Paradox Point

       Omniscient of Nescience?             Awhile back I concocted a philosophical conundrum. I consulted Dana Leslie, a friend and a philosopher; he in turn recommended that I contact Robert West. He did not disappoint; for Robert West resolved the paradox in not just one, but two ways, and those ways in subtle but severe contradiction! As a paralogician, I enjoy this. I first stated the paradox like this: “Can an omnipotent being truly understand what it is like to lack power?” I rephrased this colloquially as, “Can God grok wimphood?” By ‘grok’, I mean intuitive understanding; a point I’ll revert to shortly. Robert West noted that this is really about omniscience, not omnipotence; so I reformulated it to: “Does an omnipotent being possess the power to understand powerlessness?” But perhaps “the power to understand” is a quibble. So better yet: “Can omniscience know nescience?” That i...

           Plato, Meet Russell   Plato spoke of ideal Forms, of which the entities around us are imperfect examples. Thus there are frogs, and there is the Form of all frogs, and the Form of all frogs is not a frog. But there is also the Form of all Forms, which is itself a Form. Therefore some Forms are examples of themselves, and some are not. Now consider Russell’s Form R, of all forms, and only those forms, that are not examples of themselves:   For any form F,    F is an example of R     =     F is not an example of F   Is Russell’s Form R an example of itself? Substitution yields:   R is an example of R     =     R is not an example of R   A Russellian paradox! Here is another paradoxical Form: G, the Groucho Form, which is the Form of all Forms, and only those Forms, that the Groucho form is not an example of:   For any ...

Mathematics of Local Optimism   The theory of Local Optimism assumes that there are many possible worlds; most are virtual, not lasting long enough to be observed; a few last long enough to be observed, and are called real.           Local optimism states that any real world is a local optimum; it is the best of all sufficiently similar possible worlds. Call such a possibility-neighborhood the “circumstances”; meaning “that which stands around”; then local optimism says that this is the best possible world, under the circumstances.           This resembles Leibnitzian Optimism, which states that this is the best possible world of all . Leibnitz says that this world is a global optimum; whereas Local Optimism says that this is a local optimum. According to local optimism, there may be many local optima, some better than ours, some worse. This leaves open the question of what is bei...

Local Optimism   Voltaire mocked Leibnitz (in the guise of Dr. Pangloss) for proposing that this is the ‘best of all possible worlds’. But Leibnitz, co-inventor of the calculus, knew the difference between local and global maxima. A global maximum is the largest value that a function reaches, for any input; whereas a local maximum is the largest value that a function reaches, in some neighborhood of the locally-maximizing input. I therefore propose this modification of Panglossian optimism; Local Optimism, which states that this is the best of all sufficiently similar possible worlds. Any stable world locally optimizes; it’s the best of all nearby possibilities.           Local optimism suggests that there may be many stable worlds, some better than ours. There may also be inherently unstable worlds, that are the worst of all sufficiently similar possible worlds.           Any continu...