References
[Editor’s notes are in blue. Readers who prefer to ignore the links in the text and follow the notes on a separate page, may open a separate page with the references here.]

* The title refers to Nathaniel Branden’s lecture “The Concept of God,” from his lecture series “The Basic Principles of Objectivism.” That lecture is fully transcribed in his book The Vision of Ayn Rand: The Basic Principles of Objectivism (Gilbert, Ariz.: Cobden Press, 2009), chapter 4. Partial and perhaps complete audios seem to be available throughout the Internet. See also R.A. Childs, “The Epistemological Basis of Anarchism,” Note 19.

[01] Webster’s Third, under “modus tollens.”
  Britannica 3, Micropedia, under “modus ponens and modus tollens.”
  Britannica (1961), under “logical glossary” see “modus tollens” and “indirect proof” and “reduction.”
  Encyclopedia of Philosophy, ed. Paul Edwards (Macmillan 1967) under “logical terms, glossary of” see “modus tollens” and “indirect proof” and “reduction.”
  For a discussion and endorsement by Aristotle, see his Prior Analytics, 45a23-45b11, and 62b29-63b21 (ii.14).
  For use by Euclid, see the Elements, Book I, Propositions 6-8 et passim.
  [URLs supplied by the editor. The Sudoku puzzle was not well known when James wrote his Revisions, but it has since become fairly popular. “Modus tollens” is a primary tool for solving Sudoku puzzles.]

[02] AS [Atlas Shrugged] 139x-140u [paperback] (142jj-143hh) [hardback].
  [James Taggart to Francisco at a party]
  “Well, first of all, that nationalization — what are you going to do about it?”
  “Nothing.”
  “Nothing?!”
  “But surely you don’t want me to do anything about it. My mines and your railroad were seized by the will of the people. You wouldn’t want me to oppose the will of the people, would you?”
  “Francisco, this is not a laughing matter.”
  “I never thought it was.”
  “I’m entitled to an explanation! You owe your stockholders an account of the whole disgraceful affair! Why did you pick a worthless mine? Why did you waste all those millions? What sort of rotten swindle was it?”
  Francisco stood looking at him in polite astonishment. “Why, James,” he said, “I thought you would approve of it.”
  “Approve?!”
  “I thought you would consider the San Sebastián Mines as the practical realization of an idea of the highest moral order. Remembering that you and I have disagreed so often in the past, I thought you would be gratified to see me acting in accordance with your principles.”
  “What are you talking about?”
  Francisco shook his head regretfully. “I don’t know why you should call my behavior rotten. I thought you would recognize it as an honest effort to practice what the whole world is preaching.... I have carried out every moral precept of our age. I expected gratitude and a citation of honor. I do not understand why I am being damned.”

  AS 474x-ee [paperback] (505h-o) [hardback].
  [Dagny to a board of directors]
  “Got what you’ve been asking for all these years, gentlemen?”
  ... [7 lines]
  In the silence of the next moment, she felt their resentment like a starch thickening the air of the room, and she knew that it was not resentment against Mr. Weatherby, but against her.

[03] Allan Calder, “Constructive Mathematics,” Scientific American, October 1979, pp. 146-71. [This article is available from the Scientific American website to subscribers and at jstor.org for a fee. The first page of the article is available at jstor as a teaser.]

[04] AS 191p-r, 315v-z, 913ff-vv [paperback] (199e-g, 331aa-ee, 984s-ii) [hardback].

[05] A. Rand, “Collectivized Ethics” 2/1/4e-f [References of this form refer to The Objectivist Newsletter, so that volume 2, number 1 would be January 1963. After volume 4, the name of the publication was The Objectivist. The page numbers for the latter are those of the original format, not those in the bound volume. James seems to have erred in his Objectivist Newsletter citation here. The correct lines are dd-oo.] and VOS [The Virtue of Selfishness (paperback)] 85.
  And if you wish, give him the following example of the ideals he advocates. It is medically possible to take the corneas of a man’s eyes immediately after his death and transplant them to the eyes of a living man who is blind, thus restoring his sight (in certain types of blindness). Now, according to collectivized ethics, this poses a social problem. Should we wait until a man’s death to cut out his eyes, when other men need them? Should we regard everyone’s eyes as public property and devise a fair method of distribution? Would you advocate cutting out a living man’s eye and giving it to a blind man, so as to “equalize” them? No? Then don’t struggle any further with questions about ...

A. Rand, “The Nature of Government” 2/11/49gg-50b. [December 1963; I have been assuming that James’s letters refer to a line count — a-z for lines 1-26, aa-zz for lines 27-52, aaa-zzz for lines 53-78. If that is true, James has erred in his citation here, which should read 2/12/49dd-50i] and VOS [paperback] 112-13.
  A recent variant of anarchist theory ... is ... called “competing governments.” ...
  Ask yourself what competition in forcible restraint would have to mean....
  One illustration will be sufficient: ... a squad of Police A proceeds to Mr. Jones&146; house and is met at the door by a squad of Police B.... What happens then? You take it from there.

A. Rand, “IAD: Patents and copyrights” 3/5/19cc-dd. [Intellectual Ammunition Department, May 1964; James’s line count is wrong. The text that he is citing is in the second column, lines q-s.]
  Consider what would happen if ... we had to pay royalties to the descendants of ... the inventor of the wheel....

WTL 385-388 [We the Living, 1959 edition, paperback] & FNI 60-62 [For the New Intellectual, paperback].
  (Kira to Andrei on the consequences of altruism — modus tollens)

FH 684 [The Fountainhead, paperback, the later Signet edition bearing the renewed copyright date of 1971; it is page 676 in an earlier Signet edition designated as the “nineteenth printing”] & FNI 83 (paperback).
  The leaders of collectivist movements ask nothing for themselves. But observe the results.

AS 936tt-937b [paperback] (1010j-p) [hardback] & FNI 117-18 [paperback].
  You have destroyed all that which you held to be evil and achieved all that which you held to be good. Why, then, do you shrink in horror from the sight of the world around you? That world is not the product of your sins, it is the product and the image of your virtues. It is your moral ideal brought into reality in its full and final perfection. You have fought for it, you have dreamed of it, you have wished for it, and I — I am the man who has granted you your wish.

AS 398gg-ii [paperback] (422z-bb) [hardback].
  “Why James,” said Francisco, smiling, “what’s the matter? Why do you seem so upset? Money is the root of all evil — so I just got tired of being evil.”

[06] A. Rand, “Cashing In: The Student Rebellion” 4/7-9. [July-September, 1965] & TNL [The New Left: The Anti-Industrial Revolution] 13-57. [TNL was later revised and updated to include Ayn Rand’s essay “The Age of Envy” and then later issued under the title Return of the Primitive: The Anti-Industrial Revolution. It contained additional essays by Ayn Rand (“Racism” and “Global Balkanization”) and an Introduction and additional essays by Peter Schwartz.]
  A. Rand, “The Roots of War” 5/6 [June 1966].
  A. Rand, “The Wreckage of the Consensus” 6/4-5 [April-May, 1967].
  A. Rand, “Apollo and Dionysus” 8/12 - 9/1 [December, 1969 - January, 1970] & TNL 57-81.
  A. Rand, “The Anti-Industrial Revolution” 10/1-2 [January-February, 1971] & TNL 127-51.

[07] AS 858tt [paperback] (925gg) [hardback].

[08] A. Rand, “Introduction to Objectivist Epistemology,” 5/9/2c. [September 1966] [References of this form refer to The Objectivist Newsletter, so that volume 5, number 9 would be March 1966. After volume 4, the name of the publication was The Objectivist. The page numbers for the latter are those of the original format, not those in the bound volume.] and IOE 38 [Introduction to Objectivist Epistemology. (And the reference here is to the original paperback monograph reprinting the articles from the periodical. However, James has erred in his pagination, and the correct page number is 31; the corresponding page number for the Expanded Second Edition containing additional material by Harry Binswanger and Leonard Peikoff (New York: NAL, 1990) is 29.)]

  AS 942g-p [paperback] (1015jj-ss) [hardback].
  Existence exists — and the act of grasping that statement implies two corollary axioms: that something exists which one perceives and that one exists possessing consciousness, conscious being the faculty of perceiving that which exists.
    If nothing exists, there can be no consciousness: a consciousness with nothing to be conscious of is a contradiction in terms. A consciousness conscious of nothing but itself is a contradiction in terms: before it could identify itself as consciousness, it had to be conscious of something. If that which you claim to perceive does not exist, what you possess is not consciousness.

  AS 966i-l [paperback; the quotation actually begins on line h; no hardback citation is given].
  The day when he grasps that the reflection he sees in a mirror is not a delusion, that it is real, but it is not himself, that the mirage he sees in a desert is not a delusion, that the air and the light rays that cause it are real, but that it is not a city, it is a city’s reflection....

[09] N. Branden, “Self-Esteem,” [Part V of a 5-part series] 6/9/8b [September 1965]. [There is a parallel passage in The Psychology of Self-Esteem: A New Concept of Man’s Psychological Nature, page 140 (New York: Bantam, 1971). James did not cite material Branden published after his break with Ayn Rand (May 1969), even when it was presented in terms identical to his earlier work, but only material presented before that break, the idea being that he didn’t want to create an opening for the objection Branden’s later work did not correctly state principles of Objectivism.]
  Rationality does not guarantee infallibility.

  N. Branden, “IAD: The psychological primacy of the choice to think” 3/4/14bb [April 1964]. [The cited text is in the second column, lines g-i; there appears to be no parallel passage in POS.]
  ... when a man is awake and his brain and nervous system are structurally normal, he is conscious — if only passively.

  FNI 19.
  Since no man can fully escape the conceptual level of consciousness, it is not the case that Attila and the Witch Doctor do not think....

[10] AS 942vv-yy [paperback] (1016cc-ff) [hardback].
  The task of his senses is to give him the evidence of existence, but the task of justifying it belongs to his reason, his senses tell him only that something is, but what it is must be learned by his mind.

  A. Rand, “Intro. to Object. Epistemology,” 5/7/g [July 1966] & IOE 6. [Actually, page 11. Expanded edition, page 6.]
  A sensation is a sensation of something.... A sensation does not tell a man what exists, but only that it exists.

  A. Rand, “A Letter from a Reader,” 5/10/13c [October 1966].
  ... it is our job to tell people what Objectivism is, it is your job to tell them that it is.

  A. Rand, “Intro. to Obj. Epistemology,” 5/12/5a [December 1966] & IOE 78 [page 55; Expanded edition, page 59].
  The concept “consciousness” does not indicate what existents one is conscious of: it merely underscores the primary fact that one is conscious.

[11] N. Branden, “The Roots of Social Metaphysics,” 6/10/2e [October 1967; parallel passage at POS, page 175].
  Man’s mind is fallible; he can make an error at any step of the thinking process....

  N. Branden, “Self-Esteem and Romantic Love,” 7/2/2a [February 1968; modified parallel passage in POS, page 214].
  It is a fact of reality that man is neither omniscient nor infallible.

  N. Branden, “The Contradiction of Determinism,” 2/5/17jj [May 1963]. [The correct lines are rrr-vvv in the second column. The parallel passage in POS is on pages 54-55. Other parallel passages may be found in the YouTube except from Lecture 5 on free will at 4:15-4:39, and in N. Branden, The Vision of Ayn Rand, page 136.]
    Man is neither omniscient nor infallible. This means (a) that he must work to achieve his knowledge, and (b) that the mere presence of an idea inside his mind, does not prove that the idea is true; many ideas may enter a man’s mind which are false.

[12] N. Branden, “The Contradiction of Determinism,” 2/5/20h [May 1963, page 20, correct line is aaa]. [Parallel passages may be found in POS on pages 56-57, and in The Vision of Ayn Rand, page 139. The YouTube excerpt ends before this passage.

[13] A. Rand, “Man’s Rights,” 2/4/13jj [April 1963; the correct citation should be for line ooo in the second column.] & VOS 94.

[14] I am indebted to Dr. Alan Wilson, formerly of the University of Wisconsin, for this formulation.

[15] See George Smith, Atheism: The Case against God (Nash, Los Angeles, 1974, out of print [hardback, pages 119 ff.]; Prometheus, 1980, 120 f. [paperback]).
  Smith’s discussion of coin-flipping as a means of obtaining knowledge is lucid and concise, as are his discussions of many other points. This is not an endorsement of every statement in the book.

[16] N. Branden, “The Contradiction of Determinism,” 2/5/20a [May 1963] & POS 55. [Parallel passages are to be found in The Vision of Ayn Rand, page 137, and in the YouTube excerpt, 7:42-7:48.]
  One of the defining characteristics of psychosis is loss of volitional control over rational judgment....

[17] N. Branden, “The Contradiction of Determinism,” 2/5/17jj [May 1963; rrr-sss] & POS 54-55. [Parallel passages are to be found in The Vision of Ayn Rand, page 136, and on YouTube 4:15-4:39.]
  Man is neither omniscient nor infallible. This means (a) that he must work to achieve his knowledge, and (b) that the mere presence of an idea inside his mind, does not prove that the idea is true; many ideas may enter a man’s mind which are false.

  AS 391uu-392i [paperback]; (415n-aa) [hardback].
  “Señor d’Anconia,” declared the woman with the earrings, “I don’t agree with you!”
  “If you can refute a single sentence I uttered, madame, I shall hear it gratefully.”
  “Oh, I can’t answer you. I don’t have any answers, my mind doesn’t work that way, but I don’t feel that you’re right, so I know that you’re wrong.”
  “How do you know it?”
  “I feel it. I don’t go by my head, but by my heart. You might be good at logic, but you’re heartless.”
  “Madame, when we’ll see men dying of starvation around us, your heart won’t be of any earthly use to save them. And I’m heartless enough to say that when you’ll scream, ‘but I didn’t know it!’ — you will not be forgiven.”