The Possibility of Necessity

By: Dr. Sam Vaknin

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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:

  1. Is every LP also PP?
  2. Is every LP also PA?
  3. Is every PP also PA?
  4. Is every PP also LP?
  5. Is every PA also LP?
  6. Is every PA also PP?
Every PP must be also LP. The physical world is ruled by the laws of nature which are organized in logical systems. The rules of nature are all LP and whatever obeys them must also be LP. Whatever is PA must be PP (otherwise it will not have actualized). Since every PP is also LP – every PA must also be LP. And, of course, nothing impossible can actually exist – so, every PA must also be PP.

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:

  1. Logical (something is possible if its negation constitutes a contradiction, a logical impossibility).
  2. Metaphysical (something is possible if it is consistent with metaphysical necessities)
  3. Nomological (something is possible if it is consistent with scientific laws)
  4. Epistemological (something is possible if it sits well with what we already know)
  5. Temporal (something is possible if it is consistent with past truths)
  6. Something is possible if it is conceivable to a rational agent
Most of these modes can be attacked on various grounds.
  1. There are impossible things whose negation would also yield a contradiction.
  2. We can commit errors in identifying metaphysical necessities (because they are a-posteriori, empirically derived). A metaphysical necessity is an objective one and is stronger than a logical necessity. Still it can be subject to an a posteriori discovery, from experience. And experience can lead to error.
  3. Scientific laws are transient approximations which are doomed to be replaced by other scientific laws as contradicting data accumulates (the underdetermination of scientific theories by data)
  4. What we already know is by definition very limited, prone to mistakes and misunderstandings and a very poor guide to judging the possibility or impossibility of things. Quantum mechanics is still considered counter-intuitive by many and against most of the things that we “know” (though this is a bad examples: many things that we know tend to support it, like the results of experiments in particles).
  5. The temporal version assumes the linearity of the world – the past as an absolutely reliable predictor of the future. This, of course, is never the case. Things are possible which never happened before and do not sit well with past “truths”.
  6. This seems to be the strongest version – but, alas, it is a circular one. We judge the possibility of something by asking ourselves (=rational agents) if it is conceivable. Our answer to the latter question determines our answer to the former – a clear tautology.
To answer the first three of the six questions that opened our article – we need to notice that it is sufficient to answer any two of them. The third will be immediately derivable from the answers. Let us concentrate on the first and the third ones : Is every LP also PP and is every PP also PA?

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 call: “civilization”.