Is the veracity of a statement contingent on the veracity of the converse of said statement?

Your mom goes to college.

My cat can eat a whole watermelon.

It certainly could be. I never took a formal course in logic, so I have no received wisdom on this. It seems intuitively true, but I am suspicious of it nonetheless (because I trust very little that is posed as a universal truth or generalization) and am trying to think of exceptions.

Meanwhile, putting “veracity of a statement contingent on the veracity of the converse” into Google (without quotes) brought up some interesting links and introduced me to the term “metaphoricity,” so I’m off to pursue digressions.

I’m sorry.. I am feeling slow this morning. :) Could you give me an example?

@3or4monsters

If holding a gun makes a weak person feel powerful, does holding a gun make a person weak? (This is the original context)

No. Holding a gun makes a person powerful. That’s why it’s called fire power. How they feel is irrelevant.

No. Given only the statement that A ->B, then (not B) -> (not A), but B (does not ->) A. Thus, the first statement is true if A and B are both true, in which case the converse is true, and it is also true if B is true and A is false, in which case the converse is false. For the truths of the two statements to be interdependent, you would have to explicitly make the converse part of the statement; the statement must be A -> B AND B -> A

To build on what @Jayne said:

We take the statement: “Holding a gun makes a person powerful,” and rephrase it as, ”if a person is holding a gun, then he feels powerful.” The converse of this, made by switching the antecedent (if…) and consequent (then…) parts of the phrase, is, ”if a person feels powerful, then he is holding a gun.” (The converse of the statement “A implies B” is “B implies A.”)

@grog, what you have there is the contrapositive—the contrapositive of “A implies B” is “not A implies not B.” The contrapositive of “if a person is holding a gun, then he feels powerful” is “if a person is not holding a gun, then he does not feel powerful.”

The truth or falsehood of the original statement does not have any necessary relationship with the truth or falsehood of the converse or the contrapositive. It’s trivial to find an example of this, such as the statement: If it is Sunday, the post office is closed. The converse of this is, if the post office is closed, it is Sunday. But this is not true on national holidays—on Memorial Day, for instance, the post office is closed, and it is not Sunday. The contrapositive is, if it is not Sunday, the post office is not closed. But again, on Memorial Day—a Monday—the post office is closed.

(Logic is much easier to discuss if you avoid emotionally loaded subjects like guns.)

I feel like having a beer now…

@Poser

How they feel can be very relevant, powerless people suddenly feeling a false sense of power can be very dangerous.

No. A statement can exist and be true in isolation.

@grog Either a gun makes them powerful or it doesn’t. How they feel about that power (or lack thereof) is irrelevant to the existence of said power, though it certainly has an effect on what they do with that power.

okay, I shouldn’t feed :(

@TaoSan Maybe, but many questions can accidentally lead to good discussions, as per our previous encounter
Philsophers through the ages have written thousands of words about the nature of “truth”. It is not a subject that can be easily determined here, but the answers that use formulaic (sp?) equations come closest.

What can I say, I smell the MS Office Thesaurus from a mile away :)

Sadly, when transitives are involved…. oh whatever….

@TaoSan hehehehe, Thesaurus is one of my favorite resources, but I like it for the variety it offers, unlike the pretenders we often encounter.

@Yarnlady

:)

No. If it rained, the car is wet does not make true, If the car is wet, it rained.