Double negation equals affirmation

[Vera_Ljuba]

Simple, even elementary logic, but it has long reaching consequences. Your thoughts?

 

[edward_george]

Not necessarily. The difference between “what we can’t not know” and “what we can know” is so vast as to comprise separate disciplines in philosophy. The former implies near inevitability, so as relates to knowledge it would be things that are innate. The latter refers to possibility. So the former might be an apt description of natural law (it is the title of J. Budziszewski’s book on the subject), while the latter could be said to describe epistemology.

-Fr ACEGC

 

[dshix]

Simple, even elementary logic, but it has long reaching consequences. Your thoughts?

I agree with the above poster. Double negation can be equivalent to affirmation, but because of the quirks of language and logic there are times that the meaning can be extremely different.

 

[DaveBj]

Multiple negation can also mean emphasis. Language is not mathematics.

“It’s NOT UNusual” – what about that double negative?

In Russian, multiple negation is not only allowed; it’s required:

Я НИчего НИкому НИкогда НИгде НЕ дал – I did NOT give NOthing to NO one NOwhere at NO time.

 

[dshix]

Я НИчего НИкому НИкогда НИгде НЕ дал – I did NOT give NOthing to NO one NOwhere at NO time.

That’s a pretty funny sentence.

“I did NOT give NOthing” - does this imply he did, in fact, give something to no one? Or does grammar work differently in Russian?

 

[Vera_Ljuba]

I was talking about the laws of logic, not linguistic word games. A proposition “P” expresses something. The proposition “~P” represents its negation. The proposition “~~P” is the equivalent of the original proposition “P”.

Of course linguistic games have their place under the sun, especially for entertainment purposes. Here comes one:

The teacher explains to the class the concept of double negation. He tells that double negation is an affirmation, however a double affirmation is not a negation. One of the students mumbles “Yeah! Right!” and everyone starts laughing.

Seriously, however. There is no difference between “agreeing” with something and “not disagreeing” with it.
“I am not unaware” == “I am aware”.
“I do not reject” == “I accept”.
and zillions of other examples.

 

[Vera_Ljuba]

I was talking about the laws of logic, not linguistic word games. A proposition “P” expresses something. The proposition “~P” represents its negation. The proposition “~~P” is the equivalent of the original proposition “P”.

Of course linguistic games have their place under the sun, especially for entertainment purposes. Here comes one:

The teacher explains to the class the concept of double negation. He tells that double negation is an affirmation, however a double affirmation is not a negation. One of the students mumbles “Yeah! Right!” and everyone starts laughing.

Seriously, however. There is no difference between “agreeing” with something and “not disagreeing” with it.
“I am not unaware” == “I am aware”.
“I do not reject” == “I accept”.
and zillions of other examples.

 

[dshix]

I was talking about the laws of logic, not linguistic word games. A proposition “P” expresses something. The proposition “~P” represents its negation. The proposition “~~P” is the equivalent of the original proposition “P”.

Of course linguistic games have their place under the sun, especially for entertainment purposes. Here comes one:

The teacher explains to the class the concept of double negation. He tells that double negation is an affirmation, however a double affirmation is not a negation. One of the students mumbles “Yeah! Right!” and everyone starts laughing.

Seriously, however. There is no difference between “agreeing” with something and “not disagreeing” with it.
“I am not unaware” == “I am aware”.
“I do not reject” == “I accept”.
and zillions of other examples.

Well, if we choose to exclude the connotations of language from the discussion, then you are, of course, entirely correct.

Now I’m not sure that there’s anything further to be said now that the objective truth has been identified and affirmed.

 

[Rhubarb]

Elementary logic isn’t as useful for a wide range of arguments. And there are plenty of advanced logics that do not allow for negation elimination. Specifically logics that don’t follow the law of the excluded middle.

 

[sko]

The proposition “~~P” is not necessarily equivalent to “P” – it depends on the logic. In mathematics, there is a wealth of constructive logics which have the fact that “~~P” does not always imply “P” as their basic property and are, in some ways, actually much more useful that the “ordinary” ones.

And if you want to step outside the precise world of formal logic and into the mess that is the “real” world, I could say that I can indeed not disagree with X, for instance by being unaware that X exists, but that does not imply I actually agree with X.

 

[Vera_Ljuba]

Well, if we choose to exclude the connotations of language from the discussion, then you are, of course, entirely correct.

Word games, especially puns are fun. But I was serious when I presented the OP.

Now I’m not sure that there’s anything further to be said now that the objective truth has been identified and affirmed.

I would say that “AN objective truth has been identified and confirmed”, instead of “THE objective truth… etc.” There are infinitely many “true” statements. However there is an important corollary to all this. Many times people argue that the fact that “God permits something” does not imply that “God accepts it (or agrees with it)”. But according to the principle stated, if God “does not disapprove of something”, then “God approves it”.

That is the point of this thread. Simple logic and elementary grammar, nothing else.

 

[DaveBj]

That’s a pretty funny sentence.

“I did NOT give NOthing” - does this imply he did, in fact, give something to no one? Or does grammar work differently in Russian?

I told you in post #4 – the multiple negatives are for intensification. They don’t mutually cancel each other out. And on a cultural level, that’s the way it works in English, too. When a 10-year-old tells you, “I didn’t do nothin’!”, he really means it.

Trying to apply mathematical logic to the non-mathematical, non-logical construct that is language is a mistake from the get-go.

 

[tee_eff_em]

Seriously, however. There is no difference between “agreeing” with something and “not disagreeing” with it.

I can neither agree nor disagree with this statement.

tee

 

[Wesrock]

Word games, especially puns are fun. But I was serious when I presented the OP.

I would say that “AN objective truth has been identified and confirmed”, instead of “THE objective truth… etc.” There are infinitely many “true” statements. However there is an important corollary to all this. Many times people argue that the fact that “God permits something” does not imply that “God accepts it (or agrees with it)”. But according to the principle stated, if God “does not disapprove of something”, then “God approves it”.

That is the point of this thread. Simple logic and elementary grammar, nothing else.

Funnily enough, your “I do not reject” = “I accept” example from earlier was one I had qualms with. Now I just wish I decided to post before you got to your point…

Edit: Deleting the bulk of this post as it’s a tangent and not related to the double negative discussion.

 

[Vera_Ljuba]

I told you in post #4 – the multiple negatives are for intensification. They don’t mutually cancel each other out. And on a cultural level, that’s the way it works in English, too. When a 10-year-old tells you, “I didn’t do nothin’!”, he really means it.

Just because a 10 years old cannot (or does not) speak proper English that fact does not create a valid philosophical argument.

Trying to apply mathematical logic to the non-mathematical, non-logical construct that is language is a mistake from the get-go.

So you don’t care if a proposition adheres to the laws of logic or not? Shall we get rid of that pesky logic and the useless rules of grammar… so anything can mean whatever you want is to mean?

I will stick to the three laws:

1. A is A - everything is itself. (The law of identity)
2. A and ~A = 0. (The law of non-contradiction)
3. A or ~A = 1. (The law of excluded middle)

Without these laws there cannot be a meaningful conversation.

I recall a nice proposition: “We the willing, led by the unknowing are doing the impossible for the ungrateful. We have been doing so much for so long with so little, that now we are qualified to do everything with nothing”. A fun slogan of the wall of your cubicle, that is for sure…

 

[tuffsmurf]

Grammatically it differs from language to languages. In french you are supposed to use double negation:
Je ne sais pas, je ne regrette rien, and so on.
In Swedish(my mother tongue) you can never use double negation. In english it differs depending on accent. “I ain’t got nothing to do” is used in some areas.

When it comes to formal logic, ~~P always equals P, but first order language and natural language is different.

 

[thephilosopher6]

The proposition “~~P” is not necessarily equivalent to “P” – it depends on the logic. In mathematics, there is a wealth of constructive logics which have the fact that “~~P” does not always imply “P” as their basic property and are, in some ways, actually much more useful that the “ordinary” ones.

And if you want to step outside the precise world of formal logic and into the mess that is the “real” world, I could say that I can indeed not disagree with X, for instance by being unaware that X exists, but that does not imply I actually agree with X.

Actually, in basic propositional logic, ~~P is logically equivalent to P.

 

[Darryl_B]

Simple, even elementary logic, but it has long reaching consequences. Your thoughts?

It is not logic, it is language. Double negative means even more No, except in English for some reason. And I am not not not not not not not not not not going to see it any other way.

 

[inocente]

Seriously, however. There is no difference between “agreeing” with something and “not disagreeing” with it.
“I am not unaware” == “I am aware”.
“I do not reject” == “I accept”.
and zillions of other examples.

“I agree” and “I don’t disagree” are not the same. The latter says I neither agree nor disagree, it’s neutral.

Similarly “I do not reject” doesn’t imply I accept. Follow the words, it means I’m not committing either way.

 

[edward_george]

Think of how in court one can be “guilty,” that is, proven to have committed the crime beyond a shadow of a doubt, or “not guilty,” so not proven to have committed the crime. Not guilty does not necessarily mean innocent. One can still have committed the crime, but it just can’t be legally demonstrated beyond a shadow of a doubt.

-Fr ACEGC