Which logical fallacy is this?

[Gfactor]

@John Mace

The last sentence in what you quoted from me is why.

To show, mathematically, that AC = UM (or not).

Just a quibble, but math and logic are different. You can’t prove a logical statement, “mathematically.” Though, mathematical proofs sometimes involve symbolic logic. I get what you mean though.

I’m afraid I am too tired today, to give you a definitive answer (getting old sucks). Generally, they are getting at different things. But if you read the site about translation, you may find a way to answer the question.

[Gfactor]

@John Mace

The last sentence in what you quoted from me is why.

To show, mathematically, that AC = UM (or not).

Ok. Here, more to the point.

All giraffes are tall=All A are C
All John Maces are tall=All B are C
Therefore all John Maces are giraffes=All B are A

Or more formally,
If A, then C
If B, then C
Therefore, if B, then A

AC would be

If A, then C
C
Therefore A

And here is a long quote explaining UM

Undistributed Middle Term

AKA:
Undistributed Middle

Type:
Syllogistic Fallacy

Form:
Any form of categorical syllogism in which the middle term is not distributed at least once.

Example:
“[O]ne patient…concluded that there are money-trees because ‘money is green [in the United States] and so are trees, so money must grow on trees.’”
Context of the Example

Counter-Example:
"The 29 students in Mr Strang’s classroom gravely considered the two sentences scrawled across the freshly washed blackboard:

All A’s are C’s.
All B’s are C’s.
"‘The apparent conclusion–that all A’s are B’s–does have a certain allure, a kind of appealing logic.’
"Mr Strang blinked myopically, his wrinkled face resembling that of a good-natured troll. Then he whirled, and his chalk drew a large screeching X through both sentences.

“‘Of course,’ he snapped, ‘it’s also dead wrong. Its error can easily be verified by substituting “teenager” for A, “ostrich” for B, and “two-legged” for C in the original premises. Thus, all teenagers are two-legged, all ostriches are two-legged, and therefore all teenagers are ostriches. I doubt you’d accept that conclusion.’”

(William Brittain, “Mr Strang Accepts a Challenge”, from The Mammoth Book of Locked-Room Mysteries and Impossible Crimes, pp. 349-50.)

Syllogistic Rule Violated:
In a valid categorical syllogism, the middle term is distributed in at least one of its occurrences.

Exposure:
Undistributed Middle is one of the most famous fallacies, and is sometimes used as a synonym for “fallacious argument”, that is, some people know that an undistributed middle is somehow logically bad, and mistakenly think that any bad argument must have one. In other words, they seem to reason as follows:
All arguments with undistributed middle terms are bad arguments.
This is a bad argument.
Therefore, this argument has an undistributed middle.
This argument is a bad argument because it has an undistributed middle term, namely, “bad arguments”!

I say they are different.

[David_Simmons]

@hegel

I cannot remember the name of this logical fallacy: “I am tall; giraffes are tall; therefore; I am a giraffe.”

John Mace is correct. It is the fallacy of the undistributed middle. The class of tall things is undistributed in that not all tall things are giraffes.

Guilt by association arguments are of this type.

[John_Mace]

@Gfactor

Just a quibble, but math and logic are different. You can’t prove a logical statement, “mathematically.” Though, mathematical proofs sometimes involve symbolic logic. I get what you mean though.

I’m afraid I am too tired today, to give you a definitive answer (getting old sucks). Generally, they are getting at different things. But if you read the site about translation, you may find a way to answer the question.

Yes, sloppy wording on my part. I wasn’t exactly sure how to state it precisely, but as you said, you got what I meant. Thanks for the cites. I’ll give them a look. Guess I was hoping someone would just walk me thru it.

[summerjack]

Ionesco pointed this out in Rhinoceros as a syllogistic fallacy. I think like “undistributed middle” though.

[hyjyljyj]

All giraffes are tall.
I AM a giraffe.
Therefore, I’m having a devil of a time typing this.

:^D) I’m being facetious, of course. I’m having someone else type it for me in exchange for letting them play with my 12-inch blue tongue.

---

Thanx to all for clarification of the syllogistic fallacy discussed in this thread.

[ccwaterback]

In the set of tall things we find you and a giraffe. Two things belong to the same set therefore they are equal? This is most definitely a logical fallacy.

Isn’t this the same thing?: A implies C, B implies C therefore A = B. There are cases where A = B is true, but the statement is general is false.

[ccwaterback]

Example 1:

2 oranges + 2 oranges is a group of 4 oranges.
1 orange + 3 oranges is a group of 4 oranges.

I think we can agree: 2 oranges + 2 oranges = 1 orange + 3 oranges.

Where on the other hand …

2 oranges + 2 oranges is a group of 4 round things.
1 basketball + 3 basketballs is a group of 4 round things.

But certainly …

4 oranges are not the same round things as 4 basketballs.

So, in this case, it depends on the definition of the group.

Example 2:

This flame is exactly hot enough to boil water.

This other flame is 100 degrees C and it is exactly hot enough to boil water.

The two flames are the same temperature, the temperature that is exactly hot enough to boil water, and they belong to the set of all things at least hot enough to boil water.

So in this case, A implies C, B implies C and A is indeed equal to B.

[shijinn]

hegel, a Registered User, posts on the sdmb;
i also post on the sdmb; therefore, i am a Registered User?

[Urban_Ranger]

@shijinn

hegel, a Registered User, posts on the sdmb;
i also post on the sdmb; therefore, i am a Registered User?

That’s correct.

If you derived “I am hegel” though, that’d be a fallacy.

[shijinn]

but i’m not a Registered User! i’m only a member like everyone else.

[Urban_Ranger]

@shijinn

but i’m not a Registered User! i’m only a member like everyone else.

That’s because all Members are Registered Users.

[Gfactor]

@ccwaterback

In the set of tall things we find you and a giraffe. Two things belong to the same set therefore they are equal? This is most definitely a logical fallacy.

Isn’t this the same thing?: A implies C, B implies C therefore A = B. There are cases where A = B is true, but the statement is general is false.

Ok. There are really three concepts getting mixed up here.

Implication–A implies B. If A implies B, then B is true every time A is true. Put another way either B is false, or A is true.

Mathematical Equivalence–A=B. The numerical value of of A is the same as B. Again, this can be true or false. But it has little place in symbolic logic.

Material equivalence. A, if and only if, B. This means that A implies B and B implies A. They go together, and if one is true, then so is the other.

In the example given above, A and B may be true. A=B is probably a meaningless statement, becuase A and B are not numbers, but truth valued statements about the world, and A implies B is false because we can have B without A.