Forget about the Venn diagram. That's just for illustration but it seems to only be confusing you more. (For the record though, I'm not saying you have to apply different rules to the outside area, but that if you find yourself talking about the outside area, you can conclude you must be talking about an empty set, because there's no other way to dealing with something out there, to have none and all simultaneously, unless "all" is zero).

Let's talk about a more concrete example instead. There's a room with a number of things in it, bearing in mind that zero is a number so the room might have zero things in it, or it might have more than zero, I'm not specifying either way.

If we know that everything in the room is red,
then we know it is not the case that something in the room is non-red,
and we know it is the case that nothing in the room is non-red.
(All = not some not = none-not).

So far as we know in this case it could either be the case that somethings in room is red, or that nothing in the room is red. If there is something in the room at all, we know it must be red, but there might be nothing in the room at all, in which case it's still true that everything (all zero things) in the room are red, i.e. nothing in the room is non-red. All we know is that if something is in that room, it is red.


On the other hand if we know only that something in the room is red,
then we know it is not the case that nothing in the room is red,
and we know it is not the case that everything in the room is non-red.
(Some = not-none = not-all-not).

We know for sure in this case that there is something in the room, because if there is something red in the room there has to be something in the room. But we don't know if everything in the room is red or not. It might be, if there are no non-red things in addition to the red things (this is the case the Venn diagram was meant to illustrate, and that @khaled sums up nicely above: that something doesn't imply not everything, although a phrase like "only some things" would); but it might not be everything, if there are some non-red things in addition to the red things.

"Something" and "everything" can but don't have to overlap. You can have:
neither something nor everything (if there are things to be had but you have none of them).
something but not everything (if there are some things you don't have and some you do),
both something and everything (if there are things to be had and you have all of them),
not something but still everything (if there are zero things to be had and you have all zero of them),


Lastly, if we know that nothing in the room is red,
then we know it is not the case that something in the room is red,
and we know it is the case that everything in the room is non-red.
(None = not-some = all-not).

This illustrates perhaps most clearly why "everything" and "nothing" can apply at the same time, if you have zero things. If nothing in the room is red, then everything in the room is non-red, and vice versa. If nothing in the room is non-red, then everything in the room is red, and vice versa. So if nothing in the room is red and nothing in the room is non-red, you can conclude that there must be nothing in the room at all. And if everything in the room is red and everything in the room is non-red, you can likewise conclude that there is nothing in the room at all, because (aside from the fact that otherwise there would be a contradiction) each of those "everything" statements translates into a "nothing" applied to the negation of its operand.

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

Don't worry about it.

Something as at least one could also mean everything which is at least one

Everything doesn't imply at least one thing, because there might be zero things to begin with, in which case everything in that set of zero things is less than one thing.

Logicians are well aware that this sounds very weird to the untrained ear, but that's just because we pretty much never have reason in normal life to talk about empty sets. But strictly speaking this is how the logic works out when you don't forcibly exclude them.

Something as at least one could also mean everything which is at least one — TheMadFool

No, being at least one is a property of everything (in this universe) not its definition.
Something: At least one thing
Everything: Everything (which is also at least one thing)

So something is a subset of everything. Being a subset, something CAN MEAN everything but it doesn't have to. Example: The set of all cars, and the set of all cars I own. The set of all cars I own is a subset of the set of all cars but it IS possible for the sets to be equivalent, if I own every car ever. Similarly, it is POSSIBLE for something to mean everything, if the person using "something" had in mind every thing

It is probable that you own every time-traveling car ever built on Earth, and that you also own none of the time-traveling cars ever built on Earth, because there are probably no time-traveling cars that have ever been built on Earth.

Other than that, spot on.

So something is a subset of everything. Being a subset, something CAN MEAN everything but it doesn't have to. — khaled

That's all I mean.

Forget about the Venn diagram. — Pfhorrest

Why? It has proof value. Your proposition has been disproven by a proof-value tool. Why proceed from there?

If we know that everything in the room is red, — Pfhorrest

You specified that the room may contain no objects. Only objects can be red. Nothing cannot be red. Therefore your first premise is wrong. The rest of your argument can be discarded.

On the other hand if we know only that something in the room is red, — Pfhorrest

Again, this invalidates the possibility that the room is completely empty; yet you specifically stated that that assumption must be true.

You can't cherry pick your assumptions as you go along, you must stick to one or the other, if they are contradictory.

You are playing a dangerous game, purely in a philosophical sense, my friend. (-: You set up goal posts and you demolish them temporarily and re-erect them as they fit your purpose. Socrates or Aristotle would have made minced meat out of your arguments. (I am joking, but only semi-joking. Please reconsider carefully what I said, using reason: you set out the example as "may or may not contain any objects" (paraphrased) and in some parts of your proof you say "the room must necessarily contain objects" (paraphrased). These two claims, or premises, are fully contradictory, therefore your argument fails.)

Please stop with the condescension. This is standard logic I’m trying to teach you, not my own argument I’m putting forth for debate. You can read all about this in any logic text you care to search for too, probably explained better than I am doing.

Why? It has proof value. Your proposition has been disproven by a proof-value tool. — god must be atheist

It has not, and I did address your point, but that explanation seemed to be raising more questions than it answered for you so it’s clearly not the best educational tool for this job.

objects can be red. Nothing cannot be red. Therefore your first premise is wrong. The rest of your argument can be discarded. — god must be atheist

You don’t seem to understand the structure of what I was saying. I was giving three different cases involving the things that may or may not be in the room. In one of those cases we know there is at least one thing in the room. In the other two cases we don’t know how many things are in the room at all, only that IF anything is in the room THEN it is... whatever.

That’s the point of the explanation: “all A are B” is equivalent to “if something is an A then it’s a B”. So “everything in the room is red” is equivalent to “if something is in the room then it’s red”, or “nothing in the room is non-red”. But there might not be anything in the room at all, and that’d still be true.

And back to the original point: if something in the room is red, and nothing in the room is non-red, then everything in the room is red, so it can easily be the case that both something and everything in the room is red. But that doesn’t make “something” and “everything” equivalents, because it could instead be the case that some things in the room are red and other things are non-red, in which case something but not everything in the room is red. You seem to want to restrict “something” to only this case, but that’s just not how the word works. You’d have to say “only some things” or such to get that meaning.

What i am objecting to is that you use at least two different scenarios to prove a general point, and the two scenarios are not identical in nature.

I hope to make you understand that if you want to create an a priori rule that applies to ALL scenarios, then your premises can't be exchanged between two paths of reasoning, in a way that the one currently in use is the only premise that applies to the situation and the other premis currently not in use is forbidden to apply to the situation. Yet you do that.

What I read is not that you use separate specific cases, with the same rules, and with the same mechanism of logical constructs to arrive at a conclusion; but instead you use separate specific cases each with their own specific and non-overlapping different rules. And you can't, must not, unify these rules, because the mechanisms you apply in the different cases are also different; yet you claim that your unifying the rules are valid.

More specifically:

1. You claim all rules are applicable to empty sets and to non-empty sets.
2. You use one specific way of showing how on specific the rule applies to non-empty sets.
3. You use another, different specific way of showing how a different specific rule applies to empty sets.
4. You claim that the rules you used in 2. and in 3. are not only compatible, but point at the same result.

No, they don't.

This was illuminated first in your Venn diagram example, where inside the circles the meaning was only meanigful if something existed, while outside the circles it was meaningful only when nothing existed (in the set).

This was illuminated in your second example, when you used a whole bunch of negations to arrive at your points, but each of the three sets used different negations of different things. It would have only been meaningful if you used the same logical steps in all three scenarios and arrived at the same conclusion, that is, at a unified rule. But you did not.

To be completely honest, I did not read your third explanation yet, I'll do it later. But I don't know why you don't see that your methodology does not cut the mustard, so to speak. If the same rule only applies to empty sets when one condition is met but the other condition is not met, and the same rule only applies to non-empty sets when another condition is met, but not the first one, then it's not the same rule, but a modification of the same rule in the two separate instances. And if you modify a rule so it becomes different from its original form, then it is not the same rule.

Someone else tag me out, this guy can’t be taught.

Someone else tag me out, this guy can’t be taught. — Pfhorrest

I am a student who uses his head. Years of indoctrination in the wrong logic hasn't touched me. I hope it never will.

Okay, I'll give this one more try, because I'm a sucker for difficult students apparently.

There are three people, Alice, Bob, and Chris. Each of them has a storage unit. To start with, we don't know what if anything they each have in their storage. But then, each of them tells us something about what they each have in their storage.

Alice tells us that nothing in her storage is red.
We still don't know whether she has anything at all in her storage.
Because we don't know if she has something non-red in her storage instead.
But we do know that she does not have something red in her storage.
And we equivalently know that everything in her storage is non-red.
The bolded bits are all equivalent:
Nothing is = not-something is = everything is not.

Bob tells us that something in his storage is red.
We don't know if he has anything non-red in his storage.
So we don't know whether or not everything in his storage is red (though it might be, if in addition to having something red, he also has nothing non-red. This is the only point I've really been trying to get through to you.)
But we do know that he does not have nothing red in his storage.
And we equivalently know that not everything in his storage is non-red.
The bolded bits are all equivalent:
Something is = not-nothing is = not everything is not.

Chris tells us that everything in their storage is red.
We still don't know whether they have anything at all in their storage (because "everything" might be nothing, if they don't have anything at all in their storage. This seems to be what you're getting hung up on, missing the point above.)
All we know is that nothing in their storage is non-red.
Or equivalently, that they do not have something non-red in their storage.
The bolded bits are all equivalent:
Everything is = nothing is not = not-something is not.

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. — TheMadFool

"Not everything" is not "not anything".

@Pfhorrest, at some stage one has to suppose that the unwillingness to learn displayed here is wilful. When one reads:

Years of indoctrination in the wrong logic hasn't touched me. I hope it never will. — god must be atheist

the only sensible thing to do is to walk away.

Chris tells us that everything in their storage is red.
We still don't know whether they have anything at all in their storage (because "everything" might be nothing, if they don't have anything at all in their storage. — Pfhorrest

This equivalence between everything and nothing troubles me as well.

There must be something red in the storage in order for everything in the storage to be red. If nothing is in the storage then it cannot be the case that everything in the storage is red.

Aristotle had a problem with that as well, but modern logicians have generally agreed that it's really not a problem because practically speaking we never really talk about empty sets, and it's really useful mathematically to have a DeMorgan dual of "something" (a function that just means "not-something-not"), and the sense of "everything" that you and Aristotle want to use is really, really close to that, except in the practically unused case of talking about empty sets. The Aristotelian sense of "everything" is "not-something-not, and also, something", which only differs from "not-something-not" simpliciter when you're talking about an empty set, which we generally never do in practice.

Good to know I'm not alone. I'm not at all on board with what god must be atheist has been arguing, yet something was worth being said...

...(if there are zero things to be had and you have all zero of them), — Pfhorrest

Practically unused cases like the above?

Take the domain of discourse as everything in storage, and hence "everything is red".

Now derive "something is red"...

Can't be done.

All one can derive is that it is not the case that something is not red.

Universal instantiation does not help, since there may be no individuals in the domain of discourse.

(Happy to have someone show me that this is wrong. Old brain has difficulty with formal logic.)

I don't know Banno. Once you've committed to a domain, you can no longer use common sense...

There must be something red in the storage in order for everything in the storage to be red.

Right?

That's not a derivation, but it's true nonetheless.

Yes, that's exactly the kind of case. I brought it up to make a logical point, but in practice (hence practically unused) when do we ever talk about how much of a set of zero things some predicate applies to?

:up: but that is a little circular as you're employing the very logic that's being questioned here. Aristotelian logic basically had "everything entails something" as an axiom (not that it was really an axiomatic system, but loosely speaking). The modern, axiomatized logic you're employing looked at that and say "ehhhh that's not really necessary and it's a cleaner system without it".

Sure.

"everything entails something" — Pfhorrest

...became universal instantiation - which (should have) cleared up what was going on.

There must be something red in the storage in order for everything in the storage to be red. — creativesoul

Do you want to be able to claim to have a red nothing in storage?

There must be something red in the storage in order for everything in the storage to be red.
— creativesoul

Do you want to be able to claim to have a red nothing in storage? — Banno

:brow:

That's pure unadulterated nonsense when one realizes and works from the supposition that everything and nothing are not equivalent. Realizing it is easy enough.

There must be something red in the storage in order for everything in the storage to be red.

Right?

Yes, that's exactly the kind of case. I brought it up to make a logical point, but in practice (hence practically unused) when do we ever talk about how much of a set of zero things some predicate applies to? — Pfhorrest

The case is itself one of what we must do as a means of remaining coherent in order to be able to say other things.

...(if there are zero things to be had and you have all zero of them), — Pfhorrest

The above presupposes and/or requires us to draw an equivalence between everything and nothing.

If we draw the actual distinction between everything and nothing, we arrive at a much different different account...

If there are zero things to be had, then you have nothing.

If there are zero things to be had, then you have nothing. — creativesoul

That is also true on the modern account. Because “everything” is equivalent to “nothing not”: nothing is not red if and only if everything is red. That’s pretty uncontroversial isn’t it? It only becomes an apparent problem if there is nothing whatsoever in the universe of discourse. Because then nothing is not red, and nothing is red, because there is nothing whatsoever; but since everything is red iff nothing is not red, then in that circumstance everything is red, and since everything is non-red iff nothing is red, then everything is non-red in that circumstance too. It would be a contradiction if there was some thing that was both red and non-red, but thankfully we’re not saying something is red or something is non-red, we’re saying nothing is non-red and nothing is red, which just says that there’s nothing at all.

Looks like an equivocation of the term "nothing" to me. Sometimes used as a means to refer to all things in a set(as a means to talk about what's not the case regarding them), and sometimes used normally.

No, same sense. If you want to say nothing is older than 15 billion years in formal logic, you’d use the same symbols (either not-something or everything-not) as you would to say nothing in that room is red, you just wouldn’t specify a set you’re picking from on the first case. You select a number of subjects (possibly zero) and apply a predicate to them either way. To select all, you can select zero and apply the negation of the predicate you want applied to all.

If you want to say that nothing is older than 15 billion years, then that's what you say. If you want to say that everything is younger than 15 billion years, then that's what you say.

If you want to say that nothing in the room is red, then that's what you say. If you want to say that everything in the room is not red, then that's what you say.


If I have understood you, then the above two pairs of statements are both equally amenable to the logical notation you're advocating here. Is that right? Both pairs consist of two different statements that mean the same thing?

That's correct, provided we can take "younger than 15 billion years" to be equivalent to "no older than 15 billion years". (Technically we can't, because cases where things are exactly 15 billion years differ between those two formulations, but I think you probably meant the latter).