Sunday, December 30, 2007
Boundary conditions of the world – the Cartesian view.
1. On First Cause
2. First steps: The General Principle of Equivalence
3. Building a sturdy ontology.
4. The cataclysm that attends the General Principle of Equivalence
5. On the structure available to possible worlds.
6. Boundary conditions of the world - the Cartesian view.
7. On denoting and the laws of thought.
8. Something for nothing, and why this is not absurd.
6. Boundary conditions of the world – the Cartesian view.
Given the problem of bundling previously mentioned, the meditator seeks to find a world that can hold together in some complex form. Is a complex form possible? One place to start is to consider boundary conditions, conditions that can only be the case, with which the domain of discourse (the world) must conform. We note several constraints that apply to the ontology necessarily.
1. Any variation in assets expresses a different omnet (by the General Principle of Equivalence).
2. There is only one Totality, because any variation would imply a difference in assets (follows from 1).
3. The Totality and everything within it complies with the General Principle of Equivalence at every level.
4. Only the General Principle of Equivalence has the power to bring compresence to pure assets, pure assets lack this power in and of themselves (previously shown through the problem of bundling).
Because these follow from the General Principle of Equivalence, they are not axioms. Rather, they are necessary truths, boundary conditions that may stand in for axioms.
As meditator, I am concerned about these truths. In the first instance, does not item 1 imply that the world cannot undergo change, as Parmenides and Zeno argued? I find myself flung into a state of empiricist denial. My refuge, as Cartesian meditator, is to say that the necessity of these truths suggests that my understanding of the Totality is not well formed. Regardless of the duality between the presenting world and Item 1, I cannot deny the truths so presented because they are as indubitable as the General Principle of Equivalence which gave rise to them. In the positive, the existence of this duality of interpretations is useful, because a logical theory may be tested by its capacity for dealing with puzzles (Russell 1905).
To explore the implications of the boundary conditions on the Cartesian system (the system of omnets and assets that present to the Cartesian meditator), I aim to develop a means of referring to the system of omnets, and a means to test supposed qualities of this system. If my terms do not properly denote, or are not constrained by the General Principle of Equivalence, further effort may founder on a lack of exactitude. The first task is to develop a system of denotation, the second to develop a form of logic to stand in for the Laws of Thought. I do this in the next blog.