For instance, take two distinct contradictions, A ∧ ¬A and B ∧ ¬B, where A and B express ordinary, contingent propositions.
In particular, in any system with K and RM, (OBp & OB~p) ↔ OB⊥ is a theorem.[2] But it seems odd that there is no distinction between a contradiction being obligatory, and having two distinct conflicting obligations.
To accept no idea as certain that is not clear, distinct, and free of contradiction (mathematicism).
If to say that x and y are the same person is to say that x and y are persons and are (absolutely) identical, and to say that x and y are different passengers is to say that x and y are passengers and are (absolutely) distinct, we have a contradiction.
Frege quickly added an Appendix to the second volume, describing two distinct ways of deriving a contradiction from Basic Law V.
If g is a rational function but not a polynomial, by Lemma 2.2, then (g^{n}g^{ k)}-a=0) at least has two distinct zeros, which is a contradiction.
There is no contradiction between retaining a distinct cultural identity and identifying with Britain".
But there is no contradiction between retaining a distinct cultural identity and feeling a sense of belonging with Britain.
They also brought to it a distinct gloss with a built-in contradiction, depicting India as a classically timeless culture but one in sad decline.
The nuances and contradictions of the various distinct cultures surrounding us are slowly becoming more apparent, enriching our understanding of this region.
The seeming contradiction between functional cooperation and distinct subcellular localization of epithelial CEACAMs and integrins has been nicely resolved.
