# Peikoff Homework on Definitions

More Peikoff Logic Homework

## Intro

The following consists of my answers for one of the homework sets in 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. These exercises start on page 13 in the handout.

I used β where Peikoff agreed (basically, on the essential point) with some portion of my answer and β where I got a different answer from Peikoff and agreed with Peikoff's reasoning at the end of the day. I used π€ for disagreements with Peikoff's answer or for stuff I was unclear on. For some questions I may use multiple emoji and the reason why should be clear upon reading my answer (typically, it's something like I got one point correct but missed another). When I put a β or β in a particular place within my answer and not others, it means that Peikoff spoke to that part but not to the rest of my answer. If I didn't put a β or β in a particular place, it probably just means that I forgot to do that.

For problems 8, 14, 17, 20, and 22, the approach was different than from the other problems. Instead of just analyzing the existing definition for defects, people were asked to come up with a positive definition, and various possibilities were discussed before Peikoff offered his own analysis. I didn't grade these.

## Definition Terminology & Rules

Peikoff lays out some rules for formulating proper definitions. These rules are apparently part of traditional logic.

### Terminology

#### Genus & Differentia

A genus is a class wider than the concept to be defined which represents the basic identity of the concretes in question. For example, in "Man is a rational animal", the genus is "animal".

A differentia is a characteristic which distinguishes the concretes in question from all other members of the genus. For example, in "Man is a rational animal", the differentia is "rational".

A definition must consist of a genus and differentia.

#### Definiens & Definiendum

A definiens is a word, phrase, or symbolic expression used to define something, especially in a dictionary entry, or introduce a word or symbol into a logical system by providing a statement of its meaning. E.g. in "man is a rational being", "rational being" is the definiens.

A definiendum is the termβword or phraseβdefined in a definition. In the defining statement "A lake is a large, landlocked, naturally occurring stretch of water", "lake" is the definiendum, "stretch of water" is the genus, and "large", "landlocked" and "naturally occurring" are the differentia.

### Rule of Equivalence

The Rule of Equivalence says that the definiendum and the definiens must be logically equivalent.

So the definition must be true of ALL and ONLY members of the class being defined.

Definitions can violate the Rule of Equivalence by being too narrow. E.g. "Morality is a theory which teaches you to sacrifice for others." Doesn't include all moral theories.

Definitions can also violate the Rule of Equivalence by being too wide. E.g. "Morality is the subject concerned with the principles of action." Doesn't exclude psychology, economics, even physics.

Can do both at the same time. E.g.

"Happiness: the emotional state that results in achieving a promotion."

Too narrow - misses most of happiness.

Too wide - people can have other emotions over promotion, like anxiety.

### Rule of Fundamentality

A definition must state fundamental characteristics. You have to choose the most significant characteristic. This is the fundamental characteristic β the characteristic which is responsible for the greatest number of an entity's distinctive characteristics.

Examples of failing to comply with this rule:

• Defining man "as featherless biped with broad nails."
• Defining man as "the animal who uses language." Ability to use language is expression of rational faculty.

Only apply this rule to reject a definition when no other rule applies.

### Rule of Circularity

The Rule of Circularity states that a definition must not directly or indirectly define the subject by itself. A definition must not contain any content to understand which presupposes the definition you are supposed to be providing.

Forms:

• Reusing same or similar word.
• Using synonyms (e.g. "Man is a human being.")
• Misuse of correlatives. Correlatives are things so related that one implies the other (e.g. husband and wife). If you define one in terms of the other, you might wind up in circularity (e.g. if you say a husband is "a man who has a wife" and then a wife is a "woman who has a husband" that's circular). Instead define the relationship involved (e.g. a husband is a man who is married and then you define marriage).

### Rule of Negatives

Where possible, a definition must be positive, not negative.

E.g. "an ornament is something not necessary for practical use" = bad definition.

But e.g. "bachelor" as "a man who is not married" is fine cuz bachelor is a negative concept.

### Rule of Obscurity

Definitions must be stated literally, clearly and as simply and economically as possible.

No metaphors, not too ponderous or complex.

### Peikoff's approach for defining terms.

1. Consider if you have a particular usage in mind and specify that.
2. Don't look for common denominators for totally different meanings (like "trunk" for part of an elephant and for luggage).
3. Find common denominators when they do exist. E.g. "morality" covers "a code of values accepted by choice" even if the codes are as varied as Oism and Xianity.
4. "Revolution" is a trickier case than "trunk" or "morality". You might say that "revolution" is basically political and that stuff like "sexual revolution" or "industrial revolution" are metaphorical uses. Or you could say "revolution" is actually broad and try to come up with a definition that covers the industrial revolution, sexual revolution etc.
ββ1. Peikoff says if you're not sure, start with hypothesis that the concept is a broad one and try to come up with a definition. Remember the purpose of a definition (differentiation and integration) and then ask if your definition is too general and thus useless or whether it's actually a helpful integration of stuff.

### Checklist for Definitions Homework

• Does the definition consist of a genus and differentia?
• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?
• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?
• Is the definition unnecessarily defined in negative terms?
• Is the definition metaphorical, ponderous or complex?
• Is the Rule of Fundamentality violated?

## Homework

Note that Peikoff said referring to dictionaries was fine in answering these so I'm doing that.

### Problem 1 βπ€

An editorial is an expression of opinion in a newspaper.
• Does the definition consist of a genus and differentia?

Yes.

"in a newspaper" is the genus (there are many things in newspapers, so it is a wider class) and "expression of opinion" is the differentia (we're only interested in the expressions of opinion appearing in newspapers).

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

β The definiendum and the definiens are not logically equivalent. The definition is too wide. It covers e.g. letters to the editor, or expressions of opinion from the man on the street being reported in a news article.

π€An additional issue that came up in the class discussion: Peikoff claims that there are editorials in other mediums such as TV and so it's also too narrow. The dictionaries I checked seemed to confine editorials to newspapers, magazines and other written forms of communication.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

N/A since it wasn't even logically equivalent.

What would a better definition be?

My initial attempt (based on newspaper context): An editorial is an expression of opinion run by or on behalf of an editor of a newspaper on an issue of the day.

Peikoff basically agrees, says you need to indicate whose opinion it is, and that it's the opinion of the people who run or own the paper.

### Problem 2 βπ€ β

Science is any information acquired by the use of mathematical and/or experimental methods.

Peikoff says lots of people operate on this definition. My guess is he's talking about instrumentalists.

• Does the definition consist of a genus and differentia?

Yes. The genus is "information" and the differentia is "acquired by the use of mathematical and/or experimental methods."

• Are the definiendum and the definiens logically equivalent?

No.

• If not, is the definition too narrow, too wide, or both?

The definition is simultaneously too wide and too narrow.

β It is too wide because an experiment could generate huge volumes of incidental/unimportant data that might qualify as information but would not be relevant to the investigation of any scientific question and should thus not be classified as science.

Peikoff gives a good example: if you add up the entries on your credit card bill, the sum would be a piece of information acquired by mathematical methods but is obviously not science.

Peikoff says that science involves a systematized knowledge of some area according to general principles.

β It is too narrow because a good definition of science should mention talking about trying to understand the natural world or investigate natural phenomena or something. The given definition doesn't say what the point of science is.

(This would actually be an argument that it is too wide).

π€Peikoff says it's too narrow cuz it excludes stuff like philosophy or history which he counts as sciences.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated? (Only analyze if no other issues found)

N/A.

• What would be a better definition?

Mine: The use, guided by certain norms and practices, of conjecture and experiment in order to understand and investigate the natural world.

Dictionary: the systematic study of the structure and behavior of the physical and natural world through observation, experimentation, and the testing of theories against the evidence obtained.

Interesting, I almost said "systematic" too.

Peikoff: The problem with the definition is it takes physics and uses that as a model for all science. Peikoff says that in a proper definition you'd need to include that science is systematized and that the method is reason based on observation.

### Problem 3 βπ€

Independence is the characteristic of not needing other people.
• Does the definition consist of a genus and differentia?

β Yes. The genus is "characteristic" and the differentia is "of not needing other people."

• Are the definiendum and the definiens logically equivalent?

No.

• If not, is the definition too narrow, too wide, or both?

β Too narrow.

Someone could "need" others for mutually beneficial transactions but still be independent in the sense of acting on their own initiative and according to their own judgement. Depends on how you take "need". (Peikoff specifically brought up division of labor society).

π€ Peikoff says it's too wide cuz e.g. a corpse doesn't need other people.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms? β

Yes.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

I think so, but we don't analyze it since we found more specific violations.

• What would be a better definition?

My initial attempt: Independence is the virtue of being able to act on one's own initiative and according to one's own judgment.

In lecture, Peikoff said not to build "virtue" into the definition since you're prejudging whether it is a virtue right in the definition. But whether it is a virtue is a question that you need to arrive at ethics to analyze.

So my second attempt: Independence is the ability to act on one's own initiative and according to one's own judgment.

### Problem 4 β

Hypochondria is a condition where a person worries a great deal about his health.
• Does the definition consist of a genus and differentia?

Yes. "Condition" is the genus and "where a person worries a great deal about his health."

• Are the definiendum and the definiens logically equivalent?

No.

• If not, is the definition too narrow, too wide, or both?

βIt is too wide. It includes someone e.g. worrying about their health a lot because they just got a cancer diagnosis. (Peikoff mentioned my cancer example specifically).

There needs to be something to limit it to irrational fears.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No..

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

N/A.

Peikoff says you'd need to say it's some sort of neurosis and not just a "condition".

### Problem 5 β

Happiness is what you feel when you get what you want.
• Does the definition consist of a genus and differentia?

Yes. The genus is "what you feel" and the differentia is "when you get what you want."

It fails to actually say what happiness actually is though - like that it's a positive emotion.

• Are the definiendum and the definiens logically equivalent?

No.

• If not, is the definition too narrow, too wide, or both?

It is too wide. Sometimes people get what they want and are disappointed. That would not be happiness but is included in the definition.

It is too narrow. It is vaguely written but arguably doesn't include longer-term happiness/content from living life well overall.

Peikoff uses Roark in the quarry as a counterexample to the definition. He's not getting what he wants (to work in architecture) but is happy.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

N/A.

Peikoff says a proper full distinction of happiness would have to refer pleasure experienced on a metaphysical level that's related to a confidence in your ability to achieve your values.

### Problem 6 β

A poison is anything which is virulent in its action or effect upon a living creature.
• Does the definition consist of a genus and differentia?

β Yes. Genus is absurdly broad "anything" (should be something like "substance") and differentia is "which is virulent in its action or effect upon a living creature."

• Are the definiendum and the definiens logically equivalent?

No.

-If not, is the definition too narrow, too wide, or both?

Too wide. Includes viruses.

• Does the definition directly or indirectly define the subject by using the same words or synonyms?

βFor some dictionary definitions, yes. E.g. dictionary.com gives as a the first definition for "virulent" something that is "actively poisonous; intensely noxious:". So the definition above could be read as "A poison is anything which is actively poisonous in its action or effect upon a living creature."

• Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

N/A.

### Problem 7 β

Capitalism is the social system based on competition and the profit motive.
• Does the definition consist of a genus and differentia?

Yes. "Social system" is the genus and "based on competition and the profit motive" is the differentia.

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

I tentatively think so. I can't think of another social system that would qualify as capitalism other than the one described, so it's not too wide.

And it doesn't exclude any examples of capitalism, so it's not too narrow.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

βYes. Competition and the profit motive are secondary points. I think that the private ownership of the means of production, the price system and the enforcement of contracts come first and make other aspects of capitalism possible.

Peikoff agrees that it's a Rule of Fundamentality issue and that private property is an essential missing point. He also mentions free individual action as a prerequisite for competition. Peikoff mentions that making competition a primary means people can say that govt using force to prevent monopolies is defending capitalism.

### Problem 8 - Revolution

The term under consideration is "revolution".

For this one and a few others, Peikoff asked people to come up with definitions.

My attempt: A sudden change in the politics of a country occurring outside of the normal political process, potentially involving violence, and resulting in a change in the country's political leadership and potentially its political constitution.

Peikoff's approach:

• he started out with the hypothesis that "revolution" was a broad, general concept. He thought of various examples of things called revolutions. American Revolution and Industrial Revolution would be included, but the revolution of the earth around the sun was clearly a different concept and so it would not be included in the definition.
• Genus was some type of change in human attitudes or actions.
• We are trying to differentiate revolution from evolution. Different is speed of change. So revolutions have to be sudden. They also have to involve something important. They also need to involve many people.
• Peikoff doubts this is a useful concept. He says there's no metaphysical basis for it.
• So then he switches to a political definition. He says a revolution is some sort of change in a country's government. And it needs to be successful, cuz an unsuccessful revolution is just a failed rebellion or something like that.
• And it needs to not have happened through normal procedures (like Hitler's rise to power).
• And it needs to have broad support (unlike a coup).

Peikoff's definition: A fundamental change in the nation's government brought about by a forcible uprising with widespread popular support.

### Problem 9 ββ

A piece of sculpture is a man-made object in a gallery or museum, which has three dimensions, reviews in the press, and no practical purpose.
• Does the definition consist of a genus and differentia?

Yes. "man-made object' is the genus and various differentia are given.

• Are the definiendum and the definiens logically equivalent? β

Yes. I can't think of any obvious cases unreasonably included or excluded if you conjoin these things together. Note that Peikoff broke the differentia apart and analyzed them separately.

Paraphrasing Peikoff's analysis: the genus is too wide since it should be art or visual art and not man-made object. Being in a gallery museum is irrelevant and too narrow since some sculptures aren't in a gallery museum. Everything physical has three dimensions so that's not a great criteria. It'd be different if art was in the genus. Press reviews is too wide and too narrow (not true of all sculptures or only of sculptures).

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms? β

Partially, maybe? "No practical purpose" is a negative definition.

Paraphrasing Peikoff: No practical purpose is a negative formulation trying to get at the fact that it's art.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated? β

Yes. It has listed some concretes without even trying to get at the essence.

### Problem 10 β π€

Random House Dictionary, College Edition: A sacrifice is βthe surrender or destruction of something of value for the sake of greater gain.β
• Does the definition consist of a genus and differentia?

Yes. The genus is "the surrender or destruction of something of value" and the differentia is "for the sake of greater gain.β (this would distinguish it from pointlessly destroying something for no gain).

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

βπ€ It is too wide because it fails to distinguish a sacrifice from an exchange (e.g. if you surrender money for the sake of something you value more, that would seem to fit within the definition).

Peikoff says this definition is just wrong. It's not too wide because to say it's too wide is to say it's true of sacrifices and other things, but the definition is just wrong. I agree the definition is wrong. Lots of these definitions are wrong though. I'm not sure what the dividing line is between applying our analytic framework to criticize a definition and just saying a definition is wrong.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

N/A.

### Problem 11

The spiritual element in man means the part which is non-material.
• Does the definition consist of a genus and differentia?

Yes. "part" is the genus and "which is non-material" is the differentia.

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

I don't see any obvious issues with the logical equivalence.

• Does the definition directly or indirectly define the subject by using the same words or synonyms?

Yes. "Spiritual' and "non-material" are synonyms. (Peikoff didn't mention)

• Is the definition unnecessarily defined in negative terms?

(Heard Peikoff say this before writing my answer). Yes, non-material is negative.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

N/A.

### Problem 12

Plato: Time is βthe moving image of eternity.β
• Does the definition consist of a genus and differentia?

Yes.

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

It's too poetic and vague for me to comment.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

### Problem 13 β

Anger is a wrathful, irate emotional state, often expressed in rage.
• Does the definition consist of a genus and differentia?

Yes. The genus is "emotional state" and the differentia are irate, wrathful, often expressed in rage.

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

I have an intuition that perhaps it's too wide because it fails to distinguish anger from other emotions, but I'm not sure how well one can even do that.

• Does the definition directly or indirectly define the subject by using the same words or synonyms?

β Yes. "Wrathful", "irate" and "rage" are all synonyms.

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

N/A.

### Problem 14 - Fascism

The term under consideration is "fascism".

For this one and a few others, Peikoff asked people to come up with definitions.

The example of a fascism definition in the handout is:

Fascism is a totalitarian system of government characterized by brutality, anti-Semitism, and private property.

This seems like as good a place as any to start with in terms of getting our bearings. I think that it's definitely a system of government. "totalitarian" seems fair but I'll withhold final judgment on that for the moment. Anti-semitism seems like an incidental feature only of some fascist regimes.

"private property" is mistaken as a differentia. I think the essential characteristic of fascism is a particular way of implementing the violation of private property. Namely, you put the use, trade in, and disposal of property under total government control, but you let individuals retain titular ownership (and whatever benefits might accrue based on such ownership to the extent the state is not interested in those benefits). Fascism is thus essentially a form of socialism.

Because fascism is a form of socialism, one might ask if "totalitarian" or "brutality" necessarily follow as correct descriptions. I think that while socialism involves force, it doesn't necessarily involve the especially notable brutality of, say, the Nazis. So I think that's out. "totalitarian" is trickier though. I can't think of a non-totalitarian fascist regime but I'm not sure I want to build it into the definition. Let's focus on the nature of property under fascism.

So then we have something like:

"Fascism is a system of government characterized by the government leaving titular ownership of property in the hands of individuals while having full rights of control over that property."

Thinking about my attempt at a definition some more, I think that it should say something about the way the government is organized. If you had a system where people retained some titular private ownership to property but the use of the property was being decided democratically, that seems like it'd be some variant of socialism but not fascism specifically. A key element of fascism is having some sort of autocrat deciding things. So an amended definition:

"Fascism is an autocratic system of government characterized by the government leaving titular ownership of property in the hands of individuals while having full rights of control over that property."

Peikoff's remarks: regarding the initial definition we're presented with, he says that any autocracy involves brutality so you don't need to specify brutality. He says "anti-semitism" is much too narrow since it wasn't a characteristic of fascism in Italy or Japan. And the private property point is simply false.

Then Peikoff moves onto his method. First, he decided to define it generally, and not merely as related to, say, Mussolini's system (which was the first system called fascist, per Peikoff).

Peikoff says that social system could be a valid genus but a type of collectivism is better.

Peikoff says talking about it as a form of socialism is optional and that it depends on how you are using socialism. Peikoff prefers the term collectivism.

Peikoff says that fascism is a form of totalitarianism. It doesn't limit its scope to some aspects of a citizen's life but seeks to control every aspect. Someone else in the class had an economically-focused definition very similar to mine and he says that the economic stuff is just one aspect of fascism.

Peikoff says we need to distinguish fascism from communism. One point is the facade of private property in fascism. Another is the nature of the collective being appealed to. Under fascism, it's a racial or national group, but under communism, it's a class.

Peikoff says you reasonably define fascism a couple of different ways. If you think the economic point is not central, you could say "Fascism is a form of collectivism which is totalitarian and racist or nationalist." If you think the economic point is central, you could say "Fascism is a form of collectivism which is totalitarian, racist or nationalist, and preserves a facade of private property."

### Problem 15 β

Sleep is a loss of consciousness which occurs repeatedly, especially when one is in bed.
• Does the definition consist of a genus and differentia?

Yes. The genus is "loss of consciousness" and the differentia is "which occurs repeatedly, especially when one is in bed." (distinguishing it from e.g. being put under anesthesia or losing consciousness after an accident).

• Are the definiendum and the definiens logically equivalent?

No.

• If not, is the definition too narrow, too wide, or both?

βI'm not quite sure, but I think part of the issue is that it doesn't specify that sleep 1) typically occurs at night, or 2) is restful/necessary. Dreams might be worth mentioning also.

Peikoff says it's too wide, includes comas, feinting, being knocked out.

Peikoff also says it's too narrow because it limits sleep to beds (good point). Animals sleep also.

Peikoff: need to say it's a natural or normal rest (e.g. not a coma), involves suspension of volitional consciousness and external action, and some physiological details.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

Perhaps? It does seem to miss some of the essential issue.

### Problem 16 β

A cause is any agent or action which brings about a consequence or result.
• Does the definition consist of a genus and differentia?

Yes. "any agent or action" is the genus and "which brings about a consequence or result" is the differentia (distinguishing causes from passive agents or potential actions).

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

It's arguably too wide assuming you want to talk about a cause that's fairly "close" to the result you're talking about. As written, you could potentially say the Big Bang was the cause of the egg shortage of 2022-2023, since (by a very long chain of events) the Big Bang, in some sense, ultimately brought about the result of the egg shortage.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

β No.

Note: I had some intuition that there was a problem here but rejected it for some reason.

Correct answer (per Peikoff): "consequence or result" are synonyms for "effect". If you define "cause" in terms of "effect" (or a synonym), you risk then defining "effect" in terms of cause.

Also, "bring about" just means "cause".

So the statement means "A cause is any agent or action which causes something that comes from a cause."

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

No.

### Problem 17 - Freedom

The term under consideration is "freedom".

For this one and a few others, Peikoff asked people to come up with definitions.

#### My Initial Analysis

The example of a freedom definition in the handout is:

Freedom is a state in which a man can do what he wants to do.

If a thug or dictator is in a position where he can harm a victim he wants to harm, this definition would include such a condition within freedom. I think that is too wide.

It would also include a slave who actually wants to be a slave and perform slave tasks within the concept of freedom. So I think that is too wide as well.

Peikoff has a good example: If someone wants to become POTUS and can't then they aren't free.

The term freedom is often used in specific contexts β like freedom of religion or freedom of speech. So there's an element of not having the government (or other people) interfere with your action.

But it's more than just a negative concept denoting an absent of government interference with self-determined action in some area, although that's a part of it. It's the self-determination of action itself. Like when a slave was granted their freedom, that meant they could direct their own life and choices instead of having their life controlled by someone else.

But your choices have to not violate the rights of others. So that's three elements: self-determination, lack of government interference, and respecting the rights of others.

So a working definition might be: "The ability to determine one's beliefs and actions free of external coercion and in accordance with the rights of others."

#### Peikoff's Analysis

Peikoff considered ideas like a free man, free will, free fall, free minds.

Peikoff started with a very broad definition. "Freedom is an absence of impediments, hindrances, or barriers to action." Peikoff says this applies to the cases he started with:

1) free man: the government doesn't hinder or restrict him.

2) free will: no factors outside your control governing you and forcing you to act a certain way.

3) free fall: nothing hindering object's fall.

4) free mind: one that isn't weighed down by anxieties or conflicts.

Peikoff notes that what counts as a hindrance or obstacle isn't specified. This raises the possibility that people could misuse the concept due to faulty conceptions of what constitutes a hindrance. E.g. Peikoff says existentialists say that no man is free because we can't leap to the moon unaided. Law of gravity hinders human freedom. People can construe reality itself as the enemy of freedom.

Peikoff says that trying to build in a qualification to the definition that what constitutes a hindrance must be construed with the facts of reality and morality raises problems. People will ask what that means and you have to explain a bunch of philosophy. So it's better to use different terms (e.g. volition for free will).

It seems like Peikoff might think there are a few legitimate uses of freedom but he starts talking specifically about the political definition. For political definition, it has to pertain to human action, and the hinderer is going to be the government. But it only counts as a violation of freedom if the govt initiates coercion against innocent men (e.g. non-criminals).

Peikoff's working definition is therefore: "Freedom is the political condition in which an individual is not subject to the initiation of governmental coercion."

### Problem 18 β

A Republican is an American interested in politics, who is not a Democrat or an Independent, does not favor capitalism or socialism, and tries to win elections.
• Does the definition consist of a genus and differentia?

Yes. The genus is "an American" or "an American interested in politics" and the differentia is the remainder.

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

Too wide: Would include as Republicans people who are members of some centrist third party.

Too narrow: Would exclude strongly capitalist Republicans, or Republicans who run as protest candidates. Peikoff: There are apathetic Republicans who don't care about winning elections.

Just wrong: I think Republicans can reasonably said to, in some sense, favor capitalism over socialism.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms?

β Yes. "who is not a Democrat or an Independent, does not favor capitalism or socialism" are both negative.

• Is the definition metaphorical, ponderous or complex?

It's fairly complex given the number of criteria specified.

• Is the Rule of Fundamentality violated?

Yeah. It's not getting at the essence of the matter. I think a definition should indicate some identification with the Republican party and its broad overall policies, rather than framing things in negative terms. Something like "A Republican is someone who identifies as and/or is a registered member of the Republican Party in the United States and broadly supports the political program of said party."

Peikoff: no ideological common denominator, so you'd have to define it in terms of being a member of the party.

### Problem 19 π€

(Not sure I agree with Peikoff on this one).

Logic is manβs method of knowledgeβthe one which, properly used, assures reliable conclusions.
• Does the definition consist of a genus and differentia?

π€ I think you could argue there is though I'm not sure. My argument would be that "method of knowledge" is the genus and "man's" is the differentia (distinguishing this method of knowledge from what an animal might use?). One issue: I think that animals don't really have a method of knowledge, per se (which implies a method for dealing with knowledge/creating new knowledge), but some knowledge that's been hard-coded into them. Also, this doesn't account for the role of the part of the definition after the dash.

Peikoff: Differentia is problematic because it is not fundamental. Genus is fine; logic is man's method of knowledge. Better definition would indicate what the method is β that it involves non-contradictory identification.

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

π€ It's way too wide wide. Logic is a specific tool for solving certain issues and is only part of rationality. If applied properly, one can come to reliable conclusions, but only within the delimited sphere of logic, not in general.

A better definition might be "A system for analyzing the validity of arguments by determining whether the form of an argument conforms to the rules of logic."

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

No.

### Problem 20 - Propaganda

The term under consideration is "propaganda".

For this one and a few others, Peikoff asked people to come up with definitions and discusses them before offering his own analysis.

#### My Analysis

The example definition given is:

Propaganda is any attempt to persuade other people to accept your ideas.

This would include thoughtful essays and books, calm and reasoned discussions, etc within propaganda. So it's way too wide.

People often use propaganda in a way restricted to the government but I think that's too narrow.

Some characteristics of propaganda:

1. It's partisan, biased, unobjective, one-sided. If it were a totally fair and balanced discussion of the issue then that wouldn't be propaganda.
2. It often tells lies or at least half-truths.
3. It's based on appeals to things other than reason, like emotional appeals.
4. It's directed at a mass audience as opposed to a specific individual.

So a definition might be: Propaganda is a partisan persuasive effort directed at a mass audience which attempts to persuade by means of emotional appeals and misleading or false accounts of facts.

#### Peikoff's Analysis

Peikoff starts off by saying he's doubtful that propaganda is even a legitimate concept.

Peikoff defined his genus as a body of ideas and then looked to the etymology (which derives from propagate) to determine that the body of ideas is being spread publicly in order to further some cause. There has to be an active attempt to spread to distinguish propaganda from education (note that he means like teaching arithmetic education, and not using "education" as a tool of propaganda.) Peikoff says a lawyer trying to persuade a jury isn't propaganda because there's an element of widespread public dissemination in propaganda.

Propaganda has pejorative connotation. Peikoff believes there's some sort of philosophical skepticism at play causing people to equate propagating an idea with corrupt methods of doing so. He nonetheless considers whether such the concept of propaganda, if confined to the case of people using irrational methods to spread ideas, might be valid. Peikoff says that irrational methods covers a lot of stuff and that makes the concept harder to automatize. I did not find his arguments on this point persuasive.

### Problem 21 β

John Dewey: βInquiry is the controlled or directed transformation of an indeterminate situation into one that is so determinate in its constituent distinctions and relations as to convert the elements of the original situation into a unified whole.β
• Does the definition consist of a genus and differentia?

Uh, perhaps? I guess you could say "controlled or directed transformation" is the genus and the rest is the differentia?

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

The definiens is such a mess I can't really tell.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

Let's try a simplified version.

Inquiry is the controlled [...] transformation of an indeterminate situation into one that is [...] determinate [...].

I don't think so. I don't think the definition makes much sense, but I don't think it's using synonyms.

• Is the definition unnecessarily defined in negative terms?

No.

β - Is the definition metaphorical, ponderous or complex?

Yes. It's like a parody of academic writing.

Peikoff: In Dewey's defense, he is giving an accurate definition from the perspective of his philosophy. Translated into English, this would be something like: Reality itself, apart from man, is nothing in particular. It lacks any identity. It is indeterminate metaphysically. Inquiry is the process by which human beings create identity and make it into something particular.

### Problem 22 - Sandwich

The term under consideration is "sandwich".

For this one and a few others, Peikoff asked people to come up with definitions and discusses them before offering his own analysis.

#### My Analysis

The example definition given in the handout is:

A sandwich is bread surrounding another ingredient.

I actually found an amusing "sandwich alignment chart" here that captures a lot of the range and potential ambiguity of sandwich definitions:

In addition to the structure and ingredient issues covered in the chart, what the "bread" or wrapper for ingredients is made out of is also an issue. I'd say that choco tacos and pop tarts are out just on the grounds of their "bread" not counting as bread for sandwich purposes, aside from structural or ingredient issues.

But if you wanted to argue about the example definition above, I'd say that it's too wide because it'd include some rolled up buttered toast or something like that. It could even include filled donuts, I think.

Some concretes that we'd want to include:

• normal sandwiches (BLTs, ham and cheese)
• sweet sandwiches (PB+J)
• submarine sandwiches (including if they're only made from 1 cut-out piece of bread)
• normal structure sandwiches but having weird ingredients

and stuff we'd want to exclude:

• chicken wraps/burritos (those are a different kind of food)
• desserts in general (donuts, pop tarts, choco tacos)

Hot dog is kind of a borderline case and i don't think it matters too much if it's excluded or excluded.

One thing about sandwiches is the filling faces out of the sandwich on at least three sides (if a submarine sandwich has bread cut out for the filling, you still have the meat facing out on one long side + the front and back of the sandwich). So the bread being on the top and bottom of a filling is pretty universal (it's just also sometimes enclosed on one more side too, as in a sub sandwich cut-off to have filling). So you generally don't have the bread fully enveloping or wrapping the filling. This excludes wraps, burritos, rolled up jam butties, filled donuts, pop tarts etc).

Also toppings/condiments (e.g. tomato, mustard, mayo) are very common and should be mentioned.

My definition: A sandwich is a food item consisting of a filling of ingredients enclosed on the top and bottom by bread and potentially including toppings and condiments.

#### Peikoff's Analysis

Lol Peikoff comes up with some wild examples to criticize the example definition (baking bread around a piano was one).

Peikoff says you have to make a decision about what you're going to include because there are club sandwiches (multiple pieces of bread) and open sandwiches and ice cream sandwiches. My proposed definition handles club sandwiches okay but would exclude open sandwiches and ice cream sandwiches, which I'm fine with.

Peikoff says he wants to just define the plain old garden variety sandwich and so he's fine with limiting his definition to two slices of bread.

Peikoff says he likes to give the genus as "food preparation" because that specifies that you're talking about an item of food prepared by human beings and not something as it exists in nature. Good point imho.

Peikoff says you can exclude a couple of things from the potential ingredients. One is bread itself lol. The other is liquid foods (no milk sandwiches lol). Ok fair.

Peikoff's definition: a food preparation consisting of two slices of bread with a layer of solid food other than bread between them.

### Problem 23 π€

Certain means free from doubt.
• Does the definition consist of a genus and differentia?

If you take "free" as indicating "freedom", then that could be the genus, and the differentia could tell you what sort of freedom you have (from doubt).

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

Very tentative: It's maybe too wide, since while people think that certain people can be wrong, you wouldn't typically apply the concept of certainty to some random person who thought they were the King of England. People would talk about "delusion" or something in that case. So someone being "free from doubt" that they're the King of England or Jesus Christ or whatever shouldn't qualify as certainty. But OTOH, if you just think of certainty as the state of being free from doubt, then maybe it's okay.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

I don't think so.

• Is the definition unnecessarily defined in negative terms?

π€ I'm not sure. I checked dictionaries and lots of them actually defined certainty in terms of a freedom from doubt or a lack of doubt.

I think you could define certainty positively. One definition might be "a confident judgment arrived at through a process of reasoning." I'm not certain that defining it negatively here is wrong, though.

Peikoff: It's unnecessarily negative. Proper definition should have genus of "evidential status" or "cognitive status" and differentia is where all of the available evidence favors a conclusion. (I disagree with Peikoff on the epistemological point here).

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

No.

### Problem 24 β

God is an infinite, supernatural Being transcending time, space, and matter.
• Does the definition consist of a genus and differentia?

I think so.

Argument that it does: The genus is being and the differentia is a being that is infinite, supernatural, etc. This distinguishes God from beings that aren't infinite and supernatural.

Argument that it doesn't: The differentia fails to actually differentiate God from other beings since it describes impossible characteristics.

Counterargument: For the purposes of analyzing whether a definition meets the basic criteria of being a definition, it's reasonable to take the attributes described in the differentia as true.

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

I think you need to specify as context that you're talking about a Christian or Abrahamic conception of God. Otherwise the definition could be viewed as too narrow (for e.g. excluding the Greek pantheon).

I don't think it's too wide because I don't see how it includes anything that shouldn't be included.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms?

β No.

Peikoff: This definition violates the negative rule 5 times. It says that God is something which is not finite, natural, temporal, spatial, or material. (I agree with Peikoff on this one.)

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

I think so because this doesn't mention that he's the supposed Creator of the universe, and that's a big part of the idea of God.

### Problem 25 ββ

Education is any process of acquiring knowledge.

(was on the right track with this one but missed an important point Peikoff pointed out)

• Does the definition consist of a genus and differentia?

Yes. "Process" is the genus and "of acquiring knowledge" is the differentia.

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

My intuition is to say it's too wide, but I think it depends on how broadly you want to define "education".

You could conceive of education very broadly, in such a way that would include practical experience and more traditional education (like classes). I think defining it that broadly would reduce the usefulness of the concept, though. So I guess it's too wide.

I looked at a few dictionaries. A key part of education definitions appears to be instruction, and that is missing from the definition above.

I guess you could also say the definition above is too narrow in that it excludes from the definition of education cases where someone went through the educational process (went to classes, was instructed) but didn't actually learn much.

(Missed this Peikoff point, so I gave myself an β) Peikoff: This definition would imply that if you look up a number in a phone book, that's education. And therefore there's no uneducated men, since everyone goes through some process of acquiring knowledge.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

Proposed definition: a process of instruction with the purpose of instilling knowledge in the person receiving the education.

Peikoff: good definition of education has to involve systematic acquisition of knowledge of general principles and development of powers of reasoning.

### Problem 26 βπ€

(I skipped going through the entire checklist on this one and this is the one that didn't have a genus!)

Garbage is what you throw out after a meal.
• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

βThis is too narrow in that it excludes from the definition of garbage things that are thrown out at times other than after a meal.

π€ Peikoff: It's too wide because anything you throw out after a meal would be considered garbage. (Not sure about this one)

• Is the Rule of Fundamentality violated?

Yes. It's tying it to a specific meal and not getting at the general idea of being stuff that's waste/that people don't want anymore.

Peikoff: No genus.

### Problem 27 β

Chance is the fortuitous or accidental events in the world.
• Does the definition consist of a genus and differentia?

I think "events" is the genus and "fortuitous or accidental" is the differentia. "in the world" doesn't actually tell you anything (where else would the events be?).

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

I think the definition is just wrong. Chance isn't particular events themselves but some hypothetical element behind the scenes that causes things to come out a certain way.

Also, too wide. There are lots of fortuitous or accidental events that go unnoticed in the world. Maybe a meteorite smashes somewhere uninhabited and you could say that was the result of chance. But chance is typically a concept that relates to unpredictable elements of life from the perspective of human beings. So even if you accept an event-focused definition, I think it's not quite right.

Peikoff: for a good definition of "chance", you'd need to determine whether you're using it in metaphysical or epistemological sense. In metaphysical sense, it means an uncaused effect (which, under Objectivism, is not a thing). In the epistemological (valid) sense, chance means an event whose cause is unknown by human beings. E.g. if you throw dice and you say it came up 7 by chance, you're saying you don't know all the original conditions and pressure factors and so on.

• Does the definition directly or indirectly define the subject by using the same words or synonyms?

β Yes. "fortuitous" and "accidental" are both related to "chance".

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

### Problem 28 β

To read is to move oneβs eyes in order over a written or printed series of words in a language one knows.
• Does the definition consist of a genus and differentia?

You could say the genus is the action of moving one's eyes, and the differentia is the other details (which distinguish this instance of moving your eyes from other cases like rolling them or giving someone a sidelong glance)

• Are the definiendum and the definiens logically equivalent? If not, is the definition too narrow, too wide, or both?

βIt's too wide because one could perform the mechanical action described without actually reading (comprehending) the material.

• Does the definition directly or indirectly define the subject by using the same words or synonyms? Are correlatives used?

No.

• Is the definition unnecessarily defined in negative terms?

No.

• Is the definition metaphorical, ponderous or complex?

No.

• Is the Rule of Fundamentality violated?

Yes. Doesn't mention comprehending or understanding the text. Reduces reading to a mechanical action.