Writing Out Arguments and Logical Forms Facillitates Understanding

 Thhe following could apply to learning a language too.

It seems that the logical memory device known as "Cesare" goes like this:

1) No P are M

2) All S are M

3) Ergo, no S are P

The argument's validity can be demonstrated by means of a reductio ad aburdum argument (also known as reductio per impossibile):

1a) No P are M

2a) Some S are P

3a) Ergo, some S are not M

3a) contradicts 2) and 2a) contradicts 3). Notice the false conclusion as well in the reductio example.

So, it helps to write these things out and clarifies what's happening in arguments and language. Consulting Aristotle's square of opposition might shed some additional light on what's happening in these arguments.