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.

Dear Bruno,

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: http://plato.stanford.edu/entries/substance/#DesSpiLei

"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 entity.

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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