Are different values of nothing equivalent?

Question

Are different values of nothing equivalent? Is 'no tigers' the same as 'no zebras'?

Numbers are an abstraction to reality. Our "consciousness brings them to life (for us) because we are able to understand it. " The nothingness equals two different things." Cannot be because numbers are an abstraction to "reality". — jkohn, Sep 13 '11 at 20:03
It's true because for every a, 0a=(1-1)a=1a-1a=a-a=0 (by the standard axioms of a field http://en.wikipedia.org/wiki/Field_%28mathematics%29) — Rom, Sep 14 '11 at 03:53
No. Even for zero quantities, measurement units matter. Zero volt may still mean 100kg. Mathematics has not measurement unit (is not applied yet to anything). Please do not confuse 0 (abstract, maths) with 0 tigers (concrete, physics or whatever). — fubra, Sep 25 '12 at 11:19
Context. Its moot point. If you have 0 of something and 0 of anything, you still have a measure of 0. If you apply context and subtract the unit of measure then yes you are dealing with two seperate entities.. thus you can apply a weighting against the purchase of the unit of measure dpeending on — Scott Barnes, Sep 16 '11 at 03:51
The tigers ate all the zebras and then they starved to death. — Scott Rowe, Mar 14 '22 at 23:15

score 20 · Accepted Answer · answered Sep 12 '11 at 20:35

It depends on how you are using the term 0. In your question you used it as both a predicate (a property of an object) and as a existential "flag" (non-predicate).

In other words, you could use to it refer to the existence of something, i.e. with 0 essentially representing the existence or non-existence of something:

1 apple = an existing apple  
0 apple = a non-existing apple

Or, you could also (in a way) use it as a descriptive characteristic, like a property; in this regard it might be seen as a property all things share. I.E. All existing things share in their non-nothingness; all non-existing things are equal in their nothingness. However in many philosophical contexts, existence is not seen as a property of an object; it is simply viewed a relation between objects (the subject and the object). In other words, it doesn't really say anything about an object's features/characteristics to say that it exists or not.

The overall point here is that you should be careful to avoid linguistic traps with the concept of 0.

E.G.

The Devil is greater than nothing.

Nothing is greater than God.

Therefore, the Devil is greater than God.

See the brief but useful section on Language and Logic on Wikipedia about this. You might also be interested in philosophical discussions of nothingness in the article from SEP.

nothing explains everything! – Arnis Lapsa Sep 16 '11 at 06:46 — Arnis Lapsa, Sep 16 '11 at 06:46

score 18 · Answer 2 · answered Sep 13 '11 at 16:40

18

You're missing the point because you're conflating values-with-units and values-without-units.

0 = 0

therefore

0 apples = 0 oranges

Okay. But then

1 = 1 = 1 = 1

therefore

1 lemon = 1 aircraft carrier = 1 snowman = 1 blog post

Wha?

Of course all things that you have none of are connected in the most ephemeral sense of you-not-having-any, just like all things that you have one of are connected in that sense. Not very interesting.

But if you are wondering how to turn lemons into aircraft carriers, you need to notice that you can't conflate unitless quantities with unit-containing quantities. Zero lemons is no more like zero aircraft carriers than one lemon is like one aircraft carrier when you care about the units. If you don't care about the units, zero is just as much like zero as one is like one. If you confuse the two--with units and without--you'll be confused.

answered Sep 13 '11 at 16:40

Rex Kerr

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I think that answer is a little too pat; it's possible (of course) to argue that having no lemons is different than having no snowmen, but you'll have to make that case, not simply assert it. The obvious reference here is the joke told in Ninotchka, about a man who goes into a Parisian cafe and orders "One coffee, no cream" only to be told "I'm so sorry, we're all out of cream-- I can give it to you with no milk..." – Michael Dorfman Sep 13 '11 at 19:05
@Michael Dorfman - You mean I should give a tutorial on units? My point, stated differently, is that the question seems to confuse quantity with quality, and we already have a well-worked-out system for separating quantity from quality, namely measurement units. – Rex Kerr Sep 13 '11 at 19:32
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No, I'm suggesting that from a philosophical perspective, the units disappear when we are talking absence; we have no way to distinguish coffee-without-cream from coffee-without-milk (which would surely be the identity-criteria in this case). If we wish to put this in mathematical terms and keep the reference to units, 1 Coffee + 0 Milk = 1 Coffee + 0 Cream, but 1 Coffee + 1 Milk <> 1 Coffee + 1 Cream. Even if you keep the units, zero is a special case, and has some unusual properties. – Michael Dorfman Sep 14 '11 at 07:05
@Michael Dorfman - I guess we just disagree about the use of units. 0 Milk <> 0 Cream if we view the items as units. If there is no gravity, you don't say that the gravity is zero joules or zero moles or zero meters. It's still zero m^2/s; anything else is a unit error. Zero does have some unusual properties, but dropping units isn't one of them, not when you're doing calculations (not unless you want to risk getting confused). No gravity (0 m^2/s) is not the same as extremely cold (0K) in any useful sense. I propose that this is exactly the misunderstanding in the original question. – Rex Kerr Sep 14 '11 at 07:20
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Ah, but here we get into the difference between measurements and countables. A countable thing has properties, but these properties are manifest only if the thing actually exists in the determined context; if the things are absent, the properties (which define the thing) are also absent. So an apple is not a banana, but zero apples is indistinguishable from zero bananas. The units only come into play if we actually have units; if we are dealing with absences, this isn't necessarily the case. (This particular dispute goes back to Parmenides, at least.) – Michael Dorfman Sep 14 '11 at 09:38
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@Michael Dorfman - Agreed. My impression is that the question was conflating "I measure zero apples" with "no-apples is just like no-bananas", which is solved by paying attention to units. Multiplying measurements makes some sense; multiplying by a particular object doesn't so much. – Rex Kerr Sep 14 '11 at 14:18
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Nice discussion here in the comments. I feel kind of silly, but this show how important logic and mindful observance is. I really mixed up some things. The weakness of language is its inaccuracy. Thanks for your thoughts. – Stephan Schielke Sep 14 '11 at 19:04
Michael said: "from a philosophical perspective, the units disappear when we are talking absence" which is interesting because from a programming point of view, the units do not disappear, or they do, depending on what language you use, namely, if the language has generics or not, e.g. in PHP, two empty arrays are equal to each other since they have no idea what kind of objects they will be filled with, but in C# an array meant to hold objects of type apple will not be equal to an array meant to hold objects of type orange. – Edward Tanguay Sep 16 '11 at 02:25
@RexKerr check out my answer. ;) – Shelby Moore III Jul 22 '15 at 17:50
@Rex: I don't understand how 1=1=1=1 implies the next statement, even if we agree on the previous implication. what operation did you perform? I don't see what is inconsistent in having the first three statements true, but the last false. – Dror Speiser Oct 05 '15 at 18:34
@DrorSpeiser - The operation is "apply whatever unit you want to each number". – Rex Kerr Oct 05 '15 at 19:53
so there's a hidden premise that the reason for the first implication is "apply...". but it needn't be. – Dror Speiser Oct 05 '15 at 20:09
@DrorSpeiser - The original (longer) question made it (more) clear that the poster was trying to manipulate or think about the numbers in a way that doesn't make sense unless you have units attached. – Rex Kerr Oct 06 '15 at 12:42

score 5 · Answer 3 · answered Sep 13 '11 at 07:07

First, that was not a question, so this is not an answer per se.

If I have an apple zero times, it becomes zero. It is equal to nothing! I never understood that.

It's really not that hard. If you have an apple zero times, you have zero apples. You have no apples. The state of being appleless is really not terribly profound.

In my opinion the 0 is the ultimate connection between everything. The nothingness equals two different things.

Believe it or not, this is actually reasonably close to some interpretations of the primary teaching of the Madhyamaka school of Buddhism. The key term of art used there is Śūnyatā, usually translated by "emptiness", which is also the word for "zero". This, if framed properly, actually is quite profound.

"The state of being appleless is really not terribly profound." Definitely got me cracking up here :D — eflorico, Sep 13 '11 at 13:39

score 2 · Answer 4 · answered Sep 13 '11 at 11:17

0X = 0 is a loose statement. If you intend to represent a mathematical equality then this is true: 0 (number of units of a countable thing) x Multiplied by (zero value ) = 0 (number of units of a countable thing)

so 0x = 0 should be stated as: 0x=0 of x, which is the same as 0x=0x

holoidal · Answer 5 · 2011-10-22T23:31:31.170

I distinguish between emptiness (Buddhism) and Void (Taoism) as two types of nonduality. they both use the idea of zero, or negativity as their idea of how to point toward nonduality. But I have found in my research that there is a difference between what I call even and odd zero. And my evidence for that is that there is a difference between what comes before the first 1 in the Pascal Triange, and the empty places within the triangle, and this is the difference between emptiness and void.

Thus I believe that O does not equal 0.

And in fact there is a theory of Domain Walls that comes from the study of Bose-Einsein Condensates that backs this idea up, that space can have domain walls that differentiate various domains of empty space. So space within a domain wall enclosure is essentially different from space with no domain walls. And this is essentially what we are seeing in the Pascal triangle example.

Zero: The Biography of a Dangerous Idea by Charles Seife

The Nothing that Is: A Natural History of Zero by Robert Kaplan and Ellen Kaplan

Signifying Nothing: The Semiotics of Zero by B. Rotman

score 2 · Answer 6 · answered Dec 09 '11 at 16:33

Intuitions of correctness can be misleading and these intuitions come to mind easily without explanations of their source and may be substituting an answer to a different but related question. I realized if I think of the problem in terms not having 1 apple when I desire an apple, it is certainly different than not having 1 orange when I have no desire for an orange. It is the wanting that throws me off. But not having something I want is more like having -1 of that thing. I only really have 0 apples when I have 0 desire for apples and in that case it is much easier to equate with 0 of anything I do not desire.

Lie Ryan · Answer 7 · 2011-09-14T00:30:55.053

Are these statements equivalent?

This basket contains apples and pears, there is 0 apples in this basket.  
This basket contains apples and pears, there is 0 pears in this basket.

Consider also:

This basket only contains apples, there is 0 apples in this basket.
This basket only contains pears, there is 0 pears in this basket.

The first one is definitely different assertion. Asserting that there is 0 apples does not directly imply that there is 0 pears.

On the second version, the statements are equivalent. Asserting that there is 0 apples/pears implies that the basket is empty, and both are asserting that the basket is empty, therefore they are equivalent.

Therefore, whenever we see statements that only asserts

There is 0 apples in this basket.
There is 0 pears in this basket.

we had to distinguish by context whether it asserts the first case or the second one.

score 1 · Answer 8 · answered Sep 16 '11 at 03:51

My personal thought is that 0 oranges != 0 apples.

I much prefer apples and so having 0 apples is of greater concern to me that having 0 oranges, ergo they're not the same in this case. As such, I'd say it depends on what you're talking about and whether you care about the items in question.

Similarly 0 != 0 beers, because 0 beers may indicate that your glass is empty and needs to be refreshed.

score 0 · Answer 9 · answered Sep 16 '11 at 03:53

When we have units of something we're counting 'things': 0 apples.

When we have 0 apples, in a way we're saying that we have spaces for apples but those spaces are empty.

By that logic 0 apples != 0 oranges.

0X = 0Y can still follow when X and Y are values of unknown numerical quantities. In that case we don't have any units, just numbers.

Shelby Moore III · Answer 10 · 2015-07-22T17:48:04.760

Your question is not philosophical; rather is question of logical relation.

An equivalence function inputs a counted set. The type (units) of any counted set is the disjunction of the types in the set; thus the type parameter of a counted set is contravariant. Thus the type of the set of the disjunction of all types (a.k.a. in computer science as ⊥ or bottom) obeys the Liskov Substitution Principle for functions on sets as an input to an equivalence function testing equivalence to a set of type (or even types).

Thus nothing (set without a type, thus the set of the disjunction of all types) is equivalent to any set of no thing (where thing is a type). But no thing(s) is not equivalent to no another thing(s), unless thing(s) and another thing(s) have a common disjunctive relationship.

Are different values of nothing equivalent?

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