Wednesday 18 November 2009
To follow on a few arguments I had at some blogs like Gödel’s Lost Letter, vetta project, Machine Learning (Theory) and The n-Category Café I think I need to clarify the matter about my personnal stance on "objects" and ontologies, this also for my own benefit.
I am strongly anti-platonist because all evidence points to the irrelevance of metaphysical postures for the actual practice in mathematics and engineering.
There is no need to question and look and check for the actual existence of objects and concepts (which are also objects, supposedly abstract and immaterial) "in reality" because objects and concepts are NOT part of reality but part of our representation of reality (whatever one's view of reality is).
We shoudln't fear to be lacking of any sort of objects as representations (including pink unicorns) because as shown by the "existence" of the Rado Graph any fancy (countable) structure can be found.
The only trouble we can have is improper use of language (mathematical or otherwise) in our attempts to pin down "an object", that is a lack of definedness, mistakenly expecting that a sentence (or any sort of syntactical construct) actually points (denotes) an object (one and the same) in a consistent manner.
As I hinted the only purpose of objects is to serve as carriers of properties in our discourse.
Think about it for a moment, how could we organize any display of information if it were not possible to refer to the "same thing" at two or more distinct places in a discourse of any kind?
This is why objects must be intemporal (eternal), we already have enough trouble with the shifting of meanings due to the fuzziness of actual communication practices without having an indeterminacy "in principles".
This leads the Platonists to believe in the existence of abstract objects as some ghostly duplicates (non-physical and non-mental) of material objects, this is only a clumsy projection of folk intuition.
Objects are referents not "things" in the lay meaning of the word.
Furthermore ANY POSSIBLE OBJECT potentially exists, any piece carved out of the Rado Graph can serve as a referent, a label, a pointer in a discourse, being both recognizably distinct and unique (up to isomorphism).
Trying to sort out which objects "exist" like the Platonists do is devoid of any meaning, because all do exist.
Which doesn't mean that we should have an interest in every of them or will ever meet them all.
As René Thom said "Truth is not limited by falsity, but by insignificance".
Therefore what's the point with ontologies?
Ontologies are not just lists of "existing objects" they necessarily involve some language with wich they define the objects and their relationships.
And this is the valuable part of ontologies, they establish the basis for some discourse.
They also enforce a somewhat arbitrary partition of the "reality" they aim to be about, what is known in linguistic as the Sapir-Whorf Hypothesis.
However there is no one true right ontology it all depends on the problems at hand and even for the same one problem (or class of problems) there are many possible ways to "ontologize" it, like foundational problems in mathematics.
What makes the difference is the convenience of the ontology relative to the questions sought for.
This is why quasi-religious haggling about the "right way" to talk or think about this or that is pretty pointless.
Yet, shifting our perspective (swapping/altering ontologies) is something we do so naturally and with so much ease (if not rigor ) that we forget how critical it is for our thinking process.
The many different proofs of any given theorem require such "translations" between sligthly different perspectives, at least with respect to the lemmas used in the proof which, though may be defined inside a same general framework, are not necessarily related in an obligatory manner. And, may I remind you, lemmas ARE OBJECTS ON THEIR OWN, they have names, they can be recognized and beside terminology quarrels they have unicity.
It is this ability to build objects tailored to a purpose which is the key to our ability to deal "intelligently" with the world, what Barwise & Etchemendy call heterogeneous reasoning.
As far as I know The Mutilated Checkerboard problem is still NOT solved in AI except by brute force because it requires (so called...) human creativity in choosing a clever approach, i.e. shifting the perspective.
This is why I object to the simplistic view of Marcus Hutter and als, that AI is about sequence prediction.
I also deem all "foundational quarrels" in mathematics entirely irrelevant.
What needs to be done is to figure out what we are exactly doing when we shift perspectives and juggle wit h ontologies, because WE DO IT (successfully...)
Submitted by Kevembuangga