Thought for the Evening: Incipit and Desinit
An incipit operator indicates that something begins to be;a desinit operator indicates that something comes to an end. Suppose we use <Inc> for incipit and <Des> for desinit. Then for <Inc>:
~<Inc>~X indicates that not-X does not begin to be (literally: Not-Begins-Not-X).
<Inc>X, of course, indicates that X begins to be. It is consistent with, but not required by, ~<Inc>~X (because the latter could be the case if ~X has been going on for a while).
<Inc>~X indicates that not-X begins to be. It is inconsistent with <Inc>X and also with ~<Inc>~X.
~<Inc>X indicates that X does not begin to be. It is inconsistent with <Inc>X, it is consistent with, but not required by, ~<Inc>~X and <Inc>X.
And for <Des>:
~<Des>~X indicates that not-X does not come to an end.
<Des>X indicates that X comes to an end; it is consistent with, but not required by, ~<Des>~X (because the latter is consistent with X never having been).
<Des>~X indicates that not-X comes to an end; it is inconsistent with <Des>X and also with ~<Des>~X.
~<Des>X indicates that X does not come to an end, and is inconsistent with <Des>X. It is consistent with, but required by ~<Des>~X and <Des>X.
The two can be related, since X beginning to be also tells us that not-X is coming to an end, and X coming to an end tells us that not-X is beginning to be, and so forth. Then:
~<Inc>~X is the same as ~<Des>X.
<Inc>X is the same as <Des>~X.
~<Inc>X is the same as ~<Des>~X.
<Inc>~X is the same as <Des>X.
Therefore if we wanted to say that Socrates begins to be wise, where 'Socrates is wise' is W, then we can say <Inc>W or <Des>~W.
Everything so far, however, overlooks the fact that we have stronger and weaker forms of both beginning and ending. So, for instance, we could mean 'X is beginning' in the sense that X is at some point in some process of beginning; that's a weaker form. Or we could mean that X has properly begun, which is the stronger form. The difference is that the stronger form implies "X is", while the weaker form does not -- in the weaker form, it could still be true that X does not exist (but there is a process such that X will be). We can call the stronger incipit <Inc1> and the weaker <Inc2>, and do the same, mutatis mutandis, for <Des>. Then we can say that <Inc1> implies <Inc2>, and <Des1> implies <Des2>, but not vice versa.
Various Links of Interest
* Manuel Vargas discusses parochialism in philosophy.
* Philip Kosloski notes that St. John Paul II's Luminous Mysteries are probably due to St. George Preca.
* Josh Blackman on what actually counts as a constitutional crisis.
* Beaney and Chapman, Susan Stebbing, at SEP.
* Gerard Bradley, Religious Liberty and the Common Good
* Carlo Rovelli argues against mathematical platonism: Michelangelo's Stone (PDF).
* Penelope Maddy, Set-theoretic Foundations.
Teresa of Avila, The Life of Saint Teresa of Avila by Herself
Teresa of Avila, The Interior Castle
C. S. Lewis, Present Concerns
Satischandra Chatterjee, The Nyaya Theory of Knowledge
Vladimir Soloviev, The Justification of the Good
Gregory Palamas, Dialogue Between an Orthodox and a Barlaamite