In comments and replies concerning the Ontological Argument, a debate opponent made a claim about controversial rule S5 in Modal Logic. I had been rebutting the fallacies of the Ontological Argument, but he was claiming intellectual high ground with this, so I went to his source, the online Stanford Encyclopedia of Philosophy and read on Modal Logic. It didn’t seem difficult, so I read quickly through to S5. I did not see a problem in its formal presentation, but I did with an explanatory example.
I objected on these bases to my correspondent, and he derisively dismissed me, charging that I could not understand these matters so quickly, since he had been studying Modal Logic for many years. I sent an email to the maintainers of the site, and got an ambivalent reply, and reference to some book. I also speculated that S5 in Modal Logic had been invented for the purpose of supporting the Ontological Argument, to which my critic accused me of being a biased, ignorant, obstinator, though not in those words. This morning, in fact-checking myself, I learn that Modal Logic was founded by C.S. Lewis, a well-known apologist for Theism, and for Christianity, in particular.
Since then, I have been pondering this, off and on, but this morning I synthesized my criticisms into this evaluation: Modal Logic is beset with sophistry.
The first problem I had was with the definition of Modal Logic, or, rather, a resort in justifying or explaining it to a Possible Worlds Scenario, without defining ‘possible’. In looking through other resources, I find that ‘possible’ is defined as “existing in some possible world(s)”. This is a circular definition, containing the word that is to be defined. Moreover, the positing of more than one possible world that is not the real world violates the Principle of Parsimony, called Occam’s Razor.
‘Possible’ means being not self-contradictory. Some concept, such as a god, in some definition, may be possible if and only if when all effects, all ramifications of the details of the definition are found to not be self-contradictory, to not be impossible.
The phrase ‘possible world’ was also not defined, but I intuit that it means ‘a set of conditions imagined to be consistent, not self-contradictory’.
Modal logic also deals with the word ‘necessary’, which is defined as ‘existing in all possible worlds, including the real world’, and with constructions of sequences containing ‘necessary’ and ‘possible’. This inclusion is the biggest invitation to sophistry I can imagine, because to say that something is ‘necessarily possible’ or ‘possibly necessary’ is sophisticated ambiguity, the first being redundant, and the second being a contradiction in terms.
Since to be ‘necessarily possible’ means that in all possible worlds, some proposition is seen as possible. At best, this means that in no possible, self-consistent set of conditions, can this proposition be seen as impossible. This is unnecessarily (meaning, ‘not needed’) slamming words together, and multiplying entities, because the only imaginary “world” required is the one in which the proposition is not self-contradictory.
To say that something is possible, in the Possible Worlds Scenario, is to confine it to an imagined ‘world’. To then apply ‘necessary’ to that something breaks it out of that scope, and requires it to be real. Why bother having posited it in a “possible world” to all? One ought just admit to assuming reality of the proposed “something”.
It seems to me that Modal Logicians are wrapped up in their formalism, and fail to apply the common meanings to their words enough to realize that, beyond the basics, their work is sophistry.
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