What logic is and how it do

Logic is like math using language. Which is rad for me, because language on its own can be too abstract sometimes, and numbers are just annoying.

Trying to find counterexamples

When I was going through 1.5, I tried for about 15 minutes straight to find a counterexample for #8 in section I of the exercises. I failed.

Some T are H

Some H are U

--------------

Some T are U

For instance, the example we used in class with T as lizards, H as reptiles, and U as animals. I also tried replacing T with plants/animals, H with flowers/mammals, and U with dandelions/dogs, respectively

I worked out six possible ways that the argument could be laid out:

Only in the case of the last two is the argument invalid. But so far I can't find a counterexample that would follow either 5 or 6. Frustrating.

EDIT: Just after publishing, I thought of a counterexample that works:

Some lizards are reptiles

Some reptiles are snakes

-------------------------

Some lizards are snakes.

So it is invalid. Problem solved...

[From Friday's 'Boston Globe,' Letters To The Editor]

P1: Peer Nielson's observations observations enable us to begin to gain a useful understanding of China.
P2: Achieving an appropriate mindset is crucial in developing useful foreign policy.
C: Nielsen's op-ed would help to keep US policy toward China om a benign and mutually profitable basis.

Thoughts On Language

The next sentence is true.

The previous sentence is false.

And now we are confused.

Suppose one day human beings were to develop a perfect form of communication? One that is completely logical, where everyone expresses exactly what they mean with no chance whatsoever for misunderstanding, and verbal paradoxes such as the above are literally impossible? Would it be an improvement on our current state, or is the constant interpretation that we all have to perform every waking moment the only thing that keeps us from getting bored?