On 11/3/2012 5:26 AM, Bruno Marchal wrote:
The arithmetical property of numbers are innate to the numbers, logic
and the laws we assume.
How? How are properties innate? This idea makes no sense to me, it
never has as it does not allow for any explanation of apprehension of
properties in my consideration... The only explanation of properties
that makes sense to me is that of Leibniz: Properties are given by
relations. We might think of objects as "bundles of properties" but this
is problematic as it implies that properties are objects themselves. I
think of properties similar to what Leibniz did:
"Leibniz's substances, however, are the bearers of change (criterion
(iv)) in a very different way from Aristotle's individual substances. An
Aristotelian individual possesses some properties essentially and some
accidentally. The accidental properties of an object are ones that can
be gained and lost over time, and which it might never have possessed at
all: its essential properties are the only ones it had to possess and
which it possesses throughout its existence. The situation is different
for Leibniz's/monads/---which is the name he gives to individual
substances, created or uncreated (so God is a monad). Whereas, for
Aristotle, the properties that an object/has to/possess and those that
it possesses/throughout its existence/coincide, they do not do so for
Leibniz. That is, for Leibniz, even the properties that an object
possesses only for a part of its existence are essential to it. Every
monad bears each of its properties as part of its nature, so if it were
to have been different in any respect, it would have been a different
Furthermore, there is a sense in which all monads are exactly similar to
each other, for they all reflect the whole world. They each do so,
however, from a different perspective.
For God, so to speak, turns on all sides and considers in all ways
the general system of phenomena which he has found it good to
produce...And he considers all the faces of the world in all
possible ways...the result of each view of the universe, as looked
at from a certain position, is...a substance which expresses the
universe in conformity with that view. (1998: 66)
So each monad reflects the whole system, but with its own perspective
emphasized. If a monad is at place p at time t, it will contain all the
features of the universe at all times, but with those relating to its
own time and place most vividly, and others fading out roughly in
accordance with temporal and spatial distance. Because there is a
continuum of perspectives on reality, there is an infinite number of
these substances. Nevertheless, there is internal change in the monads,
because the respect in which its content is vivid varies with time and
with action. Indeed, the passage of time just is the change in which of
the monad's contents are most vivid."
The difference in my thinking to that of Leibniz is that a monad is
never "at place p at time t" (location is defined solely interns of
mutuality of perspectives) and monads are only "substances" in that they
are eternal. I find it best to drop the idea of substance altogether as
it can be completely defined in terms of invariances.
After I wrote the above I can see how you would think of properties
as being innate, but I see this as just a mental crutch that you are
using to not think too deeply about the concept of property. The
situation is the same for your difficulty with my hypothesis of meaning.
We learn to associate meanings to words so that words are more than just
combinations of letters, but this is just the internalization of the
associations and relations within our thinking process.
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