Presented by Ratio Christi TAMU
LOGIC, DEBATE, AND REASONING
WHAT IS LOGIC

The science of analyzing arguments?

The science of good

Tagore
A
reasoning in general?
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.
ROADMAP
Types of Arguments
• Inductive
• Deductive
Bad Arguments
• Formal Fallacies
• Informal Fallacies
Tactics
• Analysis
TYPES OF ARGUMENTS

Inductive
in a high probability that the
conclusion is true.
 Common in science
 Results

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
probable
certain, only
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
VALIDITY AND SOUNDNESS

Validity
 An

argument is valid if it has the correct
Sound
 An
argument is sound if it is valid
and the premises are true
form
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:
 Minor Premise:
 Conclusion:

All men are mortal;
Socrates was a man;
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;
√
X
 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.
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)
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)
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
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
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)
ROADMAP
Types 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:

X

 All
communists are leftists.
 No conservatives are communists.
 Therefore, no conservatives are leftists.
Ex:
X
 All
dogs are animals.
 No cats are dogs.
 Therefore, no cats are animals.
AFFIRMING THE CONSEQUENT
Improper modus ponens
 Ex:

X
 If
God exists, then objective morals and duties exist
 Objective morals and duties do exist
 Therefore God exists
DENYING THE ANTECEDANT
Improper modus tollens
 Ex:

 If
X
God does not exist then objective values and duties do
not exist
 God does exist
 Therefore objective values and duties exist
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
AD HOMINEM
Meaning: “To the man”
 Favorite of politicians
 Ex:

X
 "All
politicians are liars, and you're
just another politician. Therefore,
you're a liar and your arguments are
not to be trusted."
RED HERRING

An irrelevant fact intended to divert
attention from the real issue
X

 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!
STRAW MAN

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
X

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
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
X
gives very
strong evidence for evolution.
 But Ray Comfort says
evolution is false!
SLIPPERY SLOPE

Argues that by permitting A to occur, a farfetched Z will occur.
 Only

fallacious if Z is not a likely consequence of A
Ex:
 Colin
X
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
WEAK ANALOGY
If using an inductive analogy, the analogy must
be strong or the argument is fallacious
 Ex:

 Cars
X
and motor-boats both
have engines and steering
wheels.
 Cars have wheels
 Therefore boats must
have wheels as well
HASTY GENERALIZATION

Drawing a conclusion about a whole group
based on a few members of that group
 Not

all generalizations are hasty
Ex:
X
 Both
of the politicians I have met were liars
 Therefore, all politicians are liars
FALSE CAUSE

Post hoc ergo proctor hoc (After this
therefore because of this)
 Correlation

does not imply causation
Ex:
 Pointing
X
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
APPEAL TO IGNORANCE

Draws a conclusion from a lack of evidence
 Absence
of evidence is not necessarily evidence of
absence
 Ex:
X
 You
arguments have failed to show that God exists;
 Therefore, God must not exist.
BANDWAGON

Everyone knows that…

X
Ex:

Everyone knows that Stephen Hawking disproved God…
GENETIC FALLACY

Claiming a belief is false because you can
explain why someone believes it
 “Why
X
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
BEGGING THE QUESTION

X
How do I know the Bible is true?
 Because
the Bible says it is true, and I believe it!
Argument from Emotion


X
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 witchhunts…” –Richard
Dawkins
SPECIAL PLEADING

Exempting your claims from your own requirements


X


Everything that exists has a cause
God exists
So what caused God?
A: God doesn’t count because He’s uncaused!
EQUIVOCATION

Using the same word with two different
meanings
 Define
your terms!
SELF REFUTING STATEMENTS

The argument
proves itself to
be wrong
ROADMAP
Types 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?

ANALYSIS
X
X

 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!
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
