What is the "term" for a logical argument that states A = B, but B does not necessarily = A?

Question

For instance:

All Catholics (A) are Christians (B), but not all Christians (B) are Catholics (A).

I'm going insane trying to remember what type of logical argument that is. Any help?

Answer 1

http://en.wikipedia.org/wiki/Affirming_a_disjunct is this it? ive been interested in this subject for a while now

okay that might not be it try http://www.nizkor.org/features/fallacies/ wikipedia is confusing the hell out of me lol

Answer 2

The argument in the form A=B, but B not equal to A is not a valid argument. If one states something to be equal, then the inverse has to be equal too. I think the correct relational form to use is rather =>, which means to imply, and sets the implied factor as a function of the other.

The functional effect means that if A implies B, then B does not neccesarily imply A. However, B is a direct function, or product, of A.

The impact of this relationship structure is that if B is removed, then A is removed as well, in this context. So remove the Christians from your example, and the Catholics have no relational value in this context.

I don't know what sort of logic this is, but it can be found in relational theory, as applied to systems analysis.

The philosophical reasoning is one of reductionism, or decomposition.

Answer 3

This is not a "formal" argument structure, but rather a type of categorical proposition called a particular affirmative statement. "Some B are A."

The formal logical argument structure in its most basic form is typically a three part statement of two propositions and a conclusion. An example of a valid argument using the parameters you outline might read:
All Catholics are Christians.
The Pope is a Catholic.
Therefore the Pope is a Christian.

An example of an invalid logical argument might read:
Some Christians are Catholics.
The Pope is a Christian.
Therefore the Pope is a Catholic.

Answer 4

The closest term for what you describe is the 'law of antisymmetry', which states:

If all A are B, all B are A if and only if A=B.

If someone asserted that because all A are B that necessarily means that all B are A, that would be a kind of 'formal fallacy' - the conclusions do not logically follow from the premise.

Hope that's what you're looking for!

Answer 5

The nearest is perhaps.....

Transposition (logic)

Grammatically speaking
A grammatical example traditionally used by logicians contrasting sufficient and necessary conditions is the statement "If there is fire, then oxygen is present". An oxygenated environment is necessary for fire or combustion, but simply because there is an oxygenated environment does not necessarily mean that fire or combustion is occurring. While one can infer that fire stipulates the presence of oxygen, from the presence of oxygen the converse "If there is oxygen present, then fire is present" cannot be inferred. All that can be inferred from the original proposition is that "If oxygen is not present, then there cannot be fire".

Answer 6

This is a job for a Venn Diagram!