Monday, January 19, 2009

Fundamentals

Psychological time is a notoriously malleable quantity. I hardly seem to spend any time waiting in supermarket checkout queues these days, but that's mainly because I tend to slip into a type of absent-minded reverie. Sometimes I imagine winning the Monaco Grand Prix from 17th place on the grid; on other occasions, I come from 4-down with 5 holes to go to beat Tiger Woods and win the Ryder Cup for Europe. On very rare occasions, I ponder more difficult tasks, such as answering Martin Heidegger's question: What is the thingness of a thing? In other words, What is it for a thing to exist?

Someone in front seems to have something with a barcode missing, so I've got the opportunity to recall that there's a number of concepts which can be identified as fundamental in the human conceptual system:

(i) Objects.
(ii) Properties and relationships.
(iii) The possession of properties and relationships by objects.
(iv) Existence.

All other concepts appear to be built from these, but are these concepts independent, or can we define them in terms of each other, and reduce the number of fundamental concepts?

First of all, properties and relationships can themselves possess properties and relationships, hence properties and relationships can be treated as special types of objects. One could define zeroth-order objects to be objects which are not predicated of other objects; first-order objects (properties) to be those which are predicated of other objects; second-order objects (binary relationships) to be those which are predicated of pairs of other objects, and so on.

Conversely, however, one can define objects to be merely bundles of properties. Moreover, if existence is merely absence from contradiction, then an object exists by virtue of the fact that the bundle of properties which define it is free from contradiction. This would re-define existence as a logical property of bundles of properties. Whilst existence might not be a property of zeroth-order objects, it could be a property of the bundle of properties which defines a zeroth-order object.

(I'm vaguely irritated by the fact that some silly person in front wants cashback). Even the possession of properties by objects can be re-cast as a relationship itself, but a relationship between objects and properties rather than a relationship between (zeroth-order) objects.

There is no need for one of these approaches to be right, and the others to be wrong; it may be that the human conceptual system is cyclic, in the sense that each one of the fundamental concepts above can be defined in terms of the other concepts. But just as this idea solidifies, it's time to ask for some plastic bags, and to admit once more that, no, I don't have a Sainsburys Nectar card thanks.

3 comments:

elberry said...

i'm usually thinking about pork pies and how nice they are.

Gordon McCabe said...

Mmmmmm, pork Pi.

elberry said...

Great Kate Bush song about pi on 'Aerial', but perhaps it was really about pie...?