Monday, 7 May 2018

On Coherence

Every lecture or series of lectures, should start with a reminder of our fundamental rule: a rule that is both intuitive and experimental, and which sits at the root of formal systems of logic or pragmatic rules/causal-based systems of thought.

In everyday language we call the rule 'coherence', and we regard it more highly than any other rule.

Coherence is found in all sorts of places. Hamlet spoke to himself in William Shakespeare's play

"To be, or not to be, Ay there's the point,
To Die, to sleep, is that all? Aye all:
No, to sleep, to dream, aye marry there it goes,
For in that dream of death, when we awake,
And borne before an everlasting Judge,
From whence no passenger ever returned,
The undiscovered country, at whose sight
The happy smile, and the accursed damn'd."

This version of the soliloquy (you may not have seen it in this older form) is the theater script, which subsequently was cleaned up for publication as the more recognizable: "To be, or not to be, that is the question".

Lots of actors and English academics agonize over this bit of writing, which is very clever, and which sets out a complex argument about coherence: you cannot be dead and alive at the same instance. If you appear to be dead and alive at the same instance you are probably just asleep. But, if you wake up dead, you aren't in Texas anymore.

The soliloquy in fact derives from the writing of a medieval thinker, William of Ockham, a Franciscan monk and troublemaker. You may have come across the 'Name of the Rose', a great medieval whodunit about a monk named 'William of Baskerville' - who in character and mission looks a lot like Ockham. Originally written by Umberto Eco (a troublesome Italian professor of semiotics), the story was then put to film by Jean-Jacques Annaud (starring Sean Connery as William of Baskerville).

William of Ockham is famously remembered for his method of thinking. Today we remember him through 'Ockham's Razor', a principle that is sometimes summed up as "one should always accept as most likely the simplest explanation that accounts for all the facts", although William stated it differently:
"It is vain to do with more what can be done with fewer"
"Plurality should not be assumed without necessity"
"No plurality should be assumed unless it can be proved by reason, experience, or infallible authority."
Sherlock Holmes is credited with less obvious corollary, "when you have eliminated the impossible, whatever remains, however improbable, must be the truth".

In fact, a lot of William's razor sharp thinking was suppressed by the medieval church as a bit of a by-product of William's troublesome nature (he had a naive belief in the good and truth and thought they would always prevail) and the great debate of the time about whether the Christ, Jesus lived in poverty because he thought that was a good thing or whether it was just a bit of bad luck, and whether all the wealth of the 'poor' Franciscan order was not owned by the Franciscans but owned by the Church of Rome.

At the forefront of William's thought is the central tenant of coherence, the proposition that: All things are possible for the Divine, except those that involve a contradiction (Quodliberta VI, q6). He made two other important observations. Firstly, the Divine can do all things directly that might be seen indirectly (Reportatio II, q19). Truth is only self-evident, revealed, experienced, or deduced by reason (Ordinatio, d30, qIE).

The statement of coherence runs through most ancient, medieval and modern thought, from Aristotle to Boethius to William to Shakespeare to Eco.

I frequently use a form of symbolic language called Deontic logic (Gk: "that which is proper") to map complex legal statements or explore ethical propositions. In deontic logic, coherence (which is there regarded as a 'fundamental axiom') is expressed pictorially as in the image below. The image 'translated' means:
D: (not) (Ox (and) O(not)x)
The symbols mean:
Ox – It is obligatory that x
O(not)x – It is obligatory that not x

As a fundamental principle of law, you should not be obliged to do 2 mutually inconsistent things. Similarly, in formal logic, there is no thing which is one thing and (not) that thing. If you find an example which appears to contradict this rule, a short examination will discover that 'the thing' has been mis-described or the attribution is mistaken.

(Introduction to lectures on Customary Legal systems in South Eastern Australia, Canberra 2017)
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