Wikipedia: History of Goedels ontological proof

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Changed: 13,22c13,23

The proof uses [modal logic]? which distinguishes between
necessary truths and contingent truths. A truth is necessary
if it cannot be avoided, such as 2 + 2 = 4; by contrast, a contingent truth "just happens to be the case", for instance "more than
half of the earth is covered by water". In the most common
interpretation of modal logic, one considers "all possible worlds". If
a statement is true in all possible worlds, then it is a necessary
truth. If a statement happens to be true in our world, but is not true
in all other worlds, then it is a contingent truth. A statement that
is true in some world (not necessarily our own) is called a
possible truth.

The proof uses [modal logic]? which distinguishes between necessary truths created by definitions and
contingent truths inferred from observations of a world.
A truth is necessary if it cannot be avoided, such as 2 + 2 = 4;
by contrast, a contingent truth "just happens to be the case",
for instance "more than half of the earth is covered by water".
In the most common interpretation of modal logic, one considers "all possible worlds".
If a statement is true in all possible worlds, then it is a necessary
truth.
If a statement happens to be true in our world, but is not true
in all other worlds, then it is a contingent truth.
A statement that is true in some world (not necessarily our own) is called a possible truth.

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Changed: 37c39

# If P₁, P₂, P₃, ... are positive properties, then the property (P₁ and P₂ and P₃ ...) is positive as well.

# If P₁, P₂, P₃, ... are positive properties, then the property (P₁ AND P₂ AND P₃ ...) is positive as well.

	Revision 8 . . October 21, 2001 6:45 am by Damian Yerrick [another angle on necessary vs. contingent]
	Revision 7 . . October 20, 2001 10:55 pm by (logged).253.128.xxx [Fix typos]