Double negation equals affirmation

[Vera_Ljuba]

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

Thank you.

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.

If you separate language from logic, all you get is gibberish. There are some perfectly clear ways to put special emphasis on something. If you really want to express your disagreement in a heightened way, you can always use: “I strongly disagree”, or “very strongly disagree”, but never with “I do not disagree”.

Or one can use the construct of Newspeak. For “bad” one can say “ungood”, for strong disagreement comes “plusungood” and for very strong disagreement one can say “doubleplusungood”.

Of course we are all familiar with a playful way to say that the dish served was very tasty, by saying “it was not too bad” accompanied by a smile, but that is just a linguistic play. We all know that “not too bad” does NOT mean “it was pretty bad, but still edible”.

“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.

There are people who - for some strange reason - do not want to be explicit - and they play word games. Just imagine the intonation of “weeeell, I don’t reeeealy disagreeeee…”, when expressing agreement feels “uncomfortable”.

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.

The language of the law has special rules - for obvious reasons. The language of philosophy does not. Here ~~P always equals P.

As a matter of fact, this reminds me of something. When you leave a hospital after a long stay, there is an accepted procedure (at least here in the States) that a nurse puts you in a wheelchair, and rolls you out to your car - even if you could simply walk out the door. Presumably this procedure was instated because if you would just walk out, then someone might mistakenly think that you were actually healed of your problem, and then other people would also expect to be healed, too. Reality frequently takes a back seat when it comes to appearances.

But to get back to serious business. If you are in the position to prevent an atrocity (especially if you could do it without jeopardizing your own safety) and fail to do so, then you cannot use the defense: “Don’t blame me! I did not agree with this action; I merely allowed it to happen”. No rational person will accept this obvious “cop-out”. Actively committing an act or passively allowing it to happen are logically the same.

 

[DaveBj]

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

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…

I could not fail to disagree with you less.

 

[Vera_Ljuba]

I could not fail to disagree with you less.

Bad grammar. It translates into “I strongly agree with you”. Of course, if you wanted to say that you “strongly disagree”, then you discard the laws of logic, and as such are unworthy of consideration.

It is quite entertaining to see these conversations. No matter what I say (or any other atheist says), you guys disagree in a nice Pavlovian fashion. If I would start a thread with the topic that the “sky is blue”, I am sure that you guys would disagree with that as well.

 

[dshix]

No matter what I say (or any other atheist says), you guys disagree in a nice Pavlovian fashion. If I would start a thread with the topic that the “sky is blue”, I am sure that you guys would disagree with that as well.

Strawman much?

 

[Vera_Ljuba]

Strawman much?

Nope. Having good, reliable memory.

 

[Rhubarb]

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

And that would be fine of basic propositional logic is the only logic that we use. But there are a host of logics that we use for various reasons because the basic simple ones like prepositional calculus doesn’t get the job done.

Any anyone who has made a study of logic should have been taught that a system of logic is merely a formal language were we stipulate the rules of syntax, so we can look at the semantics only of statements and arguments. The operators aren’t plucked from some ontological shelf - in logic WE stipulate the rules and it just so happens that frequently (but not always) the operators we stiplate map onto words of natural language. There are lots of theories in meta-logic and philosophy of language that try to figure out how and why there is this disconnect between logic and language.

And as the previous poster mentioned, there are plenty of intuitionist and constructivist logics that do not allow double negation and the law of the excluded middle. These logics were developed because previous logics were not dealing properly with sentences and arguments the developer was working with.

 

[inocente]

“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.

There are people who - for some strange reason - do not want to be explicit - and they play word games. Just imagine the intonation of “weeeell, I don’t reeeealy disagreeeee…”, when expressing agreement feels “uncomfortable”.

You seem to think it’s binary, that you either must agree or must reject. But there are other possibilities, such as not having decided, or being non-committal. “I don’t reject” is saying you don’t disagree but don’t want to commit to agreeing. The meaning is explicit in the words themselves, there’s no game.

No matter what I say (or any other atheist says), you guys disagree in a nice Pavlovian fashion.

Vera: The Moon is made of cheese. Also black is white, and 2+2 = 93.17658.

Us guys: Nope.

Vera: No matter what I say (or any other atheist says), you guys disagree in a nice Pavlovian fashion.

 

[Vera_Ljuba]

And that would be fine of basic propositional logic is the only logic that we use. But there are a host of logics that we use for various reasons because the basic simple ones like prepositional calculus doesn’t get the job done.

Any anyone who has made a study of logic should have been taught that a system of logic is merely a formal language were we stipulate the rules of syntax, so we can look at the semantics only of statements and arguments. The operators aren’t plucked from some ontological shelf - in logic WE stipulate the rules and it just so happens that frequently (but not always) the operators we stiplate map onto words of natural language. There are lots of theories in meta-logic and philosophy of language that try to figure out how and why there is this disconnect between logic and language.

And as the previous poster mentioned, there are plenty of intuitionist and constructivist logics that do not allow double negation and the law of the excluded middle. These logics were developed because previous logics were not dealing properly with sentences and arguments the developer was working with.

If one denies the three basic laws of logic, there can be no meaningful discussion.

Without the law of “A” is “A” there can be no agreement about what the terms mean. (The law of identity)
Without the law of “A and ~A = 0” there can be no true or false propositions. (The law of non-contradiction)
Without the law of “A or ~A = 1” there can be no Kolmogorov space of propositions. (The law of excluded middle)

Now, the law of excluded middle must be formulized carefully. It does not mean that A is either true or false, it means that A is either true or not true, and this gives way some ambiguity. A proposition may be neither true nor false, it may be incoherent, meaningless.

Sure, there is “fuzzy” logic and other constructs, but what of it?

Moreover, Matthew 12:30 says:

Whoever is not with me is against me, and whoever does not gather with me scatters.

 

[Vera_Ljuba]

You seem to think it’s binary, that you either must agree or must reject. But there are other possibilities, such as not having decided, or being non-committal. “I don’t reject” is saying you don’t disagree but don’t want to commit to agreeing.

True, many people are unwilling to show their hands, they prefer to hide their views. Especially when being explicit puts them into opposition to something that they do not want to oppose. Human weakness, I suppose.

The meaning is explicit in the words themselves, there’s no game.

Actually, there is no “intrinsic” meaning of words, we assign meaning to them by mutual agreement. But this is a very different discussion.

 

[Rhubarb]

(1) If one denies the three basic laws of logic, there can be no meaningful discussion.

Without the law of “A” is “A” there can be no agreement about what the terms mean. (The law of identity)
Without the law of “A and ~A = 0” there can be no true or false propositions. (The law of non-contradiction)
Without the law of “A or ~A = 1” there can be no Kolmogorov space of propositions. (The law of excluded middle)

Now, the law of excluded middle must be formulized carefully. It does not mean that A is either true or false, it means that A is either true or not true, and this gives way some ambiguity. A proposition may be neither true nor false, it may be incoherent, meaningless.

(2) Sure, there is “fuzzy” logic and other constructs, but what of it?

Moreover, Matthew 12:30 says:

Whoever is not with me is against me, and whoever does not gather with me scatters.

I’ve put bolded marks to organize my thoughts.

1. It doesn’t sound like you quite understand what logic actually is. Or, perhaps, you are conflating it some parts of natural language. There are nuanced problems between language and logic. You don’t have to take my word for it, the material is out there for studying. And arguments in intuitionist and constructivist logic are plenty meaningful and productive. Otherwise they wouldn’t exist. The operator CONJUNCTION does not map perfectly onto our concept of AND. Neither does disjunction, implication, or even negation. The information about this is out there too, if you want to find it. Paul Grice wrote a book on trying to resolve the tension between language and logical operators.
2. I don’t want to make assumptions but on the face of it, I can only assume you are denigrating other logics because you don’t understand them. Someone who spent their whole life studying simple propositional logic would find first order logic, or modal logics ‘fuzzy’. These systems were created because they work and they solve problems.

 

[inocente]

True, many people are unwilling to show their hands, they prefer to hide their views. Especially when being explicit puts them into opposition to something that they do not want to oppose. Human weakness, I suppose.

I don’t think there’s any subterfuge in such phrases, the meaning is clear.

Actually, there is no “intrinsic” meaning of words, we assign meaning to them by mutual agreement.

If you only just worked that out, then that explains.

 

[Vera_Ljuba]

And that would be fine of basic propositional logic is the only logic that we use. But there are a host of logics that we use for various reasons because the basic simple ones like prepositional calculus doesn’t get the job done.

Correct. People use all sorts of “logic”.

Some people use “military logic”, which can be illustrated with the following example: “If one soldier can dig a foxhole in 5 hours, then assigning 3000 soldiers to the task would accomplish the same result in 6 seconds”.

Or some people use “apologist logic”, which would be: “If someone has the power to prevent an undesirable act without any personal harm, but fails to do so, then the person is innocent of any harm-doing”.

 

[Rhubarb]

Correct. People use all sorts of “logic”.

Some people use “military logic”, which can be illustrated with the following example: “If one soldier can dig a foxhole in 5 hours, then assigning 3000 soldiers to the task would accomplish the same result in 6 seconds”.

Or some people use “apologist logic”, which would be: “If someone has the power to prevent an undesirable act without any personal harm, but fails to do so, then the person is innocent of any harm-doing”.

When I say ‘logic’ I mean formal systems to analyze statements and arguments. You are using it in a colloquial non-specific manner. I don’t know if you’re confused, or purposely trying to muddy the waters.

 

[thenobes]

And that would be fine of basic propositional logic is the only logic that we use. But there are a host of logics that we use for various reasons because the basic simple ones like prepositional calculus doesn’t get the job done.

Any anyone who has made a study of logic should have been taught that a system of logic is merely a formal language were we stipulate the rules of syntax, so we can look at the semantics only of statements and arguments. The operators aren’t plucked from some ontological shelf - in logic WE stipulate the rules and it just so happens that frequently (but not always) the operators we stiplate map onto words of natural language. There are lots of theories in meta-logic and philosophy of language that try to figure out how and why there is this disconnect between logic and language.

And as the previous poster mentioned, there are plenty of intuitionist and constructivist logics that do not allow double negation and the law of the excluded middle. These logics were developed because previous logics were not dealing properly with sentences and arguments the developer was working with.

Does “excluded middle” mean that only true or false can be the result of an analysis of a statement? In propositional logic that may be true, However in analysis of discrete or continuous values, a 0 value, if existing, may be neither negative nor positive, (or both?!) by definition, and so, “not positive” implies negative or 0, and “not negative”, positive or 0.

Thus, the sentiment of agreement, if looked at through the continuum of values from strongly agree to strongly disagree, passes a point of neither agree nor disagree (0).

So double negation implies affirmation only if no 0 value of affirmation exists, Else it can imply "affirmation -or- “neither afiirmation or negation”.

Or am I missing something more basic in your question?

peace
steve