LOGIC, DEBATE, AND REASONINGPresented by Ratio Christi TAMU

WHAT IS LOGIC 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 A FORMAL ARGUMENT 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 probable given the premises.

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ROADMAPTypes of Arguments• Inductive• Deductive

Bad Arguments• Formal Fallacies• Informal Fallacies

Tactics• Analysis

TYPES OF ARGUMENTS Inductive

Results in a high probability that the conclusion is true.

Common in science

Deductive Arguments If the premises are true,

and the structure is correct, the conclusion must be true.

INDUCTIVE ARGUMENTS 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

STATISTICAL SYLLOGISM 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

GENERALIZATION Assumes a sample has

the same attributes as a population

10% of the survey were Democrats

Therefore, 10% of people are Democrats

ANALOGY 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

PREDICTION 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

DEDUCTIVE ARGUMENTS 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

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VALIDITY AND SOUNDNESS 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

TYPES OF DEDUCTIVE REASONING Categorical Logic Propositional Logic Modal Logic

CATEGORICAL LOGIC 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 S are P No S are P Some S are P Some S are not P

Can be combined into groups of three called a syllogism

CATEGORICAL SYLLOGISM 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

(middle term) P1: All men are mortal; P2: Socrates was a man; C: Therefore Socrates was mortal.

CATEGORICAL SYLLOGISMS 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.

X

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PROPOSITIONAL LOGIC The most basic logic dealing with conditionals If then statements, etc.

More powerful than simple categorical syllogisms 9 basic rules

RULE #1 MODUS PONENS

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)

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RULE #2 MODUS TOLLENS

If P, then Q Not Q Therefore, not P

Valid, example: If it is raining, the ground is wet The ground is not wet Therefore it is not raining

(This one may be unsound as well)

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RULE #3 HYPOTHETICAL SYLLOGISM 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 #4 CONJUNCTION P Q Therefore P and Q

Example John is a good student Mary is a good student Therefore John is a good student and Mary

is a good student√

RULE #5 SIMPLIFICATION P and Q Therefore P

Example John is a good student and Mary is a good

student Therefore John is a good student

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RULE #6 ABSORPTION 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 raining and

the road is wet√

RULE #7 ADDITION P Therefore P or Q

Example It is raining Therefore if it is raining or the sun is

shining√

RULE #8 DISJUNCTIVE SYLLOGISM P or Q Not P Therefore, Q

Example It is either raining or the sun is shining It is not raining Therefore, the sun is shining√

RULE #9 CONSTRUCTIVE DILEMMA If P then Q and If R then S P or R Therefore, Q or S

Example If it is raining the streets are wet, and if it

is sunny the streets are dry It is either raining or sunny Therefore, the streets are wet or the

streets are dry

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EXAMPLE If God exists and 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, Then Einstein’s theory is

wrong (However this may be unsound)√

ROADMAPTypes of Arguments• Inductive• Deductive

Bad Arguments• Formal Fallacies• Informal Fallacies

Tactics• Analysis

FORMAL FALLACIES Result from errors of logical form

May have true conclusions But the conclusion does not follow from the

premises

INCORRECT CATEGORICAL SYLLOGISM Many types: Ex:

All communists are leftists.  No conservatives are communists.  Therefore, no conservatives are leftists.

Ex: All dogs are animals.  No cats are dogs.  Therefore, no cats are animals.

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X

AFFIRMING THE CONSEQUENT Improper modus ponens Ex:

If God exists, then objective morals and duties exist

Objective morals and duties do exist Therefore God exists

X

DENYING THE ANTECEDANT 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

X

INFORMAL FALLACIES Mistakes in reasoning that arise from

the content of the argument⁻ 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

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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

“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

STRAW MAN

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X

APPEAL TO ILLEGITIMATE AUTHORITY 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!

X

SLIPPERY SLOPE 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

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WEAK ANALOGY 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

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HASTY GENERALIZATION 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

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FALSE CAUSE 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

X

APPEAL TO IGNORANCE 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.

X

BANDWAGON Everyone knows that…

Ex: Everyone knows that Stephen Hawking disproved

God…X

GENETIC FALLACY 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

X

BEGGING THE QUESTION How do I know the Bible is true?

Because the Bible says it is true, and I believe it!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

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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

EQUIVOCATION Using the same word with two different

meanings Define your terms!

SELF REFUTING STATEMENTS The argument

proves itself to be wrong

ROADMAPTypes of Arguments• Inductive• Deductive

Bad Arguments• Formal Fallacies• Informal Fallacies

Tactics• Analysis

ANALYZING ARGUMENTS Arguments are rarely stated in simple

syllogisms We must take complex arguments and

break them down into simple parts we can analyze

EXAMPLE 1 What would happen if we get down on our

knees and pray to God in this way: Dear God, almighty, all-powerful, all-loving

creator of the universe, we pray to you to cure every case of cancer on this planet tonight. We pray in faith, knowing you will bless us as you describe in the Bible. In Jesus' name we pray, Amen.

We pray sincerely, will anything happen? No. Of course not

http://godisimaginary.com/i1.htm

ANALYSIS What was the argument Maybe…

God promises to answer all prayers God didn’t give me what I prayed for Therefore God does not exist

ANALYSIS False premise

God promises to answer all prayers

Christians do not necessarily believe this, so the argument is unsound

ANALYSIS What was the argument?

If I pray and God exists, then God will answer my prayer

I prayed God didn’t answer my prayer Therefore God does not exist

This is valid, but Christians may disagree with the premises

EXAMPLE 2“We could learn to live with people from all races and not immediately hating and wanting to kill someone just because they believe in a different god.Yes, a world without God would be a far better, friendlier and happier place. A world without religion would also be a safer place for innocent children, who have been abused by the religious-lot for centuries and continue to be abused.” –god-does-not-exist.org

ANALYSIS This argument was an argument from

emotion It did not provide facts or evidence It only claimed that religion harms

children

EXAMPLE 3 To understand why "God does not exist" can be a legitimate

scientific statement, it's important to understand what the statement means in the context of science. When a scientist says "God does not exist," they mean something similar to when they say "aether does not exist," "psychic powers do not exist," or "life does not exist on the moon."

All such statements are casual short-hand for a more elaborate and technical statement: "this alleged entity has no place in any scientific equations, plays no role in any scientific explanations, cannot be used to predict any events, does not describe any thing or force that has yet been detected, and there are no models of the universe in which its presence is either required, productive, or useful."

ANALYSIS What is the argument:

There is no empirical evidence that can only be attributed to God

If God exists, then he will produce empirical evidence

Therefore God does not exist.

ANALYSIS What is the argument:

There is no empirical evidence that can only be attributed to God

If God exists, then he will produce empirical evidence

Therefore God does not exist. This is deductively valid (maybe) But is it True?

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ANALYSIS There is no empirical evidence that can

only be attributed to God If God exists, then he will produce

empirical evidence Therefore God does not exist.

We would disagree with the first premise, and maybe even the second premise!

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CONCLUSION Logic can be a useful tool in

understanding arguments But arguments are rarely in logical form Therefore, it is useful to be able to

analyze arguments in logical form to find errors