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If zero is the representation of nothing, then nothing must me something because it is being represented, correct?

Now, if the above is incorrect, and zero is actually nothing, then why is it that after every 9 numbers when we count we use zero to increment to the next set of 1-9 IE:

[1,2,3,4,5,6,7,8,9,10<-,11,12,13,14,15,16,17,18,19,20<-]

Because if zero is actually nothing, then aren't we simply looping through 1-9 over and over again?

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  • While it seemed on the face of it this question was a metaphysics (ontology of numbers) question, it seems to read by the end more as an epistemology question. That is, knowledge representation... The short answer is that you can still have the idea of something without that concept actually reflecting anything in reality, but different philosophers will have different things to say about that. – stoicfury Oct 17 '12 at 16:45
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We use zero to represent a piece of information: that is, that there is zero of some collection. Nothing is not "a thing", but it is usually a state of affairs which is distinguishable from something.

In the same vein, in computer science, we denote the value of a bit usually by either 0 or 1; but here '0' doesn't mean 'nothing' nor does 1 mean 'one thing', but rather they represent two distinguishable states of a physical system, such as a voltage in a wire. Furthermore, these values are used to represent 'false' and 'true' respectively, in reference to some proposition (e.g. "The computer is connected to the network".) In this case, 'true' and 'false' are also no more than the distinguishable states of affairs about a proposition which has two polarized, distinguishable configurations: one which satisfies the proposition, and one which does not. Our notion of "truth" and "falsehood" in the bivalent picture comes from trying to draw such polarized distinctions in the world around us, and to comprehend the world in terms of such polarized distinctions.

As to numerical representation: we do not use '0' to 'increment' to the next set of digits 1–9, any more than we use '1' to increment from "1" to "11". Instead, what we are doing is representing a number using a sequence of symbols, of which '0' is one of them; and the symbols represent the number of items in a hypothetical collection. We take the right-most digit to represent the number of items in a collection of individuals; the next right-most digit to represent the number of items in a collection of groupings of ten individuals, and so on. We may write 007 for 7, but this is redundant and uninformative; while the right-to-left nature of our convention makes the two zeroes in 700 more informative, because it causes the 7 to denote the number of groupings of one hundred in the numeral. But 0 is no more special here than any other digit; the 7 in 736 also represents 7 groupings of one hundred, together with other amounts of tens and individuals.

Our symbols represent information which may be of interest to us; and the information that is of interest to us sometimes is that some collection is empty. The same applies to the word "nothing", or "vaccuum", similarly. But the ontological status of "information about a system", if it can be said to have ontological status at all, is not a property of the system itself as it is a property of our (or someone else's) interaction with the system. That interaction hopefully reveals something about how the system is; but this does not mean that there is an esoteric, occult sort of object as "no apples" or "no koalas" if for example I find that my office is devoid of either apples or koalas. I merely find in my interaction with my office that it seems not to have the features that it would have if there were apples or koalas in it; and I communicate this information to you my stating that there are zero of each, hoping that you understand that there are no zeroapples or zerokoalas in my office.

As always, it is important to distinguish reality from how we speak of it, to not mistake propositions for facts, or words for properties, however we usually endeavor to have the former represent the latter.

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