Friday, 21 November 2014

Coherence

I use Deontic logic (Gk: that which is proper) - a form of symbolic logic - to map legal statements. 

A fundamental axiom of deontic logic is coherence: you should not be obliged to do 2 mutually inconsistent things. 




This axiom of deontic logic is expressed as:
                                 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



My friend  has reminded me of the wonderful soliloquy from Hamlet:

To be, or not to be: that is the question:
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles,
And by opposing end them? To die: to sleep;
No more; and by a sleep to say we end
The heart-ache and the thousand natural shocks
That flesh is heir to, 'tis a consummation
Devoutly to be wish'd. To die, to sleep;
To sleep: perchance to dream: ay, there's the rub;
For in that sleep of death what dreams may come
When we have shuffled off this mortal coil,
Must give us pause: there's the respect
That makes calamity of so long life;
For who would bear the whips and scorns of time,
The oppressor's wrong, the proud man's contumely,
The pangs of despised love, the law's delay,
The insolence of office and the spurns
That patient merit of the unworthy takes,
When he himself might his quietus make
With a bare bodkin? who would fardels bear,
To grunt and sweat under a weary life,
But that the dread of something after death,
The undiscover'd country from whose bourn
No traveller returns, puzzles the will
And makes us rather bear those ills we have
Than fly to others that we know not of?
Thus conscience does make cowards of us all;
And thus the native hue of resolution
Is sicklied o'er with the pale cast of thought,
And enterprises of great pith and moment
With this regard their currents turn awry,
And lose the name of action. - Soft you now!
The fair Ophelia! Nymph, in thy orisons
Be all my sins remember'd.

I have sat here wondering of the precision of his thinking, so long ago. The expression with which it starts might appear to be framed as:
                                       E:  (Ox (or) O(not)x)  
But, of course, here the bard uses OR as exclusive - you cannot 'be' and 'not be' at the same time - a precise reduction to the principle of coherence:
                                      D: (not)  (Ox (and) O(not)x)  

I remembered Lewis Carroll's other book, the one that no one reads:   http://www.gutenberg.org/files/28696/28696-h/28696-h.htm. 




Peter Quinton
Palerang
November 2014
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