What hath God Wrought?

I suppose I'm destined to become that which I hate - A person with a blog who does not bother to update it. Despite the fact that there are hardworking people out there desperately trying to avoid doing hard work. They need blogs to divert their productivity. And I will likely fail them.

About the title

I stumbled into the phrase “Vacuously True” in a class. It was a term used in passing. I decided to look it up and it tickled me. The context I originally saw it in was first order logic.

If p implies q, and not p. Then p implies q is true whether or not q is true.

A truth table might help clear that up for the mentally deranged.

The term basically means “Ok, yeah, that’s technically true, but it doesn’t really tell you anything.

For a more linguistic example try substituting these phrases for the p’s and q’s

p = “There is steak on the table”
q = “Dawn will eat it”

So in the first row of the truth table where both p and q are true, so p→q would read:
“If there is steak on the table then Dawn will eat it”. True enough.

The second row would read:
“If there is steak on the table then Dawn will not eat it.” This is obviously false and the third column confirms it.

The third row simply states:
“If there is not steak on the table then Dawn will not eat it.” This would cover the rare case of us not having steak and Dawn not being in the mood for steak.

The forth row is the interesting row:
“If there is no steak on the table then Dawn will eat it.” Does Dawn bend the rules of logic to win a free steak dinner? This statement is vacuously true. It basically says that she will eat all the steak that isn’t there.

The statement is true but gives you no real information. You can use that as a metaphor for this blog.

Also don’t try to use first order logic as a way to dupe a Dawn into thinking they just had a steak dinner if there is no steak on the table. That can get you a pretty nasty bite.