# Identify the fallacy: X has red hair. Females have red hair. Therefore, X is female

Person A has trait X, therefore person A is group Y.

Therefore, anyone with trait X is group Y.

What I'm trying to show is that Person A has red hair. Females have red hair. Therefore, person A is female. This is obviously not true, hence what is the fallacy of this called?

Referring to Aristotelian Syllogism, a "typical" case of fallacy is the Fallacy of the undistributed middle.

The argument :

All z is B

All y is B

Therefore, all y is z

is not valid.

In your case you have an individual term in place of a general one, but the fallacy is basically the same; the argument :

All Chinese are men

Socrates is a man

Therefore, Socrates is a Chinese

is not valid.

• But this is not the syllogism in play. He is taking "All A are X", and "Some Y are X", and getting "All A are Y". Which is even less valid.
– user9166
Oct 8, 2015 at 19:10

What you have is the following:

A is B, Some C are B. Therefore, All A are C.

We cannot use 'All C are B' because 'All females have red hair' is not true. Also, it does not yield a contradiction. Structurally there is nothing wrong with: 'A is B, All C is B. Therefore, All A are C'.

If 'A is B', it means they have a property in common, in this case B [the property of being redheaded]. We can treat them as equal, A = B.

Some C are B = Some C are A

Thus, we can rewrite it as:

Some C are A. Therefore, All A are C.

We have now found the contradiction, namely:

'All' ≠ 'Some'

Structurally,

A is B, Some C are B. Therefore, All A are C.

is not valid. We cannot use this structure to deduce a conclusion.

Edit:

The fallacy is called the undistributed middle. In this case the problem is:

All Z is B, Some Y is Z Therefore, all Y is B

If we add the Z and Y to

All A is B Some C is B Therefore, All A is C

we get:

All A is B [Z] Some C [Y] is B [Z] Therefore, All A is C [Y]

We rearrange and compare:

All Z is B, Some Y is Z Therefore, all Y is B

with

All B [Z] is A, Some C [Y] is B [Z] Therefore, All C [Y] is A

and conclude that the problem is related to the fallacy of the undistributed middle.

• A is B, where B is an adjective, is nothing like A = B, where A and B are both nouns. "X is red-haired" does not mean that X is just like all the red-haired or that any other the red-haired person necessarily has anything beyond that in common with X.
– user9166
Oct 12, 2015 at 19:24
• @jobermark Is Socrates like all mortal men? Does all mortal men like the same food? Does all mortal men love the same woman? Oct 15, 2015 at 8:50
• Exactly, having a property in common is not being the same. So "We can treat them as equal, A = B" is misleading. Also "Structurally there is nothing wrong with: 'A is B, All C is B. Therefore, All A are C'." makes no sense, unless "A is B" means A = B, but it only means that when A and B are both objects. Structurally it is incorrect when B is a property, which it is.
– user9166
Oct 15, 2015 at 14:54