Introduction

# Intro to Logic ## St Athanasius College ## 2025

### Why think about logic?

1 Logic is unavoidable -- to think is to think according to norms

2 Logic is undeniable -- to deny logic is to use it

3 Logic works -- some truths are necessarily true, and some relations between propositions are necessary

4 Logic underlies all knowledge -- this includes science, philosophy, theology, psychology, engineering, art, etc.

### Why think *about* logic? ### Because we think *with* logic

### The One Thing You must get The fundamental structure of all reasoning is the movement of the mind from premises to a conclusion. The conclusion is what you are trying to prove to be true; the premises are the reasons or evidence for the truth of the conclusion.

### The One Thing You must get The conclusion is the truth claim. (For example: “Obama is the 44th president” can be a conclusion.) Premises are statements that, if true, support or prove your conclusion. (For example, statements that support the claim above might be: “Obama won the presidential election” and “there were 43 U.S. Presidents before 2004.”) The conclusion is the whole point of the argument. Always ask yourself, “What am I being asked to believe?” That is the conclusion of the argument. Everything else is a premise.

### Three "3"s * 3 Acts of the mind * 3 Products: Terms, judgments, arguments * 3 Laws

### Act 1: Simple Apprehension - Conception - Naming - Identifying - Cognizing & recognizing - Result = Terms - Good terms = *clear*

### Act 2: Judgment - Proposition - Statements - Relating two concepts - Result = Sentences - Good judgments = *true*

### Act 3: Reasoning - Arguing, Proving, Demonstrating - Surmising, Guessing - Generalizing - Result = Arguments - Good arguments = Valid

### Memorize this | Act | Result | Virtue | |---------------|-------------|--------| | Apprehension | Term | Clear | | Judgment | Sentence | True | | Reasoning | Argument | Valid |

### Three Laws Some truths are self-evident foundations of thinking. For example, the classical “laws of thought”: 1. Every thing is identical to itself (A=A) 2. No thing can be A and not A at the same time in the same respect. (X cannot be A and not-A) 3. Every affirmation is either true or false. (A=true or A=false)

### Three Laws These laws are *necessary truths*. 1. Impossible 2. Contingent but false 3. Contingent and true 4. Necessarily true Some truths are necessary -- they have to be true and can be known with certainty. ![possible](http://www.possiblefutureworlds.com/img/logic.png)

### In a word... >Logic is the science of arguments. An argument is a proof composed of premises (that support the conclusion) and a conclusion. Arguments are composed of words. Good arguments have clearly defined words, true premises, and a valid inference to the conclusion. Fallacies are bad arguments. A good argument *necessarily* entails the conclusion; a good argument is the most scientific form of rational proof.

### Questions?

### Pop Quiz! >All men are bipeds and Edgar is a man, so Edgar is a biped. - What is the conclusion? - Valid inference? true premises? clear terms?

### Example 2 >Jean Jones is seven feet tall because all San Franciscans are seven feet tall and Jean Jones is a San Franciscan. - Valid inference? true premises? clear terms?

### Example 3 > 1. All Oakland Raiders are football players. > 2. Ken Stabler is a football player. > 3. Ken Stabler is an Oakland Raider. - What is the conclusion? - Valid inference? true premises? clear terms?

### Example 4 > 1. I want my daughter to marry a good man. > 2. Shia Labeouf is a good actor. > 3. I want my daughter to marry Shia Labeouf. - What is the conclusion? - Valid inference? true premises? clear terms?

### Example 4 >It is obvious to anyone thinking logically that minimum wage should be increased. The current minimum wage is an insult and is unfair to the people who receive it. The fact that the last proposed minimum wage increase was denied is proof that the government of this state is crooked and corrupt. The only way for them to prove otherwise is to raise minimum wage immediately. - What is the conclusion? - Valid inference? true premises? clear terms?

### Review 1. Logic is inevitable and useful 2. Premise and conclusion 3. 3 acts of the mind: conceiving, judging, reasoning 4. 3 laws of thought are necessary truths, identity, non-contradiction 5. To evaluate an argument, search for the conclusion first 6. Then examine the clarity of the terms, the truth of the premises, and the validity of the inference

## Day 1 WRAPPING UP * Questions? * Exercises

# Logical Fallacies

### Two Logics 1. Symbolic (Math-y) 2. Aristotelian (Language)

### Two Branches of Logic - Material (content of thoughts) - Formal (organization of thoughts)

### Induction, Deduction, Abduction - Induction: generalization - Deduction: specification - Abduction: hypothesis

### Induction - Simple apprehension, plus induction is used to form basic propositions: - grass is green, tables are hard, the sky is blue, Mom is kind, Fido is soft.

### Deduction Deduction extends these basic propositions to the unknown. If all dogs are mammals, and your pet is a dog, your dog is a mammal.

### Abduction Abduction is guessing or explaining. - E.g., The ground is wet. If it was raining, the ground would be wet. So maybe it was raining. - Deductively invalid, but still important (Maybe sprinklers were on, or the fire hydrant is open, etc.) - Perhaps the whole earth is round (it is). Maybe your mom is kind, too (she is). Perhaps all grass is green (it's not). Maybe all dogs are soft (they're not).

### Fallacy A fallacy is any mistake in reasoning - Formal fallacies: mistaking the structure - Material fallacies: mistaking the content

### Fallacy - Formal fallacies = your argument is invalid. - Material fallacies = something else is wrong with your argument.

### 23 of the 100s of Fallacies 1. Equivocation 2. Amphiboly 3. Ad Hominem (to the man) 4. Appeal to Ignorance 5. Appeal to Irrelevant Authority 6. Ad Populum (Appeal to Majority) 7. Appeal to Motive 7. Faulty Analogy 8. Group Think 9. Hasty Generalization 10. Composition and division 11. Straw Man

### 23 of the 100s of Fallacies 13. Non Sequitur (doesn't follow) 14. Slippery Slope 15. False Cause 16. Petitio Principii (begging the question) 17. False Dilemma 18. Loaded Question 19. Hedging 20. No True Scotsman 21. Nothing Buttery 22. Confusing Accident / Essence 23. Confusing Quality / Quantity 24. Confusing Abstract / Concrete

### So what are some themes / categories?

### Fallacies of Language - **Equivocation**. An equivocation trades upon the use of an ambiguous word or phrase in one of its meanings in one of the propositions of an argument but also in another of its meanings in a second proposition. Example: "Really exciting novels are rare. But rare books are expensive.Therefore, Really exciting novels are expensive."

- **Amphiboly**. An amphiboly can occur even when every term in an argument is univocal, if the grammatical construction of a sentence creates its own ambiguity. Example: "A reckless motorist Thursday struck and injured a student who was jogging through the campus in his pickup truck. Therefore, it is unsafe to jog in your pickup truck."

- **Spin/Slant**. Arguing by the positive or negative definitions or connotations of one's words. - Pro-choice vs. “Anti-choice” - Pro-life vs. “Anti-Life”. - "Terrorist" vs. "Freedom fighter". - "Radical" vs. "Pious" Believer. - "Rat" vs. "Whistle-blower"

![out-group](https://github.com/user-attachments/assets/35011a87-ea5b-48e3-9b64-919a14ab7184)

### Fallacies of Relevance 1. **Ad Hominem.** (Attacking the person): This fallacy occurs when, instead of addressing someone's argument or position, you irrelevantly attack the person or some aspect of the person who is making the argument. The fallacious attack can also be direct to membership in a group or institution. Example: "Socrates' arguments about human excellence are rubbish. What could a man as ugly as he know about human excellence." "No, I will not reply. I see no need to defend my views against the objections of ignoramuses."

2. **Appeal to Ignorance**. This fallacy occurs when you argue that your conclusion must be true, because there is no evidence against it. This fallacy wrongly shifts the burden of proof away from the one making the claim. Example: "You know that scientists can't prove that UFO's do not visit the Earth, so it makes sense to believe in them." "Since all who have tried to prove freedom of the will have failed, we are safe in assuming we are not free."

3. **Appeal to (Irrelevant) Authority**. You appeal to authority if you back up your reasoning by saying that it is supported by what some authority says on the subject. Most reasoning of this kind is not fallacious, and much of our knowledge properly comes from listening to authorities. However, appealing to authority as a reason to believe something is fallacious whenever the authority appealed to is not really an authority in this particular subject, when the authority cannot be trusted to tell the truth, when authorities disagree on this subject (except for the occasional lone wolf), when the reasoner misquotes the authority, and so forth. Example:"The moon is covered with dust because the president of our neighborhood association said so." "Pacifism is a good idea because the brilliant scientist Einstein advocated it."

- **Ad Populum (Appeal to the People, Appeal to Majority, Ad Numerum, Appeal to the Gallery, Appeal to the Masses, Argument from Popularity, Argumentum ad Populum, Common Practice, Mob Appeal, Past Practice, Peer Pressure, and Traditional Wisdom.)**.

- **Ad Populum**. This fallacy claims that the conclusion is correct simply because it's what most everyone believes. Agreement with popular opinion is not necessarily a reliable sign of truth, and deviation from popular opinion is not necessarily a reliable sign of error, but if you assume it is and do so with enthusiasm, then you are using this fallacy. The "too strongly" mentioned above is important in the description of the fallacy because what most everyone believes is, for that reason, somewhat likely to be true, all things considered. However, the fallacy occurs when this degree of support is overestimated. Example: "You should turn to channel 6. It's the most watched channel this year."

- **Appeal to Motive**. This fallacy assumes a motive behind the speaker arguing the conclusion, and then dismisses the conclusion as false. Examples: "You're only arguing that taxes should be abolished because you are an anarchist and hate the government." "You're just saying that education is important for children because you are a principal and you'd lose your job if we saw through the lies."

- **Faulty Analogy**. This fallacy consists in assuming that because two things are alike in one or more respects, they are necessarily alike in some other respect. Examples: "Medical Student: "No one objects to a physician looking up a difficult case in medical books. Why, then, shouldn't students taking a difficult examination be permitted to use their textbooks?" "Because human bodies become less active as they grow older, and because they eventually die, it is reasonable to expect that political bodies will become less and less active the longer they are in existence, and that they too will eventually die."

- **Group think**. A reasoner uses the Group Think Fallacy if he or she substitutes pride of membership in the group for reasons to support the group's policy. If that's what our group thinks, then that's good enough for me. It's what I think, too. "Blind" patriotism is a rather nasty version of the fallacy. Example: "We K-Mart employees know that K-Mart brand items are better than Wall-Mart brand items because, well, they are from K-Mart, aren't they?"; "97% of scientists agree that human caused climate change is real."

### Inductive Fallacies - **Hasty generalization.** This fallacy occurs when we we make a generalization on the basis of insufficient evidence. This may occur when we rely on too small of a sample or an unrepresentative sample to support the generalization. Example: "Children of faculty are brats. I baby-sit for one of my professors and his children are spoiled and demanding."; "You don't want to take history from a man. They always have a sexist bias."

- **Composition and Division.** This fallacy attributes properties of the parts to the whole or properties of the whole to the parts. - Examples of Composition: "Each person in America is a citizen, therefore the country is a citizen." "Each brick in the church is a rectangular. Therefore the dome of the church is rectangular." "The 9/11 bombers were Muslims therefore Islam is a violent religion." - Examples of Division: "The Church as a whole is a spotless bride. Therefore I am a spotless bride." "The human race is thousands of years old. Therefore I am thousands of years old."

- **Straw man**. Your reasoning contains the Straw Man Fallacy whenever you attribute an easily refuted position to your opponent, one that the opponent wouldn't endorse, and then proceed to attack the easily refuted position (the straw man) believing you have thereby undermined the opponent's actual position. Example: "Opponent: Because of the killing and suffering of Indians that followed Columbus's discovery of America, the City of Berkeley should declare that Columbus Day will no longer be observed in our city. Speaker: This is ridiculous, fellow members of the city council. It's not true that everybody who ever came to America from another country somehow oppressed the Indians. I say we should continue to observe Columbus Day, and vote down this resolution that will make the City of Berkeley the laughing stock of the nation."

- **Non Sequitur**. When a conclusion is supported only by extremely weak reasons or by irrelevant reasons, the argument is fallacious and is said to be a Non Sequitur. However, we usually apply the term only when we cannot think of how to label the argument with a more specific fallacy name. Any deductively invalid inference is a non sequitur if it also very weak when assessed by inductive standards. Example: "Nuclear disarmament is a risk, but everything in life involves a risk. Every time you drive in a car you are taking a risk. If you're willing to drive in a car, you should be willing to have disarmament."

- **Slippery Slope**. In a slippery slope argument, a course of action is rejected because, with little or no evidence, one insists that it will lead to a chain reaction resulting in an undesirable end or ends. The slippery slope involves an acceptance of a succession of events without direct evidence that this course of events will happen. Example: "We can't permit the sale of marijuana by doctor's prescription, because that will lead people to believe it's an acceptable drug; this will open the floodgates to the complete legalization of the drug for use by every pothead in the country."; "If Texas adopts a personal income tax, I'm moving away. An income tax at the state level is just a first step to communism."

- **Post Hoc, Ergo Proper Hoc (False Cause)**. In the false cause argument, you cite event A as the cause of event B simply because B came after A. Example: "Every time I wear my green socks, we win the game." "The President's policies are so risky, the stock market bubble crashed as soon as he was elected."

### Fallacies of Presumption 1. **Petitio Principii (Begging the Question).** The fallacy of begging the question occurs when an argument's premises assume the truth of the conclusion, instead of supporting it. In other words, you assume without proof the stand/position, or a significant part of the stand, that is in question. Begging the question is also called arguing in a circle. Example: "Erica: "How do you know that the bible is divinely inspired?" Pedro: "Because is says right in the third chapter of II Timothy that 'all scripture is given by divine inspiration of God.'; "People who deny the truth of Marxism are simply dancing to the tune of their capitalist masters, as Marx understood so well."

2. **False Dilemma**. When you reason from an either-or position and you haven't considered all relevant possibilities you commit the fallacy of false dilemma. Examples: "Are you a Republican or a Democrat?" "Good students will study and learn without the threat of an exam, and bad students won't study and learn even with the threat of an exam. So, exams serve no purpose."

3. **Loaded question**. Assuming something false as a premise of a question. Example: Prosecutor to defendant: "So how did you feel when you robbed the bank?" Reporter to politician: "When will you stop being a racist?"

4. **Hedging**. You are hedging if you refine your claim simply to avoid counterevidence and then act as if your revised claim is the same as the original. Example: "Samantha: David is a totally selfish person. Yvonne: I thought we was a boy scout leader. Don’t you have to give a lot of your time for that? Samantha: Well, David’s totally selfish about what he gives money to. He won’t spend a dime on anyone else. Yvonne: I saw him bidding on things at the high school auction fundraiser. Samantha: Well, except for that he’s totally selfish about money."

5. **No True Scotsman**. This error is a kind of Ad Hoc Rescue of one's generalization in which the reasoner re-characterizes the situation solely in order to escape refutation of the generalization. Example: "Smith: All Scotsmen are loyal and brave. Jones: But McDougal over there is a Scotsman, and he was arrested by his commanding officer for running from the enemy.Smith: Well, if that's right, it just shows that McDougal wasn't a TRUE Scotsman."

### Metaphysical Fallacies

### Nothing Buttery - "A star is a big ball of burning gas" (no, a star is *made of* burning gas) - I am reading "words words words" (no, you're reading *content*, *with* words)

### Confusing Accident / Essence - adding race into definition of 'human person' - removing male-female parents from definition of 'family' - "A great nose indicates a great man" - "There is an incredible amount of empty space in the universe... And as to mass: the sun weighs about 2 followed by 27 noughts tons... it is not very easy to retain a belief in one's own cosmic importance in view of such overwhelming statistics."

### Confusing Quality / Quantity - Intelligence = # IQ test score - Beauty = # of dates - Goodness of a Product = # of people who buy it - The number 7 = divine number

### Confusing Abstract / Concrete - Abstract Beauty, Justice, etc. = Concrete forms - Concrete Tom, Dick, Jane = Abstract "humanity"

### Some Others ### Fallacies of Oversimplification Jeremiah 11:29 says the Lord knows the plans he has for me, plans to prosper. Therefore every Christian can expect to be prosperous in this life. ### Fallacies of Argumentation: - Contradictory premises: " Even if the fetus is a person, I still believe in abortion because I believe in every person’s right to control her body." ### Procedural Fallacies

## Day 2 WRAPPING UP * Questions? * Exercises

## Day 3 WRAPPING UP * Questions? * Exercises

## Day 4 WRAPPING UP * Questions? * Exercises

## Day 5 WRAPPING UP * Questions? * Exercises

1 Logic is unavoidable -- to think is to think according to norms, rules, laws

2 Logic is undeniable -- even to deny logic is to use it

3 Logic works -- some truths are *necessarily* true, and some relations between propositions are necessary relations... this alone blows the mind.

4 Logic underlies all knowledge -- this includes science, philosophy, theology, psychology, engineering, art, etc.

### Demonstrative syllagisms (230) *

### Categorical syllogisms, terms, premises - Not quite induction, either: - Grass is green, tables are hard, the sky is blue, Mom is kind, Fido is soft. - Perhaps the whole earth is round (it is). Maybe your mom is kind, too (she is). Perhaps all grass is green (it's not). Maybe all dogs are soft (they're not).