# ここでの論理的な誤りは何ですか？

ここでの論理の誤りはどこにあり、それはどれですか？

A. Whatever is not normal is abnormal.

B. Sleeping is normal.

Conclusion: Being awake is abnormal.

より良い例：

A. Whatever is not normal is abnormal.

B. Being an Asian is normal.

Conclusion: Being a Caucasian is abnormal.

Conifold is right to draw attention to the fact it involves an equivocation of the copula 'is' for starters.

Let's look at the argument with enthymemes and some clarification

P1 The opposite of 'normal' IS-BY-DEFINITION abnormal. (a priori claim)
P2 'Sleeping' IS-BY-FREQUENCY normal. (a posteriori claim)
E1 [The 'opposite' of sleeping IS-BY-DEFINITION being awake.] (a priori claim)
C If sleeping is normal, and then it's opposite being awake must have the opposite of its properties. (a priori claim)

But in fact, the property of normality applied to either state is a question of frequency, that is to say, it is an empirical fact that is normal for humans to sleep and to be awake. The properties aren't analogues.

But the equivocation only undermines the rule for drawing the conclusion, which itself would seem to be a false analogy. That is to reason that both terms have opposites means that their opposites share the same properties.

Let's look at another example:

P1. Not in the kitchen is the opposite of being in the kitchen. (a priori claim)
P2. Socrates IS-BY-EXPERIENCE in the kitchen. (a posteriori claim)
E1. [Socrates IS-BY-DEFINITION the opposite of his wife.] (a priori claim)
C. Therefore, Socrates's wife is not in the kitchen.

Here again, the copula is used in two different senses, and we cannot presume that the location of Socrates's wife is the opposite of his, because men and women are in a sense paired in a marriage.

It's a false analogy to presume that two different entities that are opposites have opposite properties.

You've added a second example, and stated correctly, it's not a fallacy.

P1. Whatever is not normal IS-BY-DEFINITION abnormal. (a priori claim)
P2. Being Asian IS-BY-FREQUENCY normal (say, in Asia). (a posteriori claim)
E1. [Among a mixed group of Asians and Caucasians, if you are not Asian, you ARE-BY-DEFINITION Caucasian and vice versa.] (a priori claim)
C. Being a Caucasian (say, in Asia) IS-BY-FREQUENCY abnormal. (a priori claim).

In this case, the argument is correctly analogical because the frequency of two groups DO have opposite properties. In this case, the majority population by definition has the opposite property of the minority population.

This looks like a fallacy of equivocation, exploiting the ambiguity between the "is" of predication and the "is" of identity, as in the following argument:

1. Alice is human
2. Bob is not Alice
3. Therefore, Bob is not human

The ambiguity here is between interpreting premise 1 as "Alice has the property of being human" (predication) and interpreting it as "Alice is identical to 'human'" (identity). Clearly, the former is the correct interpretation, but the argument proceeds as if it were the latter.

The underlying assumption you need to close the argument seems to be that

`if A is B, then the contrary of A is not B`

which is clearly not valid (even if I am not sure about how we may define in general the contrary of)