Every poem about thunder was written under the protection of a roof, or, at the very least, an empty sky Nov 23, 2009

"Every poem about thunder was written under the protection of a roof, or, at the very least, an empty sky" asserts that something is true about each poem ever written about thunder. Specifically, that such poems were written under an empty sky or under the protection of a roof. Symbolically:

p ( Pp (Rp Sp) )

where

Px x is a poem about thunder
Rx ≡ x was written under the protection of a roof
Sx ≡ x was written under an empty sky

The truth of this sentence is time-dependent. It may have been true in 1872, but once Johannes Heimmacher stepped out of his front door and started jotting on that napkin in the rain, it became false. It seems so likely that someone, over the course of human history, has written a poem about thunder while outside on even a cloudy day, that it seems this statement is surely false. More rigorously, it is easier to prove this sentence's falsity than its truth. To show that it is false, we only need to display one poem about thunder which was neither written under an empty sky, nor under the protection of a roof. To show that it is true, we must demonstrate that no such counterexamples exist—i.e., know the conditions under which every poem about thunder was written. Even if we had this information for the whole of humanity, we are still left with an infeasible task unless we can prove that extra-terrestrial life-forms do not exist or that they exist but that none have written poetry about thunder (which includes but is not limited to the cases that they do not conceive of thunder, that they do not have poetry, or that they do not write their poems). Additionally, assuming that there are areas of the universe extant beyond our current perception, due to light and thus information not yet reaching us, it seems impossible that we could make the necessary observations. And that's leaving out all arguments revolving about meaning and interpretation of the predicates themselves, such as would be involved if we found a planet with a poem about thunder encoded as craters in its surface.

Thus I am confident in asserting the opposite,

¬∀p ( Pp → (Rp ∨ Sp) )
= p ( ¬(Pp → (Rp ∨ Sp)) )
= ∃p ( Pp ¬(Rp ∨ Sp) )
= ∃p ( Pp ∧ ¬Rp ∧ ¬Sp )

= There exists a poem about thunder which was neither written under the protection of a roof nor was it written under an empty sky.

So let me return to the original statement. For convenience, I shall take WUROS to mean "written under the protection of a roof, or, at the very least, an empty sky." Thus the original statement is: "Every poem about thunder was WUROS." A more difficult statement to resolve would be one that incorporates the time-dependence, such as: "There has been a time when every poem about thunder was WUROS." If we assume that time can be ordered (i.e., for any two moments we can decide which came first), then it follows that there was a first poem about thunder which satisfied the writing conditions. That is, unless two or more such poems were written at the exact same moment. However Einstein's relativity throws a wrench in here—according to the relativistic model, we cannot order time alone. Luckily, I believe it is possible to order spacetime. Assuming that, we have: "There has been a spacetime when every poem about thunder was WUROS." Of course, now we hit the difficulty we experienced with the original statement—it is impossible for us to check this due to the possibility of a counterexample existing beyond our perception.

Exercise to the reader: Consider the metaphysical possibility of eternal recurrence, against whose circularity 'ordering' seems to have little meaning.

Now consider the opposite: "There has been no spacetime when every poem about thunder was WUROS." Equivalently: "At any spacetime, there had been a poem which was not WUROS." It follows that this statement asserts that there are an infinite number of non-WUROS poems, extending into the 'past'. To disprove it, we would need to show that there are only a finite number of such poems, which is again impossible due to our limited perception. Of course it is easy to construct such statements: "There was a spacetime when raincomplex didn't ever exist." You can't prove I didn't.

dedicated to Bertrand Russell