Nothing, Something and Everything
The dictionary defines nothing as the following:
1. Zero (the mathematical 0)
2. Not anything which I take to mean not everything
The logical meaning of everything/all is the entire collection of things which in our case is the universe itself
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 indubitably 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.
Given the above definitions of nothing, something, and everything I'd like to know what are the antonymical relationships between these three concepts.
The old chestnut "why is there something rather than nothing?" suggests something is an antonym of nothing.
Then there are all too familiar conversations like below:
John: Can I eat the cake?
Jane: Yes, but not everything.
The fictitious conversation above makes something an antonym of everything.
So, nothing is the antonym of something and something is the antonym of everything.
Also what's established by the definitions I provided above is nothing is also the antonym of everything in that it is not anything.
It can thus be inferred that nothing is the antonym of both something and everything in everyday discourse. Is this a normal state of affairs in re antonyms?
As defined, an antonym of a word is supposed to have an opposite meaning to the word itself i.e. if one is applicable the other is not. We must remember this point that the words themselves aren't as important as the meanings of these words - antonyms are about meanings being opposite.
Now consider the words "hot" and its antonym "cold" which are simple enough for the discussion and what applies to this case can easily be generalized to all antonyms. One can immediately see that hot and cold are logical contraries i.e. both can't be true but both can be false e.g. it can be room temperature (neither hot nor cold). However, what's interesting is room temperature (neither hot nor cold) isn't considered an antonym of hot or cold. The same applies to other words e.g. the antonym of "good" is "bad" and "amoral" isn't part of the picture.
What the above means is that antonyms come in pairs - there are always two, no more no less. Even if meaning wise there are other alternatives all of them are ignored and only two are chosen, one being the antonym of the other.
If that's the case then it's wrong to think nothing is the antonym of something AND everything because antonyms have to come in pairs and even if there are other alternatives they're to be ignored.
What is the correct antonym for nothing?
Something OR Everything OR
1. Zero (the mathematical 0)
2. Not anything which I take to mean not everything
The logical meaning of everything/all is the entire collection of things which in our case is the universe itself
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 indubitably 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.
Given the above definitions of nothing, something, and everything I'd like to know what are the antonymical relationships between these three concepts.
The old chestnut "why is there something rather than nothing?" suggests something is an antonym of nothing.
Then there are all too familiar conversations like below:
John: Can I eat the cake?
Jane: Yes, but not everything.
The fictitious conversation above makes something an antonym of everything.
So, nothing is the antonym of something and something is the antonym of everything.
Also what's established by the definitions I provided above is nothing is also the antonym of everything in that it is not anything.
It can thus be inferred that nothing is the antonym of both something and everything in everyday discourse. Is this a normal state of affairs in re antonyms?
As defined, an antonym of a word is supposed to have an opposite meaning to the word itself i.e. if one is applicable the other is not. We must remember this point that the words themselves aren't as important as the meanings of these words - antonyms are about meanings being opposite.
Now consider the words "hot" and its antonym "cold" which are simple enough for the discussion and what applies to this case can easily be generalized to all antonyms. One can immediately see that hot and cold are logical contraries i.e. both can't be true but both can be false e.g. it can be room temperature (neither hot nor cold). However, what's interesting is room temperature (neither hot nor cold) isn't considered an antonym of hot or cold. The same applies to other words e.g. the antonym of "good" is "bad" and "amoral" isn't part of the picture.
What the above means is that antonyms come in pairs - there are always two, no more no less. Even if meaning wise there are other alternatives all of them are ignored and only two are chosen, one being the antonym of the other.
If that's the case then it's wrong to think nothing is the antonym of something AND everything because antonyms have to come in pairs and even if there are other alternatives they're to be ignored.
What is the correct antonym for nothing?
Something OR Everything OR
Comments (87)
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.
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.
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.
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.
Why would that be a problem? I don't see anything "incomplete" here.
I think that everything exists except thinghood itself.
Or else explain what is it about anything that makes it a thing rather than not.
These are not the same.
If you asked me to hand you anything, you are not asking me to hand you everything.
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.
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.
Well, no, since the universe of discourse is presumably the cake...
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.
Quoting 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.
Quoting 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.
Quoting god must be atheist
[quote=Stanford Encyclopedia of Philosophy]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.[/quote]
Quoting 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".
Quoting 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.
Quoting 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 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.
What exactly do you mean by context and that the meaning of words depend on it?
Firstly, when I said,
Quoting 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.
Quoting 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.
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.
:rofl: :rofl: :up: :up: Don't do drugs but merry christmas to you
I guess it's as futile as you make it out to be. Thanks.
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.
It ain't, and that's it.
As soon as you turn nothing into something, you go from making sense to talkin no sense
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.
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.
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.
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.
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.
No? How is there no difference? One is a subset of the other.
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.
Don't worry about it.
Something as at least one could also mean everything which is at least one
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.
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
Other than that, spot on.
That's all I mean.
Why? It has proof value. Your proposition has been disproven by a proof-value tool. Why proceed from there?
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.
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.)
Quoting 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.
Quoting 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.
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.
I am a student who uses his head. Years of indoctrination in the wrong logic hasn't touched me. I hope it never will.
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.
"Not everything" is not "not anything".
the only sensible thing to do is to walk away.
Quoting 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.
Quoting Pfhorrest
Practically unused cases like the above?
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.
: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".
...became universal instantiation - which (should have) cleared up what was going on.
Quoting creativesoul
Do you want to be able to claim to have a red nothing in storage?
: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?
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.
Quoting 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.
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.
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?
Actually I had overlooked and/or neglected cases where something is exactly 15 billion years of age, but I think I've understood the logical notation you're advocating here. That example didn't quite fit, but could have had I not employed "younger" and instead said something like "everything in the universe is not older than 15 billion years", or "there is not something in the universe that is older than 15 billion years". Both of these are semantically equivalent to "nothing in the universe is older than 15 billion years".
When everything is X, then nothing is not X. When everything is not X, then nothing is X.
In both cases, the term "nothing" is semantically equivalent to "everything". This happens as a result of shared common referents(both terms pick out the same things), regardless of what's being said about them(aside from contradiction). So far, all of this seems fine by me.
My issue involves...
Quoting Pfhorrest
Saying "you have all zero of them" neglects the fact that in order to have all of anything requires that there first be something to have. Having all of something requires at least one thing. Zero things is not at least one thing. Zero things is nothing, and not in the same sense as when the term "nothing" is used as a means to pick out everything.
It’s weird, yeah, but that’s because we don’t usually talk about empty sets, because there’s almost no practical need to.
Banno, the preceding page that has posts since the post of the above quote shows that I am not stupid, or unwilling to learn. It ought to show you the error of your way of reasoning. It is not my "unwillingness to learn" that is the stupid thing around here; the "stupid" was the ill logic that PfHorrest was trying to teach me. You, PfHorrest and CreativeSoul have argued a page worth preceding this post of mine, without resolution. Because, basically, if you stick to your wrong guns, and you are emotionally committed to stick by them, then you can't be convinced of your wrongness in logical terms. And I put it to you, Banno and PfHorrest, that you two are committed emotionally to the wrong argument.
What happened here? This:
PfHorrest showed me a Venn diagram that was self-contradictory or nonsensical. When I told him that, he said, "forget the Venn diagram".
Then later CreativeSoul pointed out to you and to PfHorrest that to have everything red in a box, you must have at least on thing in the box, because nothing (in case of an empty box) can't be red. You two, PfHorrest and Banno, tried to deny this with logical arithmetics, which was a futile and -- between us -- unthinking move.
This is where the impasse occurred, and I saw this happening, yet you, Banno, and PfHorrest, THOUGHT OF ME IN A VOCALIZED (WRITTEN) WAY AS THE STUPID ONE WHO IS UNWILLING TO LEARN, whereas what happened was that I saw the error of your ways, which you two are still unwilling to see or to admit to.
I pulled out of this futile thread, because you are unwilling to admit to obvious facts, and I was actually hurt and dismayed and filled with bitterness when YOU TWO, BANNO and PFHORREST called me stupid (not verbatim, but in so many other words).
... strike "becasue there's almost no practical need to" and replace it with "because it blows our theorem to pieces making minced meat out of it."
I did explain briefly why it was not self-contradictory before moving on to a different approach, but since you're so hung up on it I can explain in more detail here.
To recap, the left circle is cases where you have "something" and the right circle is cases where you have "not everything". In other words, the left circle is cases where there are things that you have, and the right circle is cases where there are things that you don't have.
In the left crescent are cases where you have something but not not everything, or in other words both something and everything: there are some things you have, and no things you don't have, so you have all of the things there are to be had, and there are some to be had. This is the ordinary use case for "everything", but there is another we'll get to later.
In the middle intersection are cases where you have something but not everything: there are some things you have, and some things you don't have. These are the cases that you want to restrict "something" to, but in normal language and formal logic both Aristotelian and modern, "something" also applies to the left crescent: you can have something and everything, or something and not everything. I like to call this case "merely something", where the "mere" conveys the not-everything part of it.
In the right crescent are cases where you don't have something, and you do have not-everything: there are no things that you have, and there are things that you don't have. This is the ordinary use case for "nothing".
But in the outer area are the weird cases, or rather, the one single weird case: where you don't have something, and you don't have not-everything, or in other words, when you have nothing and everything: because there are no things that you have, and no things that you don't have, because there are no things at all, because the only case that falls out here is the case of an empty set.
I drew a picture:
If everything is red in the box, and everything is non-red in the box, that is reductio ad absurdum as long as something is in the box. But reductio ad absurdum also means that no such thing is possible. And lo and behold: the box is empty, therefore "everything is red" and "everything is non-red" is satisfied with no object, therefore with nothing, so there.
I eventually had to do something to try to agree with you, PfHorrest and Banno. But your reasoning did not penetrate my capacity for logic.
This reductio ad absurdum, however, proves the same thing, so I believe you now, although the steps you took to arrive at what you were trying to say are still beyond me.
Quoting Pfhorrest
You're still neglecting the facts here.
In order to have all of anything, there must be something to have. Something is not equivalent to nothing. Nothing is not all of something. Nothing is not all of anything.
You say:
"All of it"???
"The most out of zero"???
:brow:
All of IT is all of something, because "it" always refers to something. Something is not equivalent to nothing. Yet, that is precisely how you've been employing the term "nothing". I said much earlier that it looked like an equivocation fallacy to me. Now, it's certain.
It's not just weird. It's incoherent at best, and utter nonsense at worst. Either way, it's an equivocation of the terms "zero" and "nothing". That much is certain.
All meaningful use of "the most" presupposes "the least". "The most" makes no sense whatsoever unless there is also "the least". These two notions are both existentially and semantically dependent upon one another.
This is just plain old common sense.
"The most" and "the least" are always in direct inverse proportion to one another when dividing a whole into two unequal portions. That comparison gains complexity when dividing something into more than two unequal proportions, but the meaning of both "the most" and "the least" are still - and always are - established by comparison between a plurality of shares/portions/etc.
We talk about "the most" and "the least" after, and only after, we have something being dividing into a plurality of unequal (pro)portions. Otherwise, both notions are rendered utterly meaningless. There is no possible referent for either, unless there are referents for both.
And yet...
You've talked of "the most" of both nothing and zero, as if there is a meaningful quantitative difference to be drawn between the most of nothing and the least of nothing; as if there is a meaningful quantitative difference to be drawn between the most of zero and the least of zero.
There is not, and such talk is nonsense.
The most of zero is exactly the same as the least of zero. The most of nothing is exactly the same as the least of nothing. There is no distinction to be drawn here between the most of nothing(zero) and the least of nothing(zero) because they both have precisely the same numerical and/or quantitative value.
That's exactly the point. Out of a set of nothing, of zero things, there is no difference between the most of it and the least of it. But only in the case of a set of nothing, of zero things, an empty set. It is precisely because there is no difference between the most things from that set and the least things from that set that that all of it, everything from it, is the same as none of it, nothing from it. Any percent of zero is the same thing: zero. 100% of 0 = 0% of 0. In general, 100% of x ? 0% of x, except when x = 0. That is the only case when all of x is none of x, when x is an empty set.
Alice: Well, I haven't had any yet, so I can't very well take more."
How can there be anything without 'Firstness'?
How can 'nothing' be a concept at all, unless you start from the perspective of 'something'?
Top down versus bottom up thinking?
We are limited because from the perspective of self we can only know what is now, the top place to start when thinking from top to bottom. We have no concept of what the bottom may be. What we can only comprehend is that there is always something.
'Nothing' is the complete absence of Firstness. Capturing the in-between of nothingness to somethingness (the birthing of being, an idea, etc) is not an opposite or contrary, it is an emergence of continuity, perhaps from outside in to inside out. Two sides of a spinning coin. Nothingness is the exact image of the edge of the coin, when it is neither heads nor tails.
Just my thoughts.
Which renders both notions meaningless. In addition, as I've already mentioned, there's an equivocation of both terms "zero" and "nothing" as a result of using them to mean different things.
You'll have to explain this supposed equivocation between "zero" and "nothing", because I'm not seeing what you're talking about. If it helps, I'm not saying that the number zero is itself nothing; I'm saying that zero is the number of things in a set that has no things in it.
Aside from the meaninglessness I've shown...
Seems that there are brilliant people that have already shown the inherent issues in Set Theory, and they have done so on it's own terms... Russell comes to mind. Barbers and haircuts or something similar???
There are no empty sets.
This is standard mathematics, and the "terminological use I'm advocating" is standard logic. I'm not putting forward anything of my own here, I'm just trying to help you understand the normal way professionals on this subject understand things.
You've said that that's the point.
You've also claimed that everything in mathematics is based upon set theory. That's utter bullshit. We were using maths long before, so...
While it may be true that current conventional understanding of maths employs set theory, it is quite simply not the case that all math is based upon set theory.
Math existed prior to. That which exists prior to something else cannot be existentially dependent upon that something else.
Anyway...
Yeah. So you're promoting conventional understanding. Good for you.
Grounded in... based upon...
As if there is a difference here that matters? You've already shown a penchant for rendering terms meaningless and/or incoherent. Now you're drawing distinctions that make no difference.
When something is grounded in something else it cannot exist prior to that something else. Math was prior to set theory. Math cannot be grounded in something that did not exist at the time we began using math.
Quoting Pfhorrest
Here again, you've rendered otherwise meaningful terms incoherent and/or meaningless.
Following the above and applying it to the current discussion, math would be called "higher level" and set theory would be called "lower level". Set theory is far more complex than simple counting. So you're calling the more complex of the two "lower-level" and the most basic, rudimentary and foundational of the two "higher level".
Incoherent, meaningless, nonsense.
Furthermore, the comparison itself is bogus. Genes existed in their entirety prior to our knowledge of them. Set theory did not.
Likewise, mathematics works for some reason or another, and that reason was in question for thousands of years, but we didn't need to know that in order to just add and stuff. We did that first, and only last century started coming up with strong rigorous explanations of why that stuff works, which explanations today universally rely on some kind of set theory.
No. You miss the following point:The analogy falls apart upon direct application to this discussion of ours. That's not the only one you've missed.
As already mentioned, you've exhibited a penchant for equivocation and/or incoherency.
You're calling higher level complexity things "lower", and lower level complexity things "higher". You're using the term "nothing" when referring to something. You're using the term "all" to refer to nothing.
This is the short list...
If this is what it takes in order to 'explain' how math works, then someone... somewhere... has gone horribly wrong.
The problem with "zero-nothing" is that, it always contains information in the sense that it is a limited possibility within all possibilities. If one considers limitations of what something can be information and considers that an existing thing then "zero-nothing" just means zero amount and not true nothingness.
Quoting creativesoul
Do you care to answer these direct charges? Do you understand them?
Have I written the word "higher" when talking about things with far less complexity while simultaneously using the term "lower" to refer to other things with far more?
You're trying to convince me of the inductively sound nature of the logic of zero in terms of nothing when nothing means something, everything, and all.
I'm telling you that nowhere in your account have you explained the role that thought and belief play here. The discussion is skirting around the differences in our respective opinions concerning the type and amount of value that each of us places upon mathematical theory.
Numbers are names of quantities. Some of those quantities existed in their entirety prior to our naming them. Others... not so much. Which of the two are more basic, foundational, and/or simple?
Where does zero land?
That gets at the heart of the equivocation of the term "nothing".
What do you mean by that? How does zero contain information?
Imagine a set, {dog, 9, $, F}.
If I remove 9, I have removed something but what I'm left with is {dog, $, F} which is still something and definitely not nothing.
If now I remove everything, I'm left with { }, the empty set aka nothing.
So, shouldn't the opposite of nothing be everything instead of something? :chin:
Now imagine that there's nothing, { }. Suppose {dog, 9, $, F} is everything. Now, I take 9 which is a something and add it nothing, it becomes {9} and nothing is no longer nothing. Shouldn't the opposite of nothing be something instead of everything? :chin:
Paradox alert!
If there was only black empty space it would be true nothing. Because there wouldn’t be something there to observe it as something. But you couldn’t even call it “nothing” because nothing to is as a word that has significance and indicates something. If you add something (mass-energy) then suddenly space is the “thing” that is not other things.
It is by contrast that things exist. No contrast, no polarity or dichotomy or pairs of extremes , then true nothing. But because energy is a spectrum there must stuff.
Just as zero is the same as -1 +1 energy time space and mass could simply be the property of true nothingness.
Or think of it as a double negative. Logically if “nothing” does not exist then something must exist.