Sunday, December 30, 2007

The cataclysm that attends the General Principle of Equivalence

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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.

4. The cataclysm that attends the General Principle of Equivalence.

On pure/minimal assets
By the General Principle of Equivalence, assets are what omnets have. Because assets are also omnets under the initial construct, then by symmetry if there is an internal difference within an asset or omnet, that implies a difference in assets. This implies directly that all omnets are composed of (possibly finite, possibly uncountably many) minimal assets for which further segregation has no proper ontological foundation. That is, such base assets are indivisible. Let's call these 'pure' assets. That all omnets are a compresence of such follows from the nature of the principle.

The number of these assets is irrelevant to the argument. This is not an iterative process where one divides an omnet into two or more assets then does so again and again. If it were, then the argument would be invalid. Rather, it follows from the GPE because it is just a recognition that an asset is an omnet and any two assets differ in some way, else they would be the same. Also it doesn't matter whether assets are properties, or tropes, or relations or some other more metaphysically bamboozling element. The beauty of the Cartesian view is that we aren't in a position to even consider such fine detail yet, for everything but the GPE and our own existence in the Totality is suspect.

For example, if there is a line, it might be made up of a finite number of line segments, or an infinity or transfinite number of points, or infinitesimals or perhaps something else. None of this matters, for it is made up of what it is made up of, and any difference along the line is due to a difference in assets, and any internal difference within such asset is likewise based on different assets immediately, not iteratively. So at the base level the elements are pure assets.

No matter what we suppose to be the case from the comfort of the World-of-Seeming, whether nothingness or anything else, each omnet is no more than pure assets. In this context, every complex omnet is a bundle of indivisible assets, where ‘bundle’ means pure assets in compresence (exactly the term that refers to the ontological condition implied by there being complex omnets).

This is parallel in meaning to the ‘bundle’ of bundle theory (see Armstrong 1978b), for which four central themes are evident, as these might apply to substances (Robinson 2004). The themes are
1. The concept of substance can be analysed in terms of some relation between properties conceived as universals.
2. The concept of substance can be analysed in terms of properties conceived of as individuals, e.g., as property-instances or tropes.
3. Substances are in fact no more than bundles of properties conceived of as universals.
4. Substances are in fact no more than bundles of properties conceived of as individuals.
Here substance is that which ‘stands under or grounds things’ (Robinson 2004, n.p.). For the Cartesian meditator, the idea of substance might equate to assets, but also may be an unnecessary layer of presupposed structure. The Pyrrhonian sceptic would argue that all these options reduce to opinion, for there is no clear determinant for any particular choice. Fortunately the meditator has no need to judge which might be the case, for all are suspect. To hold these concepts in abeyance is the right path for the Cartesian meditator, for strictly speaking, one cannot be sure that there are such complex omnets. The challenge is for the meditator to find some basis to re-admit such complexes into the actual ontology, through further consideration of universal conditions.

Why things can't hold together unless they are built from the GPE as constructor.
The difficulty comes when the Meditator looks for a basis for this bundling to rescue complex omnets from a sea of minimal (pure) assets. One needs to find a means of association but, prima facie, all such associations are themselves composed of minimal assets. To explain the current concerns with respect to this, I will consider a measure of recent philosophical commentary.

On compresence and bundling
Armstrong (2005) hints at a problem for bundle theories when he favours universals against tropes. A universal is a property that is essentially shared by whatever has it. For example all red things share the same red property. Tropes apply to individuals alone. A particular red ball has that red, but does not share it. He is prepared to forego the simplicity of tropes because identities across particulars (that is, universals) seem to be necessary to hold the world together.
Bundle theories, considered in detail in Armstrong (1978a), have ‘great difficulty with the metaphysics of the uniting principle or principle of bundling,’ (Armstrong 2005, p. 311) but he admits that a similar problem applies to the alternative view of properties as attributes of particulars.
Further, he wonders what might bundle ‘dispositions’, and expresses that this problem is one of the most confounding for metaphysics. For this reason, he likes the idea that every property should bestow power, presumably because this would provide some connection between cause and effect. It is not clear, however, how properties might achieve such power within themselves, given that they, being different from other properties, are not directly connected to other properties, and so require to be bundled by something other than themselves.
But compresence, according to Grupp (2004) must be a special bundle itself. He holds that this leads to an infinite regress, with respect to finding what bundles the special bundle. This is no different to the result just shown to follow from the General Principle of Equivalence, that all possible worlds are founded on minimal assets, but such assets have separate identity, otherwise they would be the same, which is essentially the argument of Heidegger (1969).

The problem is not with the possibility of assets, for we see evidence of such everywhere through the differences that must have some basis (such differences being differences in assets for this is all that omnets have). The problem is in the understanding of how these assets find a means of association. The existence of assets does not in itself say anything about these assets in some way forming an omnet at any level more complex than pure assets. For example, assets of bigness, redness, catness, or being two metres from another cat (should any of these be well-founded assets), are different to each other and different to the omnet in which they are compresent, they do not in themselves imply the existence of a big red cat with its relations, bundled in some way, making them 'in esse' to complete a big red cat resting in space.
An appeal to universals does not in itself rescue the omnets as they present to us, for they too have no ability to hold the world together, because if there are omnets, they reduce to minimal assets. The question that then attends the development is how such assets can form complex omnets, meaning omnets with more than one pure asset.
Our initial adventure showed that the General Principle of Equivalence is necessarily true, and reflects a global tautology. As such it should be relatively innocuous. However, taken to its natural end, pure assets constrained by the General Principle of Equivalence noumenon (meaning the condition of the world that the GPE models) are all that an omnet has, and the means of association is likewise composed of pure assets. As such there is a challenge as to what holds the world together.

To put this pointedly, because the GPE applies to all that is, it implies that everything in the world (energy, matter, words, ideas) should collapse to simples, unless there is some necessary truth that cannot collapse. But of course this is the GPE itself, for it is indefeasible, whatever is, even if the world is empty, relies on the GPE.

In my next post I will show that this implies that there is a unique origin for the world and that its origin is inescapable.

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