The Logical use of ANY

Philosophical, mathematical and computational logic, linguistics, formal argument, game theory, fallacies, paradoxes, puzzles and other related issues.

The Logical use of ANY

Postby BadgerJelly on October 13th, 2020, 11:40 pm 

I’m having a hard time accepting this interpretation:

(20)
a.
I’m {not happy/*unhappy} with the plan, I’m ecstatic!
b.
You didn’t eat {some/*any} of the cookies, you ate them all!


Note: (*) means contradiction.

I COMPLETELY disagree with example (b) as ‘any’ can just as easily mean ‘a’ - so the above could just as easily be interpreted as saying “You didn’t eat a cookie, you ate them all!” So there is nothing wrong with (b).

To further back up this point if you were to ask me “When can we meet next week?” And I reply “Anytime” I do NOT mean, and nor do you take that to mean, that I we’re going to spend the entire week together. It does mean that I am available on everyday, but it doesn’t mean that ALL the days are free for said meeting (this is explicitly understood by both parties).

Ergo the quote above (b) is incorrect as it makes too many assumptions - which are especially flexible in irregular negations!

Anyone care to disagree? If so how?
User avatar
BadgerJelly
Resident Member
 
Posts: 5739
Joined: 14 Mar 2012


Re: The Logical use of ANY

Postby Serpent on October 14th, 2020, 12:32 am 

Is it okay if I say something?
Serpent
Resident Member
 
Posts: 4324
Joined: 24 Dec 2011


Re: The Logical use of ANY

Postby Positor on October 14th, 2020, 12:54 am 

A few random thoughts:

1. I think "I'm not happy with the plan, I'm ecstatic!" is a contradiction. Being ecstatic is a form (an extreme form) of being happy. To avoid the contradiction, one should say "I'm not merely happy with the plan, I'm ecstatic!"

2. "Not...any" is ambiguous. It normally means "none", but (with suitable emphasis) it could mean "not an unrestricted choice" ("You can't have any of the cookies, but you can have these ones"). So:

(a) In its normal meaning of "none", "you didn't eat any" contradicts "you ate them all".

(b) In its meaning of "not an unrestricted choice", "you didn't eat any" still contradicts "you ate them all", since by eating them all the eater gave him/herself an unrestricted choice!

3. Logically, "You didn't eat some of the cookies, you ate them all" is a contradiction, since "all" entails "some" (i.e. not none). "Some" does not necessarily imply "not all".
Positor
Active Member
 
Posts: 1179
Joined: 05 Feb 2010


Re: The Logical use of ANY

Postby BadgerJelly on October 14th, 2020, 1:10 am 

Positor -

I should’ve posted this in linguistics me thinks!

The example you’ve given is an instance of Irregular Negation. There is nothing contrary about saying “I’m not happy, I’m ecstatic!”

The unusual linguistic cases of irregular negations are to do with the use of NOT.

It is contradictory to say “I’m unhappy, I’m ecstatic!” and this is where “not happy” is used to create an Irregular Negation “I’m not happy, I’m ecstatic!”

This is a semantic issue. My qualm is with the interpretation of ANY in the above quote.
User avatar
BadgerJelly
Resident Member
 
Posts: 5739
Joined: 14 Mar 2012


Re: The Logical use of ANY

Postby Positor on October 14th, 2020, 9:12 am 

BadgerJelly » October 14th, 2020, 6:10 am wrote:The example you’ve given is an instance of Irregular Negation. There is nothing contrary about saying “I’m not happy, I’m ecstatic!”

Ecstatic = extremely happy [dictionary definition]

So what about "I'm not happy, I'm extremely happy"? Is that a contradiction? I would say yes.


With regard to your point about "any":

If you do spend the entire week together with someone, and I ask "Did you spend any time together?", the correct answer is "Yes". "We did not spend any time together" would be untrue. "Not...any" (in its normal sense, as here) contradicts "all" – because "not...any" means "none", and "none" contradicts "all".
Positor
Active Member
 
Posts: 1179
Joined: 05 Feb 2010


Re: The Logical use of ANY

Postby BadgerJelly on October 14th, 2020, 10:48 am 

Positor -

You’re just not getting this.

I’ve not made up the term Irregular Negation. There has been a reasonable amount written about different types of negation.

As a turn of phrase people say things like “I’m not happy, I’m ecstatic!” And no one asks them what they mean. Whereas if they said “I’m unhappy, I’m ecstatic!” People would not accept it as a ‘proper’ turn of speech.

To show my point more clearly regarding ANY:

(a) “I don’t have some degree of happiness about this, I have every degree of happiness!”

(b) “I don’t have any degree of happiness about this, I have every degree of happiness!”

The point being ‘any’ can easily be framed as a singular reference (a specific one). As another example:

(c) “I don’t have any degree of happiness, I have the highest degree of happiness!”

If you still have no idea what I‘m talking about look here: https://plato.stanford.edu/entries/negation/#NegPol
User avatar
BadgerJelly
Resident Member
 
Posts: 5739
Joined: 14 Mar 2012


Re: The Logical use of ANY

Postby TheVat on October 14th, 2020, 11:25 am 

That OP opening paragraph [ETA: now removed by poster request] made me want to gnaw my foot off. But the rest was understandable. I remain uncertain as to why anyone would be so concerned that "any" has different meanings based on context. It's clear what speakers mean when they use the word. In some areas, speakers often put "just" in front to clarify a specific item. Or typing, italicize "any. "

I don't have any bananas. (the plural makes meaning clear)

I don't have just any banana. (I have a special banana, genetically engineered to glow in the dark)

I don't have any banana. (same idea)
User avatar
TheVat
Forum Administrator
 
Posts: 7819
Joined: 21 Jan 2014
Location: Black Hills


Re: The Logical use of ANY

Postby BadgerJelly on October 14th, 2020, 12:19 pm 

Did I accidentally copy and paste that by accident or did you add it in for context?

I mean this bit:

The descriptive/metalinguistic distinction is supported by converging linguistic diagnostics suggesting that metalinguistic negation operates on a different level, whence its failure to incorporate morphologically or license negative polarity items:


I didn’t mean to post that if I did? Did I? Anyway, it’s certainly a bit of a niche topic!
User avatar
BadgerJelly
Resident Member
 
Posts: 5739
Joined: 14 Mar 2012


Re: The Logical use of ANY

Postby TheVat on October 14th, 2020, 12:33 pm 

Yes, that was in your OP. And I didn't realize it was a quote at first (and was a bit worried for you, lol). I can remove that, if you didn't mean to include it. I would not add material to anyone's post without consulting with them first.
User avatar
TheVat
Forum Administrator
 
Posts: 7819
Joined: 21 Jan 2014
Location: Black Hills
BadgerJelly liked this post


Re: The Logical use of ANY

Postby Serpent on October 14th, 2020, 3:26 pm 

Human language, unlike machine code, is not constructed on logical principles. Like any [each particular example of an] organic entity, it evolves; it adapts to environments; it changes and grows. While it has discernible and explicable systems - plural, because there are many languages and each has more than one application - of logic, this is the logic of social interaction, not of a philosophical artifice.
Like any [each particular example of the category] versatile tool, language can be employed to convey specialized information with great precision, but is not restricted to that function. Aside from the obvious specialized applications, such as liturgical, legal, commercial and medical, a particular word or phrase is understood, not only in the context of a sentence or subject matter, but also in the context of its intent, which may be jocular, peremptory, persuasive, cryptic, deceptive, lyrical, etc..

An example such as "I'm not happy. I'm ecstatic!" is intended as jocular hyperbole.
'Not happy' isn't synonymous with 'unhappy'. 'Unhappy' has one, and only one specific meaning, which is a definite existing emotional state from which all forms of happiness are excluded. 'Not happy' is ambiguous by the very absence of a definite state: it allows for all other emotions, including all the permutations of joy and delight. It is not a contradiction, because one could clarify the first statement by one word: "I'm not merely happy; I'm extremely happy." just as one might say, without contradiction, "I'm not just unhappy; I'm profoundly unhappy; I'm lower and bluer than a mandril's backside."
Therefore, when one says, "I'm not happy," the hearer is likely to, and is generally expected to infer a state of discontent, and feel let down. This is intended to lend the impact of surprise to the punchline that follows: "I'm ecstatic!" to lift him up higher than would have been the case if one simply said, "I'm ecstatic."

The case of 'any' is quite different. Any is short for any one. It refers to an individual specimen, of whom/which the particular identity is not [currently] known. "Pick a card, any card." is universally understood to mean a single rectangle of paperboard. "Pick any card." still means the same: one card only. The 'any' there means that no individual has been identified by the speaker; all individual specimens of the category are eligible: the other person is invited to select one particular specimen.
It's the same with time. "Call me any time," means "You choose the [one particular] moment at which you call me." It is not synonymous with "Call me all the time." It still works the same with a plural word ending. "Are any of you ladies from Texas?" is a question directed at each individual within a designated group of adult females who fits the criterion. And "I didn't see any bears on my camping trip." means all of the individual specimens of the category 'bear' eluded the speaker; it would be contradictory if he then added, "I saw all of them." However, if he intended jocular hyperbole for dramatic effect, he might say : "I didn't see a single bear on my camping trip.(pause) They were all married, with children!"

A great deal of poetic, dramatic and humorous effect is grounded in the ambiguity of an expression which is imprecise enough to imply, or allow the hearer to infer, a common usage that is not the strict or exclusive meaning of the word.
Serpent
Resident Member
 
Posts: 4324
Joined: 24 Dec 2011



Return to Logic

Who is online

Users browsing this forum: No registered users and 5 guests