Peikoff Logic Homework on Informal Fallacies

The following consists of my answers for the first homework sheet of Leonard Peikoff's Introduction to Logic course. The handout with the exercises is freely available on the Ayn Rand Institute's website for the course. Note that I'm using the YouTube version of the lectures because I'm using certain Chrome Extensions as I read them (particularly Youtube Transcript Extractor, which generates an in-browser clickable transcript).

I used ✅ where I and Peikoff agreed, ❌ where I got a different answer and agreed with Peikoff's reasoning at the end of the day, and 🤔 for more complicated cases or significant disagreements or differences in reading of the prompt. For some questions I use multiple emoji and the reason why should be clear upon reading the question.

Note that I disagree with Peikoff's approach to what he calls the "argument from ignorance" or "argumentum ad ignorantiam", as I explained here and here. I've still named that fallacy below if I think it's the best guess as to the answer Peikoff was looking for.

I didn't include the names of the fallacies cuz transferring them over from my markdown flashcard note system would have been too much work. The below might therefore not make much sense unless you already know informal fallacies and are taking the course. I still present them below, as they might be helpful for someone also taking the course. One brief note about terminology: Peikoff's use of "Argumentum Ad Populum" for "Appeal to Other People's Emotions" seems to vary from current convention – most people seem to use Ad Populum to describe what he calls the quantitative type of Appeal to Authority (where you say that something is true because most people agree with it).

Problems

1 ✅

Until you are omniscient about yourself, you cannot know for sure whether or not some part of your motivation, presently unknown to you, is basically evil. For the present, you have no proof on this point either way. You must, therefore, admit that it is possible that you are, to some extent, basically evil.

Peikoff would say this is argument from ignorance. It demands that because you can't disprove that you are evil that you concede that you are evil (or possibly evil).

I would criticize the statement on different grounds. (One is bias – it's asking you to concede that you're possibly basically evil based on an unknown, rather than asking you to concede that you're possibly basically good or possibly basically neutral).

2 ✅

John Stuart Mill, Utilitarianism: “. . . each person’s happiness is a good to that person, and the general happiness, therefore, a good to the aggregate of all persons.”

Composition. Reasoning from something true about individual happiness to something true about some general or collective happiness.

3 ✅

"Long hair is superior to short hair, as proved by the consensus of distinguished youth leaders."
"How do you determine who is a distinguished youth leader?"
"That's easy. They all have long hair."

Arbitrary definition (petitio).

Initially, it appears that "distinguished youth leaders" has a meaning apart from needing to have long hair, but then it is later defined as necessarily involving long hair.

4 ✅

Your arguments against Red China's system of government are completely worthless, because you haven't even been there.

Ad hominem (abusive). Attacking the advocate of criticisms against Communist China due to a personal detail about them.

Peikoff: If you claimed to give an eyewitness account of facts and hadn't been to the location where you would have supposedly acquired such eyewitness knowledge, then someone bringing up the fact that you hadn't been there would be valid. But arguments against a system of government don't require you to be an eyewitness.

5 ✅

The American people are fundamentally opposed to the tactics of violence and lawlessness. The Weathermen, therefore, being Americans, must be champions of law and order.

Division. Statement is erroneously reasoning from a truth about Americans generally to a truth about some particular Americans.

6 ✅

My friends, the only cure for the present energy crisis is the nationalization of all oil and coal companies. Once and for all, we must put an end to the diabolical conspiracy of the profit-mad, power-lusting vultures of Big Business. Don't let the tycoons wrap their slimy tentacles around our nation's economy, and squeeze it dry for their own aggrandizement. Don't let them sink their blood-drenched claws into the helpless, exposed flesh of the American people.

Argumentum Ad Populum. Using emotional language in place of argument.

Also arguably question-begging epithet (assumes without argument that e.g. nationalization is a cure, there is a conspiracy of Big Business and so on).

7 ✅

"Every person acts at every moment to achieve the maximum personal pleasure. That is the sole human motivation."
"What about Mr. X? He just went into the desert for 10 years to mortify the flesh and lie on a bed of nails."
"That's no argument against me. That's his way of achieving personal pleasure."
"How do you know that that's his way of achieving pleasure?"
Well, it's obvious. After all, every person acts at every moment to achieve the maximum personal pleasure. That is the sole human motivation."

Circular reasoning. Arrives at the conclusion it started with by a serious of steps.

Possibly arbitrary redefinition. Arguably, a certain meaning of "maximum personal pleasure" was implied at the beginning that did not involve mortification of the flesh. And then the definition was switched mid-way to encompass such mortification.

Peikoff says he intended arbitrary redefinition.

8 ✅

Nobody is smarter than Einstein. You are smarter than nobody. Therefore, you are smarter than Einstein.

I think this is an amphiboly. If the first two sentences were drafted as "Einstein is smarter than everyone. You are smarter than no one." then the third sentence would clearly not follow, so the issue is arising from the grammatical construction or something. (Peikoff used similar reasoning but grouped this under equivocation)

✅ The other possibility is equivocation around "nobody".

9 ✅🤔

Croce, Philosophy of the Practical: "The Inquisition must have been justified and beneficial, if whole peoples invoked and defended it, if men of the loftiest souls founded and created it severally and impartially, and its very adversaries applied it on their own account, pyre answering to pyre.

✅ "if whole peoples invoked and defended it" is the quantitative type of argument from authority. It's saying that if whole peoples could do something, it must be justified. If accepted, that would justify, among many other horrors, the Holocaust.

✅ "if men of the loftiest souls founded and created it severally and impartially" is the qualitative type of argument from authority. It's saying that if certain men of lofty souls could found and create something, then it must be justified.

🤔"its very adversaries applied it on their own account" is also some type of argument from authority (the authority of the adversaries, who the author is implying wouldn't adopt some method if it were unjustified).

Notes

Peikoff read "its very adversaries applied it on their own account" differently than I did. He read it as Circumstantial ad hominem, basically saying that since the adversaries adopted the technique of the inquisition, you can ignore their arguments against the Inquisition, since they contradicted themselves (the error here being that the author is basically taking one side of the contradiction). I read it as essentially saying that the Inquisition was true because even its adversaries used its technique. It struck me as sort of similar to that line of reasoning that's common in political debate where you cite someone on "the other side" – a conservative might cite Jon Stewart or Bill Maher for example – and say "See? Even Bill Maher concedes X", with the implication that this supports or lends credibility towards establishment X.

Peikoff conceded that "if men of the loftiest souls founded and created it severally and impartially" could be an argument from authority but had in mind that it was a Petitio ("Until you know that it was justified, how do you establish that it was lofty men who did it impartially?" Maybe they were bad people who did it for bad reasons).

10 ✅

Are you a progressive who is in favor of basically changing the American political system, or are you one of those conservatives who believe that nothing in our present political system should be changed in any way?

False alternative lol. You could e.g. be in favor of making certain targeted changes but leaving the basics of the political system in tact.

Peikoff says complex question would also be valid but false alternative is better.

11 ❌

Marshall Tito of Yugoslavia: “There really isn’t very much difference between the political systems of America and Yugoslavia; after all, America has two major political parties and Yugoslavia one, a difference of only one party.”

Accent (emphasizing that there's only a difference of one party but not discussing the significance of a one-party state, instead just treating it like a trivial difference).

Peikoff said neglected aspect. I agree that that's a better fit. I think I was thinking of the prompt initially as emphasizing "one" party or something, but I don't think it's a good fit.

12 ✅

But this piece of music simply must be beautiful. There is not one ugly phrase in it from start to finish.

Composition. Just because each part of the music is okay doesn't mean the whole is.

13 ✅

Smith will give you a number of arguments as to why you should vote for the Democratic candidate. Don't fall for them. Remember that Smith has been hired by the Democrats and that he himself votes Republican.

✅ Ad hominem (abusive) - the fact that Smith has been hired by the Democrats is used to try to impeach his argument. But that fact is irrelevant to judging his argument.

✅ Ad hominem (circumstantial) - The fact that Smith votes Republican and that this contradicts his advocacy is brought up in a biased way to take one side of the contradiction (namely, to argue that Smith's arguments about the Democrats should be treated as unpersuasive).

14 ✅

Obviously, hard work is undesirable. A poll has just been taken which shows that the great majority of people definitely dislike hard work.

Quantitative argument from authority.

15 ✅

My lawyer, Mr. Green, says that I should settle out of court and not prosecute, because the law in this case favors my opponent. Since Green has a law degree from Harvard, 30 years of experience in the field, and a large and successful legal practice, I guess he should know I what he's talking about. The chances are that his advice is correct.

Not a fallacy but instead a proper treatment of the authority of an expert.

16 ✅

Of course, it's wrong to argue against conscription. You'll be drafted if you do.

Argumentum Ad Baculum if read as asserting that the truth of conscription is somehow upheld by the force involved if you disagree with it.

NOTE: If read as an argument regarding the most self-interested action (in other words: "It's unwise in the context of your life to publicly argue against the draft, because you'll be drafted if you do") then it would not be a fallacy.

17 ✅

My teacher tells me that we must be completely honest during the examination. My neighbor has just asked me to let him copy my entire examination. What can I do to resolve such a clash of interests except to let my neighbor copy just a part of my examination?

Misuse of the mean. Tries to rationalize assisting in cheating by positioning it as the middle of the road between two extremes.

18 ✅

All men want love, no matter what they say--because man's need for love is universal.

Restatement (petitio form). Saying that all men want love is just another way of saying that man's need for love is universal.

19 ✅🤔

“The best advice I can give you, in regard to your forthcoming job interview, is: Be yourself.”
“That’s ridiculous. How could I be anything else?”
“I mean: Be natural.”
“That’s foolish, too. I can hardly be supernatural.”

🤔Appeal to laughter (by means of repeated equivocations.)

Peikoff disagrees that it's appeal to laughter, because he says that the argument does not rest on invoking laughter. Earlier he described the appeal to laughter as trying to refute some viewpoint by turning ridicule against it. I read this dialogue as doing that, so I disagree with Peikoff.

✅"Yourself" is used to indicate that one should reflect one's personality honestly, and also in the sense of you as opposed to other people.

✅"Natural" is used to indicate that one should reflect one's personality honestly, and also to discuss the natural (as opposed to supernatural) world.

20 ❌

Peikoff says this one is super tricky.

Something cannot become nothing. The soul is something. Therefore, it cannot become nothing. Thus, the soul will always exist—i.e., it is immortal.

Well this argument is wrong factually but I'm not sure what the fallacy is.

One guess: "immortal" is a concept that pertains to living entities, but a soul is supposedly a disembodied spiritual essence that can endure in the absence of a living entity. So perhaps bringing immortality in at the end is a non-sequitur?

Peikoff

Peikoff says that there is equivocation. In the first sentence, "something" refers to a tangible thing, like an apple. In the second statement, there's no commitment to the soul being a substantial entity. (Note that Peikoff says we can take soul as being a faculty of consciousness and not necessarily mystical). The notion that "something cannot become nothing" doesn't mean that a faculty can't go out of existence. You can e.g have a faculty of vision and go blind. "Something cannot become nothing" has as its scope matter, substance, stuff, that sort of thing. It means that stuff can't vanish into nothing. But particular configurations of stuff that give rise to a capacity can change their configuration and then the capacity vanishes.

Peikoff also says that there's a non-sequitur in moving from "Therefore, it cannot become nothing. Thus, the soul will always exist". Because, given the meaning of "Something can't become nothing" we just discussed, the fact that something can't literally vanish doesn't mean that it will always exist (an apple can't become nothing but it can break down such that it's no longer an apple).

21 ✅

After the admiral read his young son a story, he was tucked into his crib with his favorite teddy bear.

Amphiboly? Seems more like a grammar issue to me than a bad argument. It's ambiguous as to whether the admiral or the young son is being tucked in.

22 ✅

Proposed subject for research project: Do the creatures who live in UFO’ s employ ESP?

Loaded question. Assumes that there are UFOs.

23 ✅

If a young hoodlum heaves a brick through the window of a baker’s shop, he creates business for some glazier. The glazier, with the money he will receive for fixing the window, will be able to buy, for instance, a suit—and thus he will create business for some tailor. And the tailor will be able to use the money he received to buy something from someone else. And so on. The smashed window will go on providing business indefinitely. We can only conclude that the man who broke the window actually helped the economy by doing so.

Neglected aspect (ignores e.g. the suit the baker could have bought).

24 ✅

How can you possibly argue against the validity of socialized medicine? Every civilized country in the world either has it already or is moving rapidly to enact it. On this question, the facts are clear: the trend of history has rendered a decisive verdict.

Argument from authority (quantitative and qualitative). Claims that a bunch of countries are doing it and so therefore it is correct (quantitative), and also that in particular civilized countries are doing it and therefore it's correct (qualitative).

Note: Peikoff didn't mention the qualitative aspect but I think it's there.

25 ✅

I am completely unprejudiced. Go ahead and tell me your vicious argument in favor of modern art, and I'll judge whether it is valid or not.

Question-begging epithet (Petitio form). Calling the argument "vicious" in advance of having heard it is assuming the point at issue (whether the argument is any good) before proof has been offered.

26 ✅

You must sign the legislation raising price supports for farm products, Mr. President. It is a perfectly sound law. Remember that farm organizations in five states have announced that if you veto this bill, they will work for your opponent in the coming election.

Argumentum ad baculum (appeal to force). The implied claim is that the law is sound because of the threat of the farm organizations.

27 ✅

From The New York Times: “Supporters of Mr. Sandman, the 1973 Republican candidate for governor of New Jersey are counting on logic. To this end they have constructed the following syllogism: A majority of the voters oppose an income tax. Mr. Sandman says he will save them from one. It follows, then, that a majority of the voters will vote for him.”

✅ Neglected aspects (Do the voters believe Mr. Sandman? Do they care about any other issues?).

Peikoff: could also be non-sequitur.

28 ✅

Genghis Khan must have been evil at birth because, after all, a man is born either fundamentally good or fundamentally evil, and Genghis Khan is clearly not in the former category.

False alternative. People could be neither good nor evil at birth but form their character later.

29 🤔

You ask me to give you a valid argument to prove the truth of the Law of Contradiction? That's simple. Whatever is presupposed by all knowledge must be true, and the Law of Contradiction is presupposed by all knowledge. Therefore, I infer that the Law of Contradiction must be true.

My Answer

The form is:

1. Whatever is presupposed by all knowledge must be true.
2. The law of contradiction is presupposed by all knowledge.
3. Therefore, the law of contradiction must be true.

Superficially this appears okay because it looks like the famous Socrates syllogism. You make a general statement about a category, identify a concrete as being a member of that category, and then state a consequence of the concrete due to membership in the category.

My guess is that Peikoff will say you can't prove an axiom, you need to start with it.

One thought about this: if we treat "The law of contradiction is presupposed by all knowledge" (which I will call "X" for the purposes of this paragraph) as true, then X is a bit of knowledge (meaning X is some factual detail or description about the state of the world). But if X is true, then X needs to be presupposed by all knowledge, including X! And a thing can't be its own mandatory presupposition. Thus, if we assume X is true, we need X to be both be knowledge (in order to be an accurate description of the state of the world, which is an implication of X being true) and not knowledge (so that we don't try to have X be its own supposition). A thing can't be both X and not X at the same time and in the same respect.

As to which specific fallacy to categorize this in, I'm honestly not sure but I think it'd be some petitio principii. Perhaps circular reasoning?

Peikoff

Peikoff says it's a petitio but a miscellaneous type that wasn't covered.

He says that any argument ultimately depends on an appeal to the law of contradiction (I think he means the law of non-contradiction). E.g. (my example)

1. Socrates is a man.
2. All men are mortal.
3. Since the law of contradiction is true and therefore Socrates can't both be a man and not mortal,
4. Socrates is mortal.

In this case, the structure of the reasoning is

1. Whatever is presupposed by all knowledge must be true.
2. The law of contradiction is presupposed by all knowledge.
3. Since the law of contradiction is true,
4. Therefore, the law of contradiction must be true.

The point at issue, the thing you are trying to prove, is assumed in the argument (hence petitio) but it is not assumed as one of the formal assumptions but is instead assumed in the very act of reasoning.

Peikoff says this illustrates that any attempt to prove the laws of logic would commit a petitio.

30 ✅

Communism means dictatorship; laissez-faire capitalism means dog-eat-dog competition. But we don’t have to accept either of these radical systems. Isn’t the wisest course to combine the advantages of each—i.e., to have a mixed economy?

✅ Misuse of the mean. Assumes the correct economic system is in between the two systems identified.

31 ✅

There are no real differences among people; basically, they all want the same thing: strength. For instance, Napoleon wanted a strong army, Adam Smith wanted a strong economy, Aristotle admired strong arguments, and my Senator loves strong liquor.

Equivocation re: "Strength" (as in "effective/powerful/large" for army, "robust/growing" for economy, "sound/valid/persuasive" for arguments, and "high in alcohol" for liquor).

32 ✅❌

You don’t believe in government regulation of the economy? But then you must be an anarchist.

✅ ❌ Irrelevant conclusion, extension subtype (straw-manning a laissez-faire person's views).

Peikoff says false alternative is better/more specific and I agree.

33 ✅

Of course, this is an important news story. The New York Times gave it six columns on the front page.

Argument from authority (qualitative). The claim is that it's an important news story because the prestigious New York Times says so.

34 ✅

Philosophers have tried for millenia [sic] to prove the existence of a supernatural dimension. I admit that all their arguments so far have been invalid. But no one has yet disproved their viewpoint, either. Maybe, therefore, they are right.

Peikoff would say this is an argument from ignorance. It says that since we've failed to disprove something, maybe it's right.

I would say that the flaw here is that it offers no criticism of the criticisms of supernaturalism.

35 ✅

“Bill is a marvelous person. I always enjoy myself in his company.”
“I disagree. I think he’s awful. It depresses me just to be in the same room with him.”

Appeal to one's own emotions. The fact that the second person has an emotional response is being used to demonstrate Bill's character.

36 ✅

The development of literature—both fiction and non-fiction—is a great milestone in the progress of civilization. Mein Kampf was one of the most widely read books in world literature. We must, therefore, give it due credit for its civilizing influence on the world.

✅ Division. Starts with information about literature in general and then uses that as the basis for a statement about a particular book.

Could also be neglected aspect (neglects specific content of Mein Kampf) or irrelevant conclusion.

37 ✅

Karl Marx and F. Engels, The Communist Manifesto: “But don’t wrangle with us so long as you apply, to our intended abolition of bourgeois property, the standard of your bourgeois notions of freedom, culture, law, etc. Your very ideas are but the outgrowth of your bourgeois production and bourgeois property just as your jurisprudence is but the will of your class made into a law for all, a will whose essential character and direction are determined by the economic conditions of existence of your class.”

✅ Ad hominem ("bourgeois" ideas and criticisms of Marxism are wrong because the advocates are bourgeois).

Possibly argument from authority (non-bourgeois ideas having authority). (Peikoff did not address this)

38 ✅

More people now become ill from smallpox vaccination than from smallpox itself. This clearly demonstrates the futility of vaccination.

Neglected aspect – the facts are compatible with smallpox being so effective that it has reduced deaths from smallpox enormously.

39 ✅

You say that man should aspire to perfection? That’s impossible. Of course, I don’t believe that one should be depraved, but isn’t moderation the best policy? You know, we’re all gray—nobody is morally black or white.

Misuse of the mean.

Peikoff: Also cliched thinking re: "nobody is black or white".

40 ✅

You argue that happiness is possible to man? Well, you're wrong. Wait until you've lived.

Pretty vague.

Speaker could be appealing to his own emotions? (Peikoff did not address)

✅Or ad hominem against person based on their supposed lack of experience?

41 ✅

When I consider the massacres in Russia, I realize how evil slavery is. That’s why I’m going to quit going to college. In college I’m a slave to the chronic routine of attending lectures, studying, taking exams, and so on. How much better it would be to be free!

Equivocation around "slavery", which has a different meaning a communist society compared to just doing stuff you don't like in college.

42 ✅

Newspaper headlines:
(1) Mayor Attacks Obscenity at Junior League Tea.
(2) Master Chef Likes Dessert More than Wife.

Amphiboly?

I think maybe the first sentence is intended to be ambiguous as to whether the mayor is criticizing the use of obscenity at the tea or himself used obscenity at the tea. The latter reading might be better punctuated as "Mayor Attacks! Obscenity at Junior League Tea."

The second statement could mean that the chef prefers his dessert to his wife or that he enjoyed the dessert more than did his wife.

43 ✅

Of course, it's a great movie. I loved it.

Appeal to one's own emotions. The fact that the person liked the movie is being used as a proof that it was a great movie.

44 ✅

I don’t care how powerful your reasoning is. You can’t be certain of your conclusion on this (or any) question. Since man is fallible, how do you know that you didn’t make a mistake?

I think Peikoff intends this as an Argument from Ignorance.

I think it's a bit vague as written and could be read in both a fallacious way and a reasonable way (depending on how you take "certain" and your epistemological ideas), but I don't want to go into a big tangent on that.

45 ✅

Aristotle defined the laws of logic in ancient Greece. We are living in the twentieth century. Obviously, things have changed enormously since then, and his logic is now deficient.

Ad hominem (saying Aristotle's ideas are wrong because he lived a long time ago). Peikoff: specifically, abusive)

46 ❌

Capitalism is the right system of government because it promotes the freedom of the individual. Individual freedom is good because it enhances the individual’s ability to produce. And production is a good thing because, without it, we could never maintain the free enterprise system.

Shorter restatement:

Capitalism is right because it promotes freedom.

Freedom is good because it helps production.

Production is good because we need it for capitalism.

I don't think this is circular because the final statement isn't "capitalism is right" but "we need it for capitalism." Things can be interrelated and have connections between each other and that's not circular.

Peikoff:

Disagrees and thinks it's circular reasoning.

47 ✅

Material entities are made up, ultimately, of subatomic particles, each of which is rigorously determined in its action by scientific law. The human body, too, is made up of such particles. Consequently, a man’s actions are rigorously determined. Free will is a myth.

Composition. Reasoning that because something is true of parts that a human is made out of, it must be true of the whole.

48 ✅

There will never come a time when all men agree about everything; there are always going to be disputes and disagreements. For this reason, war can never be eradicated.

Non-sequitur. Just brings up war as inevitable. Implied argument seems to be that disputes and disagreements necessarily lead to war.

49 ✅

Professor, you must raise my grade in this course. Otherwise, I won’t be able to graduate, and that means I’ll lose my job—and then what will happen to my two sick children?

Appeal to pity. Claim is grade should be raised cuz this guy is a sad case.

50 ✅

Obviously, machines cause unemployment. Every time a machine does a job that a man could be doing, the man is thrown out of work.

Neglected aspect. E.g. a power shovel can enable a single man to do way more than a bunch of men could, which increases productive and could lead to tons of new jobs as the price of projects drops.

51 ✅❌

You can ignore his arguments against religion. As soon as he confronts his own weakness, he’ll forget them himself. You know the old saying: There are no atheists in foxholes.

Cliche thinking. There are plenty of atheists in foxholes.

Peikoff mentions, and I missed, that the first two sentences are making a circumstantial ad hominem argument (he will be personally inconsistent and thus you can ignore his arguments).

52 ✅

Watergate proves that the American system of government cannot survive if the President continues to have unlimited power. We must give that power to Congress.

False alternatives. Why does any branch need to have unlimited power?

53 ✅

How do you explain the telekinetic abilities demonstrated at Duke University?

Complex/loaded question. Assumes telekinetic abilities exist.

54 ❌

If a person is in love, he wants to communicate with the person he loves. He hasn’t telephoned me for two days. Therefore, he doesn’t love me.

Equivocation about the meaning of "communicates" perhaps? "Communicates" is a pretty broad term that could encompass a range of frequencies of communication, but then the person is saying that failure to call for two days proves no love.

Peikoff says it's just a non-sequitur.

55 ✅

Pornography is disgusting. There should, therefore, be a law forbidding it.

I said non-sequitur.

56 ✅

“I want to see a movie downtown on Thursday.”
“Do you have the money?”
“Yes.”
“Do you intend to go to the theater and purchase the ticket?
“Yes.”
“Are you sure there is a movie playing downtown on Thursday?”
“Yes.”
“Then I can only conclude that, barring some unforeseen circumstance or a change in your plans, you will see a movie on Thursday.”

Solid reasoning. No fallacy.

57 ✅

This man claims that he remembers his former life, in which he was the Pharaoh of Egypt. I believe him. And you can’t prove that he wasn’t.

Appeal to one's own emotions (Peikoff did not address).

✅ Peikoff would say argument from ignorance. The guy is appealing to his belief and also seems to be saying that because you can't disprove the claim, you should accept it.

58 ✅

Employee: “What is the reason for filling out these forms in triplicate?”
Employer: “You’ll be fired if you don’t.”

Appeal to force. Employee asked for a reason, not a description of the consequences of failure.

59 ✅

If you don’t believe in God, then you must believe that the order in the universe is a result of blind chance. But that is ridiculous. Therefore, there is a God.

False alternative.

60 ❌

Societies disagree profoundly with one another as to what constitutes good and evil. This shows that objective truth in ethics can never be known by man.

The fact that people disagree doesn't show that objective truth is unknowable. At most, such disagreement might indicate that the available argument about the point are lacking in some way.

I think that Peikoff might say it's an Argument from Ignorance. A way of reading it is that there is an implied premise that if societies agreed with one another as to what constitutes good or evil, then that would establish an objective truth in ethics. But since they disagree, we can't prove an objective truth in ethics, and therefore this shows that we can't know an objective truth in ethics.

It's not quite an argument from ignorance cuz it's not saying that because you can't prove X is false therefore its true.

Peikoff

The implicit premise is that you need to consult society to know the truth. Appealing to society to determine the truth is an appeal to authority.

61 ✅

In a free country, men agree to abide by majority rule. The majority in this country regards abstract philosophy as a waste of time. Therefore, as a man dedicated to freedom, you must accept and abide by the majority’s view on this question.

Equivocation about "majority rule". Accepting majority rule means you accept the determination of the majority as to political questions. It does not mean you accept whatever the majority thinks is true.

Bonus: Equivocation ✅❌

1. What happens every day is a usual event.
2. Unusual events happen every day.
3. Unusual events are usual events.

Tricky. Here's a true version:

1. If some particular event happens every day, it is a usual event.
2. Some particular unusual event happens every day.
3. Therefore, some particular unusual event happening is a usual event.

And here's one reading of what the original implies (fallaciously):

1. If some particular event happens every day, it is a usual event.
2. Some particular unusual event happens every day.
3. Therefore, all unusual events happen every day and are thus usual events.

So I think the equivocation is around "unusual events". Due to the ambiguous writing, on the second line, one can read the meaning as that some particular unusual event happens every day. And then one can make a fallacious leap in the third line to saying that all unusual events happen every day. This would arguably also be composition (going from a truth about a particular unusual event on a particular day to a purported truth about every unusual event on every day).

Peikoff focuses on "happens every day" but his analysis is very similar. I gave myself partial credit here.