Antonyms versus Negations

[fast]

Antonyms are mutually exclusive but not collectively exhaustive, so third options exist.
Negations are both mutually exclusive and collectively exhaustive, so third options don't exist.

A rock is neither happy nor unhappy, so a rock is both not happy and not unhappy, so "not happy" is not always equivalent with "unhappy". Anything that can't be the case won't be the case.

I'll put it another way. A rock is not the kind of thing that can be happy, and if something can't be happy, then it won't be happy. At the same time, a rock is not the kind of thing that can be sad or unhappy. It's not within its nature to have feelings one way or the other. To say x is happy is to assume the possibility of happiness, and so too is the case that to say x is unhappy is to assume the possibility of happiness. Saying x is not happy doesn't carry with it that assumption.

Another example, "innocent" and "guilty" are not collectively exhaustive while "guilty" and "not guilty" are collectively exhaustive; however, if we exclude things that can be neither (like rocks and such), haven't we just eliminated the distinction between a negation and an antonym?

The reason there exists a difference between "false" and "not true" is because of the third option. "False" implies "not true", but "not true" does not imply "false," for things that can neither be true or false are still not true (and not false for that matter), but if we lay aside all third options due to possibilities, it seems to me like we can treat antonyms like negations--so long as mutual exclusivity implies exhaustivity in the absence of third options.

That being said, a person that is not guilty of a crime is innocent of a crime. Of course, a legal finding of guilt and thus judged guilty in no way implies guilt; after all, if I was incorrect about that, we couldn't find innocent people that have been convicted of crimes.

At the same time, it makes sense to not infer that a person is innocent just because one hasn't been found guilty, so a judgement of not guilty doesn't imply innocence--but it's still nevertheless true that a person who is not guilty is in fact innocent--not in the broad scoped meaning (innocence and purity of a child) but rather in the more narrow sense (innocent of a particular crime).

 

[Speakpigeon]

a person that is not guilty of a crime is innocent of a crime.

Sure, a person not guilty of a crime may well be guilty of a crime.

What you meant, I guess, was that a person that is not guilty of a crime is innocent of this crime.

Of course, a legal finding of guilt and thus judged guilty in no way implies guilt; after all, if I was incorrect about that, we couldn't find innocent people that have been convicted of crimes.

We certainly find people we now think, or even the judiciary now think, are innocent that had been previously judged guilty. However, just as a legal finding of guilt doesn't imply guilt, a finding of innocence, legal or otherwise, doesn't imply innocence (you said yourself as much later). So even if a legal finding of guilt implied actual guilt, we might very well still find people previously judged guilty and now not.
EB

 

[fast]

When I said, "a person that is not guilty of a crime is innocent of a crime," I meant just that. It may well very be that a person not guilty of a crime is also guilty of a crime, but if one is not guilty of a crime, then one must be innocent of a crime-at least the one crime that one is not guilty of.

I still hold the view that while "innocent" implies "not guilty," "not guilty" doesn't imply "innocent," but I nevertheless infer innocence from not being guilty, and I do this in defiance of my view. Even though a logical implication may be absent, the inference isn't.

 

[fast]

When I said, "we couldn't find innocent people that have been convicted of crimes," the idea is that the people found are innocent and therefore not guilty despite the legal finding.

I do not hold the view that a legal finding of guilt implies guilt. It suggests guilt, but "implies" is a strong technical word that is supposed to guarantee an inference. For instance, Bobby says that he hates black people. That suggests racism, but we cannot logically infer that he is racist based on that. After all, Bobby also says he hates all people, white, Hispanic, Mexican, Vietnamese, Russian, etc etc etc.

 

[Speakpigeon]

When I said, "a person that is not guilty of a crime is innocent of a crime," I meant just that.

You say so but I can't believe that. What you say is, according to English syntax, ambiguous. Further, it is either logically inconsistent or false depending on how you choose to solve the ambiguity. The only way out is by replacing the second "a" by "this" as I suggested earlier.

It may well very be that a person not guilty of a crime is also guilty of a crime,

Good to me.

but if one is not guilty of a crime, then one must be innocent of a crime-at least the one crime that one is not guilty of.

Sure but that is precisely why I said you need to remove the ambiguity. Yes a person is innoncent of the crime she is not guilty of but may be she isn't innocent of another crime. Your initial sentence does not make that clear. We can understand your idea because we can assume you're not an idiot based on your attention to language but the sentence on its own is useless.

I still hold the view that while "innocent" implies "not guilty," "not guilty" doesn't imply "innocent,"

How being not guilty of a crime doesn't imply being innocent of this crime? And if that's not what you meant then I don't think what you meant was at all expressed cogently by what you said.
EB

 

[Speakpigeon]

When I said, "we couldn't find innocent people that have been convicted of crimes," the idea is that the people found are innocent and therefore not guilty despite the legal finding.

But then it is not the case that you can hold for certain that we did find innocent people when we came to think that we had found innocent people. Innocence is a metaphysical notion. All we may have are beliefs that some people are innocent. We can't even be certain of our own innocence.

I do not hold the view that a legal finding of guilt implies guilt.

Of course not.

It suggests guilt, but "implies" is a strong technical word that is supposed to guarantee an inference. For instance, Bobby says that he hates black people. That suggests racism, but we cannot logically infer that he is racist based on that. After all, Bobby also says he hates all people, white, Hispanic, Mexican, Vietnamese, Russian, etc etc etc.

More generally, we cannot make a proper deduction from one set of facts to another which wouldn't include the first one.
EB

 

[fast]

You say so but I can't believe that. What you say is, according to English syntax, ambiguous. Further, it is either logically inconsistent or false depending on how you choose to solve the ambiguity. The only way out is by replacing the second "a" by "this" as I suggested earlier.

I don't think I should say, "this" because I didn't specify a crime. Let me go at it differently. If I am not guilty of crime1, then there is a crime I'm not guilty of. If I am not guilty of crime1, then I'm innocent of crime1, and if I'm innocent of crime1, then I'm innocent of a crime; therefore, if I'm not guilty of crime1 and innocent of crime1, then I'm both not guilty of a crime and innocent of a crime.

I said, "I still hold the view that while "innocent" implies "not guilty," "not guilty" doesn't imply "innocent," and you said, "
How being not guilty of a crime doesn't imply being innocent of this crime? And if that's not what you meant then I don't think what you meant was at all expressed cogently by what you said."

Draw a rectangle, and within that rectangle, draw two large circles such than no line touches or overlaps. Label one circle A, label the other circle B, and label the remaining area in the rectangle C. Label A as innocent, and label B as guilty. Clearly, if you're innocent of 'this' crime, then you're not guilty of 'this' crime. Also, if you are guilty of 'that' crime, then you're not innocent of 'that' crime.

But notice, not A is more than just B. It includes C as well. Also, not B is more than just A. It includes C too. The same reason I hold what I do about the distinction between "false" and "not true" lies at the heart of what I'm saying.

 

[fast]

By the way, my whole underlying idea of treating negations as antonyms in the absence of sentences that fail to express propositions might of been shot down by my dang self with the thought experiment of a person in a coma neither being happy or sad.

 

[ronburgundy]

The general point seems to be that a negation of a thing is merely the absence of that thing, and is not the same of the presence of an opposite thing.

Is that about right?

That's generally correct, however it depends upon the "thing". True is not a thing in itself but always a property of some other thing, namely a propositional idea or claim. True means that the idea accurately describes to reality to which the idea in meant to refer. "False" does not have any meaning other than "not true". Thus, any claim that is not true (the property of accuracy is absent) is also false. Some "things" don't really have an opposite thing. What is the opposite of a tree? There is no antonym for tree, only a negation of it. So, maybe my point is that many things and concepts have no true antonym but we often think of the negation as though it is the opposite.

 

[Speakpigeon]

The general point seems to be that a negation of a thing is merely the absence of that thing, and is not the same of the presence of an opposite thing.
Is that about right?
That's generally correct, however it depends upon the "thing".

Outside of logic, anythng goes but in standard logic, there's no such a thing as the negation of a thing. Unfit is not the negation of fit, it is the opposite. Negations only apply to statements (propositions, predications), not to objects and concepts, thus: I am happy v. I am not happy. In classical logic there are only two possibilibies: A is F and A is not F.

Antonyms, or opposites, have a more general application: empty/full, fast/slow etc. Antonyms have opposite meanings where it is possible to have a range of possibilities between the two opposite extremes: empty, half-empty, full; white, shades of grey, black.

Thus, negating a statement will often produce a result different from that of using an antonym.

"I am not happy" is different from "I am unhappy" essentially because the first one is a negative statement (I am not X), while the second one is a positive statement (I am X) and given the nature of happiness and unhappiness, it just happens that you may be neither happy nor unhappy but something in between.

There is also a more subtle difference. You can say cogently that a rock is not happy, not that it is unhappy because the latter but not the former suggests that a rock could be happy.

True is not a thing in itself but always a property of some other thing, namely a propositional idea or claim. True means that the idea accurately describes to reality to which the idea in meant to refer. "False" does not have any meaning other than "not true".

The meaning of false is not "not true". "False" has its own meaning, which is that the statement or idea fails to refer anything in the real world. "True" and "false" are antonyms, i.e. opposite. However, if your logic is bi-valued (truth/false), then of course "false" implies "not true" and vise versa, but "implies" is not a true synonym of "means", although we often use the latter for the former.

There is also the problem of statements which are not true but not false either because they are not categorical, or if they are because they are not meaningful. "The dream in the distance waited for her to cost a length" is neither true nor false, nor untrue, but not true and not false.

Thus, any claim that is not true (the property of accuracy is absent) is also false.

Claims which are meaningless are neither true nor false. Also, a claim may be neither true nor false in trivalued logics.

Some "things" don't really have an opposite thing. What is the opposite of a tree? There is no antonym for tree, only a negation of it.

There's no negation of a tree or of the word "tree". There is only the negation of a statement affirming the existence of a tree.
EB