Saturday, July 17, 2010

The General Principle of Equivalence

This post identifies the first premise upon which all other premises rely. I call it the General Principle of Equivalence. My argument is, and I will gradually show, that from it all other certain knowledge comes. At the outset it may seem just too simple to say anything worth considering, but this is only because, like so many things, it is so close to us that we do not see them. As you come to understand it, you will see that it is no more than an expression of our innate understanding of equivalence and difference.

Accepting, for reasons already given (see my post Foundation 1: Equivalence and Difference), that our notion of equivalence founds understanding, one can begin to study, from first philosophy, the nature of the world. This will provide insight into the validity and nature of the domain of discourse, namely the terms that refer to possible structures in the possible ontology (see my post Foundation 3: A Constructional Ontology).

Using the terms ‘omnet’ and ‘asset’ permits a fundamental shift in the nature of Leibniz’s Law from an effectively synthetic, contingent proposition to a global tautology, here named the General Principle of Equivalence:
Every omnet that has all the assets of that omnet, is that omnet.
Now this is the simplest of concepts, no more than the global tautology. In some ways, if one assumes the innate idea of equivalence, the proposition may be reduced to a word, ‘omnet’. However, and most importantly, while for any particular tautology, the statement is essentially vacuous to the Meditator, the globalised concept, I believe, is wholly different. It can be shown to be true transcendent of doubt and this changes it from an apparent truth to a truthmaker, a constructor, and a sieve of the possible ontology (explained in Foundation 3). That this is true will become evident in fur

Why the General Principle of Equivalence is immune to doubt.
Descartes introduced radical grounds for doubt to suspend judgment about the whole domain of discourse, with the intention to ‘establish something lasting in the sciences’ (Broughton 2002, p. 97). Emulating an architect’s method, he excavated back to the foundations. He did so in the understanding that, by utilizing the strong maxim that one should doubt all that can be doubted (rationally) Descartes would have ‘the power to go up against the authority of common sense’ (Broughton 2002, p. 97). And it is in common sense that philosophy has foundered for a very long time.

Up to the limits of rational discourse, to doubt, one must have rational grounds for doubt, even if these are radical or ‘hyperbolic doubts’ (Broughton 2002; Newman, L. 2005). Such doubts include for example those put by Descartes: the dream argument, the evil genius argument, the lunacy argument and the fate or chance argument (Broughton 2002). However, even if one addresses each argument in turn, there is no guarantee that another basis for doubt will not be raised at some future time, unless all such arguments are struck down universally, so that there is no possibility of raising rational doubt. Success in this then, ought to be an end to criticism. It then rests with the Meditator to understand, accept and commit to the General Principle of Equivalence (see my post Skeptical Commitment and the Modern Meditator).

The great value in Broughton’s interpretation of the foundation of Descartes’s method of doubt, whether this was what Descartes meant or not, lays in the recognition that one is not justified in holding a doubt about some proposition if that doubt relies on the truth of the proposition for the doubt to be valid.

The indefeasibility of the General Principle of Equivalence follows directly from this. While the GPE is self-evidently true, such self-evidence is insufficient for our purpose. Rather, the GPE is indefeasible exactly because every proposition (true or false) to be that proposition, must have all the assets it purports to have, and not other than these assets, otherwise such is not the proposition it purports to be. Then each proposition assumes the GPE to be true for it. Then any proposition that expresses doubt against the GPE, is reliant on it being true for it. Hence all propositions (true or false) are epistemologically dependent on the truth of the General Principle of Equivalence.

Immediately we see why tautologies are necessarily true, beyond self-evidence, because the GPE makes it so due to necessity (this does not imply that the supposed content of the tautology has a referent of course, but that is a story for another time).

So, all propositions, at minimum, rely on the truth of the GPE, and all propositions purport to model a condition of the world. Then, firstly, the GPE models an actual condition of the world, and it is ontologically prior to all other conditions of the world. Consequently, the GPE models the origin of all that is.

Future posts will focus on how the GPE implies a unique origin to structure, then explore the nature and evolution of that initial structure.

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