If it has rained all day, it must be very wet outside.

[…] the night is far gone, the day is near. Let us then lay aside the works of darkness and put on the armor of light.

In which sense does ‘∀p ~(p & ~p)’ cause the tokening of the belief in the subject?

The nation was also at peace. The Cold War had ended before Bill Clinton took the helm, and his presidency had experienced nothing that could be called a major international crisis. Turmoil in the Balkans and Middle East was nothing new. Iraq required attention but no massive deployment of Americans. There had been devastating, but fortunately isolated, terrorist attacks in Africa and in Oklahoma City. But the North Koreans had not invaded South Korea, nor had they lobbed one of their missiles in our direction. Communist China did not invade Taiwan. Libya remained quiet.