Thursday, September 01, 2005

Sorities Paradox

The problem of vagueness is derived from the sorities paradox. Here is a typical example of a sorities paradox:

(1) One grain of sand is not a heap.

(2) If one grain of sand is not a heap. [n + 1 is not a heap]

(3) Therefore, 100,000 grains of sand is not a heap.

The step that I reject is (2) maybe 3 or 4 grains of sand is a heap but there seems to be some point at which several (many) grains of sand becomes a heap. Another move made is the reverse march.

(4) 100,000 grains of sand is a heap.

(5) If 100,000 grains of sand is a heap, then 99,999 grains of sand is a heap [n - 1 is a heap]

(6) Therefore, one grain of sand is a heap.

I'm not quite sure where grains of sand become a heap, but there definitely seems to be some type of cutoff where sand becomes a heap.

3 comments:

Anonymous said...

My bling bling ring? Um, prolly 2007. My stud won't be home until fall of 2006 so proposal and wedding will follow in 2007. Yeah, I got a long time to wait. :-(

When's your wedding again? And where will it be?

Di

Justin said...

December 10 in Stanford, IL which is near Bloomington/Normal IL

Anonymous said...

Right, Diana doesn't mind referring to herself in third person. She especially hates it when people refer to themselves in third person while talking baby talk or whispering sweet nothings in their lovers' ears or whatever. Diana thinks these people are bonkers. Diana is now going to stop referring to herself in third person.

HA!