Entertain a proposition:
It is impossible that there be impossibility.
another:
There can be no state X such that the existence of X is impossible.
or
It is impossible that the statement, “There can be no state X such that the existence of X is impossible” is false
Are these equivalent expressions? What are the truth values?
To the first question, no they are not all equivalent- not by a long shot. To the second question the second proposition is trivially true iff we grant a theory of multiverse alternalities. To the first proposition, the truth value is to be determined, but not be emperical means, but by logic.
The first proposition might seemingly lead to an apparent paradox by the familiar avenue of self-referentiality.
There are so many things, states, and conditions that we use the “impossible” descriptor with:
Impossible configurations. Emperical impossibilities. Syntactic impossibilities. Mathematical impossibilities. (Ethical impossibilities? Aesthetic impossibilities? Epistemic impossibilities?) Physical impossibilities.
Does what cannot be, far far outnumber what can be or is?
Look at the metaphysics of forecasting: doesn't the number of possible outcomes astronomically outnumber the set of probable outcomes? Further, doesn't the universe of impossible outcomes far far outnumber the universe of possible outcomes? This by reason that they are not bound by obedience to physical or even logical restrictions? If this is so, then the actual world we occupy, where all things are not only lawful and possible, but highly probable as well, is a microscopically small region in a vast universe of improbabilities and impossibilities. What is the likelihood we should find ourselves in such a small neighborhood? Sounds a little like that self-validating Anthropic Principle of which we all should be skeptical.
Suppose, referring back to the second proposition, we are asked to point to an instance of something impossible. We could not do so obviously. Anything that could be pointed out as existant and impossible would by definition not be both. So the second proposition is trivially true. If that is the case then the third proposition is necessarily true. What about the first?
It is impossible that there be impossibility.
What a lot of difference a universal quantifier makes! Suppose we rephrase it to an equivalent expression:
There is no possible world where the term “impossible” refers to any existent state of affairs
In plain language wouldn't that translate to saying that “impossibility” having no possible referent is meaningless? Just nonsense?
But we certainly seem to understand proposition one. It certainly seems intelligible. But that could only be if it were false.
To resolve this, let's rephrase proposition one to this:
There must be some X such that X exists.
If that's an equivalent statement rather than a corollary, our problem goes away. But how do we prove it?
Can we even prove that we exist? Descartes thought he had a demonstration, but was it just a dream within a dream?
Face it, it's highly improbable that we exist. So who's writing this? Who's reading it?
I'm changing my major to Engineering!
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(a tip of the hat to the sophists of all eras!)
Interesting ideas, Michael. A line that has been echoing in my thoughts from Red Pine's translation of "The Zen Teaching of Bodhidharma"
"Whoever knows that the mind is a fiction and devoid of anything real knows that his own mind neither exists nor doesn't exist." p.53
Perhaps you/I/we/everyone neither exist nor do not exist if that makes sense.
"Merrily doth the logick-er weave his deceitful web!"