# Gensler star test: if 'all A* is B' TF 'all B is A*' is invalid; coincidence or general rule of thumb?

Like the title asks, I wonder if the invalid conclusion would tend to work if the letters of the premise were simply flipped to draw the simple conclusion?

Trying to logically parse the statement: “Lie” means “false statement” (taken from Gensler's intro to Logic), for example, I would reason out that:

``````all L* is F
TF all F is L* (invalid)
``````

Logically invalid seems of course right, since not all falsehoods are lies per se.

But then I guess if 'all L is F' were a valid conclusion/statement, then L=F and so there would only be either L or F and not really both?

Sorry for the n00ber question, but I am just getting a start in logical thinking and trying to determine when reading single statements if there is a way to test their validity without knowing the premises upon which they were based?

• What? Can you clarify your notation and what you're trying to say? I can't make heads or tails of it other than to note that the converse of a statement need not have the same truth value as the original statement. That is, all X are Y does not imply all Y are X. Beyond that, I don't understand your question. Jan 27 '14 at 0:52
• ps -- maybe this will help. harryhiker.com/lc/docs/star.htm Jan 27 '14 at 1:06
• Even in the terms of the Gensler Test, you should still star F in the conclusion, since it is a distributed term. And in fact you should not star L in the conclusion, since it is not. This would leave you with no stars on the right hand side, which the Gensler test would suggest makes it invalid. Feb 28 '14 at 11:41

Gensler's star test is a little confusing and in cases I can think of, unnecessary.

A very simple way to check for logical validity in a structure is to substitute other words or phrases into the structure. Basically, try and find an instance in which the premises would be true and the conclusion false.

``````So here is your logical structure (basically):
P: All A is B.
C: All B is A.
``````

Can you think of a instance where the premise would be true and the conclusion false? I can:

``````P: All cats are mammals. (T)
C: All mammals are cats. (F)
``````

In this example, the premise is true, but the conclusion is false. Our initial structure has just been proven invalid.

No:

I guess if 'all L is F' were a valid conclusion/statement, then L=F and so there would only be either L or F and not really both?

"All L is F" does not entail that L=F. Otherwise "all women are human" would entail that "woman=person" but that is not so.

Yes, depending on the statement:

In standard formal logic, there are statements like A IMPLIES A that always evaluate as true (without knowing anything about the nature of "A", just based on structure), statements like A AND NOT A that always evaluate as false and contingent statements like A OR B that depend on what A and B are (or on what else has already been established).

Your statement is contingent. You can select values that make it evaluate as true, but it is not a reliable general rule.

The most common way of establishing which of the three categories a statement falls in is as follows: If the statement is self-contradictory, or can be simplified to yield a contradiction, it is "logically false". If assuming that the statement is false leads to a contradiction, it is "logically true". If neither yields a contradiction, the statement is contingent.