In Math 54 section we talked today about subspaces and that any non-empty subspace has the zero vector but any empty space contains nothing but it in itself is a space. my GSI gave the example:

*“All the elephants in this room are pink”*

Is this a true statement?

According to my GSI, it’s a true statement simply because there are no non-pink elephants to counterexample (yes, i just verb-ified that. shoot me.) this claim so it must be true, he mentioned logic as a class to further explore this, which is known formally as a “*vacuous truth.*“

**<Sys Error> Divide by zero, explodes at infinity**

As he went on, something kept bothering me and this is why I’m writing here. *There are no elephants in the room to talk about*. Intuitively, it’s like dividing about zero, seems to be a trivial statement. Perhaps it’s true in a logical sense but the absence of a counter example verifying something to be true seems to be suspiciously inductive in nature.

What is truth? surely if all there is is mathematical truth then this “flawed” kind of truth is fine. but to profess to the existence of an absolute truth as a logical universe laid out by an intelligent and infinitely wise creator, this bothers me to an extent. Sure, for now I’ll put this away and think about it when I have the time to come up for air. **For now, There are no elephants to be pink in the room.**

Closing Thoughts:

Faith is knowing something to be true and silencing the emotions that on their own accord attempt to assault those notions you know to be true”

-C.S. Lewis,

Mere Christianity(Paraphrased)

Contemplatively,

Tim

### Update (03.13.08)

My good friend has posted some articles of interest on his site actually explaining about types of truth

Types of Truth (including vacuous)

Modus ponendo ponens & Modus tollendo tollens (first 2) (“affirms by affirmation” and “denies by denial”)

Pingback: Mathematical Logic « >> Math Jesus Freak <<