'We will thus never hamper ourselves with disputes about the infinite, since it is
absurd that we who are finite should undertake to decide anything regarding it, and by
this means, in trying to comprehend it, so to speak regard it as finite. That is why we
do not care to reply to those who demand whether the half of an infinite line is
infinite, and whether an infinite number is even or odd and so on, because it is only
those who imagine their mind to be infinite who appear to find it necessary to
investigate such questions. And for our part, while we regard things in which, in a
certain sense, we observe no limits, we shall not for all that state that they are infinite,
but merely hold them to be indefinite. Thus because we cannot imagine an exception
so great that we cannot at the same time conceive that there may be one yet greater,
we shall say that the magnitude of possible things is indefinite. And because we
cannot divide a body into parts which are so small that each cannot be divided into
others yet smaller, we shall consider that the quantity may be divided into parts whose
number is indefinite. And because we cannot imagine so many stars that it is
impossible for God to create more, we shall suppose the number to be indefinite, and
so in other cases.
And we shall name things "indefinite" rather than "infinite" in order to reserve to God
the name infinite, first of all because in Him alone we observe no limitation whatever,
and because we are quite certain that He can have none, and in the second place in
regard to other things, because we do not in the same way positively understand them
to be in every part unlimited, but merely negatively admit that their limits, if they
exist, cannot be discovered by us.'
- Descartes.
(From Principles XXVI and XXVII of the First Part of the Principles of Philosophy,
trans. Haldane and Ross. Cambridge 1911)
Commentary:
the idea of the infinite only makes any logical sense as a negative concept - that which
is not finite
Descartes wants to apply these concepts - finite and infinite to substances
a finite substance that which has limits - an infinite that which does not have limits
so to substance -
that which is before its attributes - before its presentation - the 'ground' of existence
or indeed as some have held - existence itself
what is clear is that substance is an abstraction
and an abstraction that is has been seen to perform certain philosophical functions -
i.e. to give a sense of metaphysical coherence in the midst of change - to be a 'logical
ground' to perceived attributes i.e. mind and matter - etc.
what I would argue is that the concept of substance is without substance-
that substance is not the stuff of the universe - but rather that it is an organizational or
operational principle
and one that is a natural result of the relation of the conscious to the non-conscious
world
consciousness operates with such a principle in order to function
so what you have with the idea of substance is an organizational principle designed to
give some coherence to the conscious world
it is the idea of unity - of oneness - and it seems to be essential to our functioning as
human animals
it might be asked - well what is being organized when such a concept or principle is
used?
that is if we are not going to use the term 'substance' for that which is being operated
on - what do we call it?
language is a platform of description
as language users we operate on that platform - and the platform of language is very
rich an complex
so we have many and diverse 'descriptions' of the world and our presence in the world
there is no one account
as to what underlies all accounts - what is essential?
the fact of the reality of the diversity points to one thing - and that is that we don't
know
so the world as given - prior to language if you like - is unknown
and it is to this unknown that we bring consciousness
which is to say consciousness makes the unknown - known
and so for me - Descates' substance is the unknown
once this is understood and grasped - the question - is substance finite or infinite? - is
seen in its correct light -
it is not a sensible question
that is it makes no sense to ask is the unknown finite or infinite?
the unknown is just that - unknown
All of Descartes' discussion here is infected with his notion of substance -
but he nevertheless makes an interesting distinction between the infinite and the
indefinite - and he does this really to reserve the infinite for God
he sill talks in terms of substance - i.e. 'indefinite things' - and this is a shame because
if he saw the matter in the operational sense I have proposed - there would be some
conceptual movement at the station
the dividing of a line i.e. is the repetition of an operation - now the example of the line
just points to the fact that there are indeed repeatable operations - or repeatable acts
and yes they are the kind of act that can go on indefinitely
this does raise the question - well what act is not repeatable indefinitely?
and by 'act' here I mean conscious act -
to cut to the chase - there are certain operations that require repetitive acts
so the question really is - in what operational setting does indefinite repetition make
sense?
thankfully not too many and not for long
we must also realize that a human being is not capable strictly speaking of indefinite
acts of any kind - in the sense of endless
it is better here to speak of repetitive acts and repetition
yes the idea of 'God' as the infinite - as that which is not finite -
is really just a trick - a misuse of logic
every proposition can be negated
we can say that that which is not finite is infinite
it does not follow at all that the term 'infinite' here actually refers to anything
the application of the negation sign to a proposition does not create an alternative
reality
what it does (in my view) is point to the non-utility of the proposition under
consideration - that's if it is correctly used
we can of course have great fun with negation sign - we can make all kinds of realities
if we think it signifies substance
substance as I have pointed out is not the issue - the issue finally is function
and the question for us always with our concepts is - what is the appropriate context
for the use of this concept?
in what context is it designed to function?
