So, if your claim was to say that I never read the book, you could verify that (with evidence) in a number of ways.

I.e.: Prove to me that you never read 'War and Peace'

Yes, that's an example of 'proving a negative', as per the title of this thread. So what was your point, Khethil?

I'm going to make a few more attempts to help you guys understand me. I apologize if I seem obscure in my explanation, but I'm trying to be as clear as possible. What I am saying is that to claim that Caesar sneezed or didn't sneeze when he crossed the Rubicon are both false claims, because there is no evidence whatsoever to support such claims. I am not saying that it didn't happen. A claim is a statement of knowledge, and so I am saying that it is false to claim that he did or didn't sneeze.

Since the statements" Ceasar sneezed, and Ceasar did not sneeze must have opposite truth values, how could both be false? They cannot, for it one is true, then the other is false. They are what are called "contradictories". The statements, Caesar was tall, and Caesar was short, on the other hand are called, "contraries" because they both could be false, since Caesar might have been of medium height, and neither tall nor short. On the other hand, the claim the Caesar either did sneeze or did not sneeze, must be true, since it is an instance of the law of the excluded middle, either A is true, or A is false.

Kennethamy - please see posts #81-82 above. I think these may answer your point. (If they don't, I would be interested to hear your further comments.)

Since the statements" Ceasar sneezed, and Ceasar did not sneeze must have opposite truth values, how could both be false? They cannot, for it one is true, then the other is false. They are what are called "contradictories". The statements, Caesar was tall, and Caesar was short, on the other hand are called, "contraries" because they both could be false, since Caesar might have been of medium height, and neither tall nor short. On the other hand, the claim the Caesar either did sneeze or did not sneeze, must be true, since it is an instance of the law of the excluded middle, either A is true, or A is false.

Huh? Where'd this come from?



No, it actually could entail a lot; much of which has nothing to do with mathematics. What point might this serve?



Uh... yea, that was my point



I didn't have a question



Well, that's good. It's actually a great book; probably moreso at the end. I found that last 20% of it wrapped up all the minutiae of the first 80% in a clever and high-impact way. I'd wholeheartedly recommend it.



I'm not exactly sure where you're coming from or going to here. What, precisely, did you take my example for? It almost sounds like you're interested in a conversation with yourself. It seems, towards one direction or another, you've read a great deal into my statement.

Umm... good luck with that

Your logic doesn't apply to this situation because Hue-man wasn't saying contradictories are both true and false, he was trying to say (I think anyway) that no matter what is claimed to be true, if it isn't verified with observation, then any definite statement about what happened in the past is merely guessing (i.e., no statement of fact can made about the truth or falseness of Caesar sneezing).

My main objections to his points are his attempts to argue that failing to verify or prove an incident occurred means we can conclude any statement about the incident happening is false. He is mixing the concept of verification together with the false statement definition as though they are the same thing, and they aren't.

So instead of saying it is a "false statement" to claim Caesar sneezed because we have no evidence, he should say it is an "unverified statement." That's because based on the accepted meaning of "false" it would mean in this case that someone has facts that Caesar definitely did not sneeze, and no one knows that.

Mathematically it is easy to prove a negative, like the concept of nothing. In fact only a few thousand years ago the concept of zero was beyond the thought of the great minds of that time,

That is why when we still used AD for a calendar the date of Christ birth was calculated back to "year one", instead of the "year naught"

I'm saying that it is a false claim and a meaningless proposition because it is unverifiable.

If I say "I know that Caesar either sneezed or did not sneeze", is that a true claim? Is it epistemologically proper? Since my knowledge of the law of the excluded middle is verifiable, can I use it to justify the claim?

You can see in this thread Hue-man attempts to reason from certain claims of knowledge. Someone claims to experience omnipresence, and he logically tries to refute that with his argument that since he hasn't experienced omnipresence, no one has.

Were we able to decide if his epistemological claim of non-knowledge is true? No, because his reasoning was improper (just because he doesn't know how to experience omnipresence doesn't mean others haven't learned how). Are we able to say because Hue-man didn't refute claims that therefore people really do experience omnipresence? Nope, because his improper reasoning doesn't mean anybody has actually experienced omnipresence.