# Does a negative always have to be proven by a positive

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Thread starter 7 years ago
#1
Firstly, as far as I know you can prove a negative assertion. For example, the law of non-contradiction one of the three classic laws of thought is a negative proposition " contradictory statements cannot both be true in the same sense at the same time (Wiki)". Also, two times two does not equal 5. Also, . But this is proven by the positive two times two equals four...So my question is, can a negative assertion/proposition/etc... be proven on its own?
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7 years ago
#2
There are no unmarried husbands.

True by definition.
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Thread starter 7 years ago
#3
(Original post by Calvin)
There are no unmarried husbands.

True by definition.
but isn't that true because of the positive preposition: All husbands are married...?
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7 years ago
#4
So the statement "All P's are Q" is proved true by finding all instance of P and checking that they are all Q.
But if you find even one P which isn't Q then you prove it false.
That would require you to check all Ps if it's true. If it's false you might get lucky and find out it's false on the first try. But you're right that you have to check ALL the P's if it's true before you know for sure.

Now lets look at the negatative "Not all P's are Q"
For that you start checking, and as soon as you find at least one P which is Q you can stop, and you know it's true. If it's false, you again have to check all of them before you know for sure.

So they are essentially symmetrical. For the positive you have to check all of them to know it's true. For the negative you have to check all of them to know it's false.
There is no logical difference except for the conditions under which they are proved. But both are provable.

The negative "All P's are Q" is proven by the positive "There is at east one P which is not Q", so you're right.
But as we showed at the beginning, the positive is proven only by checking the negative.
So it's simply logical implication. It's not anything special about positive statements. The two are symmetrical.

Am I helping/understanding you?
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Thread starter 7 years ago
#5
(Original post by Calvin)
So the statement "All P's are Q" is proved true by finding all instance of P and checking that they are all Q.
But if you find even one P which isn't Q then you prove it false.
That would require you to check all Ps if it's true. If it's false you might get lucky and find out it's false on the first try. But you're right that you have to check ALL the P's if it's true before you know for sure.

Now lets look at the negatative "Not all P's are Q"
For that you start checking, and as soon as you find at least one P which is Q you can stop, and you know it's true. If it's false, you again have to check all of them before you know for sure.

So they are essentially symmetrical. For the positive you have to check all of them to know it's true. For the negative you have to check all of them to know it's false.
There is no logical difference except for the conditions under which they are proved. But both are provable.

The negative "All P's are Q" is proven by the positive "There is at east one P which is not Q", so you're right.
But as we showed at the beginning, the positive is proven only by checking the negative.
So it's simply logical implication. It's not anything special about positive statements. The two are symmetrical.

Am I helping/understanding you?
Yeah I got it, thanks.
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7 years ago
#6
'I don't like cheese'.

What positive would be necessary there?
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Thread starter 7 years ago
#7
(Original post by Picnic1)
'I don't like cheese'.

What positive would be necessary there?
This is not an assertion, just a personal taste.
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7 years ago
#8
(Original post by YNM96)
This is not an assertion, just a personal taste.
'I don't ever do anything that is not consistent with the laws of nature'.

What positive is necessary there? Do you really have to monitor my whole life on the off chance that I one day do a Jesus-like miracle?
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Thread starter 7 years ago
#9
(Original post by Picnic1)
'I don't ever do anything that is not consistent with the laws of nature'.

What positive is necessary there?
This statement is proven by the positive: "All actions on Earth are consistent with the laws of nature". Without this assertion your original statement wouldn't stand.
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7 years ago
#10
(Original post by YNM96)
This is not an assertion, just a personal taste.
Not so, it's either true or false. He might like cheese, and yet lie about it, so there is some condition of truth. Thus an assertion.

"Cheese is great" is personal taste. "I think Cheese is great" is a an assertion about my state of mind.
1
7 years ago
#11
(Original post by Picnic1)
'I don't ever do anything that is not consistent with the laws of nature'.

What positive is necessary there? Do you really have to monitor my whole life on the off chance that I one day do a Jesus-like miracle?
Is that a negative statement, given it is a double negative? - I don't not. Or is it a positive - "Nothing I do is inconsistent with the laws of nature" or "everything I do is consistent with the laws of nature"

Raise the great point though that OP's actual claim is not clear to begin with - what exactly counts as a negative statement?
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Thread starter 7 years ago
#12
(Original post by Calvin)
Is that a negative statement, given it is a double negative? - I don't not. Or is it a positive - "Nothing I do is inconsistent with the laws of nature" or "everything I do is consistent with the laws of nature"

Raise the great point though that OP's actual claim is not clear to begin with - what exactly counts as a negative statement?
A statement which mentions the, assumed, absence of something rather than its, possible, presence. e.g. there is no rain in England.

or, a statement that something cannot happene.g. there cannot be rain in England
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7 years ago
#13
The via negative tried to define God for what he is not as it was suggested his true nature could not possibly be described, so a positive could not qualify the negative according to the theory. However, I'm not really sure pseudo Dionysus (not sure that's the right name) actually succeeded in this.

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