If you take 'x is x', that is a propositional function which is true whatever 'x' may be, i.e. a necessary propositional function. If you take 'x is a man', that is a possible one. If you take 'x is a unicorn', that is an impossible one. Propositions can only be true or false, but propositional functions have these three possibilities..
Source:Bertrand Russell: The Philosophy of Logical Atomism, 1918.
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