# Proving a negative

## 127 posts in this topic

I cannot discuss or prove why something that is not so is not so because one cannot prove a negative.

Actually you can. One can prove there does NOT exist a pair of integers m, n such that n != 0, m and n have no common denominator other than 1 and such that (m/n)^2 = 2.. This last was proved by a follower of Pythagorus who was bumped off by some of his fellow Pythagoreans for causing them embarrassment.

ruveyn

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I cannot discuss or prove why something that is not so is not so because one cannot prove a negative.

Actually you can. One can prove there does NOT exist a pair of integers m, n such that n != 0, m and n have no common denominator other than 1 and such that (m/n)^2 = 2.. This last was proved by a follower of Pythagorus who was bumped off by some of his fellow Pythagoreans for causing them embarrassment.

ruveyn

That is an example of proving a positive that makes the opposite a contradiction.

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That is an example of proving a positive that makes the opposite a contradiction.

No It is an outright negative. It is the proof that the square root of 2 is NOT a rational number. This devistated the Pythagoreans who believed every quantity could be expressed in terms of integers. They were wrong. There is no fiddling around with double negations here. The indirect proof, or reductio ad absurdum was invented initially by the Greek geometers. Euclid's -Elements- are chock full of indirect proofs. Some indirect proofs can be used to prove the existence of things. For example if f is a continuous function, and f(a) is negative and f( is positive there is a number c between a and b where f is zero. This is proved with an indirect proof.

ruveyn

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I cannot discuss or prove why something that is not so is not so because one cannot prove a negative.

Actually you can. One can prove there does NOT exist a pair of integers m, n such that n != 0, m and n have no common denominator other than 1 and such that (m/n)^2 = 2.. This last was proved by a follower of Pythagorus who was bumped off by some of his fellow Pythagoreans for causing them embarrassment.

That is an example of proving a positive that makes the opposite a contradiction.

The assertion that there do not exist integers m and n etc. such that (mn)² =2, i.e., mn = √2, is an example of an epistemologically positive assertion. The burden of proof was on the Pythagorean who stated it to prove it, and he did. But there is no evidence that he was bumped off for it and we don't have to prove he wasn't to reject the accusation of murder.

But "discussing or proving why something that is not so is not so" is not the same thing as "proving a negative". Rick Wilmes had asked several invalid questions of the form why did something that didn't happen not happen, i.e., literally why isn't it something the opposite of what it is. It isn't because a thing is what it is, not what it isn't. The literal answer is that what didn't happen didn't happen because something else did.

Asking specific questions about the nature of something governing what it can and can't do is very different from that exchange, and in the context of "changing concepts" has in fact been discussed in detail.

That exchange between Rick Wilmes and Betsy is not anything like proving statements about what cannot be in integer relations. I think we have previously discussed why such non-existence proofs in mathematics are not "proving a negative" in the sense of where the burden of proof lies.

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That is an example of proving a positive that makes the opposite a contradiction.

Wrong sir. It is a negation of the proposition that the square root of 2 is a rational number. You can't get much more negative than that.

ruveynb

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That is an example of proving a positive that makes the opposite a contradiction.

No It is an outright negative. It is the proof that the square root of 2 is NOT a rational number. This devistated the Pythagoreans who believed every quantity could be expressed in terms of integers. They were wrong. There is no fiddling around with double negations here. The indirect proof, or reductio ad absurdum was invented initially by the Greek geometers. Euclid's -Elements- are chock full of indirect proofs. Some indirect proofs can be used to prove the existence of things. For example if f is a continuous function, and f(a) is negative and f( is positive there is a number c between a and b where f is zero. This is proved with an indirect proof.

ruveyn

An epistemologically negative statement does not mean that the statement is not grammatically negative. It means prove the negative for which there is no evidence. Clearly, that is not the case for your example. There is ample evidence of numbers being integers and evidence that some integers can be expressed as ratios of other integers.

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"Absence of proof is not proof of absence." ~ William Cowpers

It seems a bit of a cheat that, lacking omniscience, one cannot prove the non-existence of an omniscient being, e.g., that God doesn't exist. By this standard, it appears that faith is required to know anything. Proving a negative requires the positive assertion that something doesn't exist, and if that's the case, how was one aware of it to begin with? Perhaps Socrates summed it up best with, "As for me, all I know is that I know nothing."

Rational beings, aware of their fallibility, validate negative proofs by their own experience. There's no way to be positive of a negative... at least I don't think so.

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"Absence of proof is not proof of absence." ~ William Cowpers

It seems a bit of a cheat that, lacking omniscience, one cannot prove the non-existence of an omniscient being, e.g., that God doesn't exist. By this standard, it appears that faith is required to know anything. Proving a negative requires the positive assertion that something doesn't exist, and if that's the case, how was one aware of it to begin with? Perhaps Socrates summed it up best with, "As for me, all I know is that I know nothing."

Rational beings, aware of their fallibility, validate negative proofs by their own experience. There's no way to be positive of a negative... at least I don't think so.

It's hard to follow your reasoning. Since the assertion that there is an omniscient being is arbitrary, what exactly do I have to prove about him since there is nothing to point to for a demonstration? One does not know anything by faith since faith means to accept as true without evidence or contrary to the evidence. Proving a negative for which evidence can be adduced is not hard: 'there is no cat in my house' can be proven by looking around my house, knowing that I don't own a cat, and if iyou want to go to extremes, burn my house down and not find a cat body, etc. But that is NOT the meaning of "proving a negative". It means that the burden of proof is on the one who makes an assertion (whether positive or negative) and there is no logical requirement to prove the assertion is false in the absence of such evidence.

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"Absence of proof is not proof of absence." ~ William Cowpers

It seems a bit of a cheat that, lacking omniscience, one cannot prove the non-existence of an omniscient being, e.g., that God doesn't exist. By this standard, it appears that faith is required to know anything. Proving a negative requires the positive assertion that something doesn't exist, and if that's the case, how was one aware of it to begin with? Perhaps Socrates summed it up best with, "As for me, all I know is that I know nothing."

Rational beings, aware of their fallibility, validate negative proofs by their own experience. There's no way to be positive of a negative... at least I don't think so.

One more point. And just what can you say about such an omniscient being? He is smarter than me? Maybe. He is dumber than me? Maybe, too, After all, if he's so smart, he should be able to figure out a way to make me smarter than him!!! So, your left with a contradiction. What will you do with that knowledge?

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"One does not know anything by faith since faith means to accept as true without evidence or contrary to the evidence." ~ Paul's Here

This is a common misconception of the actual meaning of 'faith'**, which is firm belief* based on evidence but lacking proof. Cathedrals and recorded testamony provide historical evidence, and the fact that you refer to God as "he" (as opposed to, "duh... what?") demonstrates your awareness of it. What you do with that knowledge is up to you.

Personally, I find trying to prove a negative to be self-defeating. If for example, you know there are no cats in your house, how does attempting to persuade me to accept your proof increase our knowledge? Without being able to inspect your home, I'd have to have faith that you are telling the truth; and even if I came to visit, I'd still have to have faith that your cat wasn't being kept temporarily somewhere else.

*Definition of 'faith': firm belief in something for which there is no proof. ~ Merriam-Webster

**Definition of 'belief': conviction of the truth of some statement or the reality of some being or phenomenon especially when based on examination of evidence. ~ Merriam-Webster

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*Definition of 'faith': firm belief in something for which there is no proof. ~ Merriam-Webster

**Definition of 'belief': conviction of the truth of some statement or the reality of some being or phenomenon especially when based on examination of evidence. ~ Merriam-Webster

Considering that the "something" is primarily concrete facts/events (god, miracles, myths, etc.) that for which there is no proof is primarily that for which no evidence exists to support the conclusion. There is no proof that the word was created in 7 days obviously means there is no evidence that such an event occurred nor is there evidence that serve as a basis for a proof. Before one can prove a conclusion, one must have evidence indicating that there exists something to indicate a conclusion. For example, it might be reasonable to hold that there is (or maybe) a cat in my house because cats exist and so do houses and cats can sneak into places. But there it is an entirely untenable conclusion that the universe was created by something since that something would have had to exist prior to its creation.

I have no problem using the term 'belief' since is simply designates that someone holds something to be true without necessarily indicating the method of such knowledge. I believe there are no cats in my house, but I could be wrong since I have seen cats wandering in my neighborhood and one could be hiding out somewhere.

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"One does not know anything by faith since faith means to accept as true without evidence or contrary to the evidence." ~ Paul's Here

This is a common misconception of the actual meaning of 'faith'**, which is firm belief* based on evidence but lacking proof. Cathedrals and recorded testamony provide historical evidence, and the fact that you refer to God as "he" (as opposed to, "duh... what?") demonstrates your awareness of it. What you do with that knowledge is up to you.

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I disagree. The evidence cited is arbitrary and groundless evidence with no connection to the conclusion that allegedly lacks proof. Pointing at the Sun and saying that is evidence of a Sun God but there is no proof of a Sun God, seems like meaningless use of language. The arbitrary conclusion is already within the minds of the advocates of faith and it is they who try to find evidence to convince others.

The only evidence that cathedrals record is that that is what people believed, not evidence for any conclusion about the beliefs.

I refer to God as "he" because that is traditionally what is done. Personal pronouns are often used as collective terms designating a group, without implying anything about the members of the group. Let's not get into grammar arguments here.

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*Definition of 'faith': firm belief in something for which there is no proof. ~ Merriam-Webster

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Rand's defintiion of faith: "Faith” designates blind acceptance of a certain ideational content, acceptance induced by feeling in the absence of evidence or proof.

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The presumptions that the universe was created spontaneously, or by a Creator are just that; presumptions. We know that we are sentient and volitional creatures created by the same, and yet haggle over the original author.

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I accept Ayn Rand's definition of 'faith' as "blind faith", i.e., without any evidence. By her definition, proving a negative requires faith that something is, without any evidence of it. This certainly appears to be illogical, as how can one be aware of something without any evidence of it? One is either aware of something, or one isn't, and one certainly can't argue about that which one is entirely unaware of... OK, well some politicians do. There must be at least some catalyst to faith, else it is not only blind but irrational.

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"The only evidence that cathedrals record is that that is what people believed, not evidence for any conclusion about the beliefs." ~ Paul's Here

And yet this is exactly how trials of fact are practiced, and the lives of defendants hang in the balance; by the testimony of witnessess.

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The presumptions that the universe was created spontaneously, or by a Creator are just that; presumptions. We know that we are sentient and volitional creatures created by the same, and yet haggle over the original author.

I don't haggle over any creator. I know who created me: my parents. The presumption is that the universe was created at all.

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I accept Ayn Rand's definition of 'faith' as "blind faith", i.e., without any evidence. By her definition, proving a negative requires faith that something is, without any evidence of it. This certainly appears to be illogical, as how can one be aware of something without any evidence of it? One is either aware of something, or one isn't, and one certainly can't argue about that which one is entirely unaware of... OK, well some politicians do. There must be at least some catalyst to faith, else it is not only blind but irrational.

Imagination, fantasy, unfocused mental associations, emotional association are methods of being aware of something without evidence.

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"The only evidence that cathedrals record is that that is what people believed, not evidence for any conclusion about the beliefs." ~ Paul's Here

And yet this is exactly how trials of fact are practiced, and the lives of defendants hang in the balance; by the testimony of witnessess.

Witness testimony is known to be very unreliable. Concrete evidence is usually needed to tie the perp to the victim or the crime in some way.

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"... methods of being aware of something without evidence." ~ Paul's Here

Awareness cannot occur without evidence, i.e., perception of something. I'll have to leave it at that for now, as I'm off for a couple of weeks on a road trip. I'll check back latter...

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"... methods of being aware of something without evidence." ~ Paul's Here

Awareness cannot occur without evidence, i.e., perception of something. I'll have to leave it at that for now, as I'm off for a couple of weeks on a road trip. I'll check back latter...

Awareness is a perceptual issue, evidence is a conceptual issue. The act of being aware of something does not make it evidence of anything. The fact that an issue can be conceptualized does not automatically mean that there is evidence for it. Imagination and fantasy (as well as a host of other psychological processes) can lead to conceptualization, such as fiction and science fiction. That someone can imagine going to another planet at faster than the speed of light does not mean that the fantasy is evidence of things going faster than the speed of light. I know that some things are created, yet if I fantasize and claim that everything is created, no evidence has yet been provided for such a claim.

Have a great trip.

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Everything IS created. That something exists where nothing was before implies this truth. We might haggle over the author and process, but existence exists.

Having said this, I don't disagree with the remainder of your last comments. Apologies for the delayed response... been out on the road awhile )

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Everything IS created. That something exists where nothing was before implies this truth. We might haggle over the author and process, but existence exists.

Having said this, I don't disagree with the remainder of your last comments. Apologies for the delayed response... been out on the road awhile )

Is it possible there exists something that has always existed?

ruveyn

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I prefer probabilities and likelihoods to possibilities, but existence demonstrates change, e.g. mater to energy and energy to mater. Mass is apparently neither created or destroyed. My prior statement, "Everything IS created" was intended to mean that every object is the product of some creative process, as opposed to suddenly appearing out of nothing. As has been said, "You don't get something from nothing".

"The only constant is change" ~ Issac Asimov

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Everything IS created. That something exists where nothing was before implies this truth. We might haggle over the author and process, but existence exists.

Having said this, I don't disagree with the remainder of your last comments. Apologies for the delayed response... been out on the road awhile )

I disagree that everything is created. Such a view represents an infinite regress. And since there is no metaphysical infinity, everything is not created. Not to mention the issue of context dropping. Creation is an act of consciousness, a rearrangement of existing elements for a purpose. The causal processes of change that occur within nature are not acts of creation. They are simply a progression of change according to the nature of the entities undergoing change.