Saturday, 9 June 2012

Apoha, Universals in Buddhist Logic, Stencils and the Game of Twenty Questions



The problem of 'universals

- When you see a small feathered creature perched in a tree, how do you know it's a bird?

- When you see a fluffy long-eared creature vanishing down a hole, how do you know it's a rabbit?

- When you taste a cold, sweet vanilla-flavored food with a smooth texture, how do you know it's an ice-cream?

This is the philosophical problem of 'universals', of how our minds assign individual things to general categories, types or kinds.     


These categories, types and kinds of things are known as 'universals', whereas the individual examples are known as 'instantiations' or 'particulars'.  Thus Mungo Jerrie and Rumpelteazer are both instantiations of the universal form of cats.


Types, kinds, categories, species


The problem of universals can be split into two questions:


(i) How and where do these universals exist (assuming they even do exist)?

(ii) If universals do exist, how does our mind interact with them, to access and recognize the correct category in which to place individually observed objects?



There are three different views on how (and if) these universals exist: Essentialism, Conceptualism and Nominalism:

 

1 Essentialism

Essentialism (sometimes known as 'Platonism' or, rather confusingly, as 'Realism') states that universals really do exist outside the mind of the beholder.  There is an ideal form of 'cat' in which Mungo Jerrie and Rumpelteazer participate. Their inherent 'cattiness', which is derived from the ideal form of cat, is essential to them being what they are.  

When applied to animals and their evolution, the essentialist view is very much linked to the creationist doctrine of separate unchanging and unchangeable species.


2. Conceptualism

Conceptualism states that universals do exist, but only in the mind of the observer. 

Thus if you cut the sides of a box down a millimeter at a time, at some arbitrary time it will cease to appear as a box and suddenly become a tray.  


Similarly, Milinda's chariot came into and went out of existence depending on Milinda's arbitrary recognition of its stage of assembly and disassembly

As regards kinds, types and species of living things, conceptualism regards species not as distinct unchanging categories, but as overlapping  evolving populations.   They are not objectively real, independently of a human observer.  This view was illustrated by Richard Dawkins' famous Granny Chain thought experiment, where ancestral humans and ancestral chimpanzees hold hands all the way back to their common ancestor.


3. Nominalism

Nominalism states that universals only exist as names, and are completely dependent upon our use of language. Thus the Samis have 52 different words for types of snow and hence 52 different snowy universals.

An argument against nominalism is that we can have perfectly valid concepts of universals without the use of language.   Some of us may be able to remember early childhood when we first learned the name of a class of object, but had a concept of its type before we knew what is was called. I can remember asking my mother 'What's that?' as she reached a pan down from the kitchen shelf, and on being told it was a pan, I knew the word 'pan'  applied to all the similar utensils on the shelf.   


And as the years advance, we occasionally revert to being pre-linguistic, with the 'tip of the tongue' phenomenon, where we have a very clear concept of a thingy, or what-not, or what-d'you-call-it, but just can't remember its name.

So maybe the reason the Samis have so many different words for types of snow is they need to communicate these concepts as a result of their environment and livelihood, and not because the pre-existing structure or richness of the Sami vocabulary created these different categories of snow out of mere words.   


Language is the servant of concepts, not vice versa.


Buddhist Conceptualism

As usual, Buddhism takes the middle way between essentialism and nominalism. The Madhyamaka ('Middle Way')  rejects essentialism but nevertheless regards universals as more than mere words, they are known as 'generic images' or 'generally characterized phenomena'. They exist in the mind, but only in the mind.

So how does our mind construct, access and recognize generic images as the correct categories in which to place individually observed objects?


There are two possible ways for the mind to assign a newly observed phenomenon to a category:


(i)   Look through a mental catalog of everything that is known, and find the closest match. 


(ii)  Use a taxonomic  or cladistic approach of following a decision tree and rejecting everything that is not relevant to identifying the unknown object. This is exemplified by the game of 'Twenty Questions', where every known object can be identified by a process of exclusion using twenty or so mental operations.

Twenty iterations of a binary search will generate
a 'logical hole' corresponding to a generic image.

 "The game suggests that the information (as measured by Shannon's entropy statistic) required to identify an arbitrary object is at most 20 bits. The game is often used as an example when teaching people about information theory. Mathematically, if each question is structured to eliminate half the objects, 20 questions will allow the questioner to distinguish between 2**20 or 1,048,576 objects. Accordingly, the most effective strategy for Twenty Questions is to ask questions that will split the field of remaining possibilities roughly in half each time. The process is analogous to a binary search algorithm in computer science or successive approximation ADC in analog-to-digital signal conversion." http://en.wikipedia.org/wiki/Twenty_Questions

 

Obviously a search mechanism that can reach its target in twenty or so operations is going to be preferable to one that on average is destined to plough through half of a catalog containing everything that there is in order to find a match. (The catalog has no index, since this would be begging the question: the mind would need to already know the name of what it was looking at in order to use an index)

The evolutionary advantages are clearly with the fewest steps. In the catalog method, by the time you've recognized the long coiled thing at your feet as a snake, you're already dead.   

Of course there is a trade-off. The catalog approach is more accurate than the taxonomic method, so with the fast method you may occasionally mistake a coiled rope at dusk for a snake.
 

Buddhist philosophers claim that this binary exclusion method is in fact how generic images work. Generic images (or generally characterized phenomena)  are logical structures formed by eliminating everything that does not have the general properties of the category, rather than being a perfect description of the 'ideal form' of the category.

Thus a generic image is what's left after all else is excluded.   It is a Boolean data structure consisting of about twenty YES/NO answers to simple questions.

The generic image is a double-negative.  To quote
Geshe Kelsang Gyatso in Understanding the Mind, page 24:

"When we think of or remember an object, say an elephant, there appears to our conceptual mind an object that is the the opposite of non-elephant. This appearance is the generic image of elephant. Even though there is no actual elephant in front of us, nevertheless there is a generic image of elephant appearing to our mind. Thus our conceptual mind apprehends elephant through the generic image of elephant. We can apply this to all other phenomena"


The generic image is therefore the appearance of a non-non-elephant.

Like a toddler with one of those wooden peg puzzles, it's almost as if when I produce a generic image of an elephant, I do so not by producing a stand-alone positive image of an elephant, but by producing an image which is specified to fit into an elephant-shaped mental hole.

We can also think of non-elephant and the generic image of an elephant as being logically complementary, just as the same stencil can produce a light figure on a dark background or dark figure on a light background, with the information content being exactly the same in both cases.


Produced from the same stencil - bunny and non-bunny are informationally equivalent.

From Debate in Tibetan Buddhism by Daniel Perdue p 299 - 300

"Thought consciousnesses are not collective engagers but eliminative engagers. Thought does not comprehend its object together with all of its uncommon characteristics (the full catalog description - S.R.), but understands its object in a general way by a process of eliminating all that is not that object.  The thought consciousness apprehending a table does not comprehend a table just as it is, for it comprehends a mere mental imputation which is an elimination of non-table...

    "...The appearing object of a thought consciousness is necessarily a generally characterized phenomenon, a permanent phenomenon.  Generally characterized phenomena are so called because their characters are realized not by way of their own entities but by way of a generality. They are realized in a general way. For instance, the thought-consciousness apprehending ice cream understands it though the elimination of non-ice cream by way of the appearance of a mental image of something which is the opposite of non ice cream.  By this process ice cream is not understood  together with all of its specific qualities but merely in a general way, as the elimination of non-ice cream. Thus, a conceptual consciousness can know something in only a general way rather than appreciating its object's freshness and fullness."


So our mind identifies an object by means of a mental generic image of that object, where the generic image, not the object itself, is the appearing object of our conceptual mind.

A conceptual mind knows its object 'for what it is' through the appearance of a generic image of that object, not by seeing the object directly.

However, the generic image is the negative of a negative, a kind of 'logical hole'.


Is the universal of ice cream formed by the exclusion of non-ice cream?

And we also need to remember that we are making visual analogies of what is fundamentally a Boolean datastructure, in the form of branch points of a taxonomic tree, for example many of the identifying qualities of ice-cream are non-visual.


Madhyamaka Philosophical aspects

In terms of the Madhyamaka's rejection of all forms of essentialism, the taxonomic method clearly demonstrates how the mind recognises objects without recourse to mapping them on to some Platonic 'ideal form' or 'inherently existing other'. In fact, the generic image is a complete opposite of a Platonic Ideal Form. For whereas the Ideal Form is inherently existent, the generic image is totally and completely empty, being derived from a 'logical hole' formed by exclusion of everything else.

Platonic forms are believed to be complete and perfect descriptions of the universals, of which individual instances are imperfect instantiations.   In contrast, generic images are minimalistic specifications containing just enough information to categorize every particular instance of an object.

A positive-to-positive matching of a perceived elephant to a Platonic image of an ideal elephant would require tedious bit-by-bit matching (how many bits of information do you need to positively specify an elephant?). The method of elimination is more efficient.  



Apoha


Excerpt from 'Dharmakīrti' by Tom Tillemans in the Stanford Encyclopedia of Philosophy   


"...Let us speak about two Buddhist approaches to bridge the scheme-content gap, “top-down”, or descriptive, approaches and “bottom-up”, or causal, approaches. By “top-down” we shall mean an account which maintains that it is because of some specific (and perhaps ingenious) features of the fictional proxy, or concept, that it pertains to particular things. Even though it does not have the ontological baggage of a real universal, the fictional proxy determines the reference of the words because the descriptive content it provides does in some way have its counterpart in the objects. Thus on a top-down approach, the fictional stand-in for a universal like “blueness” would behave like a property, a sense or a meaning, that belongs to the conceptual scheme but would nonetheless qualify and serve to pick out the real blue particulars in the world. This can be accomplished, according to Buddhist Epistemologists, because the fictional proxies are, or can be analyzed to be, “exclusions of what is other” (anyāpoha), a type of double negation which applies to particular patches of blue in the sense that each such patch is non-non-blue.[37] As Dignāga had put it in his Sāmānyaparīkṣā (“Analysis of Universals”):

    A word talks about entities only as they are qualified by the negation of other things.[38]

 
In fact, Dignāga applied his analysis both to things and to the words that express them: non-non-blue is the universal-qua-object (arthasāmānya) signified by the term “blue”, and non-non-“blue” is the universal-qua-word (śabdasāmānya) that applies to particular articulations of the word “blue”. For Dignāga, the signified-signifier (vācyavācaka) relation holds between these two quasi-universals.[39]

Why are they “quasi” and not full-fledged universals? The reasoning is not explicit in Dignāga. However, it can be plausibly reconstructed. Buddhist Epistemologists generally subscribed to the principle that mere absences of properties are of a lesser ontological status than positive things. They would stress that negative facts, like x not being blue, heavy, etc., are constituted by our mere interests (i.e., we seek a blue thing at such and such a location and come away empty-handed), and are less real than the fact that x causes perceptions of blue, a fact which is what it is objectively and independently of interests. It seems that it is this general Buddhist intuition of the unreality of absences upon which Dignāga relied. As the “exclusion of what is other” is itself only a negative property/absence of something rather than a presence, we are spared commitment to there being real universals in addition to real particulars..."





- Sean Robsville

1 comment:

Anonymous said...

Hi Sean,
First of all I would like to thank you for your posts. As a Buddhist I was delighted to discover your blogs which I find extremely informative and illuminating.
By way of appreciation, perhaps I could give you some feedback which may also be of benefit?
I guess the reason I am writing this is because, to put it bluntly, I am troubled by some of the sentiments contained within some of your posts.
Whilst it makes uncomfortable reading, I guess documenting issues such as can be found within the pages of, for example, http://jihadonbuddhists.org/ is important. But of course, as you are obviously aware, anti-Buddhist sentiments (and subsequent persecution) exists in many other political cultures.
But to use the topic of Islam as an example, as a Brit living alongside Muslims, I am dismayed when I hear someone seriously expressing sentiments such as was parodied by Trey Parker and Matt Stone in Team America: World Police – especially if these views are coming out of the mouth of a Buddhist.
As I understand, no matter who or what is at issue, the Buddha did not ‘kick ass’, no matter how difficult the situation. The story of Ahinsaka who became Angulimala is testament to this; people become impoverished in many different ways.
I believe ill will or vyapada is considered to be one of the Five Hindrances. Let us deal with such matters within ourselves before we presume too much about others.
If my studies in Buddhism have taught me anything it is that there is no wisdom without compassion – the two are interdependent. The middle way, connecting the kind hearted fool to the hard hearted cynic.
Clarity alone can become a destructive force (especially partisan clarity) if not tempered by metta or compassion. This is not sentimentalism but central to a true understanding of dharma.
Peace can not be imposed it has to be experienced, to be lived.
Try it, it could become viral.