The Mathematical Theory of Black Holes (1983)

Question

De Morgan aimed to 'scrutinize and castigate' both 'heterodox ignorance' and later 'orthodox learning.' What do these two targets suggest about his underlying definition of a 'paradox,' and how might addressing both types of 'inconsistencies' shape the overall philosophical message of his work?

Synthesized answer

The passages indicate that De Morgan aimed to scrutinize and castigate both "heterodox ignorance" and "orthodox learning" [2]. This suggests his underlying definition of a "paradox" is an isolated opinion held by one or few, with its counterpart being the general opinion held by all the rest [5]. By targeting both heterodox ignorance (false or absurd isolated opinions) and orthodox learning (general opinions that may contain contradictions or inconsistencies), De Morgan treats paradox as a neutral category—neither inherently false nor true—that requires critical examination regardless of its source.

Addressing both types of "inconsistencies" shapes the philosophical message of his work by establishing a balanced, impartial critique. He does not side with either the heterodox or the orthodox but subjects both to the same "scrutiny and castigation" [2]. This approach implies that error and inconsistency can arise from any quarter, and that true wisdom requires rigorous examination of all opinions, whether they are minority views or widely accepted doctrines. The passages confirm this dual target but do not elaborate further on the philosophical message beyond this balanced critical…

Synthesized from the book passages below. Chat with the book on Feynman for follow-up.

From the book

ionum recessus se recipere ut ab adversariorum telis sententiam suam in tuto collocarent. ​ Profecto magnus ille vir ... dogma illud, quamvis apud theologos eo nomine non multum gratiæ iniverit, ita ex immotis Philosophiæ fundamentis explicat ac demonstrat, ut paucis tantum immutatis, atque additis, nihil amplius animus veritate sincere deditus desiderare possit." This is properly paradox, though also heterodox. It supposes, contrary to all opinion, orthodox and heterodox, that philosophy can, with slight changes, explain the Athanasian doctrine so as to be at least compatible with orthodoxy.…
Passage [17]
← A Budget of Paradoxes by Augustus De Morgan Introductory 1489-1599 → 134520 A Budget of Paradoxes — Introductory Augustus De Morgan PREFACE TO THE FIRST EDITION. (1872) edit It is not without hesitation that I have taken upon myself the editorship of a work left avowedly imperfect by the author, and, from its miscellaneous and discursive character, difficult of completion with due regard to editorial limitations by a less able hand. Had the author lived to carry out his purpose he would have looked through his Budget again, amplifying and probably rearranging some of its contents. He had…
Passage [2]
l difficulty of reference. Sophia De Morgan . 6 Merton Road, Primrose Hill . PREFACE TO THE SECOND EDITION. edit If Mrs. De Morgan felt called upon to confess her hesitation at taking upon herself the labor of editing these Paradoxes, much more should one who was born two generations later, who lives in another land and who was reared amid different influences, confess to the same feeling when undertaking to revise this curious medley. But when we consider the nature of the work, the fact that its present rarity deprives so many readers of the enjoyment of its delicious satire, and the…
Passage [6]
w and old books; the paradoxes had no care given to the collection of either; the arithmetical books equal care to both. The list of arithmetical books, published in 1847, divides at 1735; the paradoxes, up to 1863, divide at 1825. If we take the process which is most against the distinction, and allow every year ​ from 1847 to 1863 to add a year to 1735, we should say that the arithmetical writers divide at 1751. This rough process may serve, with sufficient certainty, to show that the proportion of paradoxes to books of sober demonstration is on the increase; and probably, quite as much as…
Passage [567]
a paper: they had the sense to ask, and I had the sense to see that none of my opinions were compromised by compliance. And I will be of any use which does not involve the status of homo trium literarum ; as I have elsewhere explained, I would gladly be Fautor Realis Scientiæ , but I would not be taken for Falsæ Rationis Sacerdos . Nothing worse will ever happen to me than the smile which individuals bestow on a man who does not groove . Wisdom, like religion, belongs to majorities; who can ​ wonder that it should be so thought, when it is so clearly pictured in the New Testament from one end…
Passage [71]

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