propositions

So the We is We hackers, who can design and build new information-contexts with different value propositions and power dynamics.

Bottom is a member of every type, so all Haskell programs correspond to proofs of trivial propositions.

These propositions could both be consistent with a specified set and yet be inconsistent with each other.

Skewness is what brings some toward riskier propositions, in hopes for a small chance of huge success.

Many classical and neoclassical economic propositions are of a fundamentally epistemological nature, not strictly positivist.

If only the Chicago and Austrian schools would change their minds when data supporting their propositions are weak or of low confidence.

These valuations are based on the philosophical underpinnings of the belief systems of the individuals in question, not on propositions subject to empirical verification.

For good and for ill, one of Bitcoin's core value propositions will always be its promise to vitiate governments' attempts to control their citizens' money.

P=NP would imply that we can relatively easily find polynomially long proofs to many hard propositions, such as the P=NP problem itself!

If coherence is consistency, the coherence theorist would have to claim that both propositions are true, but this is impossible.[1] There's an analogy to Escher's art.

Instead, they're using a lot of backwards-looking, unfalsifiable propositions.

Summary for the layperson: The Curry-Howard Isomorphism is an exact syntactic correspondence between types for lambda calculi, propositions in intuitionistic logics, and objects in closed Cartesian categories.

Essentially, constructive mathematics is mathematics done without the law of excluded middle ("for all propositions P, either P or not P").

The catch is that univalence is inconsistent with LEM at h-levels greater than -1, but assuming it is perfectly consistent for -1 types, which can be thought of as the "at most true" propositions of classical logic.

Contrast with "I think", which I think is more appropriate for statements with at least some deliberate thought behind them, or involve more concrete propositions ("I think Brand X hardware is unreliable", "I think it was last Wednesday").