Tuesday, September 29, 2009

Why omnipotence is defined in terms of the law of non-contradiction

The most basic principle of logic is, on most views, the law of non-contradiction. It is considered to be a presupposition of rational discourse. When you say "the cat is no the mat" you are implicitly denying that the cat is not on the mat, otherwise you're just making noises.

Now, you say that if God is omnipotent, and then put a bunch of noise after it, and call that true. So, omnipotence has to be defined in terms of what is coherently possible.

But what happens to the definition of omnipotence if you buy into paraconsistent logics?


Mike Darus said...

How about this:
God is powerful enough to limit Himself.

Peter Pike said...

I would say the most basic principle of logic is the law of identity. A is A. After that, LNC quickly follows, but I think you need identity first. In fact, you do so in your example. You say the cat is on the mat, and this statement of identity then denies that the cat is not on the mat. So you start with what is to determine what is not.

One Brow said...

Actually, the most basic principle of logic is the decision that, when you assign truth values to statements, each statement will get only one of only two possible truth values. Most other "basic principles" fall our of this decision.

Much like Russell's paradox, omnipotence might be an interesting concept under a different stucture than classical logic. however, there are so many choices I would probably need to think on them for a day just to list a few coherently.

Eric said...

"Actually, the most basic principle of logic is the decision that, when you assign truth values to statements, each statement will get only one of only two possible truth values."

One Brow, but doesn't this presuppose non-contradiction? If we start with your principle P and I assign both values to a proposition, you can only charge me with failing to adhere to what we had initially decided if you suppose non-contradiction obtains (i.e. I decided P and not non-P). Also, I'm not sure how a decision could be a basic principle of logic.

Gregory said...

I take it that the fundamental "laws of thought" are interdependent entities, of which there is neither priority nor preference given in the actual reasoning process. In terms of the relationship between their interdependent oneness, on the one hand, and their differentiation, on the other, you might liken them to the three Persons of the Holy Trinity. Which is only to say that the "laws of logic", though they have an interrelated unity, yet we can also diffentiate them. But that's as far as the analogy goes. Of course, there can't really be an adequate analogy between the personal and the non-personal.

Regarding the definition of "omnipotence": it is not important that we spend time offering hypothetical speculations about what "omnipotence" means, whether it's "coherent" and/or whether "omnipotence" has a logical cap/limit or not. We need only observe the enormity and complexity of the universe, itself, along with our inability to rationally comprehend it, in order for us to see that comprehension is not a prerequisite for rational assent. Since it's impossible for us to wrap our heads around the vast and complex vista of the physical world, though we have a myriad of piecemeal theories, as well as a lifetime of ordinary observations, to make a tiny bit of sense out ot it [cosmos/world]; and given the fact that God created it [cosmos], then whatever else we might say about "omnipotence", it is surely correct to say that the Creator's "omnipotence" must exceed the thing He created (i.e. the world). And, given the fact that our inability to rationally comprehend the epic scope of the universe is, in no way, a hinderance to our acknowledgment of it's [cosmos] existence, likewise, our inability to comprehend "omnipotence" need not deter us from acknowledging it's reality, either.

note: we do not derive propositional content by simply reflecting on the "guidelines" for thought (i.e. the laws of logic). At best, the laws of logic merely help us adjudicate propositions, such that we either assimilate or reject them [propositions]. What they definitely don't do for us is this: they don't furnish us with the robust propositional content necessary and sufficient for comprehensive analysis and/or philosophical reflection.

. said...

One may think an omnipotent agent exceeding its power to lift things means 'logic' is subsumed to omnipotence. But, actually it means omnipotence is subsumed to logic of limited agents.

Limited agents are so not in the merest fact/idea that they are so, but in the causes of their limitations: contingence, synthesis, and mutually dependence. They each are made of other, limited agents; the mutual bonds of which are not immutable; and the whole of which, as its ownt kind of limited agent, depends for its maintenance on a specific relation to an environment comprised of a host of other agents each of which is in some ways more powerful that it. This is how limited agents can multiply themselves, and can make other agents which are in some ways more powerful than themselves.

So, Curly plays Robin Hood’s sidekick: Grabbing for an arrow, he gets two at once without realizing it. Oblivious to having two, he nocks ‘the arrow’ to his bow, releasing ‘it’, and seeing one hit the Bull’s Eye while the other goes into the grass. In all his ‘observational acuity’, he says, ‘Hey, Mo! The target just split in half!’

The immediate coherence of the concept of omnipotence is what gives the sense that omnipotence is paradoxical: its immediate coherence is felt to pose an external, or otherwise genuine, constraint on the power of an omnipotent agent. But, such a ‘constraint’ allows us to conceive omnipotence in the first place, because the possibility of definitions is the possibility of knowledge.

If an omnipotent agent already is more powerful than itself, so as to create a stone out of...nothing that's too heavy even for it to lift, then it already is just that powerful, meaning its power to create that stone is identical to its power to lift that stone. This doesn’t make complete sense, but the point is that even in the process of ‘proving’ that the concept of omnipotence is immediately incoherent, one actually concludes that it is immediately coherent, and that the only difference is that this process is forced to this conclusion by a perfectly irrational route to its own unwilling end, with a perfectly unwelcome set of things included in that end.

The notion of power as the sense of ‘something bringing something about’, or ‘simple agency’ is logically indifferent. So, this notion can seem logically all-purpose. But, it is logically no-purpose, because it is epistemologically passive. Simple agency is the root of the paradoxical intuition about omnipotence: by which omnipotence is ‘proved’ to be irrational. But, such ‘proof’ is nothing but a description of this irrational re-conception of omnipotence.

Now, simple agency constrains our notion of omnipotence to be formulated as an agent which must be anti-identifiable except in terms of simple agency. But, this means that, for the anti-identifiable conception of omnipotence to be valid on its own terms, the very idea of ‘all identities’ must include even the negation of given positive identities, else it is allowed that such negations are proper states of affairs that are ontologically and epistemologically independent of their respective positive identities.

Given the complexity of the Cosmos, and of the contingent observer, it is axiomatic that the obverse of the law of identity includes a complex reverse: a thing not only is only what it is, it also is not all those things which it is not. But, given the possible combinations of knowledge and ignorance regarding a given topic, any number of various conflations of the two sides of this axiom is possible regarding that topic. Further, given the extent of ignorance possible regarding a topic, the extent of this conflation can be so deep that a person may have a virtually unlimited body of 'logic' upon which to seem to confirm the sense that a favored position is sound.

. said...

I would be pleased-as-punch if several us collaborated on an article or book on omnipotence. I really like some of the comments here.