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<div style="page-break-after: always;">
## Informal Fallacies
Fallacies can be thought of as errors in reasoning that are so commonplace that they were eventually given their own names. All fallacies, whether formal or informal, are just different forms of non sequitur. That is to say that all fallacies merely represent different sorts of inferential errors that challenge either the validity or the soundness of an argument.
In this first class, we will cover the top informal fallacies, with formal fallacies being covered in a later class. The following list of the informal fallacies that you are most likely to encounter.
#### 1. Red Herring
A red herring is a type of rhetorical tactic, typically used to obfuscate, that involves referring to an irrelevant point. It can be thought of as a point, reference, or example, that distracts from the main point of a discussion or larger argument.
>**Example:** "Bacon must be healthy for people because I have a 95-year old grandmother who eats bacon every day!"
#### 2. Begging the Question
Colloquially, begging the question may be understood as merely leaving certain questions unanswered after an argument is rendered. However, in philosophy, begging the question has a very different definition, and refers to a type of circular reasoning. Begging the question specifically refers to the act of presupposing the conclusion of an argument in its premises. That is to say that at least one of the premises of an argument will hinge on that argument's conclusion being true.
>**Example:** "God exists because it is stated in his own words in the Bible!"
#### 3. Strawman
A strawman fallacy is characterized by either intentionally or unintentionally misrepresenting your interlocutor's position or argument, such as to make said position or argument easier to attack. It is also the inverse of the Motte and Bailey fallacy, which is characterized by misrepresenting your own position or argument in order to make it easier to defend.
>**Example:** "People who argue for taxation are pushing communism!"
</div>
<div style="page-break-after: always;">
#### 4. Equivocation
An equivocation occurs when one uses a term with a certain meaning in one part of their argument, like the premises, but also uses the same term with a different meaning in another part of their argument, like the conclusion. This is an extremely common fallacy, and occurs often across virtually all domains of debate.
>**Example:** "The announcer said the game ended with a tie, but I didn't see any string, so the announcer must be wrong."
#### 5. Appeal to Nature
An appeal to nature is characterized by the affirmation that something is good, preferable, or desirable, merely because it is natural. This fallacy is common in the domain of human health, such as when health product advertisers claim that their product is beneficial because it either contains more natural ingredients or fewer artificial ingredients.
>**Example:** "Red meat is clearly healthy for humans if we evolved consuming it!"
#### 6. Appeal to Authority
When one appeals to authority, it simply means that one affirms that a proposition is true in virtue of it being uttered by an authority. This fallacy typically pervasive within any domain wherein there are experts who publicly profess their opinions.
>**Example:** "The carnivore diet is healthy because Paul Saladino concluded this after years of researching diet!"
#### 7. Appeal to Ignorance
An appeal to ignorance is typically defined as affirming that a proposition is true merely because it has not been shown to be false. This is common in domains of science wherein evidence for a particular research question is scant, and the gaps in knowledge can be filled with poor reasoning.
>**Example:** "It's never been shown that blueberries don't cure cancer, so we're safe in assuming that blueberries do cure cancer!"
</div>
<div style="page-break-after: always;">
#### 8. Appeal from Incredulity
The hallmark of this fallacy is assuming that a proposition is false merely because you personally do not believe, or can't imagine, that the proposition is true. This fallacy is tightly tied to the cognitive bias known as confirmation bias, which will be discussed later.
>**Example:** "That's nonsense, because I just can't believe it!"
#### 9. Muddying the Waters
Muddying the waters is less of a fallacy and more of a rhetorical device designed to obfuscate and make one's position extremely ambiguous or unclear. This is extremely prevalent in political or ethical debates, wherein it is common to vaguely gesture at your opponent with the mere appearance of disagreement rather than actually providing clear arguments.
>**Example:** "We all know those studies are bad, because you just follow the money if you want to know the truth!"
#### 10. Genetic Fallacy
The crux of the genetic fallacy is to conclude that a position is wrong merely in virtue of the one uttering the position. This type of fallacy is remarkably common, if not ubiquitous, in the political debate sphere.
>**Example:** "I know what Joe Biden says is wrong, because Joe Biden is an idiot."
</div>
---
# Hashtags
#debate
#debate_coursework

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<div style="page-break-after: always;">
## Fundamental Concepts
#### 1. Propositions
A proposition is simply a "truth-apt" statement. For a statement to be truth-apt just means that it can be either true or false. This is just to say that the statement has a truth value that can be assigned to it. Propositions are the basic components of arguments in propositional/classical logic.
>**Example:** "It is raining outside."
#### 2. Arguments
In the most basic sense, an argument is a set of premises (or even a single premise) followed by a conclusion, where the premises and conclusions are comprised of propositions. This is even true of mathematical arguments, but it's typically obscured behind shorthand and notation.
>**Example:** If it is raining outside, then the ground is wet. It's raining outside. Therefore, the ground is wet.
#### 3. Validity
Validity is a property of arguments. An argument is valid if, and only if, the conclusion logically follows from the premises. The example from the previous entry in this document (2. Arguments) is an example of a valid argument. Invalid arguments suffer from structural errors that lead to their conclusions not being deducible from their premises.
>**Valid Example:** If there are unicorns on the moon, then the world will end in 1975. There are unicorns on the moon. Therefore, the world will end in 1975.
>**Invalid Example:** If there are unicorns on the moon, then the world will end in 1975. There are unicorns on the moon. Therefore, leprechauns exist.
#### 4. Soundness
Soundness is also a property of arguments. Arguments are sound if, and only if, they are valid and their premises are all true. The above example of a valid argument is valid in its structure, but not sound. Often times an argument that is valid in structure can have untrue premises. Firstly, unicorns don't exist, and secondly, the world didn't end in 1975. So, the argument is valid, but not sound.
>**Sound Example:** All cats are mammals. Garfield is a cat. Therefore, Garfield is a mammal.
>**Unsound Example:** All cats are mammals. Garfield is not a cat. Therefore, Garfield is not a mammal.
</div>
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#### 5. Defeaters
Simply speaking, defeaters are types of responses that either significantly, or entirely, deflate the persuasive force of an argument and/or the truth value of a proposition. There are three types of defeaters:
>**Rebutting Defeaters:** An argument that directly negates a proposition and/or renders an argument unsound.
>**Undercutting Defeaters:** An argument that lowers the probability of a proposition being true and/or casts serious doubt on the soundness of an argument.
>**No-Reasons Defeaters:** An argument that demonstrates that there is no reason to believe that a proposition is true and/or an argument is sound.
#### 6. A Priori
A priori knowledge, or justification, is independent of experience or empirical evidence. It is knowledge that can be obtained through reason or logical analysis alone, and does not require any observation or experimentation to be justified.
>**Example:** Objects with three sides are triangles. Boat sails have three sides. Therefore, boat sails are triangles.
#### 7. A Posteriori
Much like the term a priori, a posteriori refers to knowledge or justification. However, unlike a priori, a posteriori knowledge, or justification, is based on experience or empirical evidence. It is knowledge that requires observation or experimentation to be justified, and cannot be obtained through reason or logical analysis alone.
>**Example:** Birds have feathers. Pigeons are birds. Therefore, pigeons have feathers.
#### 8. Analyticity
A proposition is analytic when is true by definition. It is a statement that can be deduced from the meanings of its terms, without any need for empirical evidence or experience to verify its truth or falsity.
>**Example:** Triangles have three sides.
</div>
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#### 9. Syntheticity
Unlike an analytic proposition, a synthetic proposition is *not* true by definition, but is instead true because of the way the world is. It is a statement that requires empirical evidence or experience to verify its truth or falsity.
>**Example:** Boat sails are triangles.
</div>
---
# Hashtags
#debate
#debate_coursework

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## Logic
Logic is a broad field that encompasses many different branches and sub-fields, and studies the principles and rules of reasoning, inference, and argumentation. It is concerned with the validity and soundness of arguments, and with the relationships between statements and/or propositions.
When we think of logic as it pertains to debate, we will typically be thinking about propositional logic. But this is not the only logic that exists. Propositional logic is just one branch of logic among many, and there are many other types of logics that are studied in philosophy, mathematics, computer science, and other fields. While propositional logic deals with propositions, which are statements that can be either true or false, other types of logics deal with other kinds of objects and concepts.
For example, predicate logic extends propositional logic by introducing the concept of predicates, which are statements that express properties of objects. Modal logic deals with the concepts of possibility, necessity, and contingency. Fuzzy logic deals with concepts that have degrees of truth or falsity, rather than being strictly true or false. Deontic logic deals with the concepts of obligation, permission, and prohibition. Temporal logic deals with the concepts of time and change.
Here are some examples of different types of logics:
| **TYPES** | **OF** | **LOGICS** |
|:--------------------:|:-------------------:|:--------------------:|
| Propositional logic | Predicate logic | Modal logic |
| Fuzzy logic | Deontic logic | Epistemic logic |
| Temporal logic | Non-monotonic logic | Intuitionistic logic |
| Relevance logic | Free logic | Substructural logic |
| Paraconsistent logic | Multi-valued logic | Quantum logic |
| Situation calculus | Description logic | Dialectical logic |
## Propositional Logic
Propositional logic has several "laws" or "rules" that are essentially tautologies, that is to say things that are always true on propositional logic:
1. **Law of identity:** P is always equal to P.
2. **Law of non-contradiction:** P and ¬P is never true.
3. **Law of excluded middle:** P or ¬P is always true.
Additionally, there are "laws" or "rules" that leverage different connective operators to establish different inference structures. These are called inference rules. Here are a few basic ones:
1. **Modus ponens:** If P implies Q, and P is true, then Q must be true.
2. **Modus tollens:** If P implies Q, and Q is false, then P must be false.
3. **Hypothetical syllogism:** If P implies Q, and Q implies R, and P is true, then R must be true.
4. **Disjunctive syllogism:** If P is true or Q is true, and P is false, then Q is true.
## Scientific Epistemology
Theoretical virtues of science refer to the desirable qualities that scientific theories should possess to be considered good explanations of natural phenomena. Here are some of the most commonly recognized theoretical virtues of science.
1. **Testibility:** A hypothesis is scientific only if it is testable, that is, only if it predicts something more than what is predicted by the background theory alone.
2. **Fruitfulness** Other things being equal, the best hypothesis is the one that is the most fruitful, that is, makes the most successful novel predictions.
3. **Scope:** Other things being equal, the best hypothesis is the one that has the greatest scope, that is, that explains and predicts the most diverse phenomena.
4. **Parsimony:** Other things being equal, the best hypothesis is the simplest one, that is, the one that makes the fewest assumptions.
5. **Conservatism:** Other things being equal, the best hypothesis is the one that is the most conservative, that is, the one that fits best with established beliefs.
---
# Hashtags
#debate
#debate_coursework

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<div style="page-break-after: always;">
## Tautologies
#### 1. Law of Identity
This fundamental law of logic states that every object is identical to itself. It emphasizes the consistency and predictability of entities in logical and mathematical expressions by affirming that an object or idea must always be exactly what it is and not something else.
>**Example:** Asserting that if 'x is a cat', then 'x is a cat'; self-evident identity.
#### 2. Law of Non-Contradiction
This principle asserts that a statement and its negation cannot both be true at the same time. It is a foundational rule in classical logic, ensuring that contradictions do not exist within a logically coherent system, thereby maintaining the system’s integrity.
>**Example:** For 'x is a bird', it cannot be true and not true at the same time.
#### 3. Law of Excluded Middle
This law holds that for any proposition, either that proposition is true, or its negation is true—there is no middle ground or third option. This law underpins the binary nature of traditional logical determinations, reinforcing a clear separation between truth and falsity.
>**Example:** For 'x is alive', either 'x is alive' is true or 'x is alive' is false, no third possibility.
---
## Other Principles
#### 1. Principle of Explosion
This principle states that from a contradiction, any conclusion can be validly derived. Essentially, it suggests that once falsehood is introduced, anything can logically follow.
>**Example:** Assuming P∧¬P, derive Q: From P∧¬P, infer any Q (e.g., 'unicorns exist').
#### 2. De Morgan's Law
The negation of a conjunction is equivalent to the disjunction of the negations, and the negation of a disjunction is equivalent to the conjunction of the negations.
>**Example:** Using ¬(P∧Q)≡¬P∨¬Q, an application to natural language might be like "if it's not raining outside and if it's not cold outside, then it is neither raining nor cold outside (e.g., ¬(raining∧cold)≡¬raining∨¬cold).
---
</div>
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## Formal Fallacies
#### 1. Affirming the Consequent
This occurs when someone incorrectly assumes the cause based on an effect that can also result from other causes.
>**Form:** If P then Q, Q is true; therefore, P must be true.
>**Example:** If it rains, the street is wet. The street is wet, so it must have rained. (The street could be wet for other reasons.)
#### 2. Denying the Antecedent
This fallacy arises when someone wrongly concludes the absence of an outcome based on the absence of one possible cause, ignoring other causes that might produce the same outcome.
>**Form:** If P then Q, P is false; therefore, Q must be false.
>**Example:** If I am in Paris, I am in France. I am not in Paris, so I am not in France. (I could be elsewhere in France.)
#### 3. Fallacy of the Undistributed Middle
This involves a mistaken inference that because two categories share a property, they are the same, overlooking their distinctions.
>**Form:** P implies Q, R implies Q; therefore, P implies R.
>**Example:** All dogs are mammals. All cats are mammals. Therefore, all dogs are cats.
#### 4. Illicit Major
This error is made when the conclusion improperly generalizes about all members of a category based on shared characteristics with a broader group.
>**Form:** All X are Y, all Z are Y; therefore, all Z are X.
>**Example:** All squares are rectangles. All rectangles have four sides. Therefore, all squares have four sides. (True, but the reasoning is invalid.)
</div>
<div style="page-break-after: always;">
#### 5. Illicit Minor
This mistake happens when an assumption that two subgroups share the same properties because they belong to the same larger group is incorrectly made.
>**Form:** All X are Y, all X are Z; therefore, all Y are Z.
>**Example:** All apples are fruit. All apples are red. Therefore, all fruit are red.
#### 6. Fallacy of Exclusive Premises
This involves drawing a conclusion about two groups based on their separate exclusion from a third group, which logically does not follow.
>**Form:** No P is Q, No R is Q; therefore, No P is R.
>**Example:** No cats are dogs, No birds are dogs; therefore, no cats are birds.
#### 7. Fallacy of Four Terms
>**Form:** P implies Q, R implies S; therefore, P implies S.
>**Example:** All humans are mammals. All dogs are pets. Therefore, all humans are pets.
#### 8. Affirmative Conclusion from a Negative Premise
This fallacy occurs when an argument erroneously includes four distinct terms in a categorical syllogism, preventing a proper conclusion.
>**Form:** No P is Q, All R are P; therefore, No R is Q.
>**Example:** No fish are birds, all salmon are fish; therefore, no salmon are birds.
</div>
<div style="page-break-after: always;">
---
# Hashtags
#debate
#debate_coursework

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## First session - fallacies
1. Top 10 most common fallacies
1. red herring
2. begging the question
3. appeal to nature
4. appeal to authority
5. appeal from incredulity
6. muddying the waters
7. poisoning the well
8. gish galloping
9. appeal to ignorance
10. motte and bailey
3. Homework
1. identify 5 examples of informal fallacies correctly
## Second session - intro to debate
1. Reviewing homework
2. Philosophy/debate terms
1. argument
2. proposition
3. soundness
5. validity
6. defeaters
7. a priori
8. a posteriori
9. empirical
10. analytic
11. synthetic
12. contradiction
3. Homework
1. identify 5 examples of terms correctly
## Third session - branches philosophy
1. Reviewing homework
2. Logic
1. laws of thought/classical logic
1. law of non-contradiction
2. law of excluded middle
3. law of identity
2. validity
3. soundness
4. modality
1. necessity
2. contingency
3. Epistemology
1. skepticism
2. contextualism
3. scientific method
## Fourth session - propositional logic
1. Reviewing homework
2. Arguments
1. deductive
2. inductive
3. abductive
3. Propositional logic
1. truth tables
2. writing arguments
3. formal fallacies
4. principle of explosion
4. Homework
1. create valid inferences
2. do a prop logic quiz
## fifth session - debate structure
1. Dialogue flow tree
2. Homework
1. apply the tree to a debate
## sixth session - mock debate
1. Reviewing homework
2. Mock debate
## Optional class - vegan debate
1. NTT mock dialectic
---
# Hashtags
#debate
#debate_coursework

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<div style="page-break-after: always;">
#### Fallacy 1
>"Until you show me a 50-year randomized controlled trial showing otherwise, I will continue to believe that steak is healthy."
**A)** red herring
**B)** appeal to ignorance
**C)** equivocation
**D)** appeal to nature
**E)** both B and D
#### Fallacy 2
>"You can tell me all you want that Liver King is on steroids, it just sounds ridiculous to me and I refuse to believe it."
**A)** equivocation
**B)** muddying the waters
**C)** genetic fallacy
**D)** appeal from incredulity
**E)** both D and C
#### Fallacy 3
>"We know that industrial frankenfoods made in factories are bad for you, because they're not foods that you grow yourself from the soil."
**A)** appeal to nature
**B)** strawman
**C)** begging the question
**D)** appeal to authority
**E)** both A and C
</div>
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#### Fallacy 4
>"Why would you ever believe that vegan diets were unhealthy? The Academy of Nutrition and Dietetics says they're appropriate for all stages of the life cycle."
**A)** genetic fallacy
**B)** appeal to authority
**C)** muddying the waters
**D)** red herring
**E)** both B and D
#### Fallacy 5
>"When I said that the carnivore diet cures fatty liver, what I actually meant was that it can be an effective weight loss diet for some people."
**A)** strawman
**B)** begging the question
**C)** motte and bailey
**D)** equivocation
**E)** both A and B
</div>
---
# Hashtags
#debate
#debate_coursework

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### Inference 1
>**P1)** If one becomes a lean mass hyper responder, then one has unlocked the fountain of youth.
>**P2)** Dave Feldman became a lean mass hyper responder.
>**C)** Therefore, Dave Feldman has unlocked the fountain of youth.
**P1)** ∀x(Lx→Fx)
**P2)** Ld
**C)** Fd
### Inference 2
>**P1)** If one (x) eats red meat (y), then one (x) has increased their risk of cancer (z).
>**P2)** Shawn Baker eats beef.
>**C)** Therefore, Shawn Baker has increased their risk of colon cancer.
**P1)** ∀x∀y∀z(Mxy→Cxz)
**P2)** Msb
**C)** Cso
### Inference 3
>**P1)** If fish (x) contain heavy metals (y), then eating too much fish (x) can give you heavy metal (y) poisoning.
>**P2)** Salmon contains mercury.
>**C)** Therefore, eating too much salmon can give you mercury poisoning.
**P1)** ∀x∀y(Cxy→Pxy)
**P2)** Csm
**C)** Psm
### Inference 4
>**P1)** Some people like to eat kangaroo balls.
>**P2)** Everyone who likes to eat kangaroo balls also likes to eat buffalo balls.
>**C)** Therefore, there are some people who like both kangaroo balls and buffalo balls.
**P1)** ∃x(Px)
**P2)** ∀x(Px→Qx)
**C)** ∃x(Px∧Qx)
### Inference 5
>**P1)** If the vegetables are food, then the vegetables do not have toxins.
>**P2)** Broccoli has toxins.
>**C)** Therefore, broccoli is not food.
**P1)** ∀x(Fx→¬Tx)
**P2)** ∃x(Tb)
**C)** ∃x(¬Fb)
### Inference 6
>**P1)** If one will live forever, then one is indeed a carnivore.
>**P2)** Micheal Greger is not a carnivore.
>**C)** Therefore, Michael Greger will not live forever.
**P1)** ∀x(Fx→Cx)
**P2)** ¬Cm
**C)** ¬Fm
### Inference 7
>**P1)** If a food is not healthy, then the data shows that the food increases the risk of disease.
>**P2)** RCTs show that seed oils do not increase the risk of disease.
>**C)** Therefore, seed oils are healthy.
**P1)** ∀x∀y(¬Hx→Dxy)
**P2)** ¬Dsr
**C)** Hs
---
# Hashtags
#debate
#debate_coursework
#homework

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### Inference 1
>**P1)** If one becomes a lean mass hyper responder, then one has unlocked the fountain of youth.
>**P2)** Dave Feldman became a lean mass hyper responder.
>**C)** Therefore, Dave Feldman has unlocked the fountain of youth.
**P1)**
**P2)**
**C)**
### Inference 2
>**P1)** If one eats red meat, then one has increased their risk of cancer.
>**P2)** Shawn Baker eats beef.
>**C)** Therefore, Shawn Baker has increased their risk of cancer.
**P1)**
**P2)**
**C)**
### Inference 3
>**P1)** If fish contain heavy metals, then eating too much fish can give you heavy metal poisoning.
>**P2)** Salmon contains mercury.
>**C)** Therefore, eating too much salmon can give you mercury poisoning.
**P1)**
**P2)**
**C)**
### Inference 4
>**P1)** Some people like to eat kangaroo balls.
>**P2)** Everyone who likes to eat kangaroo balls also likes to eat buffalo balls.
>**C)** Therefore, there are some people who like both kangaroo balls and buffalo balls.
**P1)**
**P2)**
**C)**
### Inference 5
>**P1)** If the vegetables are food, then they do not have toxins.
>**P2)** Some vegetables have toxins.
>**C)** Therefore, some vegetables are not food.
**P1)**
**P2)**
**C)**
### Inference 6
>**P1)** If one will live forever, then one is indeed a carnivore.
>**P2)** Micheal Greger is not a carnivore.
>**C)** Therefore, Michael Greger will not live forever.
**P1)**
**P2)**
**C)**
### Inference 7
>**P1)** If a food is not healthy, then the data shows that the food increases the risk of disease.
>**P2)** RCTs show that seed oils do not increase the risk of disease.
>**C)** Therefore, seed oils are healthy.
**P1)**
**P2)**
**C)**
---
# Hashtags
#debate
#debate_coursework
#homework

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### Inference 1
>**P1)** If I eat enough fibre, then I will have good digestion.
>**P2)** I ate enough fibre.
>**C)** Therefore, I will have good digestion.
**A)** Modus Ponens ✓
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:** P→Q
**P2:** P
**C:** Q
### Inference 2
>**P1)** If I scarf down too many ketobombs, then I will gain weight.
>**P2)** I did not gain weight.
>**C)** Therefore, I did not scarf down too many ketobombs.
**A)** Modus Ponens
**B)** Modus Tollens ✓
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:** P→Q
**P2:** ¬Q
**C:** ¬P
### Inference 3
>**P1)** If I eat a variety of fruits and vegetables, then I will get a range of nutrients.
>**P2)** If I get a range of nutrients, then I will prolong my health.
>**C)** Therefore, if I eat a variety of fruits and vegetables, I will prolong my health.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism ✓
**D)** Disjunctive Syllogism
##### Structure
**P1:** P→Q
**P2:** Q→H
**C:** P→H
### Inference 4
>**P1)** If I eat too much saturated fat, then I will increase my risk of heart disease.
>**P2)** I did not increase my risk of heart disease.
>**C)** Therefore, I did not eat too much saturated fat.
**A)** Modus Ponens
**B)** Modus Tollens ✓
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:** P→Q
**P2:** ¬Q
**C:** ¬P
### Inference 5
>**P1)** If I am a lean mass hyper responder, then I am immune to all disease.
>**P2)** I am not immune to all disease.
>**C)** Therefore, I am not a lean mass hyper responder.
**A)** Modus Ponens
**B)** Modus Tollens ✓
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:** P→Q
**P2:** ¬Q
**C:** ¬P
### Inference 6
>**P1)** If I stay on the Vertical Diet™, then I will get scurvy.
>**P2)** I stayed on the Vertical Diet™.
>**C)** Therefore, I will get scurvy.
**A)** Modus Ponens ✓
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:** P→Q
**P2:** P
**C:** Q
### Inference 7
>**P1)** I will either drink organic sheep milk or raw bison cum with my marinated ox testicles.
>**P2)** I did not drink raw bison cum with my marinated ox testicles.
>**C)** Therefore, I drank organic sheep milk with my marinated ox testicles.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism ✓
##### Structure
**P1:** M∨C
**P2:** ¬C
**C:** M
### Inference 8
>**P1)** If I eat too much processed food, then I will consume too much salt.
>**P2)** If I consume too much salt, then my heart will explode.
>**C)** Therefore, if I eat too much processed food, then my heart will explode.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism ✓
**D)** Disjunctive Syllogism
##### Structure
**P1:** P→S
**P2:** S→E
**C:** P→E
### Inference 9
>**P1)** I will either eat a salad or a soup for lunch.
>**P2)** I did not eat a salad for lunch.
>**C)** Therefore, I ate soup for lunch.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism ✓
##### Structure
**P1:** S∨X
**P2:** ¬S
**C:** X
### Inference 10
>**P1)** If I eat dingo liver, then I will get important n00trients.
>**P2)** I ate dingo liver.
>**C)** Therefore, I got important n00trients.
**A)** Modus Ponens ✓
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:** P→Q
**P2:** P
**C:** Q
---
# Hashtags
#debate
#debate_coursework
#homework

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### Inference 1
>**P1)** If I eat enough fibre, then I will have good digestion.
>**P2)** I ate enough fibre.
>**C)** Therefore, I will have good digestion.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:**
**P2:**
**C:**
### Inference 2
>**P1)** If I scarf down too many ketobombs, then I will gain weight.
>**P2)** I did not gain weight.
>**C)** Therefore, I did not scarf down too many ketobombs.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:**
**P2:**
**C:**
### Inference 3
>**P1)** If I eat a variety of fruits and vegetables, then I will get a range of nutrients.
>**P2)** If I get a range of nutrients, then I will prolong my health.
>**C)** Therefore, if I eat a variety of fruits and vegetables, I will prolong my health.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:**
**P2:**
**C:**
### Inference 4
>**P1)** If I eat too much saturated fat, then I will increase my risk of heart disease.
>**P2)** I did not increase my risk of heart disease.
>**C)** Therefore, I did not eat too much saturated fat.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:**
**P2:**
**C:**
### Inference 5
>**P1)** If I am a lean mass hyper responder, then I am immune to all disease.
>**P2)** I am not immune to all disease.
>**C)** Therefore, I am not a lean mass hyper responder.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:**
**P2:**
**C:**
### Inference 6
>**P1)** If I stay on the Vertical Diet™, then I will get scurvy.
>**P2)** I stayed on the Vertical Diet™.
>**C)** Therefore, I will get scurvy.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:**
**P2:**
**C:**
### Inference 7
>**P1)** I will either drink organic sheep milk or raw bison cum with my marinated ox testicles.
>**P2)** I did not drink raw bison cum with my marinated ox testicles.
>**C)** Therefore, I drank organic sheep milk with my marinated ox testicles.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:**
**P2:**
**C:**
### Inference 8
>**P1)** If I eat too much processed food, then I will consume too much salt.
>**P2)** If I consume too much salt, then my heart will explode.
>**C)** Therefore, if I eat too much processed food, then my heart will explode.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:**
**P2:**
**C:**
### Inference 9
>**P1)** I will either eat a salad or a soup for lunch.
>**P2)** I did not eat a salad for lunch.
>**C)** Therefore, I ate soup for lunch.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:**
**P2:**
**C:**
### Inference 10
>**P1)** If I eat dingo liver, then I will get important n00trients.
>**P2)** I ate dingo liver.
>**C)** Therefore, I got important n00trients.
**A)** Modus Ponens
**B)** Modus Tollens
**C)** Hypothetical Syllogism
**D)** Disjunctive Syllogism
##### Structure
**P1:**
**P2:**
**C:**
---
# Hashtags
#debate
#debate_coursework
#homework

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### NTT Reductio (Non-Negated Antecedent w/ Conjunction)
| <font color="CC6600">**Definiendum**</font> | <font color="CC6600">**Definiens**</font> |
|:-------------------------------------------:|:----------------------------------------- |
| <font color="CC6600">**T**</font> | a being (x) is ethical to consume |
| <font color="CC6600">**P**</font> | a being (x) has fur |
| <font color="CC6600">**Q**</font> | a being (x) has horns |
| <font color="CC6600">**R**</font> | a being (x) has hooves |
| <font color="CC6600">**a**</font> | hypothetical human |
<div style="text-align: center">
<font color="CC6600">
<b>P1)</b></font> For all x, where x is a being, they are ethical to consume if, and only if, x has fur, x has horns, and x has hooves.
<br />
<font color="CC6600">
<b>(∀x(Tx↔(Px∧Qx∧Rx)))</b>
<br />
<b>P2)</b></font> A hypothetical human has fur, horns, and hooves.
<br />
<font color="CC6600">
<b>(Pa∧Qa∧Ra)</b>
<br />
<b>C)</b></font> Therefore, A hypothetical human is ethical to consume.
<br />
<font color="CC6600">
<b>(∴Ta)</b>
<br />
<br />
</font>
</div>
[Proof Tree](https://www.umsu.de/trees/#(~6x(Tx~4(Px~1Qx~1Rx))),(Pa~1Qa~1Ra)|=(Ta))
### NTT Reductio (Negated Antecedent w/ Conjunction)
| <font color="CC6600">**Definiendum**</font> | <font color="CC6600">**Definiens**</font> |
|:-------------------------------------------:|:------------------------------------------ |
| <font color="CC6600">**T**</font> | a being (x) is ethical to consume |
| <font color="CC6600">**P**</font> | a being (x) has average human intelligence |
| <font color="CC6600">**Q**</font> | a being (x) has language skills |
| <font color="CC6600">**R**</font> | a being (x) has human genetics |
| <font color="CC6600">**a**</font> | hypothetical schmuman |
<div style="text-align: center">
<font color="CC6600">
<b>P1)</b></font> For all x, where x is a being, they are not ethical to consume if, and only if, x has average human intelligence, x has language skills, and x has human genetics.
<br />
<font color="CC6600">
<b>(∀x(¬Tx↔(Px∧Qx∧Rx)))</b>
<br />
<b>P2)</b></font> A hypothetical schmuman does not have human genetics.
<br />
<font color="CC6600">
<b>(¬Ra)</b>
<br />
<b>C)</b></font> Therefore, a hypothetical schmuman is ethical to consume.
<br />
<font color="CC6600">
<b>(∴Ta)</b>
<br />
<br />
</font>
</div>
[Proof Tree](https://www.umsu.de/trees/#(~6x(~3Tx~4(Px~1Qx~1Rx))),(~3Ra)|=(Ta))
### NTT Reductio (Non-Negated Antecedent w/ Disjunction)
| <font color="CC6600">**Definiendum**</font> | <font color="CC6600">**Definiens**</font> |
|:-------------------------------------------:|:----------------------------------------- |
| <font color="CC6600">**T**</font> | a being (x) is ethical to consume |
| <font color="CC6600">**P**</font> | a being (x) has fur |
| <font color="CC6600">**Q**</font> | a being (x) has horns |
| <font color="CC6600">**R**</font> | a being (x) has hooves |
| <font color="CC6600">**a**</font> | hypothetical human |
<div style="text-align: center">
<font color="CC6600">
<b>P1)</b></font> For all x, where x is a being, they are ethical to consume if, and only if, x has fur, or x has horns, or x has hooves.
<br />
<font color="CC6600">
<b>(∀x(Tx↔(Px∨Qx∨Rx)))</b>
<br />
<b>P2)</b></font> A hypothetical human has hooves.
<br />
<font color="CC6600">
<b>(Ra)</b>
<br />
<b>C)</b></font> Therefore, A hypothetical human is ethical to consume.
<br />
<font color="CC6600">
<b>(∴Ta)</b>
<br />
<br />
</font>
</div>
[Proof Tree](https://www.umsu.de/trees/#(~6x(Tx~4(Px~2Qx~2Rx))),(Ra)|=(Ta))
### NTT Reductio (Negated Antecedent w/ Disjunction)
| <font color="CC6600">**Definiendum**</font> | <font color="CC6600">**Definiens**</font> |
|:-------------------------------------------:|:------------------------------------------ |
| <font color="CC6600">**T**</font> | a being (x) is ethical to consume |
| <font color="CC6600">**P**</font> | a being (x) has average human intelligence |
| <font color="CC6600">**Q**</font> | a being (x) has language skills |
| <font color="CC6600">**R**</font> | a being (x) has human genetics |
| <font color="CC6600">**a**</font> | hypothetical schmuman |
<div style="text-align: center">
<font color="CC6600">
<b>P1)</b></font> For all x, where x is a being, they are not ethical to consume if, and only if, x has average human intelligence, or x has language skills, or x has human genetics.
<br />
<font color="CC6600">
<b>(∀x(¬Tx↔(Px∨Qx∨Rx)))</b>
<br />
<b>P2)</b></font> A hypothetical schmuman does not have average human intelligence, language skills, and human genetics.
<br />
<font color="CC6600">
<b>(¬Pa∧¬Qa∧¬Ra)</b>
<br />
<b>C)</b></font> Therefore, a hypothetical schmuman is ethical to consume.
<br />
<font color="CC6600">
<b>(∴Ta)</b>
<br />
<br />
</font>
</div>
[Proof Tree](https://www.umsu.de/trees/#(~6x(~3Tx~4(Px~2Qx~2Rx))),(~3Pa~1~3Qa~1~3Ra)|=(Ta))
---
# Hashtags
#debate
#debate_coursework
#namethetrait
#ntt

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# Humanity
### Genetics tho
>The trait that makes the difference is that humans have a cluster of genetics that distinguishes homo sapiens sapiens as a species, whereas non-human animals do not.
**Response:**
If a genetic test on your neighbour's kid returned the shocking result that they lack those genetics, would it be OK to kill him and eat him?
### Taxonomy tho
>The trait that makes the difference is that humans have the taxonomic classification of homo sapiens sapiens, whereas non-human animals do not.
**Response:**
If we restricted the criteria used to categorize homo sapiens to exclude some populations of people, would they be OK to kill and eat?
### Family Resemblance tho
>The trait that makes the difference is whether or not I can recognise an individual as human.
**Response:**
If we took your mother's consciousness and placed it inside of a cow's body, would it be OK to kill her and eat her?
# Cognition
### Intelligence tho
>The trait that makes the difference is that humans have human-level intelligence, whereas non-human animals do not.
**Response:**
If we found humans with the same level of intelligence as a non-human animal, would it be OK to kill them and eat them?
### Language tho
>The trait that makes the difference is that humans have the capacity to use and/or understand language, whereas non-human animals do not.
**Response:**
If we found humans with the same linguistic capacity as as non-human animals, would it be OK to kill them and eat them?
### Social Contracts tho
>The trait that makes the difference is that humans can enter into social contracts, whereas non-human animals cannot.
**Response:**
If we found humans with the same ability to enter into social contracts as as non-human animals, would it be OK to kill them and eat them?
### Moral Agency tho
>The trait that makes the difference is that humans have moral agency, whereas non-human animals do not
**Response:**
If we found humans with the same capacity for moral agency as non-human animals, would it be OK to kill them and eat them?
# Religious Belief
### Souls tho
>The trait that makes the difference is that humans have a soul, whereas non-human animals do not.
**Response:**
If we had a soul-scanner that could detect whether or not a being had a soul, and it was discovered that your neighbour's kid didn't have a soul, would it be OK to kill him and eat him?
### Image of God tho
>If we had an image-of-God scanner that could detect whether or not a being was made in the image of God, and it was discovered that your neighbour's kid wasn't made in the image of God, would it be OK to kill him and eat him?
**Response:**
What is untrue of a non-human animal that is true of a human, such that if it were made true of a human, the non-human animal would have a soul?
### Word of God tho
>The trait that makes the difference is that God's word, as articulated in the Holy Bible, permits us to consume non-human animals.
**Response:**
If the Holy Bible permitted cannibalism, would it be OK for humans to kill and eat each other?
# Norms
### Culture tho
>The trait that makes the difference is that our culture accepts the consumption of non-human animals, whereas our culture does not accept the consumption of humans.
**Response:**
If our culture developed a tolerance for the consumption of humans, would it be OK to farm humans, kill them, and eat them?
### Tradition tho
>The trait that makes the difference is that non-human animal consumption is traditional for humans, whereas human consumption is not.
**Response:**
If there was a population with a cultural tradition of cannibalism, would it then be OK to farm humans, kill them, and eat them?
### Legality tho
>The trait that makes the difference is that it is illegal to kill and eat humans, but it is not illegal to kill and eat animals.
**Response:**
If cannibalism was made legal, would it then be OK to farm humans, kill them, and eat them?
### Dominion tho
>The trait that makes the difference is that humans have dominion over non-human animals, whereas non-human animals do not have dominion over humans.
**Response:**
If space aliens had dominion over humans, would it be OK for the aliens to farm us, kill us, and eat us?
# Food
### Nutrition tho
>The trait that makes the difference is that non-human animals are rich in nutrients, whereas humans are not.
**Response:**
If it was discovered that human meat was equally as rich in nutrients as the meat of non-human animals, would it be OK to farm humans, kill them, and eat them?
### Agriculture tho
>The trait that makes the difference is that the meat of non-human animals is currently instrumental to sustaining human civilization, but the meat of humans is not.
**Response:**
If we discovered a civilization of humans who were sustaining themselves on human meat in the same way we sustain ourselves on non-human animal meat, is it OK, in your view, for them to farm, kill, and eat those humans?
### Tasty tho
>The trait that makes the difference is that non-human animals are tasty, whereas humans are not.
**Response:**
If it was discovered that human meat was equally as tasty as the meat of non-human animals, would it be OK to farm humans, kill them, and eat them?
# Hashtags
#debate
#debate_coursework
#namethetrait
#ntt

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## Operators & Symbols
| <font color="CC6600">**Symbol**</font> | <font color="CC6600">**Operation**</font> | <font color="CC6600">**Example**</font> | <font color="CC6600">**Description**</font> |
|:--------------------------------------:|:-----------------------------------------:|:---------------------------------------:|:-------------------------------------------------------------------------------------------------------- |
| → | Implies | P→Q | A proposition that is only false if either Q is false or both P and Q are false. |
| ↔ | Biconditional | P↔Q | A proposition that denotes logic equivalence, and is true when both predicates are either true or false. |
| ¬ | Negation | ¬P | A proposition that is true if and only if P is false. |
| ∧ | Conjunction | P∧Q | A proposition that is true if and only if both P and Q are true. |
| ∨ | Disjunction | P∨Q | A proposition that is false if and only if both P and Q are false. |
| ⊻ | Exclusive Or | P⊻Q | A proposition that is true if and only if either only P or only Q are true. |
| ∀ | Universal Quantifier | ∀x(Px) | A proposition that states that for all x, P is true. |
| ∃ | Existential Quantifier | ∃x(Px) | A proposition that states that there is at least one X, such that P(x) is true. |
| ∴ | Therefore | ∴Q | The conclusion of a syllogism |
| := | Definition | P:=grass is green | A general symbol used for defining propositions. |
| () | Parentheses | (P∧Q) | A means of grouping propositions together. |
# Logical Necessity
### Tautology
| <font color="CC6600">**P**</font> | <font color="CC6600">**True**</font> |
| --------------------------------- | ------------------------------------ |
| T | T |
| F | T |
# Logical Impossibility
### Contradiction
| <font color="CC6600">**P**</font> | <font color="CC6600">**¬P**</font> | <font color="CC6600">**P∧¬P**</font> |
|:---------------------------------:|:----------------------------------:|:------------------------------------ |
| T | F | F |
| F | T | F |
# Logical Possibility
### Implication (P→Q)
| <font color="CC6600">**P**</font> | <font color="CC6600">**Q**</font> | <font color="CC6600">**P→Q**</font> |
|:---------------------------------:|:---------------------------------:|:----------------------------------- |
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
### Biconditional (P↔Q)
| <font color="CC6600">**P**</font> | <font color="CC6600">**Q**</font> | <font color="CC6600">**P↔Q**</font> |
|:---------------------------------:|:---------------------------------:|:----------------------------------- |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | T |
### Conjunction (P∧Q)
| <font color="CC6600">**P**</font> | <font color="CC6600">**Q**</font> | <font color="CC6600">**P∧Q**</font> |
|:---------------------------------:|:---------------------------------:|:----------------------------------- |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F | F | T | F |
### Disjunction (P∨Q)
| <font color="CC6600">**P**</font> | <font color="CC6600">**Q**</font> | <font color="CC6600">**P∨Q**</font> |
|:---------------------------------:|:---------------------------------:|:----------------------------------- |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
### Exclusive Disjunction (P⊻Q)
| <font color="CC6600">**P**</font> | <font color="CC6600">**Q**</font> | <font color="CC6600">**P⊻Q**</font> |
|:---------------------------------:|:---------------------------------:|:----------------------------------- |
| T | T | F |
| T | F | T |
| F | T | T |
| F | F | F |
# Esoteric Logical Possibility
### Not And (P⊼Q)
| <font color="CC6600">**P**</font> | <font color="CC6600">**Q**</font> | <font color="CC6600">**P⊼Q**</font> |
|:---------------------------------:|:---------------------------------:|:----------------------------------- |
| T | T | F |
| T | F | T |
| F | T | T |
| F | F | T |
### Not Or (P⊽Q)
| <font color="CC6600">**P**</font> | <font color="CC6600">**Q**</font> | <font color="CC6600">**P→Q**</font> |
|:---------------------------------:|:---------------------------------:|:----------------------------------- |
| T | T | F |
| T | F | F |
| F | T | F |
| F | F | T |
### Material Nonimplication (P↛Q)
| <font color="CC6600">**P**</font> | <font color="CC6600">**Q**</font> | <font color="CC6600">**P→Q**</font> |
|:---------------------------------:|:---------------------------------:|:----------------------------------- |
| T | T | F |
| T | F | T |
| F | T | F |
| F | F | F |
### Converse Nonimplication (P↚Q)
| <font color="CC6600">**P**</font> | <font color="CC6600">**Q**</font> | <font color="CC6600">**P→Q**</font> |
|:---------------------------------:|:---------------------------------:|:----------------------------------- |
| T | T | F |
| T | F | F |
| F | T | T |
| F | F | F |
# Hashtags
#coursework
#logic_course
#propositional_logic

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