When1: 1905
When2: 1908
Who: Jules Henri Poincaré [Poincaré, Jules Henri]
What: mathematician/philosopher
Where: Paris, France
works\ Science and Hypothesis [1905]; Foundations of Science [1908]
Detail: He lived 1854 to 1912, helped develop intuitionism, and studied function theory, differential equations, orbits, and combinatorial topology. He found special-relativity equations [1905]. He showed how to keep distances constant as observed from different constant motions in flat space-time {Poincaré motion} {inhomogeneous Lorentz motion}, by lengthening light-cone along space dimensions and shrinking light-cone along time dimension. After systems reach largest phase-space region, they can return to all smaller regions over times much longer than universe age {Poincaré recurrence}.
Epistemology
Mathematical thinking is purely mental and so can reveal what is essential in mind. Unconscious thinking has preceded insight. Mind unconsciously selects possible solutions using innate or consciously formulated rules. Thinking appears to move in one direction and has purpose. Aesthetic value is an important creativity component.
Thinking converges on truth, but absolute truth is unattainable. Statement is possibly true if it is not necessary that it is not true. Contradictions are necessarily not true. Statements that do not involve contradiction state logical possibility. Not all contradictions are apparent. Nature contains contradictions, so contradictions can state possibilities.
Science decides what is naturally possible and naturally impossible. Epistemic possibility is what is consistent with human knowledge states. Possible truth is true in at least one possible world. Necessary truth is true in all possible worlds. Possibility and necessity are arbitrary rules about word use. Concept meaning depends on possible and impossible.
Definition can quantify over all class objects {vicious-circle principle, Poincaré} {impredicative definition, Poincaré} or not include them {predicative definition, Poincaré}.
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Date Modified: 2022.0224