# How and why is this an equivocation (logical fallacy)?

I tried this reference, but don't perceive the following, at 60%-way down this page:

"Nothing is better than"

Margarine is better than nothing.
Nothing is better than butter.
Therefore, margarine is better than butter.

pp 158 of 180, A Rulebook for Arguments, Anthony Weston
defines equivocation as 'sliding from one meaning of a term to another in the middle of an argument.'

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"Margarine is better than nothing." Here, "nothing" is referring to the absence of something.

"Nothing is better than butter." Here, "nothing" is a placeholder for anything at all.

Thus, the meaning of the word "nothing" is different in the two sentences and you have equivocation.

If you maintained the meaning of "nothing" from start to finish
(so that "Nothing" means 'absence of something' as defined in the first sentence above),
then "Nothing is better than butter" would be equivalent to "Butter is worse than nothing":

1. Margarine is better than nothing. (It is better to have margarine than to have nothing.)
2. Butter is worse than nothing. (Having butter is worse than having nothing.)
3. Therefore, Margarine is better than butter.

Here, the meaning of nothing is consistent.

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Thanks, but would you please elucidate which meaning of 'nothing' is intended in your penultimate paragraph? –  Law Area 51 Proposal - Commit Aug 22 '14 at 9:49

The equivocation is with the word "nothing." In (1) "nothing" is used in a pejorative sense; the sentence means "I'd rather have margarine if there's no other choice." In (2) "nothing" is used in a superlative sense, i.e., "Butter is the best thing." If we put those two sentences in the place of the syllogism given we get this:

1. I'd rather have margarine if there's no other choice
2. Butter is the best thing.
3. Therefore, margarine is better than butter.

I think that's clear enough why (3) doesn't follow from (1) and (2).

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I think the connotation of "nothing" is beside the point, and this answer doesn't adequately address how the actual meaning of the word changes. (Rephrasing the argument demonstrates that it must be wrong, but it doesn't explain why the original form was invalid.) –  Brilliand Aug 4 '14 at 17:14

I do not agree with some details of the above answer.

The first observation is that "nothing" is not a "name".

The logical form of :

"Nothing is better than butter"

is:

"for all x, not (x is better than butter)"

where "nothing" has been analyzed in term of quantifier and variable (a variable is "grammatically" a pronoun).

If we stay with this analysis, we can correctly apply the transitivity of the relation :

"_ is better than ..."

i.e. : if "x is better than y" and "y is better than z", then "x is better than z".

But from "Nothing is better than butter" we can infer "cheese is not better than butter" and also "margarine is not better than butter".

But in this way, we cannot conclude nothing about the "relative position" of margarine and cheese.

The second observation regards the fallacious analysis of

"Margarine is better than nothing"

in term of the the relation "_ is better than ...".

In this case the locution "is better than nothing" must be understood in "adjectival" way, like "is acceptable" or "is tolerable".

Thus, we cannot symbolize it as :

"Margarine is better than x".

Try with the quantifiers.

Clearly it is not "exists x (margarine is better than x)"; we are not saying that there is some food which is worst than margarine.

But also "not exists x (margarine is better than x)", i.e. "for all x not (margarine is better than x)", which means that margarine is (one of) the worst food.

Of course, the conclusion is the same : the "purported" syllogism does not conclude !

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the reason it is an equivocation, is that the meaning of "nothing" changes from the 1st sentence to the 2nd sentence (middle of argument), thereby meeting the definition of equivocation as given in the cited Rulebook for Arguments.

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This has to do with colloquial shorthand.

"Nothing" in the first sentence is shorthand for "having nothing (to put on your bread)". Margarine is better than having nothing.

So if we plug it into the second sentence, it doesn't make any sense: "Having nothing is better than butter".

Whoa. How'd we get to such a low view of butter? However, if we use them in the same sense that it is clear that margarine is better than butter. But to illustrate, let me substitute something we can believe we don't want on our bread: gasoline.

Margarine is better than nothing, but eating your bread with nothing is better than pouring gasoline on it. Hence margarine is better than gasoline.

In such analysis, it can be understood that "Nothing is better than butter" is in a different sense that "no thing is better than butter" (which is wrong, because bacon is the greatest member of any ordered set of foods).

Hence it's an equivocation because it tries to use a word analytically, when all we have is just the same symbol, not the same item it's referring to.

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The purported syllogism is:

1.Margarine is better than nothing.

1. Nothing is better than butter.

2. Therefore, margarine is better than butter.

A is better than B can be represented in brief (by copting mathematical notation) as A > B

So we now have:

1. Margerine > Nothing

2. Nothing >Butter

3. Margerine > Butter

its easy to see from this that the translated statement (2) is not what the original statement (2) means; which could be better put as

Butter > Nothing

But again this is the wrong interpretation. To say that Nothing is better than Butter is to say that there is no 'X' such that

X > Butter

But wait, there is more; because its a rhetorically superlative statement; if one asked a man who claimed that nothing is better a choice between a pat of fresh home made butter from a beautifully maintained organic farm and a mllion pounds; we wouldn't be surprised if he took the million pounds; and nor would we say that he has compromised his principles regarding butter - unless of course you're an extremist belonging to the Butterist Supremacy Front.

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