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Indeed, there is a deep analogy between this distinction drawn by Carnap and Feigl's distinction between the validation within an ethical system and the vindication of the ethical system (and its supreme norms) itself.
Herein lies the deep analogy with the eternal inflation model of the evolution of the multiverse in which universes repeatedly emerge as a result of a local halt of inflation caused by the decay of regions of false vacuum (Fig. 3A).
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Christian interpretation seeks to find in Shakespeare's plays a series of deep analogies to the Christian story of sacrifice and redemption.
This gives rise to a rich web of deep analogies and conjectures that underlies much of Naor's research and leads to unifying analytic insights about geometric objects that occur throughout the mathematical sciences". The Nemmers Prize is awarded biennially by Northwestern University to recognize works of lasting significance in the discipline.
A second, advanced part then discusses the deep analogies (and differences) between a geometric theory of gravity and the gauge theories of the other fundamental interactions.
By thinking over the notion of self, we can see that deep analogies exist between such notion and Leibniz's idea of monad: it is a matter of centers, unity, and activity.
In this section, I elaborate on the, apparently, deep analogies between the BBB model and the cosmological model of eternal inflation.
A deeper analogy relates tidal forces with a property of surfaces called curvature.
If you dig deeper, this analogy makes a lot of sense.
These deep quantificational analogies reflect much of the inspiration behind what is most often called "possible worlds semantics" for such logics, to which we now turn.[22] Once the analogies are noticed, this sort of semantics seems all but inevitable.
Of course, finding deeper mathematical analogy between our method and such traditional inference algorithms would be certainly interesting, but that would be beyond the scope of this paper.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com