Logic, Debate, and Reasoning

Presented by Ratio Christi TAMU Logic, Debate, and Reasoning

The science of analyzing arguments? • The science of good reasoning in general? • Tagore • A mind all logic is like a knife all blade, it makes the hand bleed that uses it What is Logic

Premises that lead to a conclusion • P1: If God exists he works all events for the good of those who believe; • P2: Some events produce no good; • C: Therefore God does not exist. • The conclusion either follows from the premises logically, or is at least probablegiven the premises. What is a Formal Argument √

Roadmap

Inductive • Results in a high probability that the conclusion is true. • Common in science Types of Arguments • Deductive Arguments • If the premises are true, and the structure is correct, the conclusion must be true.

Has premises and conclusion, but is probabilistic • 100% of biological life forms that we know of depend on liquid water to exist. • Therefore, if we discover a new biological life form it will probably depend on liquid water to exist. • Used in the scientific method • The conclusion is not certain, only probable Inductive Arguments

Statistical Syllogism • P1: Most Greeks ate fish; • P2: Socrates was a Greek; • C: Therefore Socrates probably ate fish. • Similar in form to the deductive syllogism • The conclusion is still not certain, only probable Statistical Syllogism

Assumes a sample has the same attributes as a population • 10% of the survey were Democrats • Therefore, 10% of people are Democrats Generalization

Compares two situations • Situations A and B are similar in properties X and Y • Situation A also has property Z • Therefore, B probably has property Z as well • May provide good evidence for a claim • Is not conclusive Analogy

Draws a conclusion about the future from the past • Every time in the past that an apple has been dropped, it has fallen. • Therefore, if I drop an apple now, it will probably fall • One of the foundational assumptions of science Prediction

Has premises and conclusion • P1: All men are mortal; • P2: Socrates was a man; • C: Therefore Socrates was mortal. • The conclusion is certain, but only if the premises are true and the structure is correct Deductive Arguments √

Validity • An argument is valid if it has the correct form • Sound • An argument is sound if it is valid and the premises are true Validity and Soundness

Categorical Logic • Propositional Logic • Modal Logic Types of deductive Reasoning

First formalized by Aristotle • Made up of simple statements • Not all arguments can be translated into this form • But many can be translated into this form Categorical Logic

4 types of statements • All Sare P • No Sare P • Some Sare P • Some Sare not P • Can be combined into groups of three called a syllogism Categorical Logic

Requires two kinds of premises • Major Premise: All men are mortal; • Minor Premise: Socrates was a man; • Conclusion: Therefore Socrates was mortal. • The premises must share a term (middleterm) • P1: All menare mortal; • P2: Socrateswas a man; • C: Therefore Socrateswas mortal. Categorical Syllogism

Not all combinations of terms are valid; • P1: All cats are mammals; • P2: Oreo is a Cat; • C: Therefore Oreo is a mammal. • P1: All mammals are animals; • P2: some cats are animals; • C: Therefore some cats are mammals. Categorical Syllogisms √ X

The most basic logic dealing with conditionals • If then statements, etc. • More powerful than simple categorical syllogisms • 9 basic rules Propositional Logic

If P, then Q • P • Therefore, Q • Valid, example: • If the ground is wet, it is raining • The ground is wet • Therefore it is raining • (this one is unsound because the premise is false) Rule #1 Modus Ponens √

If P, then Q • NotQ • Therefore, notP • Valid, example: • If it is raining, the ground is wet • The ground isnotwet • Therefore itisnotraining • (This one may be unsound as well) Rule #2 Modus Tollens √

If P then Q • If Q then R • Therefore if P then R • Example • If it is raining, the ground is wet • If the ground is wet, the roads are slippery • Therefore, if it is raining, the roads are slippery Rule #3 Hypothetical Syllogism √

P • Q • Therefore P and Q • Example • John is a good student • Mary is a good student • Therefore John is a good studentand Mary is a good student Rule #4 Conjunction √

Pand Q • Therefore P • Example • John is a good studentand Mary is a good student • Therefore John is a good student Rule #5 Simplification √

If P then Q • Therefore If P then P and Q • Example • If it is raining, the road is wet • Therefore if it is raining, it is rainingand the road is wet Rule #6 Absorption √

P • Therefore P or Q • Example • It is raining • Therefore if it is raining or the sun is shining Rule #7 Addition √

P or Q • NotP • Therefore, Q • Example • It is either rainingor the sun is shining • It is not raining • Therefore,the sun is shining Rule #8 Disjunctive Syllogism √

If Pthen Q and If Rthen S • Por R • Therefore, Q or S • Example • If it is rainingthe streets are wet, and if it is sunnythe streets are dry • It is either rainingor sunny • Therefore, the streets are wet or the streets are dry Rule #9 Constructive Dilemma √

If God existsand the present moment is real, then God is in time • If God is in time, then he knows what is happening now • If God knows what is happening now, then now exists • Either now does not exist, or Einstein's theory is wrong • The present moment is real • Therefore if God exists, ThenEinstein’s theory is wrong • (However this may be unsound) Example √

Roadmap

Result from errors of logical form • May have true conclusions • But the conclusion does not follow from the premises Formal Fallacies

Many types: • Ex: • All communistsare leftists. • No conservativesare communists. • Therefore, no conservativesare leftists. • Ex: • All dogsare animals. • No catsare dogs. • Therefore, no catsare animals. Incorrect categorical syllogism X X

Improper modus ponens • Ex: • If God exists, then objective morals and duties exist • Objective morals and duties do exist • Therefore God exists Affirming the consequent X

Improper modus tollens • Ex: • If God does not exist then objective values and duties do not exist • God does exist • Therefore objective values and duties exist Denying the Antecedant X

Mistakes in reasoning that arise from the content of the argument Informal Fallacies • Ad hominem • Red herring • Straw man • Appeal to Authority • Slippery Slope • Weak Analogy • Hasty Generalization • False Cause • Appeal to Ignorance • Bandwagon • Genetic Fallacy • Begging the question • Appeal to Emotion • Special pleading • Equivocation • Self refuting Statements

Meaning: “To the man” • Favorite of politicians • Ex: • "All politicians are liars, and you're just another politician. Therefore, you're a liar and your arguments are not to be trusted." Ad Hominem X

An irrelevant fact intended to divert attention from the real issue • Therefore, if morality exists, then God must exist too! • Sure, but what about slavery in the Bible? That does not sound very moral to me… • Don’t take the bait! Red Herring X

Misrepresenting your opponents position so it can be more easily defeated • “Here is the message that an imaginary 'intelligent design theorist‘ might broadcast to scientists: 'If you don't understand how something works, never mind: just give up and say God did it.” –Richard Dawkins Straw Man X • “one of the truly bad effects of religion is that it teaches us that it is a virtue to be satisfied with not understanding.” -Richard Dawkins X

If an argument is based on authority, it should be a legitimate authority, otherwise it is a bad argument • Ex: • Biogeography gives very strong evidence for evolution. • But Ray Comfort says evolution is false! Appeal to Illegitimate Authority X

Argues that by permitting A to occur, a far-fetched Z will occur. • Only fallacious if Z is not a likely consequence of A • Ex: • Colin Closet asserts that if we allow same-sex couples to marry, then the next thing we know we'll be allowing people to marry their parents, their cars and even monkeys. –yourlogicalfallacy.com Slippery Slope X

If using an inductive analogy, the analogy must be strong or the argument is fallacious • Ex: • Cars and motor-boats both have engines and steering wheels. • Cars have wheels • Therefore boats must have wheels as well Weak analogy X

Drawing a conclusion about a whole group based on a few members of that group • Not all generalizations are hasty • Ex: • Both of the politicians I have met were liars • Therefore, all politicians are liars Hasty Generalization X

Post hoc ergo proctor hoc (After this therefore because of this) • Correlation does not imply causation • Ex: • Pointing to a fancy chart, Roger shows how temperatures have been rising over the past few centuries, whilst at the same time the numbers of pirates have been decreasing; thus pirates cool the world and global warming is a hoax. –yourlogicalfallacy.com False Cause X

Draws a conclusion from a lack of evidence • Absence of evidence is not necessarily evidence of absence • Ex: • You arguments have failed to show that God exists; • Therefore, God must not exist. Appeal to Ignorance X

Bandwagon • Everyone knows that… • Ex: • Everyone knows that Stephen Hawking disproved God… X

Claiming a belief is false because you can explain why someone believes it • “Why aren’t you a Hindu? Because you happen to have been brought up in America, not in India. If you had been brought up in India, you’d be a Hindu. If you’d been brought up in Denmark at the time of the vikings, you’d be believing in Wotan and Thor. If you had been brought up in classical Greece you’d be believing in Zeus. if you had been brought up in central Africa, you’d be believing in the great Juju up the mountain.” –Richard Dawkins Genetic Fallacy X

How do I know the Bible is true? • Because the Bible says it is true, and I believe it! Begging the Question X

Argument from Emotion • An appeal to emotion • “they were religious, and that provided all the justification they needed to murder and destroy” –Richard Dawkins • “Imagine, with John Lennon, a world with no religion. Imagine no suicide bombers, no 9/11, no 7/7, no Crusades, no witch-hunts…” –Richard Dawkins X

Special Pleading • Exempting your claims from your own requirements • Everything that exists has a cause • God exists • So what caused God? • A: God doesn’t count because He’s uncaused! X

Using the same word with two different meanings • Define your terms! Equivocation

The argument proves itself to be wrong Self refuting Statements

Logic, Debate, and Reasoning