The GRE's and Logic

A friend of mine too the GRE this past saturday, and her "argumentative" essay question was pretty fascinating for us budding logicians. I'll briefly explain the argument, and go from there.

To condense the prompt, the argument is as follows:

P1. If you give students less homework, they will get better grades.
P2 The students got better grades.
Conclusion. It was because the students received less homework.


Now, that is the fallacy of affirming the consequent, which we all know is a big no-no. But, what are we to do when we come across arguments that are formally invalid? Well, I was speaking to Matt after class today, and he suggested that the next step is to allow for intellectual charity and try to help revise the argument in a way that makes sense.

I'm not sure where I was going with this post, but I found it interesting for the course!

Determining True Premises

One of the really wonderful things about formal logic is that when the argument is structured properly, and the premises are true, we can believe with great amounts of confidence that the argument is valid and therefore the answer is true. However, there is the problem of the premises themselves.

How, exactly, are we to determine whether or not a given premise is true? I mean, we can't really use Formal Logic and deductively prove a premise; that would just exponentiate the problem. Is there a particular means in logic to show that a given premise is actually true? If there isn't, what hope do we have of learning anything about the world from Formal Logic?

The Inclusive "Or"

I found it really fascinating in our class experience that the "Or" function can also include both ideas. for example PvQ could also be P and Q. Why exactly do we use that function and what sense does it really make? Obviously, it make's DeMorgan's make sense, but it seems like there must be an actual reason for the inclusion.

I'm pretty sure I read somewhere that the ancient Greek Stoics used the "Or" function in the exclusive, and it seems that modern English language conventions do the same. So, why the change?

The Merits of Logic

Wednesday in class we discussed the benefits of being able to take a given piece of text, then diagram the argument in a way that the premises flow, in order, to the conclusion. Overall we determined the benefits of applying logic to issues outside of deductive formal proofs.

However, I have a different question to ask.

Is there a way to reap the benefits to organizing formal proofs in everyday, non-philosophy classroom discussion? Do the rules of logical inference, the structure of the arguments, and formal (as opposed to informal) fallacies benefit the rest of our studies in college? I'm not sure of an answer, but I'd love to hear what you all have to say.