Monday, 15 July 2013

Buddhism, Dialetheism and the 'Mind versus Machine' Problem


How quaint the ways of Paradox
At common sense she gaily mocks!




A paradox?  A paradox!
A most ingenious paradox.
We’ve quips and quibbles heard in flocks,
But none to beat this paradox..

 - Pirates of Penzance


The classic essay Nagarjuna and the Limits of Thought by Jay L. Garfield and Graham Priest is available in pdf format at

http://www.thezensite.com/ZenEssays/Nagarjuna/NagarjunaTheLimitsOfThought.pdf

and

 http://math.stanford.edu/~mkahle/Nagarjuna.pdf


The essay shows that there are 'true contradictions' (ie real unresolvable paradoxes known as dialetheia or dialethia) at the limits of logical thought, but the limits of logical thought are not the limits of mind.

At least that's what I think it shows. When I came to the tetralemmas it made my brain hurt and I had to stop thinking and go to the pub. 

Buddhism, Dialetheism and the 'Mind versus Machine' Problem
A computer is a universal machine which can simulate any physical system including any other machine, or the software running on any other machine. If the mind can be shown to possess abilities that no machine has, or can have, then this would be evidence for the Buddhist view that the mind is non-physical.  The opposing 'materialist' view that the mind can be modelled by a computer is known as computationalism.

So is there anything that the mind can do that a machine cannot? Appreciate art? Compose poetry? Feel love and compassion? Lie detection... 

Liar Paradoxes
In philosophy and logic, the liar paradox or liar's paradox (pseudomenon in Ancient Greek) is the statement "this sentence is false." Trying to assign to this statement a classical binary truth value leads to a contradiction.

If "this sentence is false" is true, then the sentence is false, which would in turn mean that it is actually true, but this would mean that it is false, and so on without end.

Similarly, if "this sentence is false" is false, then the sentence is true, which would in turn mean that it is actually false, but this would mean that it is true, and so on without end.


There are similar sentences such as



The Ultimate Truth is that there is no ultimate truth.


Or

Postmodernism proves that all philosophical systems are invalid.


Or  

This sentense contains three erors. There are only two spelling mistakes and the sentence is grammatical so what's the third error? Well it's obviously the factual error in counting three errors when there are only two. So that explains how the sentence comes to have three errors. In which case the sentence is factually correct, hence there are only the two spelling errors. So the sentence is incorrect.


Or consider

The barber shaves everybody who doesn't shave himself. 
Who shaves the barber?

This latter is a simplified form of Russell's paradox, which is




But what's all this got to do with mind versus machine? 

Any machine will represent truth and falsity as discrete states or numerical values. A computer represents the truth of a statement as a single bit.  For exampe TRUE = 1 and FALSE = 0. 
 
You can also have fractional truth values if you are dealing with probabilities. Thus 0.5 is the truth value of an unseen tossed coin being heads. But this actually is the average of the two possible truth values. An act of observation will always resolve the coin as heads or tails. (We'll exclude the coin remaining standing on its edge by assuming we're aboard a trawler in a force nine gale).
 

Artificial intelligence requires numerically encoded truth states to be manipulated and combined to give long chains of logical reasoning.


But when we examine the statements in italics, it's apparent that their truth-states are not numerically encodable and do not lie on a scale of 0 to 1, or even on a scale of 0 to 42. In fact they're off in another dimension. These paradoxical truth-states (known as dialetheia or dialethia) have more of a qualitative, intuitive feel to them than anything quantifiable.  It seems that the human mind can access states which cannot be represented or manipulated within any machine (remember a computer is a universal machine which can simulate any physical system including any other machine).  


If dialetheist truth states were purely inconsequential curiosities, none of this would matter too much.  But as Russell and later Gödel were to show, such dialetheia lie at the very heart of mathematics.  It's also possible that the ability to deal with indeterminate truth states is an important factor in 'open-ended' or non-algorithmic mental processes such as freewill and artistic creativity.


Similar arguments, that the mind can understand what a machine cannot, have been developed by the eminent physicist Sir Roger Penrose, whose work has done much to lead to the 'rediscovery of the mind' which took place among philosophers in the 1990s. 

So perhaps Boolean logical processes implemented on any sort of physical machine are inadequate to describe the capabilities of human mental processes. This limitation will not be solved by hardware improvements. 


No matter how many terabytes, gigaflops, neural nets or iterations of Moore's law we throw at the problem of producing a machine-mind, the difficulties will remain insurmountable as long as the hardware is only capable of dealing with truth values which can be treated as binary or numeric/probabilistic.



But what other hardware architecture is there?



 
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