Notes from New Sodom

... rantings, ravings and ramblings of strange fiction writer, THE.... Sodomite Hal Duncan!!

Thursday, December 15, 2011

A Digression into Ontological Bootstrapping

Position, Supposition and Presupposition

For a while now I've been toying with the notion of what I call a suppositional logic, a model of reasoning protocols that doesn't so much drop the strictures of logic as thrashed out over the centuries as take a step back to consider that tradition in the context of natural language with its epistemic and alethic modalities, modalities of actuality and possibility. That's to say, the reasoning processes of deduction and induction don't cover the whole system with their premises and conclusions. Doubts and suspicions are a fundamental part of the reasoning process, I'd say, interrogation a driving force in reason. So I'm inclined to try and integrate uncertainty.

So, as a sortie into that, I reckon we could look at three types of logical moves, positive and negative: the epistemic position ("is (not)"); the alethic supposition ("could (not)"); the alethic presupposition ("must (not)"). The first then:

  1. +§1: There are unicorns in Africa.
  2. -§2: There are unicorns in Africaº
  • i.e. There aren't unicorns in Africa.

These are statements with an epistemic modality, true/false values to be verified epistemologically. The degrees sign is meant as a reversal of the up-down value of the period, because it's sort of a signifier of statement as is, and this fits with my approach to the other logical permutations -- to treat them as interrogatives and imperatives -- in question or not in question. I mean, one can take that position and make a supposition of it by introducing doubt, with the same positive/negative permutations.

  1. +§: There are unicorns in Africa? (implicit "Verdad?")
  • i.e. There are unicorns in Africa, aren't there?
  • i.e. There could not be unicorns in Africa, but I suppose there to be.
  • i.e. Suspicion: a positive supposition allowing the negative supposition possibility.
  1. -§: There are unicorns in Africa¿ (implicit "Really?")
  • i.e. There aren't unicorns in Africa, are there?
  • i.e. There could be unicorns in Africa, but I suppose there to not be.
  • i.e. Doubt: a negative supposition allowing the positive supposition possibility.

The reflection of natural patterns of interrogation should be clear, I hope -- the logical utility, even, of challenge as putting an alethic spin on a position. Where we want to establish knowledge, aren't these the questions we ask ourselves and/or others? That's how this very sentence is performing it's reasoning, isn't it? This one could not be using that logic, but I rather think it is. It's not a wholly ludicrous suggestion, is it? I mean this model could be flawed, but I don't think it is.

You see what I did there, right?

This seems to me a pretty straightforward and rational approach to reason, one that recognises a fundamental feature of inquiry at the heart of it. A position, I'd suggest -- i.e. I suppose this to be so -- is not reasoned unless there's supposition involved. It might be true or false or unverified; that's an epistemic matter -- whether the straight articulation maps to actuality or not. If it's established as an epistemic fact, that's all well and good, but that's experience, not reason. Where we talk of reason, what we're dealing with is this, I think, the application of doubt and suspicion to permute position into supposition. The step beyond the epistemic judgement of actuality into the alethic judgement of possibility. Laying a supposition down but allowing for the possibility that it's unsound.

Then you can start to apply logic as we more commonly know it -- inductive and deductive reasoning. Well, first you can look to confirm a context-limited suspicion or doubt -- by checking all of Africa for unicorns, say -- and thereby establish the alethic supposition as sound, turn it into an epistemic fact, the straight articulation mapping to reality. But again that's experience, not reason. Reason is about what you can do if that's impracticable. You can look to justify a suspicion or doubt with evidence, each instance where the supposition holds true increasing the probability until, by the suppositional leap of induction, you deem it just. Not sound, but just. Or you can look to dispel a suspicion or doubt by finding a fact that contradicts it, look for specific ways to do so and try them out until you succeed and, by straight deduction, can deem it unsound. Which brings us to the third type of logical move, presupposition:

  1. +§: There are unicorns in Africa!
  • i.e. There must be unicorns in Africa.
  • i.e. There could not be unicorns in Africaº
  • i.e. Acceptance: the supposition of a suspicion, with doubt dismissed.
  1. -§: There are unicorns in Africa¡
  • i.e. There must not be unicorns in Africa?
  • i.e. There could be unicorns in Africaº
  • i.e. Refusal: supposition of a doubt with suspicion dismissed.

Presuppositions are alethic imperatives, rejections of uncertainty and therefore statements of necessity, positive or negative. A presupposition is a supposition of a supposition. We can define a simple principle with all presuppositions and all alethic models based on them, indeed, the Presupposition of Soundness, which is quite simply: the supposition that a supposition holds across all contexts.

They can be understood as the repudiation of a doubt or suspicion but not on the basis of disproof. We're talking the necessity of "must" or "must not" here, of "always" or "never," not the simple "is" or "is not" of a contradictory fact. If the doubt or suspicion had been dispelled you'd have a position in the proven fact that it was/is unsound; you'd have an epistemic fact of an alethic model being unsound. To repudiate is not to dispel; rather, in dismissing the negative you adopt an attitude of acceptance or refusal, generate a supposition of a supposition, a supposition that the supposition holds across all possible contexts. This may be just according to inductive logic applied to the weight of evidence, but the presupposition is by nature a type of supposition.

There's a double edge to presuppositions for this reason. They are simultaneously a) dismissals of the possibility of being wrong, and thus a dangerous limitation of thought, and b) assumptions of potential principles, and thus extensions of thought into the speculative. They are at once a) unproven generalisations from which the most creative conceit of a model may be constructed, and b) formulated as rules and thereby constructible into models following the most rigid strictures of validity.

Working only with these gives you the traditional sort of logic -- combinations of presuppositional premises allowing deduction of presuppositional conclusions. Crude suspicions and doubts can be broken down into elementary presuppositions, reconstructed as rigorous alethic models in a search for the invalidity of an incoherent notion, a simpler lynchpin supposition that can easily be shown unsound. The utility of this approach where it abstracts out terms like "unicorn" and "Africa," formalises terms like "there" and "in," systematises the whole construction of valid abstract alethic models is... well, it's the utility of the theoretical underpinnings of science. Nuff said.

Ontological Bootstrapping

One key reason I'm inclined to break it down this way is the inherent reminder of the distinction between soundness and validity, that however coherent the presupposition, it's a type of supposition. No matter how coherent the alethic model, veracity is still an issue. A fundamental one here actually: epistemic verification is empirical observation of applicability in one context, but presupposition says it holds across all. Repeat verification can establish it as just, but it cannot be considered sound unless you verify applicability across all contexts. Hence the epistemological strategy of falsification. Where you encounter an argument that such a system is sound, I'd say, there's a good chance you're dealing with ontological bootstrapping.

The bootstrapping of ontological arguments (e.g. for the existence of God) is based on a simple trick. A presupposition can be written into a model that applies to the model itself: for the model to be valid, it must be sound. If the model can be shown to be valid, it follows that the articulation maps to actuality, is applicable across all contexts. With any valid model one constructs, it's possible to add this presupposition without affecting the validity, and thereby conclude that the model must be sound.

This presupposition only needs to be obscured. A hidden validity check can be coded in a presupposition: for the model to be a model of God (i.e. valid), it must be sound. This can then be further obscured by indirection: for the model to be a model of God, it must be perfect; for it to be perfect, it must be sound.

So, to pick as examples, two ontological arguments for the existence of God, Anselm's and Descartes, which boil down as follows:

Anselm: This is a model of that which is superior to all we can imagine. If the model is not sound, then we can construct a model of that which is superior (etc.) by dint of its model being sound. If we can construct such a model, it must be sound. Therefore, that which is superior (etc.) must exist.

Descartes: This is a model of that which is perfect. That which has an unsound model is not perfect. If the model does not premise its own soundness, it is not a model of that which is perfect. A model of that which is perfect which does not premise its own soundness is therefore contradictory. According to this model then, the model must be sound.

Descartes doesn't even hide it -- he explicitly sets out the model as invalid if doesn't have the "it must be sound" premise -- but the validity check in Anselm is maybe less obvious. If the first model is not sound, the thing is, it is not a valid model of that which is superior (etc.). If we can construct a second model of that which is superior (etc.) by dint of its model being sound, the first model is a contradiction in terms -- an ultimate model surpassed by the second model. In other words, for the model to be a valid model of that which is superior (etc.), it must be sound.

Shorter Anselm: If the model of the greatest idea is not sound because it must be, then it is not the model of the greatest idea.

Shorter Descartes: If a model is not sound because it must be, it is not a valid model of perfection.

In both cases, the bootstrapping rests on a sleight-of-hand recasting epistemic veracity as alethic necessity. The position that the model asserts (God exists) cannot be verified in one context let alone across all, so we cannot say it is sound. Without repeat verifications we can't even apply inductive reasoning in a suppositional leap and say that it is just. So instead a presupposition is written into the model whereby if it is valid, the supposition that it holds across all contexts is the only valid conclusion. Assuming it is valid, the model presupposes its own soundness.

The Model of Perfection

We could dismiss this bootstrapping out of hand simply for the circularity, but I think it's worthwhile looking at it in terms of suppositions and presuppositions just to lay bare the core problem with any such strategies.

What exactly is being done? The Presupposition of Soundness is being wired into the alethic model itself, along with a premise that if the model is valid, this must be sound. As laid out above, the PoS is the supposition that a supposition is true across all cases. It's definitive of all presuppositions and since all presuppositions are sound if and only if this is, it's decisive for all presuppositions. Since "for the model to be valid, it must be sound" makes this decision a product of deduction, with any such premise we have a supposition that an alethic model can establish the soundness of its own Presupposition of Soundness by presupposition.

If we expand this though, what do we get? The supposition that an alethic model (a system of suppositions of suppositions holding across all contexts) can establish the soundness of its own Presupposition of Soundness (the supposition that the supposition holds across all contexts) by a supposition that a supposition holds across all contexts.

Since a supposition that a supposition holds across all contexts is simply that supposition with doubt dismissed, however, we can collapse all this convoluted circularity to:

The supposition that a system of suppositions (an alethic model) can establish the soundness of the supposition that it is sound across all contexts (the Presupposition of Soundness) by supposition.

But "the soundness of a supposition that [a system of suppositions] is sound" is simply the soundness of the system, and a system of suppositions that "can establish its soundness across all contexts" must be sound across all contexts, so we can go further, reduce this to the bare essentials, where we find the basic logic of the bootstrapping trick comes down to the Presupposition of Soundness itself, Anselm and Descartes only asserting their own dismissal of doubt as regards their alethic models:

The supposition that a system of suppositions is sound across all contexts.

The problem I'm poking at then is not just the circular logic of bootstrapping but the more fundamental error of sliding modalities due to conviction and obfuscation, the confusion of position, supposition and presupposition. In part, the point is that theoretically any model could have this ontological bootstrapping wired into it. Note how neither the long form nor short form of Anselm's or Descartes' arguments specifically mention God. One might easily apply notions of perfection, greatness, completeness to a model of absolute evil:

This is a model of the perfect evil. That which does not exist has no power, but if evil has no power, it is not capable of corrupting. That which is not capable of corrupting is not perfect evil. A model of the perfect evil is therefore incomplete unless that evil is capable of corrupting. Since that which is capable of corrupting must exist, the perfect evil must exist.

Or, indeed, we can ontologically bootstrap a system of presuppositions shorn of the anthropomorphic mumbo jumbo altogether:

We can imagine a Theory of Everything that surpasses all other theories we can imagine in terms of completeness and consistency, validity and truth. If this theory is not perfect in any of these respects, it leaves an aspect of the universe undescribed and/or irrational. But if there are contradictions, gaps and/or falsehoods, this is not a Theory of Everything. We can however imagine a theory that surpasses it in any of its flaws by being perfect in all respects. Since truth is one of the requisites, this Theory of Everything must be true.

It's all about the model of perfection, it seems. We don't want to believe in perfect evil, of course, but damn we want to believe in that which is superior to all we can imagine, that it's the paragon of models, complete in having all the properties we want it to have, that it is true because it must be true, that it must be true because it is a perfect unity. But ontological bootstrapping is shoddy logic even in a wholly informal system based on supposition. You can define your faith into truth by insisting that your Presupposition of Soundness must be sound because of the validity of your presuppositions, but that ain't gonna make it so.



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