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

# Day 1 - All of Logic Overview --- **Intro to Logic, St Athanasius College, 2025** --- * Introductions * Why logic? And how? * All of logic in 2 pages(!) * Acts of the mind, big picture * Review, discussion * (Approx 28 slides + Euthyphro)

## Introductions * Who are you? * Who are me? * Will this class be worth my time?

### **Will it be awesome?** * Yes! Why? * Because... logic is *inevitable* * Five points

* A personal anecdote...

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

* **What is good logic? (Kreeft 1) 13 good reasons!** - Order - Power (proof, persuasion) - Reading - Writing - Happiness - Faith - Wisdom - Democracy - Limits of logic - Testing authority - Recognizing contradictions - Certainty - Truth

### All of Logic in 2 pages * Open to p. 26 of Kreeft. Let's read!

### **Some big picture points** **Memorize this** | Act | Result | Virtue | |---------------|-------------|--------| | Apprehension | Term | Clear | | Judgment | Sentence | True | | Reasoning | Argument | Valid |

### 3 Acts of the Mind 1st act: Simple apprehension 2nd act: Judgment 3rd act: Reasoning - Arguing, Proving, Demonstrating - Surmising, Guessing - Generalizing - Result = Arguments - Good arguments = Valid

### **Some Big picture points** 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

**Conclusions** The conclusion is the truth claim. (For example: “Trump is the 47th 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: Trump won the presidential election” and “there were 46 U.S. Presidents before 2024.”)

**Conclusions** 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 (or irrelevent).

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

### 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 * A rose is a rose. * The door cannot be both open and shut at the same time in the same respect. * The cat is on the mat -- is either true or false. It can't be neither.


### Three Laws These laws are *necessary truths*. Some truths are necessary -- they have to be true and can be known with certainty. >There's actually a whole scale of 'modality') > 1. Impossible > 2. Contingent but false > 3. Contingent and true > 4. Necessarily true

**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.

* **Discussion** * Reactions so far? Questions? * Thoughts? * Break

**Euthyphro** * Let's read a bit of Plato to show the importance of logic in thinking about God [Link to Euthyphro](https://classics.mit.edu/Plato/euthyfro.html)

**What is Euthyphro's claim #1** * Holiness (piety, righteousness) is 'whatever is loved by the gods' * Problem #1: the gods disagree

** Claim #2** * Holiness (piety, righteousness) is 'whatever is loved by *all* the gods' * Problem #2: which way does the arrow of causation go? * Do the gods recognize holiness and love it? (example, calling the car red) * Do the gods love a thing and it becomes holy? (example, painting my car my favorite color)

**Notes here on the reading!**

### Day 1 PAUSE * Questions? * Exercises...

* **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. - What's the conclusion? - 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 5** >"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?

## WRAPPING UP day 1 * Questions, comments?

# Day 2 - Acts of the Mind --- **Intro to Logic, St Athanasius College, 2025** --- * First act of the mind: understanding * Second act: judgment * Third act: reasoning * (35 slides)

### 1st act of the mind: Simple Apprehension - Conception - Naming - Identifying - Cognizing & recognizing - Result = Terms - Good terms = *clear*

### What makes man different from machine? (or animal) * Gods, men, and brutes * Gods don't question (they already know) * Brutes don't question (they don't realize they don't know anything) * Machines don't question (they have to be programmed) * *Men question (they know they don't know)* * The Aristotle story (35)

### Questions and Concepts * Our questions are: What, whether, why? * The answers to these questions require concepts, the "bits" or raw material of thought * Concepts are immaterial (transcend time and space!) * Concepts 'match' reality, they illuminate reality * Concepts are abstract (separate 'green' from the 'grass') -- separate the squareness from this or that square shape * Abstraction foster friendship (38)! * Concepts are universal (tree vs. that tree; dog vs Fido) * Relations between concepts are necessary. (Triangles necessarily have three sides) * Concepts are unchanging

### Concepts, terms and words * Concept is in the mind * A term is in the public domain -- a term is a concept in expression (transcends language though) * A word is a linguistic expression of a term (any language will do!) * The term 'love' is referred to by 'amore' 'caritas' 'amor' 'lieb' (six *words*, one term) * A term is the most basic unit of meaning * Terms are not true or false, but clear or unclear (keep your money in the river bank)

### Ambiguity * Terms for *things* that are unclear are just 'unclear': mysterious, numinous, baffling * Terms that could refer to either of two things are ambiguous: man (male or human?), bank (financial institution or river's edge?); > I saw her duck!

### Ambiguity and speciality vocab * "Tier 1" words: eg., the, a, and, he, she (8,000 words) * "Tier 2" words: eg. context, conduct, estate, invest, appreciate (570 words) * "Tier 3" words: eg. isotope, lathe, peninsula, filibuster, (100,000s of words) --- * Tier 1 words are hard to mess up. * Tier 2 words are extremely likely to become confused or confusing! Their exact meaning is sensitive to context. * Tier 3 words are extremely hard to mess up. However, they require specialized knowledge.

### Buhler's sidenote on speciality vocab * The *clarity* of tier 3 words is a likely cause of technical jargon and specialized vocab that people develop and use -- doctors, philosophers, bankers, weight lifters, etc. > Give me 50 CCs on her IV, stat! > The LTV on this DSCR is way too high after a refi, even with that ARV > Neo-Platonic realism is ecclipsed by medieval nominalism

### Buhler's sidenote on speciality vocab * Technicians and experts are not necessarily being a pedantic, snobby, or elitist by choice -- it's the natural consequence of working within a domain.

### Types of definition I. Nominal II. Real a. Essential b. Non-essential 1. By properties 2. by accidents 3. by causes 4. by effects

### Four causes * Material * Efficient (source) * Formal (kind) * Final (end, purpose)

### A good definition * Essential definition - genus and species * Clear, literal, brief, positive * Non-circular

### Good, bad, and ugly definitions (127) * Man, triangle, democracy

### Definitions - Exercises (130) * Define logic! (wee!) SO meta! I'm S o M eta T hat E ven T his A cronym

* Define science * Define deduction * Define abstraction * Define death * Define charity

Check out the definitions on 131... * Life is the most vivid of all dreams * Philosophy is unintelligible answers to insoluble problems * Justice is health of soul * "Chestertonisms"

### Universals * Forms * Nominalism

### Pause for digestion * Review / summary * Questions * Comments / where's your head at

### Extension and Intension of terms (43) * "Man = 4 billion men (males) * "Man" = 8 billion men (mankind right now) * "Man" = 50 billion men (mankind up to now) * Inversely proportional -- the bigger the extension (number of referents), the smaller the intention (detail of description) * Which has bigger extension? * Geese * Golden geese

### Extension and Intension of terms * Qualitative aspects of a term: * Comprehension, intention, connocation, meaning * Quantitative aspects: * Extension, denotation, reference

### Comprehension (generalizations) and extension * Comprehension covers what is true by nature * Extension covers what is true by factual happenstance * Comprehension (generalizations) can be true even with exceptions! (more on this later)

### **Classifying Terms** (47) * Ambiguous or unambiguous * Clear or unclear * Exact or vague * Univocal, analogical, or equivocal * literal or metaphorical * positive or negative * simple or complex * universal, particular, or singular * collective or divisive * concrete or abstract * absolute or relative Let's pick out a few of these...

### Literal, metaphorical, analogous * My dog is affectionate (analogy) * St Peter is a rock (metaphor) * God is a shepherd (metaphor) * God is good (analogy)

### Concrete & Abstract * Concrete means specific (red, spirit) * Abstract means 'taken out' (redness, spirituality) * 'Hot' is concrete; 'heat' is abstract * 'human' is concrete; 'humanity' is abstract * Exercise: You shouldn't try to love 'humanity' -- why?

### Relative v absolute **Relative** * Father (father of) * Son (son of) * Winner (winner of contest) **Absolute** * Man * Moral * Triangle

(If there's time) ### Categories * Natural and conventional * Ten categories

### Tree of Porphery (60)

### 2nd Act of the Mind: Judgment (139-156) - Proposition - Declarative statements - Relating two concepts - Result = Sentences - Good judgments = *true*

## **Subject and predicate** * Subject is what we are talking about * Predicate is what we are saying about the subject * We are "predicating" an action or adjective "of" the subject * Order matters: 2+2=4 is the same as 4=2+2, but "god is Love" is not the same as "love is god"! * S is P. Subject is predicate. S is my sermon subject, P is my sermon. S is my title, P is my essay.

## Judgment (thought), proposition (language), sentence (writing) * Judgments are *expressed* in propositions * Judgment is the act of the mind (can be inner, private) while propositions are expressed in language, math, symbols, etc. * Sentences are expressions of propositions: "Fear " * Kinds of Propositions * simple; * complex; * hypothetical, (if-then) * disjunctive, (or) * conjunctive (and)

## **Non-declarative sentences** * imperative, - interrogative, - exclamatory, - performative - (i.e., command, question, exclamation, and act)

**Only propositions contain truth!** * Words are neither true nor false * Arguments (strictly speaking) are not true or false (only the conclusion is!) * Truth resides in things too... * true money (not counterfeit) * true Van Gogh (not a fake) * true piety (not false piety) * true God (faithful, and trustworthy, and real)

**Correspondance** * Logical truth is the correspondance (of thought or word) to reality >"To say of what is, that it is and to say of what is not, that it is not"

**Four Kinds of Categorical Propositions** Memorize this: | Letter | Valence | Scope | |---------------|--------------|--------| | A | Positive | Universal | | E | Negative | Particular | | I | Positive | Universal | | O | Negative | Particular |

**Four Kinds of Categorical Propositions** Memorize this: | Letter | Example | |---------------|--------------| | A | All men are mortal. | | E | No men are winged | | I | Some men are blonde | | O | Some men are not brunette | > A shortcut: nEgO (I negate, in Latin); and AffIrmo (I affirm, in Latin)

### **Contradiction** * There are multiple ways to be 'incompatible'! * A and O *contradict* * "All holy things are "set aside" for God." * As long as there is *thing that is both holy and not set aside*, we have a contradiction. * Finding contradictions is a wonderful means to discovering truth (dismantling false beliefs)

### **Contradiction** * A and O *contradict* * E and I *contradict* No mammals lay eggs. Some mammals lay eggs. Ooops! You got [Platypused!](https://assets.wwf.org.au/image/upload/c_fill,g_auto,w_1400/f_auto/q_auto/v1/website-media/news-blogs/platypus_naturepicturelibrary?q=75)

### **Contradiction** * A and E *are contrary* though. "All logic is useful. No logic is useful." (Sounds like a contradiction but it's merely contrary.) * I and O *are compatible*. "A" * A and I *are alterns* * E and O *are alterns*

## Exercises (157) - on propositions * Let's categorize some propositions! 1. Is it a proposition or not? 2. Is it A E I or O? 3. What is the subject and what the predicate?

### Exercises (53) - on terms 1. The end of a thing is its purpose and perfection, and death is the end of life; therefore death is life's purpose and perfection. 2. Condemned prisoner to judge: "But I don't *feel* guilty.* 3. Antigravity should be easy. We disobey all kinds of laws, we should be able to disobey the law of gravity.

## **Distribution** (163) If we have time * Distribution refers to the term, whether it refers to all members of the class (distributed) * Or only some members of the class (undistributed) * Analogy of distributing pamphlets

### Tautology (189) * It is what it is * A bird is a bird * I am what I am * Only the fittest survive * You will pass if you work hard enough

* Take a breath...

# Day 2 - Review * Conception is first act of mind; simply aprehending the essence of a thing * Definitions -- good definitions are essential * Judgment is the second act of the mind; combining concepts (predication) * Conception makes us higher than animals, and computers (including LLMs!), by abstraction * Questions aim at truths, abstract truths * Judgments are expressed in propositions; S is P (or S is not P), etc. * Propositions can be simple or complex * Propositions are true or false * Propositions can be universal or particular, positive or negative (A E I O)

## WRAPPING UP day 2 * Questions? * Exercises from Kreeft (tbd)

## Day 3 - Third Act of the Mind: Arguments --- **Intro to Logic, St Athanasius College, 2025** --- * Third act: Reasoning/deduction * Syllogisms * Validity * Chains or clusters of syllagisms * Partially implied syllogisms (Entheymemes) * Intro to fallacies

## 3rd Act: Reasoning (Argumentation) (186-199) * What is reason? * "man is a rational animal" * The term 'man' is inclusive * 'rational' is inclusive too! * 'Rationality' includes wisdom, intuition, essence, conscience, self-knowledge, aesthetics -- *and math* and logic

### What can reason do? * Reason allows us to know what must be true, hypothetically (little green men on mars), beyond our experience * Reason allows us to know universal truths (2 + 2) * Reason allows us to know necessary and unchangable truths

### Deduction * Deduction is the ultimate foundation of the *syllogism* * The syllogism is the 'atom' of reasonining, the building block of arguments, the cells of the rational organism > "All planets orbit the sun. Earth is a planet. Therefore...

### Principles of Deduction (187-8) "Inherent, self-evident, necessary truths" 1. Whatever is universally true in the subject must be true of everything contained in that subject. 2. Whatever is universally false in a subject must be false of everything containing that subject. 3. Things identical with one the same third thing or identical with each other. > Notice the three laws?

### Detecting arguments (190) * Detect presence * Get into our net * Decide if edible > Take a look at the premise-indicators on 192 >

### Abduction (Explanations) 1. Buhler: Abduction (inference to best explanation) — CS. Pierce * Structure of abduction (appears like a formal fallacy!) * If A -> B, B, therefore A. * The surprising fact, *B*, is observed. * But if *A* were true, *B* would be a matter of course. * Hence, there is reason to suspect that *A* is true.

* Compare with Modus ponens: * If S is P, then Q is R. * S is P. * Therefore, Q is R. > * If Billy is a racist, then he would not celebrate Black Lives Matter day (July 13) > * Billy is indeed a racist. > * Therefore, Billy does not celebrate BLM day.

Here's a fallacy version: * If S is P, then Q is R. * Q is R. * Therefore, S is P. > * If John is a racist, then he would not celebrate Black Lives Matter day (July 13) > * John does not celebrate BLM day. > * Therefore, perhaps John is a racist!

### So what is abduction? Is it valid or not? Yes! Abduction is guessing, hypothesizing, 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.)

### Application of Abduction * Inference to best explanation (Peter Lipton) -- Philosophy, psychology, economics, sociology, etc.

### Application of Abduction Educated “Guessing” in Daily life * In daily life, we pull from background knowledge to explain what we observe. * "must be" as a clue to abduction * Eg. Why is my door open? * Eg. Why is Anne acting so shifty lately? * Eg. Why is it getting darker earlier all of a sudden?

### Application of Abduction * Hypothesizing in specialized fields * Science, philosophy, theology etc. employ domain-specific expertise to generate new guesses to be investigated * Investigation cannot produce the guess! It can only analyze the guess once proposed.

### Application of Abduction Examples > * Particle physics -- maybe there is a thing that does not obey gravity > * Philosophy -- maybe language formation (in humans) is like the construction of mathematical models (in computers) > * Law -- maybe there were two assassins > * History -- maybe the pyramids were built with sound-wave technology

### Syllogisms * Structure * Major premise, minor premise, conclusion > All men are *mortal* > *Socrates* is a man. > *Socrates* is **mortal.** "Mortal" is the major term. So the first premise is the major premise. Guess the minor term!

### Truth and validity * Arguments are either logically **valid** or **invalid**. Validity refers to the *structure* of the syllogism. * Propositions can't be 'fallacious' (nor terms) * Invalid arguments are called 'formal' fallacies (something wrong with the form!) * Informal fallacies (something else wrong besides the form) are covered next week * A valid argument gives us *certainty*

### Truth and validity Four possibilities: * (1) The premises are true and the logic is valid. * (2) The premises are true and the logic is invalid. * (3) At least one of the premises is false and the logic is valid. * (4) At least one of the premises is false and the logic is invalid * Ιn (1), conclusion is true * in (2), conclusion is UNKNOWN * In (3), conclusion is UNKNOWN * In (4), conclusion is UNKNOWN

### Truth and validity * If the premises are true, and the argument valid, we *know* that the conclusion is true. * Just because premise is false, doesn't mean we *know* that the conclusion is false > All fruit grows on trees. Avocados are fruit. Therefore, avocadoes grow on trees. > All evil spirits are birds. All sparrows are evil spirits. Therefore, all sparrows are birds. Conclusion "happens to be true (by accident)" (196)

### Arguing "backward" * If an argument is valid but the conclusion false, at least one premise must be false.

### Practicing logical NECESSITY * Imagine a spy trying to get out of East Berlin into West Berlin. In order to succeed in getting to West Berlin, he has to pass three checkpoints: Able, Baker, and Charlie. * If he fails at any of one or more of the checkpoints, he fails to get out. The spy symbolizes an argument, and escape to West Berlin symbolizes proving its conclusion to be true. The three checkpoints are the three questions of logic, one for each of the “three acts of the mind” (see the charts on pages 32-33). * Checkpoint Able checks for ambiguous terms. Checkpoint Baker checks for false premises. Checkpoint Charlie checks for logical fallacies.

### Practicing logical NECESSITY 1. If a premise is false and the argument is invalid, the conclusion must be false. 2. If a premise is false and the argument is invalid, the conclusion must be true. 3. If a premise is false and the argument is valid, the conclusion must be true. 4. Ifa premise is false and the argument is valid, the conclusion must be false. 5. If a premise is false and the conclusion is false, the argument must be invalid.

6. If a premise is false and the conclusion is false, the argument must be valid. 7. Ifa premise is false and the conclusion is true, the argument must be invalid. 8. If a premise is false and the conclusion is true, the argument must be valid. 9. If the premises are true and the argument is valid, the conclusion must be true. 10. If the premises are true and the argument is valid, the conclusion must be false.

11. If the premises are true and the argument is invalid, the conclusion must be false. 12. If the premises are true and the argument is invalid, the conclusion must be true. 13. Ifthe premises are true and the conclusion is true, the argument must be valid. 14. If the premises are true and the conclusion is true, the argument must be invalid. 15. Ifthe premises are true and the conclusion is false, the argument must be valid.

16. If the premises are true and the conclusion is false, the argument must be invalid. 17. If the argument is valid and the conclusion is false, at least one premise must be false. 18. If the argument is valid, the conclusion is false, and one premise is true, the other premise must be false. 19. If the conclusion is false, then either the argument is invalid or a premise is false. 20. If one premise is false, the conclusion true, and the argument valid, the other premise must be true.

### Kinds of "because" * Physical cause and effect * Logical ground and consequent * Psychological motive and act > * I will die because I despair > * I will die because of cancer > * I will die because all men die

### Kinds of "because" -- why this matters * I believe in God because I fear death (psychological) * I believe in God because he put the desire for eternity in my heart. (cause and effect) * I believe in God because there must be a First Cause (logical)

### Kinds of argument * Four causes (review!) * Classification of arguments * Form * Causality * Direction of movement * Length * Strategy * Cumulative

### Four causes (202) * Material * Efficient (source) * Formal (kind) * Final (end, purpose) Examples 204 Exercises 205

* Pause for break

### Arguments * Deductive (general, and inferring down) or inductive (specific, and building up) * Deductive can be simple or complex * Simple has 3 categorical propositions * Complex (wee!) can be Hypothetical, disjunctive, conjunctive (chapter 13)

### Compound Syllogisms * Linear (a river building to a destination) * Cumulative (many rivers combining to one destination)

# WRAPPING UP day 3 * Questions? * Exercises

# Day 4 - Informal Fallacies --- **Intro to Logic, St Athanasius College, 2025** --- * Review homework * Induction, abduction * Fallacies * (48 slides!)

* Review homework: predication

* Terms are 'bits' of arguments * Propositions are how we build premises (and conclusions) * Inference is the movement from premises to conclusion * Never forget: the logical relationship between premises and conclusion is where the magic happens * 'support' * 'implication' * 'proof' * 'evidence' * 'shows' * 'demonstrates' ... And where the magic *fails*!

* Review homework: predication

### Three kinds of inference - Induction: generalization - Deduction: inference - 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. > Every swan I have seen is white... And I've seen thousands! Therefore...

### **Induction** Some different types of induction: > - Generalizations: the Chinese work hard at math > - Statistics: 30% of Americans are overweight but not obese > - Categorical statements: ducks lay eggs > - Generics: humans have 32 teeth * Induction admits of exceptions! * Some Chinese don't work hard at math. 40% of Americans are obese; drakes do not lay eggs; and some people have lost teeth or genetically have extra teeth.

### **Generalizations** * We tend to favor negative or dangerous generalizations: > Always wear repellent; mosquitos carry malaria Only true of a tiny fraction of mosquitos... but because it's dangerous, it sticks in the mind.

### **Generalizations** > I would never move there; that neighborhood has high crime. LA has a violent crime rate of about 2% (i.e., maybe once a week)... 6 days of perfect peace, and yet it sticks in the mind!

### **Generalizations** * When it pays to err on the side of caution, we favor generalizations. * When we err on the side of (negative) generalizations about people, the reactions can be intense.

#### **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 * Review of abduction (guessing)

### Informal fallacies (68-108) * Errors in reasoning not due to form * Main sources: irrelevance, weak induction, presumption, ambiguity

### Absurd examples of each * Irrelevance: "It's Thursday, therefore you owe me $20." (Premise irrelevant to conclusion) * Presumption: "I know we disagree, but there's no point; you may as well concede; I've always been right in the past so you know I'm right in this case." (Premise is a re-phrasing of the conclusion: you're wrong because you disagree with me) * Weak induction: "The mall is slow, therefore every shop is going to go out of business and the mall will soon close." (Premise relevant, but not connected enough) * Ambiguity: "God is love. Love is blind. Ray Charles is blind. Ray Charles is God." ('Love' is a divine energy vs. 'love' is the human tendency to overlook faults.)

### Real life examples of each! * Irrelevance: "We live in the age of the light bulb; we know that sickness is not due to angels or demons." (Premise irrelevant to conclusion) * Presumption: "The Democratic [or Republican] party has no leadership; that's why they cannot build a strong coalition." (Premise is a re-phrasing of the conclusion: the group is not united because the group is not united) * Weak induction: "Birth rates have been dropping for over 10 years; in 50 years, the population of [Country X] will be zero." (Premise relevant, but not connected enough) * Ambiguity: "Covid deaths have increased in 2024. Therefore, Covid is still dangerous." (Does 'covid death' mean people died and also had Covid or deaths *due to Covid*)

### Difference between formal and material - Formal fallacies = your argument is invalid. - Material fallacies = something else is wrong with your argument.

### 23 of the 49 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 8. Faulty Analogy 9. Group Think 10. Hasty Generalization 11. Composition and division 12. Straw Man 13. Non Sequitur (doesn't follow) 14. Slippery Slope 15. False Cause ~~~

### 23 of the 49 Fallacies ~~~ 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 to help us understand these fallacies?

### So what are some themes / categories to help us understand these fallacies? * Relevance * Language * Presumption * Weak Induction

### So what are some themes / categories to help us understand these fallacies? * Relevance -- premises don't connect to conclusion *at all* * Language -- terms in premises moving, shifty, or vague * Presumption -- conclusion is hidden in premises * Weak Induction -- premises don't connect to conclusion *enough*

#### 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."

#### Fallacies of Language - **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."

#### Fallacies of Language - **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"


#### Fallacies of Relevance * **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."

#### Fallacies of Relevance - **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."

#### Fallacies of Relevance - 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.

#### Fallacies of Relevance - Appeal to (Irrelevant) Authority * 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."

#### Fallacies of Relevance - **Ad Populum (Appeal to the People)**, * This one has a lot of names! * 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.

#### Fallacies of Relevance - **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." * "America's favorite french fry."

#### Fallacies of Relevance - **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."

#### Fallacies of Relevance - **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."

#### Fallacies of Relevance - **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 a History [literature] from a man [woman]. They always have a sexist [feminist] bias."

### Inductive Fallacies - **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."

#### Inductive Fallacies -- 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.

#### Inductive Fallacies -- Straw Man * 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."

### Inductive Fallacies -- Non sequitur (does not follow) 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."

### Inductive Fallacies - **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*."

### Inductive Fallacies - **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. My lucky socks will give us the victory!" * "The President is pushing policies so risky, the whole stock market crashed as soon as he was elected."

### Fallacies of Presumption -- 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.

### Fallacies of Presumption -- Petitio Principii (Begging the Question) * 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.' * "Sheeple who deny the truth of Marxism are simply dancing to the tune of their capitalist masters, as Marx understood so well." * "Women who oppose feminism have internalized mysogyny."

### Fallacies of Presumption * **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."

### Fallacies of Presumption * **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?" * Philosophy prof to St Athanasius student: "Did you stop wedding the bed yet?"

### Fallacies of Presumption - 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."

### Fallacies of Presumption -- 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."

* Review / practice * What do (most) fallacies have in common?

* Good argument = premise -> conclusion * Relevance Fallacies = premise -> premise * Presumption Fallacies = conclusion -> conclusion * Love is a fallacy (114)

* A bonus section! *Metaphysical* fallacies!

### Metaphysical Fallacies (109)

### 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.

### Some Others **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."

## WRAPPING UP day 4 * Review (check outline) * Questions? * Exercises * How to write a Socratic Dialogue (344)

# Day 5 - Applying Logic --- **Intro to Logic, St Athanasius College, 2025** --- * Analyzing arguments * Pursuit of truth * St Gregory (logic and theology) * An exercise on nearly everything (336)

### Logic and theology (359) * [St Gregory example](https://www.newadvent.org/fathers/310227.htm) 27.VIII * The saints command logic! But are not limited to it

[St Gregory example](https://www.newadvent.org/fathers/310227.htm) 28.VI VI. Now our very eyes and the Law of Nature teach us that God exists and that He is the Efficient and Maintaining Cause of all things: our eyes, because they fall on visible objects, and see them in beautiful stability and progress, immovably moving and revolving if I may so say; natural Law, because through these visible things and their order, it reasons back to their Author. For how could this Universe have come into being or been put together, unless God had called it into existence, and held it together?

[St Gregory example](https://www.newadvent.org/fathers/310227.htm) VIII For every one who sees a beautifully made lute, and considers the skill with which it has been fitted together and arranged, or who hears its melody, would think of none but the lutemaker, or the luteplayer, and would recur to him in mind, though he might not know him by sight. And thus to us also is manifested That which made and moves and preserves all created things, even though He be not comprehended by the mind. And very wanting in sense is he who will not willingly go thus far in following natural proofs; but not even this which we have fancied or formed, or which reason has sketched for us, proves the existence of a God. But if any one has got even to some extent a comprehension of this, how is God's Being to be demonstrated?

[St Gregory example](https://www.newadvent.org/fathers/310227.htm) VIII Who ever reached this extremity of wisdom? Who was ever deemed worthy of so great a gift? Who has opened the mouth of his mind and drawn in the Spirit, so as by Him that searches all things, yea the deep thing of God, 1 Corinthians 2:10 to take in God, and no longer to need progress, since he already possesses the Extreme Object of desire, and That to which all the social life and all the intelligence of the best men press forward?

### Logic and theology * Euthyphro

### Your socratic dialogues

### 336 - Fatima and Tiffany * Discuss

## WRAPPING UP day 5 * Questions? * Exercises