The Possibility of Necessity
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Some things are logically possible (LP). Others are physically possible (PP) and yet others are Physically Actual (PA). The things that are logically necessary (LN) are excluded from this discussion because they constitute a meta-level: they result from the true theorems in the logical systems within which LP, PP and PA reside. In other words: the LN are about relationships between the three other categories. The interactions between the three categories (LP, PP, PA) yield the LN through the application of the rules (and theorems) of the logical system within which all four reside. We are, therefore, faced with six questions. The answers to three of them we know – the answers to the other three are a great mystery.
The questions are:
That something exists implies that it must also be possible. But what is the relationship between necessity and existence? If something is necessary – does it mean that it must exist? It would seem so. And if something exists – does it mean that it was necessary? Not necessarily. It really depends on how one chooses to define necessity. A thought system can be constructed in which if something exists, it implies its necessity. An example: evolutionary adaptations. If an organism acquired some organ or trait – it exists because it was deemed necessary by evolution. And thought systems can be constructed in which if something is of necessity – it does not necessarily mean that it will exist. Consider human society.
There are six modes of possibility:
There seems to be a wall-to-wall consensus today that every PP is also PA. One of the interpretations to quantum mechanics (known as the “Many Worlds” interpretation) claims that with every measurement of a quantum event – the universe splits. In one resulting universe, the measurement has occurred with a given result, in another – the measurement has yielded a different result and in one of these universes the measurement did not take place at all. These are REAL universes, almost identical worlds with one thing setting them apart : the result of the measurement (its very existence in one case). By extension, any event (microcosmic or macrocosmic) will split the universe similarly. While the Many Worlds interpretation remained in the fringes of institutionalized physics – not so the “possible worlds” interpretation in formal logic and in formal semantics.
Leibniz was ridiculed (by Voltaire) for his “the best of all possible worlds” assertion (God selected the best of all possible worlds because, by his nature, he is good). But he prevailed. A necessary truth – logicians say today – must by necessity be true in all possible worlds. When we say “it is possible that something” – we mean to say: “there is a world in which there this something exists”. And “this something is necessary” is taken to mean : “this something exists in all possible worlds”. The prominent logician, David Lewis postulated that all the possible worlds are actual and are spatio-temporally separated. Propositions are designations of sets of possible worlds in which the propositions are true. A property (being tall, for instance) is not a universal – but a set of possible individuals carrying this property, to whom the relevant predicate applies. Lewis demonstrated rather conclusively that is no point in using possible worlds – unless they exist somewhere. A logical necessity, therefore, would be a logical proposition which is true in all the logically possible worlds. According to Lewis’s S5 logical modality system, if a proposition is possible – it is necessarily possible. This is because if it true in some possible world – then, perforce, in every possible world it must be true that the proposition is true in some possible world. Models of T validity reasonably confine the sweep of S5 to worlds which are accessible – rather to all the possible worlds. Still, all validation methods assume (axiomatically, in essence) that necessity is truth.
Is every LP also PP? I think that the answer must be positive.
Logic is a construct of our brains. Our brains are physical system, subject
to the laws of physics. If something is LP but not PP – it would not have
been able to appear or to otherwise interact with a physical system. Only
PP entities can interact with PA entities (such as our brains are). Thus,
every logically possible thing must form in the brain. It can do so, only
if it is physically possible – really, only, if in some limited way, it
is also physically actual. The physically possible is the blueprint of
the physically actual. It is as PP (PA blueprints) that they interact with
our PA brain to produce the LP (and later on, the PA). This is the process
of human discovery and invention and a succinct summary of what we fondly