The Opposite of Nothing Is/Isn't Everything

[merjet]

0 does not have a square. 0*0 is undefined. 0^n is NOT 0*0 n times. It is 1 * n factors of zero. There is no number that corresponds to n factors of zero. 0*0 n times is just as undefined as 0*0 is. So 0^n = 1.

The above is a great and succinct example of reifying zero.

[Selene]

Reification (also known as hypostatisation, concretism, or The fallacy of misplaced concreteness) is a fallacy of ambiguity, when an abstraction (abstract belief or hypothetical construct) is treated as if it were a concrete, real event, or physical entity. In other words, it is the error of treating as a "real thing" something which is not a real thing, but merely an idea. For example: when one person "holds another's affection", affection is being reified.

Note that reification is generally accepted in literature and other forms of discourse where reified abstractions are understood to be intended metaphorically, but the use of reification in logical arguments is usually regarded as a mistake (fallacy). For example, "Justice is blind; the blind cannot read printed laws; therefore, to print laws cannot serve justice." In rhetoric, it may be sometimes difficult to determine if reification was used correctly or incorrectly.

Pathetic fallacy or anthropomorphic fallacy (in literature known as personification) is a specific subset of reification, where the theoretical concepts are not only considered alive, but human-like and intelligent.

[edit] Etymology

From Latin res thing + facere to make, reification can be 'translated' as thing-making; the turning of something abstract into a concrete thing or object.

[edit] Theory

Reification often takes place when natural or social processes are misunderstood and/or simplified; for example when human creations are described as “facts of nature, results of cosmic laws, or manifestations of divine will”. Reification can also occur when a word with a normal usage is given an invalid usage. Such "mental shortcuts" lead to ascribing substance or real existence to mental constructs or concepts, particularly treating them as live beings. When human-like qualities are attributed as well, it is a special case of reification, known as pathetic fallacy (or anthropomorphic fallacy).

A reification circle refers to the event when a norm, first seen as artificial and forced, in time becomes so accepted that even its creators start to think of it as a natural law.

Willard Van Orman Quine suggests that reification exists potentially in all linguistic categorizations and naming objects, insofar as the recognition of the same object in different spatio-temporal contexts requires abstraction from time, change, interactions and relations pertaining to the object. Already Heraclitus had observed "it was impossible to step in the same river twice", and this implies that identifying the river involves the imputation or attribution of a constancy which in physical reality does not exist.

Reification may derive from an inborn tendency to simplify experience by assuming constancy as much as possible.[1]

[edit] Reification vs hypostatisation

Sometimes a distinction is drawn between reification and hypostatization based on the kinds of abstractions involved. In reification they are usually philosophical or ideological, such as "existence," "good," and "justice."

[edit] Reification in literature

Note that reification applies to rhetorical devices, as well, such as metaphor and personification, which are not fallacies at all, but important and useful tools of language in literature. The distinction between treating abstractions as material existents rhetorically or using them in arguments that result in false conclusions, is often difficult to detect, or even to describe, especially when the fallacious use is intentional.

[edit] Examples

In philosophy, the use of the term "nothing" as if it were a special kind of something.

Another reifying use of "nothing" is found in this joke: A man walks into a bar. The bartender asks him what he wants. "Nothing," he says. "So why did you come in here for nothing?" "Because nothing is better than a dry martini."

Regarding a state or a society as a conscious being ("This product is known to the state of California to cause cancer") or assuming government is a being with desires ("Government wants to help you"). Both of these reifications are examples of the linguistic phenomenon metonymy.

The legal recognition of corporations as "individuals" may lead to fallacious assumptions. In reality, these are just organizations of capital and labor, but have been assigned the status of legal 'persons' which gives them entitlements and liabilities, such as the ability to own property or to be sued.[2] It would be fallacious to attribute other personal qualities to corporations based on this status, e.g., "Acme Explosives is a warm-hearted company." (This anthropomorphic fallacy is explored in detail in the movie The Corporation.)

Phrases

* "The universe will not allow the human race to die out by accident." (attributes intention to the universe)

* "Religion attempts to destroy our liberty and is therefore immoral." (attributes intention to religion)

* "Good and evil are forces ruling the universe." (attributes motive to the abstract ideas of good and evil)

[edit] Similar fallacies

Pathetic fallacy (also known as anthropomorphic fallacy) is a specific type of reification. Just as reification is the attribution of concrete characteristics to an abstract idea, a pathetic fallacy is when those characteristics are specifically human characteristics, thoughts, and feelings.

The animistic fallacy involves attributing intention of a person to an event or situation. This is usually not reification because the "real" attributes are given to the perceived person involved, and not the event or situation (e.g. "The train's conductor must have been impatient, so we missed the train." (animistic fallacy) compared to "The train was impatient." (reification))

Reification fallacy should not be confused with other fallacies of ambiguity:

* accentus, where the ambiguity arises from the emphasis (accent) placed on a word or phrase

* amphiboly, a verbal fallacy arising from ambiguity in the grammatical structure of a sentence

* composition, when one assumes that a whole has a property solely because its various parts have that property

* division, when one assumes that various parts have a property solely because the whole has that same property

* equivocation, the misleading use of a word with more than one meaning

[tjohnson]

Reification often takes place when natural or social processes are misunderstood and/or simplified; for example when human creations are described as "facts of nature, results of cosmic laws, or manifestations of divine will".

Interesting, I hear the expression "facts of nature" quite often on this list.

[Selene]

Yes I would love to "see" a non-fact of nature, but hmmm would that be a mystical fact of nature? - just an epistemological tongue in cheek question.

[merjet]

Roger Bissell's stipulations that 0+0 and 0*0 are undefined (or is the latter = 1 as he also indirectly said?) would not only cripple calculus and matrix algebra. They would cripple much more of mathematics, including the methods of long division and long multiplication that many or all of us learned in grade school.

[Michael Stuart Kelly]

I have the general impression that there is resistance all around to making clear meanings for concepts of method as opposed to concepts of ontology, with the resistance most strongly seen (at least to me) to making clear where the two interconnect.

Michael

[thomtg]

Roger Bissell's stipulations that 0+0 and 0*0 are undefined (or is the latter = 1 as he also indirectly said?) would not only cripple calculus and matrix algebra. They would cripple much more of mathematics, including the methods of long division and long multiplication that many or all of us learned in grade school.

I believe Roger and I stipulated what it means for something to be "undefined" earlier. (See Post #138 and Post #178.)

Edited May 28, 2009 by Thom T G

[thomtg]

I have the general impression that there is resistance all around to making clear meanings for concepts of method as opposed to concepts of ontology, with the resistance most strongly seen (at least to me) to making clear where the two interconnect.

Michael

I completely agree, Michael.

Ontologically speaking, as nothing is not another something, so zero is not another quantity. To think so is to commit the fallacy of Reification of the Zero.

[merjet]

I believe Roger and I stipulated what it means for something to be "undefined" earlier. (See Post #138 and Post #178.)

What are you trying to say? That "undefined" should be interpreted as "not operable or calculable by any process", like you say in #138? That is precisely the meaning of my remark about the consequences of Roger's stipulations for long division and long multiplication. If one encounters 0+0 or 0*0 in these algorithms, Roger's stipulation implies these expressions are incalculable and execution ends abnormally.

Ontologically speaking, as nothing is not another something, so zero is not another quantity. To think so is to commit the fallacy of Reification of the Zero.

If zero is not a quantity, then what is it? Under which of Aristotle's 10 categories does it fit? As for reifying zero, see post #226.

Edited May 28, 2009 by Merlin Jetton

[BaalChatzaf]

I completely agree, Michael.

Ontologically speaking, as nothing is not another something, so zero is not another quantity. To think so is to commit the fallacy of Reification of the Zero.

Within the domain of real and complex numbers, 0 is a real and complex number (respectively). It is also the identity element for addition which is what makes it special in terms of the structure of the real and complex numbers. It IS a quantity, as much a quantity as 1 or 2 and 3/8 or pi. You are truly a font of misinformation and disinformation concerning mathematics. But you are a master of $mathematics, a system only an avid reader of ITOE could construct. Fortunately for the world, physics and engineering use mathematics and not $mathmetics.

Ba'al Chatzaf

[tjohnson]

In mathematics numbers (including 0) represent relations. If you use them to count things then they also represent quantities. In this case it is makes no sense to speak of 0 things, however, it does makes sense, in mathematics, to speak of identity elements. There is no need to argue about this.

[Michael Stuart Kelly]

Within the domain of real and complex numbers, 0 is a real and complex number (respectively).

Bob,

That's "within the domain of real and complex numbers."

The problem is, zero-wise, we are discussing something in addition to this domain that you ignore. We are discussing how the "domain of real and complex numbers" applies to reality, i.e., the interface between the method and raw fact.

If math can build a bomb, there has to be a correspondence between the blueprint and the boom. Otherwise no boom.

Michael

[BaalChatzaf]

Within the domain of real and complex numbers, 0 is a real and complex number (respectively).

Bob,

That's "within the domain of real and complex numbers."

The problem is, zero-wise, we are discussing something in addition to this domain that you ignore. We are discussing how the "domain of real and complex numbers" applies to reality, i.e., the interface between the method and raw fact.

If math can build a bomb, there has to be a correspondence between the blueprint and the boom. Otherwise no boom.

Michael

So true and the answer is --- 0 is a quantity. It is as simple as that. If Roger and Thom think that 0 is not a quantity then so much the worse for them. That is the difference between mathematics and $mathematics (REB's proposed science).

If you had ten dollars in your bank account and you withdrew ten dollars how many dollars would you have in your bank account? Take your time now.

Ba'al Chatzaf

[Michael Stuart Kelly]

Bob,

Shift gears a bit and you will see that quantity as a concept of method and quantity as an existent are slightly different. Same word. Different meanings.

In the concept of method, zero is a symbol of quantity and there are rules that govern the symbol. (This is where you are correct.) As an existent, zero quantity means no existent at all. (This is what you are not acknowledging.)

Both are called math, although I doubt you will agree. But if you are a farmer or manufacturer, zero quantity where you would apply that phrase would most likely lean toward the ontological type of math. It would mean nothing is existing there, not that some invisible cow is there, for instance, that has special rules of being impeding it from being milked.

Like I said. Same word. Different meanings.

Michael

[thomtg]

I believe Roger and I stipulated what it means for something to be "undefined" earlier. (See Post #138 and Post #178.)

What are you trying to say? That "undefined" should be interpreted as "not operable or calculable by any process", like you say in #138? That is precisely the meaning of my remark about the consequences of Roger's stipulations for long division and long multiplication. If one encounters 0+0 or 0*0 in these algorithms, Roger's stipulation implies these expressions are incalculable and execution ends abnormally.

Ontologically speaking, as nothing is not another something, so zero is not another quantity. To think so is to commit the fallacy of Reification of the Zero.

If zero is not a quantity, then what is it? Under which of Aristotle's 10 categories does it fit? As for reifying zero, see post #226.

Thank you, Merlin, for engaging in philosophy and not arithmetics. I will answer you as soon as you answer me, under which of the categories does "nothing" fit? Meanwhile, you can take a look at your own dictionary definition of zero on page 10, Post #188, and my ontological interpretation of "zero" on the same page, Post #198.

[thomtg]

Merlin,

Others in this discussion treat pure math and applied math as if the issue were content, not intent, especially when they claim there is no correspondence between pure math and reality.

That is precisely what I question. If there were no correspondence, pure math only applies to reality in some cases by accident, but not by correspondence.

I believe this kind of reasoning is flawed.

I am surprised you have not noticed this.

Michael

[...]

I have noticed it and registered my disagreement here ( near the end) and other threads as well. It just hasn't been my focus.

Good catch, Michael.

Merlin's response at Post #68 as directed from his Post #180 (above) does not address your query.

The post shows a misunderstanding of the current proposal on the ontology of the zero. Contrary to the assertion, anything that is unitized by man can be counted (i.e. measured), not just entities. I'm sure every child would be surprised to be told he couldn't count paper lengths (an attribute) or musical durations (a relation) or dance steps (an action); and that he wouldn't be able to learn negative numbers unless he removed all thoughts related to perceptual entities. For according to Merlin's view, "some of mathematics makes no claims about reality." On this view, since on the Kelvin standard of temperature, there are no negative degrees; therefore, some math makes no claim about how to count temperatures in reality.

So, either those degrees, attributes, relations, and actions are not about reality (since children cannot count them), or this is an admission that "some" mathematics (e.g., "pure mathematics") is beyond reality. Either way, it does not register with your query: "If there were no correspondence, pure math only applies to reality in some cases by accident, but not by correspondence."

To reiterate from my Post #105,

Some people would prefer to set up an arbitrarily defined set of rules ("axioms") for manipulating symbols and then play with them, occasionally exclaiming in great surprise when their arbitrarily based manipulations produce a pattern that applies to the real world -- than to acknowledge that mathematics is an ~abstraction from~ the real world, and that, to be valid, every rule and procedure must be based on or ultimately derivable from a concrete mental operation directed toward real objects and their attributes, actions, and relations.

[...]

[...] And by this standard, axioms in science (including math, philosophy, chemistry, etc.) cannot be arbitrarily defined. They must have a basis in facts of reality. Mathematics in particular is a science of measurement. On this conception, the philosophy of mathematics needs to take cognizant both of man the measurer and of that which can be measured, in establishing criteria for determining truths in mathematics. [...]

And from Ted's Post #142,

There is no such thing as "pure mathematics" as in mathematics not instantiated by a human mind. It is the fact that humans can attempt to realize contradictions that leads to the so called problems of pure mathematics.

[...]

Mathematics isn't pure. It doesn't do itself. [...]

Edited May 29, 2009 by Thom T G

[Christopher]

This thread is long and I haven't done a lot of my homework reading it, but I was reading Objectivist Epistemology and thought this would be useful to consider:

Since axiomatic concepts are not formed by differentiating one group of existents from others, but represent an integration of all existents, they have no Conceptual Common Denominator with anything else. They have no contraries, no alternatives. The contrary of the concept "table" -- a non-table -- is every other kind of existent. The contrary of the concept "man" -- a non-man -- is every other kind of existent. "Existence," "identity," and "consciousness" [,the three Objectivist axiomatic concepts,] have no contraries--only a void.

It may be said that existence can be differentiated from non-existence; but non-existence is not a fact, it is the absence of a fact, it is a derivative concept pertaining to a relationship, i.e. a concept which can be formed or grasped only in relation to some existent that has ceased to exist. (One can arrive at the concept "absence" starting from the concept "presence," in regard to some particular existent(s); one cannot arrive at the concept "presence" starting from the concept "absence," with the absence including everything.) Non-existence as such is a zero with no sequence of numbers to follow it, it is the nothing, the total blank.

[merjet]

Thank you, Merlin, for engaging in philosophy and not arithmetics. I will answer you as soon as you answer me, under which of the categories does "nothing" fit? Meanwhile, you can take a look at your own dictionary definition of zero on page 10, Post #188, and my ontological interpretation of "zero" on the same page, Post #198.

“Nothing” is used in various ways. I can’t put it in one category to cover all cases. “Nothing” might be used to mean the absence of a substance or an action (using Aristotle’s categories). Some uses might even fit other categories. Zero is more specific – the absence of a quantity. So it fits the category quantity. Zero is quantitative. It is as much about quantity as "colorless" is about color.

I’m not sure of your point about post #188. In any case, have a look at your own post #198. There you say that zero denotes “the absence of a presumed, existing quantity”, much like the dictionary.

I’m not sure of your point about post #198. However, if it is “reification of the zero”, I refer you to post #226.

Edited May 29, 2009 by Merlin Jetton

[thomtg]

Thank you, Merlin, for engaging in philosophy and not arithmetics. I will answer you as soon as you answer me, under which of the categories does "nothing" fit? Meanwhile, you can take a look at your own dictionary definition of zero on page 10, Post #188, and my ontological interpretation of "zero" on the same page, Post #198.

“Nothing” is used in various ways. I can’t put it in one category to cover all cases. “Nothing” might be used to mean the absence of a substance or an action (using Aristotle’s categories). Some uses might even fit other categories. Zero is more specific – the absence of a quantity. So it fits the category quantity. Zero is quantitative. It is as much about quantity as "colorless" is about color.

I’m not sure of your point about post #188. In any case, have a look at your own post #198. There you say that zero denotes “the absence of a presumed, existing quantity”, much like the dictionary.

I’m not sure of your point about post #198. However, if it is “reification of the zero”, I refer you to post #226.

Merlin, I would classify "nothing" and "zero" under the derivative concept "absence," which is a "privative" in Aristotle's view of opposition, and is therefore a "relation"--an epistemological relation between a presumed existent (some entity or quantity) and a conscious awarer. Because of its dependence on a consciousness (man's or animal's), these relations can only be conceptualized by man, in my view, as methodological concepts. (See ITOE Ch. 4 on introspection.) It is the reason why you were ineffectual in placing "nothing" in any one category in reality. And if you had introspected about the nature of "absence" in opposition to the "presence" of a presumed quantity, you would have seen that "zero" too could not be a quantity. On this reasoning, any thinking whatsoever that an absence is another kind of presence in reality (or zero as another quantity, in your case) is to commit radically the fallacy of Reification of the Zero.

[Michael Stuart Kelly]

I am still confused about something.

Is there any law that says the word "zero" has to be confined to one meaning only?

Michael

[Dragonfly]

Is there any law that says the word "zero" has to be confined to one meaning only?

No, but don't try to tell the mathematician that his use of the word zero is incorrect.

[Selene]

Ahh soooooo......

"0" equals RELIGION

Whew ....Now my hair stopped hurting.

Adam

[tjohnson]

I am still confused about something.

Is there any law that says the word "zero" has to be confined to one meaning only?

Michael

No, there isn't and it means one thing in counting and another in group theory, for example.

[BaalChatzaf]

"Nothing" is used in various ways. I can't put it in one category to cover all cases. "Nothing" might be used to mean the absence of a substance or an action (using Aristotle's categories). Some uses might even fit other categories. Zero is more specific – the absence of a quantity. So it fits the category quantity. Zero is quantitative. It is as much about quantity as "colorless" is about color.

0 is a perfectly good quantity like any other real or complex number. It does have three special properties:

1. 0 + x = x

and

2. 0*x = 0

for all real (or complex) x.

3. 1/0 is not defined. Which is to say 0 does not have a multiplicative inverse.

Other than that it is a fine quantity. You can add it, multiply with it, subtract it. You can divide by it, however.

Ba'al Chatzaf

[merjet]

And if you had introspected about the nature of "absence" in opposition to the "presence" of a presumed quantity, you would have seen that "zero" too could not be a quantity.

This is a non sequitur.

On this reasoning, any thinking whatsoever that an absence is another kind of presence in reality (or zero as another quantity, in your case) is to commit radically the fallacy of Reification of the Zero.

Nowhere have I said that "an absence is another kind of presence." You are making stuff up.

But maybe I am starting to get it. In your view:

1. 0 degrees (C or F) is an absence of temperature

2. x^0 is an absence of an exponent.

3. You don't read a temperature. You somehow count it.

I would agree with post #249 if "can" in the last sentence were changed to "can't".

Edited May 29, 2009 by Merlin Jetton