More on Gödel. Gödel: ‘How did you receive your revolutionary insights?’ Einstein: ‘By raising questions that children are told not to ask’. Gödel raised questions that mathematical logicians and philosophers weren’t supposed to ask.
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More on Gödel
1. Generality is that which is accepted as true from the local perspective but possibly true and possibly false from the global perspective. A generality is, then, neither true nor false when considering both perspectives (i.e. it may be ‘falsified’ within some future timespace context). Hence classical logical principles don’t necessarily apply.
2. Particularities that are taken as true from a local perspective are not demonstrably true from the global perspective. Yet within that local perspective they are customarily construed as either true or false (i.e. classical logical principles tend to apply).
3. Possibilities stand a chance of emerging within some future timespace juncture; yet, as possibilities, some will contradict others; nevertheless, both one possibility and another mutually exclusive possibility can coexist as comfortable bedfellow. Hence classical logical principles don’t necessarily apply here either.
1. A sentence may be considered true within a local perspective (i.e. ‘Atoms are indivisible spheres’), but its truth can’t be absolutely provable. From the global perspective it is neither true nor false, for at some future timespace juncture, there is no knowing which of the range of possible alternate sentences may be considered a more viable candidate (i.e. ‘Atoms are solid indivisible spheres, they are vortices, they are like a solar system, they are a probability amplitude, etc.).
2. A particular sentence, strictly within the norms of a local context, can be considered either true or false, with the stipulation that the sentence may turn out to be either inconsistent or incomplete or both within that local context.
3. The range of pure, unactualized possibilities holds the promise that, however inconsistent and/or incomplete the sentences within a particular context that have been given generality status may be, some alternate sentence will be available for selection at some future timespace context.