The logical meaning of something is "at least one". This definition of something is incomplete because if something means just "at least one" then all/everything, because it is indubitable at least one, is also something. Since logicians aren't prone to silly mistakes like this it's probably the case that the definition of something is at least one but not ALL and it's so obvious that it's left undeclared. — TheMadFool

In systems analysis and design there is a concept where A might be said to be of type B but B is not in every case the same as A.

Logicians very often embrace a systems analysis and design approach. Its like when the wizard answers the question with "yes and no".

You can quantify analog systems (like a compact disc high sampling rate) with 1000s of data points to simulate a analog system within a digital system.

None = not some = all not = not nall not
Some = not none = not all not = nall not
All = none not = not some not = not nall
Nall = not all = some not = not none not

Also look up DeMorgan duality for more on these kinds of relationships.

What is the correct antonym for nothing? — TheMadFool

In what context? The usual construction for the antonym - hmm, def.: A word that has the exact opposite meaning of another word is its antonym.

That means you have to first know the meaning. The construction I had in mind is appending "not," as in, "not-nothing." But this is logic, not meaning itself. So, give a definition of "nothing" and I suspect it won't be too hard to find an antonym. The mistake, should there be one, might well lie in supposing that language is essentially univocal when in fact and in usage and in application it is not. That is, that the antonym that you select as appropriate for your context should apply to all contexts and usages, and that just ain't language.

2. Not anything which I take to mean not everything — TheMadFool

This is wrong. Not everything can be negated by something as well as by nothing.

Your further analysis is meaningless because you started off with the wrong premis.

Furthermore, "at least one" is not something; "at least one" is a definition of "some" in syllogisms, and in syllogisms only. In syllogisms you don't use "something".

This opening post rests on misguided understanding of the language, is my opinion.

I expect a long, elaborate and meaningful discussion by many participants who are full of opinions and have no real clue that the wrong definitions were used in the opening post, and who frightfully easily accept the wrong conclusions drawn in the opening post.

Be my guest. Go wild.

The logical meaning of something is "at least one". This definition of something is incomplete because if something means just "at least one" then all/everything, because it is indubitable at least one, is also something — TheMadFool

Why would that be a problem? I don't see anything "incomplete" here.

First, do such terms refer to anything actual.
I think that everything exists except thinghood itself.

Or else explain what is it about anything that makes it a thing rather than not.

2. Not anything which I take to mean not everything — TheMadFool

These are not the same.

If you asked me to hand you anything, you are not asking me to hand you everything.

The logical meaning of everything/all is the entire collection of things which in our case is the universe itself — TheMadFool

Is it?

Perhaps sometimes, but not always. Usually it's use is restricted by context. So if when asked if you would prefer tea or coffee, you replied "oh, anything will do", you would be deservedly surprised were you given a zebra.

It's called the Universe of Discourse.

This definition of something is incomplete because if something means just "at least one" then all/everything, because it is indubitable at least one, is also something. — TheMadFool

I can't see how that makes it incomplete. If you asked for at least one, and you receive all of them, you have by that very fact received at least one.

John: Can I eat the cake?
Jane: Yes, but not everything.

The fictitious conversation above makes something an antonym of everything. — TheMadFool

Well, no, since the universe of discourse is presumably the cake...

In systems analysis and design there is a concept where A might be said to be of type B but B is not in every case the same as A.

Logicians very often embrace a systems analysis and design approach. Its like when the wizard answers the question with "yes and no".

You can quantify analog systems (like a compact disc high sampling rate) with 1000s of data points to simulate a analog system within a digital system. — christian2017

True to what you're saying nothing, something, and everything, if quantified numerically then they can be interpreted in terms of an analog scale as follows:

Nothing = 0
Something = at least 1 but NOT all
Everything = all (the universal set)

Imagine a universe of 10 objects. In the context of these 10 objects the following relationship will hold:

Nothing (0) < Something (at least 1 but NOT all) < Everything

If one considers the general meaning of antonym as having opposite meaning and considers the pattern present in them it's usually the case that the extreme endpoints of what is actually a range/spectrum qualify as antonyms. For instance hot and cold are the extreme states of temperature and are linguistically regarded as antonyms; anything in between these extremes are ignored. If that's the case then the antonym of nothing is everything and not something.

None = not some = all not = not nall not
Some = not none = not all not = nall not
All = none not = not some not = not nall
Nall = not all = some not = not none not

Also look up DeMorgan duality for more on these kinds of relationships. — Pfhorrest

It was my initial impression that antonyms were logical entities expressible through negation but that isn't the case. A logical view of antonyms is as contraries i.e. they both can't be true but both can be false as illustrated by the example of "hot" and its antonym "cold" in the OP. So, using "not" - negation - which is more apt for contradictions doesn't get the job done.

In what context? The usual construction for the antonym - hmm, def.: A word that has the exact opposite meaning of another word is its antonym.

That means you have to first know the meaning. The construction I had in mind is appending "not," as in, "not-nothing." But this is logic, not meaning itself. So, give a definition of "nothing" and I suspect it won't be too hard to find an antonym. The mistake, should there be one, might well lie in supposing that language is essentially univocal when in fact and in usage and in application it is not. That is, that the antonym that you select as appropriate for your context should apply to all contexts and usages, and that just ain't language. — tim wood

Well, yes, the choice of the antonym for nothing seems to be context-dependent as illustrated by my examples but this isn't the usual state of affairs with other antonyms. The antonym for right doesn't change with context from wrong to something else and as far as I know this is true for all antonymical relationships.

Furthermore, "at least one" is not something; "at least one" is a definition of "some" in syllogisms, and in syllogisms only. In syllogisms you don't use "something". — god must be atheist

Modern quantificational logic has chosen to focus instead on formal counterparts of the unary quantifiers “everything” and “something”, which may be written ∀x and ∃x, respectively. — Stanford Encyclopedia of Philosophy

Why would that be a problem? I don't see anything "incomplete" here. — khaled

If I say "everything" then it doesn't contradict "at least one" right? Since something is defined as "at least one" then that means there's no difference between everything and something unless we qualify the defintion of something as "at least one but NOT all".

First, do such terms refer to anything actual.
I think that everything exists except thinghood itself.

Or else explain what is it about anything that makes it a thing rather than not. — Yohan

I refer to the commonplace usage of the words nothing, something, and everything. There is nothing special in the way I'm using these words. A lexical definition should suffice.

These are not the same.

If you asked me to hand you anything, you are not asking me to hand you everything. — Banno

You forgot to give due importance to the "not" - the negation - in "not anything". "NOT anything" negates each and every thing. There is literally no thing that nothing applies to. Surely then nothing means not everything.

The antonym for right doesn't change with context from wrong to something else and as far as I know this is true for all antonymical relationships. — TheMadFool

Really? How about left? Strong:weak, but how about mild? And so on.

Terms have have overlapping but no one coextensive meaning. “Something” just means “not nothing”; “everything” just means “nothing not”. If nothing is not whatever, but not nothing is whatever, then something is whatever and everything is whatever; but it could instead be that something is whatever, and something is not whatever.

The same relationship holds between:
some and all
something and everything
possibility and necessity
permission and obligation
disjunction and conjunction

These are all DeMorgan duals, where each is equivalent to the negation of the other of a negation. E.g. something is = not everything isn’t. Etc.

Really? How about left? Strong:weak, but how about mild? And so on. — tim wood

What exactly do you mean by context and that the meaning of words depend on it?

Firstly, when I said,

The antonym for right doesn't change with context from wrong to something else and as far as I know this is true for all antonymical relationships. — TheMadFool

I was referring to a more general conception of context Yes, "right" may be a truth-value claim in a school examination or a direction for a pedestrian but that doesn't mean I can alter the meaning of "right" simply by framing it in different contexts. For example I may be speaking of astrobiology or or a humble sandwich but the word "right" will not suddenly acquire different meanings when I use it in these disparate topics.

To the extent that I'm aware this context-sensitive nature of the meaning of words is a byproduct of the linguistic phenomenon of polysemy - one word with different meanings.While context is important in understanding words in discourse it doesn't have a direct impact on meaning itself. What I mean by that is meaning precedes context. Let's continue with the example of the word "right". If it didn't already possess the meaning of a direction then it would never appear in the context of finding your way in a city and if it didn't mean correctness it'll never be in a teacher's vocabulary.

The meaning of a word decides which contexts the word appears in. However, to decide on the meaning of polysemous words, context is indispensable. To clarify what I mean I'd like to draw your attention to two categories that can be approximated as author and reader. When an author writes a discourse she does so with only one meaning of the words she employs. If a word has the one appropriate meaning she will use it. The meaning of the word is vital to what contexts it can appear in. In other words meaning precedes context.

However for the reader, the situation is different. Since polysemy is so common a discourse will invariably contain words with multiple meanings and so to comprehend the meanings of polysemous words she needs to study the context in which polysemous words appear in.


The essential difference between the author and the reader is context is irrelevant to the former because meaning precedes context but relevant to the latter because of polysemy.

When I said what I said I meant it for an author and not a reader. An author writes based on one meaning and doesn't need to worry about context i.e. meaning is non-contextual for the author but the reader of course needs context to grasp the meaning of polysemous words.

Secondly, I accept that, as I said earlier, that meaning changes with context but what is the relationship between the two and how does it bear on the question, "what is the antonym of nothing"?

By my reckoning you want to say that meaning is context-dependent and so both something and everything can be antonyms of nothing based on context. The two examples in the OP being "good"?? illustrations of this fact

This explanation requires that nothing, something and everything have different meanings in various contexts. I'm afraid this is false. The words, "nothing", something and "everything" have definitions in only one context viz. quantification. Imagine a scale from 0% to 100% and you can see nothing = 0%, everything = 100% and 0% < something < 100%.

Whatever other context these words are used in requires the essential quantitative nature of their definitions to be applicable. So, unlike the word "right" whose meaning will alter with context (morality or directions to the bank) the words "nothing", "something" and "everything" don't have that luxury. Their definitions are fixed as quantities across all contexts.

Therefore, that words are context-sensitive while true is not applicable here to the words "nothing", "something" and "everything". When the fact that antonyms come in pairs, i.e. they're exclusively binary, is now considered in the light of what I said in the previous paragraphs, we can see very clearly that nothing can't be an antonym for both something AND everything.

“Something” just means “not nothing”; “everything” just means “nothing not”. — Pfhorrest

Antonyms can't be expressed with the negation operator.

It isn't the case that hot = not cold or good = not bad because there's always a third alternative which here are *room temperature* and *amoral* respectively.

If antonyms were negations then the antonym of good should be not-good which includes *amoral* and we know *amoral* is NOT an antonym of either good or bad.

“Something” just means “not nothing”; “everything” just means “nothing not” — Pfhorrest

You guys like to think to your guns, do you.

"Not nothing" can be something, and it can be everything. But something is not necessary everything.

For instance:

Not nothing is the user God must be atheist.

Not nothing can be the entire universe, including all matter and stuff in infinite directions everywhere, which is the only satisfactory fulfilment for the meaning of "everthing".

Yet God must be something is not infinity with matter included in all directions within infinite distance.

So clearly "something" is not "everything".

You are stuck in that groove, @Themadfool, and can't get out of there.

I invite you all to look at the fifth post on this thread. I predicted there that this nonsense will go on for a long time, with smart and learned people arguing about something that is dead wrong.

But then again, arguing about something that is nonsensical and horribly wrong, beats staring out the window at the great beyond on a Christmas day when you got no family, no friends, no nuffin', and you are too old to play with yourself, and too poor to afford any kind of recreational drugs.

But then again, arguing about something that is nonsensical and horribly wrong, beats staring out the window at the great beyond on a Christmas day when you got no family, no friends, no nuffin', and you are too old to play with yourself, and too poor to afford any kind of recreational drugs. — god must be atheist

:rofl: :rofl: :up: :up: Don't do drugs but merry christmas to you

Point to you, well argued (imo). Which point I understand to be that an antonym is not a logical negation, but is instead a very particular form that takes in the meaning of the original term and opposes that meaning. That is, the original term must be meaningful in some particular and usually contextual sense.

But for present purpose you'd like to penetrate the surface of contextuality and look at the word itself - almost always an interesting exercise. And it would seem that something, nothing, everything are already implicitly negations. And we can all work through at leisure how that works with these words, noting here only that something and everything are joined in the sense of both "opposing" nothing.

But having completed the exercise, the words return to being "always already" in a context in use that determines their meaning, even as that meaning in usage is informed by the prior meaning of the word itself.

In sum, you've lassoed language, got your rope on it, made your point. But language itself won't be wrestled to ground and tied either up or down. Nature and strength of the beast.

You’re arguing against something I didn’t say. Think of a Venn diagram. The left circle is “something”. The right circle is “not everything”. The slice of the left circle that’s not in the right is “everything” (not not everything). The slice of the right circle that’s not in the left is “nothing” (not something). The intersection in the middle is something but not everything, for which we don’t have a special word.

Point to you, well argued (imo). Which point I understand to be that an antonym is not a logical negation, but is instead a very particular form that takes in the meaning of the original term and opposes that meaning. That is, the original term must be meaningful in some particular and usually contextual sense.

But for present purpose you'd like to penetrate the surface of contextuality and look at the word itself - almost always an interesting exercise. And it would seem that something, nothing, everything are already implicitly negations. And we can all work through at leisure how that works with these words, noting here only that something and everything are joined in the sense of both "opposing" nothing.

But having completed the exercise, the words return to being "always already" in a context in use that determines their meaning, even as that meaning in usage is informed by the prior meaning of the word itself.

In sum, you've lassoed language, got your rope on it, made your point. But language itself won't be wrestled to ground and tied either up or down. Nature and strength of the beast. — tim wood

I guess it's as futile as you make it out to be. Thanks.

Addendum:

It appears that antonyms have two different logical meanings and they are:

1. As contradictions. The antonym of truth is false and in classical logic they are contradictions - mutually exclusive and mutually exhaustive in that at least one of them must be the case and there are no other alternatives.

2. As contraries. The antonym of dead is alive and these are contraries in that if one is true the other must be false but both can be false as in the case of a rock which can't be dead because it was never alive.

If antonyms had only meaning 1, as contradictions, the matter of deciding what is or is not an antonym is simple. We simply negate a word and we arrive at the antonym.

However, antonyms also carry meaning 2, as contraries, and it's here that problems arise because while hot is a contrary of cold, temperate is also a contrary of both hot and cold, resulting in confusion as to which is the correct antonym. Bear in mind that antonyms come in twos for any specific meaning of a word. One meaning, one antonym.

In logic contrariness is a relationship that admits that there's another option(s) available and if we look carefully we can see that when there are more than two options/possibilities, the most extreme options are considered antonyms. Hot and cold are extremes on the temperature scale with temperate lying in between and are considered antonyms.

Since, nothing, something and everthing are not contradictories but are contraries, we can apply the same principle that the extremes should be chosen as antonyms and so everything is the antonym of nothing.

There ain't nothin to say about nothing.
It ain't, and that's it.

As soon as you turn nothing into something, you go from making sense to talkin no sense

You’re arguing against something I didn’t say. Think of a Venn diagram. The left circle is “something”. The right circle is “not everything”. The slice of the left circle that’s not in the right is “everything” (not not everything). The slice of the right circle that’s not in the left is “nothing” (not something). The intersection in the middle is something but not everything, for which we don’t have a special word. — Pfhorrest

Then what is the area OUTSIDE of both circles, and outside their intersection? In Venn diagrams that area is also meaningful.

If "everthing" is the left of the left cirtcle, and "nothing" is only the right of right circle. the intersection is "something".

A state can only be everything, something, or nothing. Yet your Venn diagram shows a fourth state, which state is not logically possible.

Everything and something are overlapping states, as already described.

The area outside the circles is an interesting thing in modern quantitative logic. All of my children have graduated high school, but none of my children have graduated high school. This is possible because I have no children, so 100% of my 0 children have graduated high school. Since “everything is...” just means “nothing isn’t”, that area outside both circles is for circumstances like this: where it’s not something (so nothing), but also not not-everything (and so everything), which can only be the case when the set we’re choosing from is empty, like the set of my children.

There are several problems with your explanation if we apply it to things, or to the real world.

But you assure us, rightfully so, that your argument stands only for empty sets.

Why did you not start with that.

"I'm going to propose a complex and apparently wrong logical system, which works in special cases, in particular in cases of empty sets."

Because your proposal does not work for non-empty sets, does it.

I am sorry I made the mistake of not assuming your talking about empty sets. The entire conversation involving othes but you revolved around having things; empty sets, the only one for which the theory works, do not have things.

----------------------

So please, I beg you to reconsider your position for the case when things exist, and the argument is not about empty sets.

Only the fourth category you asked about involves empty sets. The rest involves any sets. And this is bog standard logic, nothing of my own invention.

It’s easier to talk about the terms all, some, and none, and then translate that into everything, something, and nothing (as everything = all the things, something = some of the things, and nothing = none of the things), so I’m just gonna do that from now on.

What is the relationship between all, some, and none? That is the question at hand here, basically.

Pretty uncontroversially, none = not some.

That requires that some = not none as well.

So we know the relationship of some and none to each other easily enough. Now what of all?

Well, if all of A are B, then none of A are not B, pretty uncontroversially.

But if there are no A at all, then it’s true that no A are B, because no A are anything.

Aristotle thought that means that “no A are not B” wasn’t a full definition of “all A are B”, and that it required an additional “and some A are B”.

Modern logicians say that’s not necessary, “no A are not B” is fine, and if that makes a weird case out of empty sets, so be it, because how often do we care to talk about empty sets.

So to modern logician, all = none not.

And since none = not some, that means all = not some not.

This is a kind of relationship called a DeMorgan duals, where one function is the negation of the other function on a negation, and vice versa.

So some = not all not. Which makes sense: if not all A are not B, then some A must be B.

And since none = not some, that means none = all not. Which also makes sense: if all A are not B, then none of A are B.

So none = not some = all not.
And some = not none = not all not.
And all = none not = not some not.

And there you go.

You can also coin the negation of all, call it “nall”, and say:

None = not nall not
Some = nall not
All = not nall
And nall = not all = some not = not none not.

Only the fourth category you asked about involves empty sets. The rest involves any sets. — Pfhorrest

But you can't take a Venn diagram and say, "this part of a given Venn diagram applies to these things, and these things only, and that part of the same Venn diagram applies to those things, and those things only, while events invovling these things and events involving those things are mutually exclusive."

Insisting that my objection is false, makes the entire Venn-diagram completely useless. The beauty of Venn diagrams is that they describe a complete set, without exceptions, and the diagram is consistent within itself. Your way of demarking the area inside either circle from the area outside of both circles defeats the very usefulness of the mechanism of Venn Diagrams.

I don't know if you can see my point. You say of the areas of the inside of either circles, "this applies to non-empty sets." then you say of the areas outside of both circles, "this applies to empty sets only." This violates the logic of the Venn, because it is supposed to be consistent with itself, and you breach that self-consistency with citing the qualities of disparate parts some of which parts the diagram's logical facts apply to, but to other parts it does not.

In other words, you must not use parts of one (only one, one and the same) Venn diagram to make it apply to empty sets, and parts of the same to non-empty sets.

If I say "everything" then it doesn't contradict "at least one" right? Since something is defined as "at least one" then that means there's no difference between everything and something unless we qualify the defintion of something as "at least one but NOT all". — TheMadFool

No? How is there no difference? One is a subset of the other.