Emergency question about a formal fallacy...

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I have a question about a formal fallacy, and need a thorough and authoritative response. Smile

A = B
C = B
therefore C = A

Is this not a formal fallacy? Is it not equivalent to :
All A is B
All C is B
therefore, All C is A?

What fallacy is this?

Also,if a persons argument is as follows :

A doohickey is a thingamajiggy.
A whatchmacallit is a thingamajiggy also.
Therefore, a whatchmacallit is a doohickey.

Is this not the same as the first example? And also the second example?

How many fallacies are there in this argument?

It takes another form as well:

If a doohickey is a thingamajiggy, and a whatchmacallit is a thingamajiggy, then a whatchmacallit is a doohickey.

Or is this a case of :
A = B
C = B
therefore C = A?

Would not the valid form be :
a = b
c = b
therefore a = c?

Seems the same argument can be put in symbolic form in two ways, one valid, the other invalid, even though it is the same argument. I know an argument cannot be both valid and invalid at the same time...

Please help somebody. I'm in the middle of a debate and don't want to stick my foot in my mouth!

peace-

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No time to actually type out the entire explanation, but I can provide a link: http://www.cuyamaca.net/bruce.thompson/Fallacies/formalfallacies.asp

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The fallacy in the argument

All A is B
All C is B
Therefore All A is C (or all C is A)

is the fallacy of the undistributed middle. for example all cats are animals all dogs are animals, yet it does not follow that all dogs are cats. membership in set A guarantees membership in B membership in C guarantees membership in B, yet A and C need not share any elements at all.

as for the argument
A=B
C=B
therefore A=C

if what you mean by this is something like things that are equal to the same
thing are also equal to each other like in Euclid's geometry. this is not a fallacy, (or if it is someone should have pointed this out long ago). If line A is equal to line B and line C is equal to line B it does not seem possible that A could not equal C (of course I am referring to the length of the segments A,B,C).
I hope this helps

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Re: Emergency question about a formal fallacy...
I see no fallacy if, when you say A = B you mean that B is A.
In fact, the three propositions can be reduced to the identity principle, A = A.

Next, you say that A = B is equivalent to "all A is B".
But that is wrong. In the first proposition you say that A and B are the same entity. In this second proposition you say the entity A is B. It is very different.
As Dev56 pointed, the second proposition can be applied to statements like: all dogs (A) are mammals (B). That doesn't mean that dogs = mammals. There are mammals that are not dogs, and being a dog is more than being a mammal.
This because the second proposition is a class proposition. As if you say: all that is A belongs to B.

But if you mean by all A is B, that B countains all that A is I think you are making an analytic proposition, like "all entities that can be defined only by the property of having three angles are triangles". And again, there is no fallacy.

But perhaps I am missing something in your statement.

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Re: Emergency question about a formal fallacy...

val wrote:

I see no fallacy if, when you say A = B you mean that B is A.

That's not what people are talking about. Saying that A is a subset of B is not the same as saying A is equal to B, and the former was clearly meant.

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dev56 is correct (and, by the way, welcome to A2K): this is the fallacy of the undistributed middle. The problem that essaias has encountered (and, by the way, welcome to A2K) is the result of confusing "is" with "equals." The term "A is B" is not the same as "A=B." Thus:

A is B C is B therefore A is Cis fallacious, since the middle term (B) is undistributed. On the other hand:

A=B C=B therefore C=Ais correct (to see why, make A=12, B=4x3, C=6x2).

In symbolic logic, one would not use the equals sign to denote "is," and so this kind of confusion would be easily avoided.

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Here's a good example this fallacy:

http://www.able2know.com/forums/viewtopic.php?p=959378#959378

I got sloppy with symbolic shorthand and committed this fallacy.

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I am also confused on this topic I recently posted a similar question. Does anyone know what a VENN DIAGRAM is?

JAne

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A diagram used in set theory. It's used to represent relations between sets.

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Venn diagrams used to be called Oiler Diagrams and looked a lot like a donut.

The outer circle might represent All Mammals and the smaller circle might represent All Dogs as a subset of All Mammals.

Venns overlap circles but not completely.

Where one circle might be All Birds and another might be All Animals with Flight. Some of those circles are going to overlap but Penquins will only be found in the bird circle and not in the Flight Circle.

TTF

TF

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Emergency question about a formal fallacy...

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