Introduction to Formal Logic Martin Cothran Introduction Logic The Basics 1 Logic The science of right thinking German philosopher Immanuel Kant called Aristotle the father of logic ID: 223391
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Slide1
Traditional Logic:Introduction to Formal Logic
Martin
CothranSlide2
IntroductionSlide3
Logic: The Basics (1)
Logic: The science of right thinking.
German philosopher Immanuel Kant called Aristotle “the father of logic.”
Formal logic has changed little since Aristotle. Slide4
Two Branches of Logic (2)
1.) Material “major”: concerned with the
content
of argumentation.
Deals with the truth of the terms and propositions in an argument.
2.) Formal “minor”: interested in the
form
of the structure of reasoning.
Truth is a secondary consideration; concerned with the method of deriving one truth from another. Slide5
G. K. Chesterton (2)
“Logic and truth… have very little to do with each other. Logic is concerned merely with fidelity and accuracy with which a certain process is performed, a process which can be performed with any materials, with any assumption. You can be as logical about griffins and basilisks as about sheep and pigs… Logic, then, is not necessarily an instrument for finding out truth; on the contrary, truth is a necessary instrument for using logic—for using it, that is, for the discovery of further truth… Briefly, you can only find truth with logic if you have already found truth without it.” Slide6
This means what? (2)
We should refer to statements as
true
or
false
, not logical or
illogical
.
Likewise, arguments are not
true
or
false
, but
valid
or
invalid
.
Validity: helps describe if an argument is logical.
Truth: the correspondence of a statement to reality. Slide7
Argument Anatomy (3)
Expect your arguments to take on the general structure:
Argument
Term
All men
are mortal
Premise
Socrates is a man
Premise
Therefore, Socrates
is mortal
ConclusionSlide8
Mental Act vs. Verbal Expression
Mental Act
Verbal Expression
Simple
Apprehension
Term
Judgment
Proposition
Deductive Inference
Syllogism Slide9
Mental Acts (3-4)
Simple Apprehension
: occurs when we first form in our mind a concept of something.
EX: thinking of your logic book
Judgment
: to affirm or deny
You think: “This book is boring.”
Deductive Inference
: when we make the logical connections in our mind between the terms in the argument in a way that shows us that the conclusion either follows or does not follow from the premises; i.e., when we make progressSlide10
Verbal Expression (4)
Term
: the verbal expression of a simple apprehension
Proposition
: the verbal expression of a statement
Syllogism
: the verbal expression of a deductive inference Slide11
Drawing everything together… (5)
Imagine moving from one room to another.
Moving your foot -> Simple Apprehension
Taking steps -> Performing judgment
Everything together -> Deductive inference Slide12
Chapter 1What is Simple Apprehension? Slide13
What is Simple Apprehension? (9)
The introduction said Simple Apprehension occurred when we first form in our mind a concept of something.
Example: Looking at a chair
1. We perceive it with our senses
2. We form an image of it with our minds
3. We conceive of its meaning Slide14
1. Sense Perception (9)
“Sense perception” is common vocabulary in all branches of philosophy
Definition: The act of seeing or hearing or smelling or tasting or touching. Slide15
1. Sense Perception (9)
We have sense perception while we are in contact with objects
Your sense perception of a chair ends when you stop looking at the chair, etc.
The sense perception of “chair” is different than the chair itself because it is in your mind Slide16
2. Mental Image (9-10)
Definition: The image of an object formed in the mind as a result of a sense perception of that object.
Occurs when an image continues after sense perception ceases
Different than both the chair itself, and the sense perception that it creates Slide17
3. Concept (10-11)
Understanding without a mental image or sense perception.
“When you grasp the concept of something, like a chair, you understand what a chair is.”
“Simple apprehension is an act by which the mind grasps the concept of general meaning of an object without affirming or denying anything about it.” Slide18
Other Terms (11)
Essence: the meaning of a thing
Abstraction: The process by which a simple apprehension is derived from a sense perception and a mental image
Helps raise a chair from the senses to the intellect
To affirm or deny a Simple Apprehension is to engage in judgment
However, thinking merely “chair” is Simple Apprehension Slide19
Chapter 2Comprehension and ExtensionSlide20
First things… (15)
This chapter will discuss the
properties
of Simple Apprehension.
Definitions explain what something is.
Properties distinguish objects from each other.
The two properties of Simple Apprehension
Comprehension: tells the essence of a thing
Extension: tells us the things to which that essence applies Slide21
Comprehension (15)
Defined as “the completely articulated sum of the intelligible aspects, or elements (
or notes
) represented by a concept.”
Note this is NOT the definition you grew up with. Welcome to life.
Not all concepts are simple.
Plato’s definition of man: a “featherless biped”
Plato later said man is a “rational animal” Slide22
What is an animal? (16)
Animals break into four simple concepts:
Substance: something rather than nothing
Material: to have a non-spiritual body
Living (self-explanatory)
Sentient: to have senses
These concepts are called “notes,” or intelligible aspects represented by a concept.
See explanation of “Comprehension.”
A chair has four notes. Slide23
What is a man? (16)
“Man” breaks into five concepts or notes:
Substance
Material
Living
Sentient
Rational
Comprehension
of man, then, equals the sum of said five notes. Slide24
The Porphyrian Tree (17)
Invented by third-century logician Porphyry
Helps us break down complex concepts into simple concepts
C
omparable
to our “Ladder of Abstraction” in terms of specificity Slide25
Porphyrian Categories (17)
Substance: material or nonmaterial
Unicorns have no substance yet chairs do. Do you know why?
Body: living or nonliving (mineral)
Organism: sentient or
nonsentient
(plant)
Animal: rational or
nonrational
(brute)
Logical species: man Slide26
Extension (19)
Extensions tells us the things to which that essence applies. Think “example!”
What is the extension of man?
All the men who have ever lived, who are now living, and who will live in the future
The greater number of notes a concept has, the less extension it has.
Man has five notes while animals have four.
“Man” is more specific than “animals”
There are more animals than man. Slide27
Important! (19)
The greater the comprehension a concept has, the less extension it has; and the more extension it has, the less comprehension.
Example: Man has five notes while animals have four. Thus, man is more specific and applies to less things.
The higher on the tree, the more to which the object applies. The lower, the less. Slide28
Simple Apprehension Wrap Up
Processes of Simple Apprehension
Sense Perception, Mental Image, Concept
Two properties of Simple Apprehension
Comprehension: a description plus categories
Extension: describes the things to which the concept applies
Next week we will have our last real vocabulary lesson! Slide29
Chapter 3: Signification and SuppositionSlide30
Overview
Term: a word or group of words which verbally expresses a concept (23).
There are two properties of “terms”
Signification: defined by if the term is univocal, equivocal, or analogous (23)
Supposition: refers to types of existence, such as verbal, mental, or real (25) Slide31
Univocal Terms
Definition: have exactly the same meaning no matter when or how they are used (23)
Latin: “
unus
” (one) + “
vox
” (voice)
EX: photosynthesis,
table saw, Phillips head screwdriver, drill
bitSlide32
Equivocal Terms (24)
Definition: although spelled and pronounced exactly alike, have entirely different and unrelated meanings
Latin: “
aequus
” (equal) + “
vox
” (voice)
Example: plane, jar, hang
“We must all hang together, or assuredly we will all hang separately.” (Ben Franklin) Slide33
Analogous Terms (24)
Definition: applied to different things but have related terms
Unlike equivocal terms, their differing meanings are related
Example: “set of wheels”
Means both “car” and “new tires”Slide34
Why does this matter? (24)
Logic requires an accurate and consistent use of the terms
The English language has many equivocal and analogous terms
In real life, language confusion is the source of many arguments Slide35
Example Argument (25)
All NBA basketball players are men
Dennis Rodman is a good NBA basketball player
Therefore, Dennis Rodman is a good man
This argument is invalid because “good” is used analogously
This problem will be explained more in detail in later lessons Slide36
Supposition (25)
Verbal existence: refers to material supposition
EX: “Man” is a three-letter word
Mental existence: logical supposition
EX: “Man” has five notes
Real existence: real supposition
EX: censored Slide37
Summary of Chapters 1-3 (26)
Three aspects of logic: simple apprehension, judgment, deductive inference
Verbally expressed by terms, propositions, and syllogisms
In future chapters we will discuss terms in propositions, then syllogisms (arguments) Slide38
Chapter 4: What is Judgment?
Chapter 5: The Four Statements of LogicSlide39
Judgment (31)
From the outset, Judgment (Mental Act) aligns with Proposition (Verbal Expression)
Judgment: the act by which the intellect unites by affirming, or separates by denying
EX: Man is an animal.
We are joining “Man” and “animal”Slide40
Uniting Concepts in Judgments (31)
Judgments are made of subjects and predicates
Subjects
: that about which we are saying something; the concept which we are affirming or denying
Predicates
: what we are saying about the subject; what we are affirming or denying about Slide41
The Proposition (32)
Definitions: (1) the verbal expression of a judgment; (2) a sentence or statement which expresses truth or falsity
Not all sentences are propositions (such as questions, commands, exclamations, etc.)
Examples
It is raining today.
There is a fly in my soup. Slide42
Elements of Proposition (32)
There are three elements to any proposition:
The subject-term (S), verbal expression of subject of a judgment
The predicate-term (P), verbal expression of a predicate of a judgment
The copula (C), the word that connects or relates the subject to the predicate; a form of “to be” such as “is” or “are” Slide43
Examples of Propositions (32)
Man (S) is (c) an animal (P).
The little brown-haired boy is very loud.
Subject: little brown-haired boy
Predicate: very loud
Notice how this is similar to algebraic statements, such as X = Y.
Modern logic takes this to an extreme, whereas Classical Logic does not. Slide44
Logical Sentence Form (33)
Sentences must be placed into a proper form to be handled logically.
EX 1: “The little brown-haired boy screams very loudly” is not in logical form.
We need to rework the predicate portion
EX 2: “The little brown-haired boy
is a child who
screams very loudly.” Slide45
The Four Statements of Logic (39)
Formal Logic has four basic categorical forms:
A: All S is P.
I: Some S is P.
E: No S is P.
O: Some S is not P.
The letters come from the Latin “
affirmo
” and “
nego
,” or “to affirm” and “to deny.”
Note: Non-categorical propositions will not be covered in this curriculum. Slide46
To Affirm or Deny? (40)
Affirmo
A: All S is P. (EX: All men are mortal)
I: Some S is P. (EX: Some men are mortal.)
Nego
E: No S is P. (EX: No men are mortal.)
O: Some S is not P. (EX: Some men are not mortal.)
Notice the pattern? Slide47
The Quantifier (40-41)
Quantifiers tell us quality and quantity
Four kinds: All, Some, No, Some… not.
Quality
: affirmative or negative?
EX: “All men are mortal” affirms about “All men.”
Quantity
: universal or particular?
Universal: refers to all, not some
Particular: refers to some, not all Slide48
Distinguishing Universals (41)
When there is no quantifier, we must determine whether they are universal or particular.
EX: “Frogs are ugly”
“All frogs are ugly”
General rule:
All
is intended unless
some
is clearly indicated.
EX: Men have gone to the North Pole.
Does not mean “all.”
“Some men have gone to the North Pole.” Slide49
Closing Thoughts
Universal/Particular cont.: In “Socrates is a man,” statement is singular (41).
We can summarize quality-quantity like this:
A: Affirmative-Universal
I: Affirmative-Particular
E: Negative-Universal
O: Negative-Particular (42) Slide50
Chapter 6: Contradictory and Contrary Statements
Chapter 7:
Subcontraries
and SubalternsSlide51
Categorical Relations (49)
Categorical statements are related via the relationship of opposition or equivalence.
The former has four relationships, the latter three.
Four ways of opposition.
Contradictory
Contrary
Subcontrary
Subalternate
Slide52
The Rule of Contradiction (49-50)
Contradictory statements are statements that differ in both quality and quantity.
Which statements differ in both quality and quantity? Slide53
The Rule of Contradiction (49-50)
Contradictory statements are statements that differ in both quality and quantity.
Which statements differ in both quality and quantity?
A
is contradictory to O.
I is contradictory to E.
What specific examples can we apply to these categories? Slide54
The First Law of Opposition (53)
Contradictories cannot at the same time be true nor at the same time false.
Does this hold for Example 1?
A: All men are mortal.
O: Some men are not mortal.
And for Example 2?
E: No men are gods.
I: Some men are gods. Slide55
Two More Rules (54)
The Rule of Contraries
Two statements are contrary to one another if they are both universals but differ in quality.
Only one pair: A vs. E (All S is P and No S is P.)
The Second Law of Opposition
Contraries cannot at the same time both be true, but can at the same time both be false.
What statements would this apply to? Slide56
The Rule of Subcontraries (61)
Two statements are
subcontrary
if they are both particular statements that differ in quality.
Which statements would these apply to? Slide57
The Rule of Subcontraries (61)
Two statements are
subcontrary
if they are both particular statements that differ in quality.
Which statements would these apply to?
I and O (“Some S is P” vs. “Some S is not P.”)
Some men are mortal. vs. Some men are not mortal. Slide58
The Third Law of Opposition (63)
Subcontraries
may at the same time both be true, but cannot at the same time both be false.
Explain the following example:
I: Some S is P.
O: Some S is not P.
Explain something more specific… Slide59
The Rule of Subalterns (63)
Two statements are
subalternate
if they have the same quality, but differ in quantity.
They are not opposite, but related nonetheless.
Which statements would fall under this category? Slide60
The Rule of Subalterns (63)
Two statements are
subalternate
if they have the same quality, but differ in quantity.
They are not opposite, but related nonetheless.
Which statements would fall under this category?
A (“All S is P”) and I (“Some S is P”)
E (“No S is P”) and O (“Some S is not P”) Slide61
The Fourth Law of Opposition (63-65)
Subalterns
may both be true or both be false. If the particular is false, the universal is false; if the universal is false, then the particular is true; otherwise, their status is indeterminate.
For A and I statements, if “Some S is P” is false, then “All S is P” is false.
For E and O statements, if “Some S is not P” is false, then “No S is P” is false. Slide62
Square of OppositionSlide63
Chapter 8: Distribution of TermsSlide64
Distribution (71)
Distribution
is the status of a term in regard to its extension.
Reminder: Extension is a description of the things to which a concept applies (19).
Reminder: Subjects and predicates.
Where is the subject in “All S is P”?
Where is the predicate in “All S is P”?
Distributed
is when a term is used universally. What, then, would
undistributed
mean? (72)Slide65
Distribution of Subject-Terms (73)
Rule:
The subject-term is distributed in statements whose quantity is universal and undistributed in statements who quantity is particular.
Look to the quantifier: All, Some, No, Some… not
Type of Sentence
Subject
-Term
A (“All
S is P”)
Distributed
I (“Some S is P”)
Undistributed
E (“No S is P”)
Distributed
O (“Some S is not
P”)
Undistributed Slide66
Distribution of Predicate-Terms (72)
Rule:
In affirmative propositions the predicate-term is always taken particularly (and therefore undistributed), and in negative propositions the predicate is always taken universally (and therefore distributed).
Type of Sentence
Subject
-Term
Predicate
-Term
A (“All
S is P”)
Distributed
Undistributed
I (“Some S is P”)
Undistributed
Undistributed
E (“No S is P”)
Distributed
Distributed
O (“Some S is not
P”)
Undistributed
DistributedSlide67
Distribution of the Predicate-Term in A Statements
All men are animals. Slide68
Distribution of the Predicate-Term in I Statements
Some dogs are vicious animalsSlide69
Distribution of the Predicate-Term in E Statements
No man is a reptile.Slide70
Distribution of the Predicate-Term in O Statements
Some men are not blind.Slide71
Different ways to Diagram I statements
Some men are carpenters.
Why are the lines dotted?Slide72
Different ways to diagram O statements
Some men are not carpenters.Slide73
Chapter 9: Obversion, Conversion, and ContrapositionSlide74
Review: Categorical Relations
Categorical statements are related via the relationship of opposition or equivalence.
Four modes of opposition: Contradictory, Contrary,
Subcontrary
, and
Subalternate
(49)
Three modes of equivalence (81)
Obversion
: works on all statements (82)
Conversion: for E and I statements (85)
Contraposition: for A and O statements (85) Slide75
Obversion, Part 1 (81)
To obvert:
(1) change the quality
and (2) negate the predicate.
(1) If affirmative, negate; if negative, affirm.
Warning: Do
not
change the quantity.
Statement
Step 1
A:
All S is P
No S is P
E: No
S is P
All S is P
I: Some S is P
Some S is not P
O:
Some S
is not P
Some S is PSlide76
Obversion, Part 1 (82)
To obvert: (1) change the quality and
(2) negate the predicate.
Place “not” in front of it.
What would this look like for each statement?
Statement
Statement
Obverted
A:
All S is P
No
S is not P
E: No
S is P
All S is not P
I: Some S is P
Some S
is not non-P
O:
Some S
is not P
Some S is not PSlide77
Double Negation of Predicate-I (82)
How do we handle “Some S is not non-P”?
Have two adjacent “not’s”
Switch the “non” and “not” (sounds better!)
Add prefix in the predicate:
im
, un, in,
ir
Rule of double negation.
EX 1: Some men are not non-mortal.
EX 2: Some Pokémon are not non-Fire-types. Slide78
Double Negation (83)
The rule of double negation says that a term which is not non negated is equivalent to a term that is negated twice (and visa-versa).
Example: “not not P” to “P”
O: Some S is not P
Some S is not not not P
Thus, and obverse O statement is equivalent Slide79
Conversion (84)
Interchange the subject and predicate.
E: No S is P
No P is S
I: Some S is P Some P is S
Partial conversion of the A
All dogs are animals
Some animals are dogs.
Why does this make sense?
Will this work for A and O statements? Slide80
Contraposition (84)
Three steps: (1)
obvert
, (2)
convert
, (3)
obvert
and the statement again.
Example for A statement: All men are mortal.
Obvert: No men are non-mortal
Convert: No non-mortals are men.
Obvert: All non-mortals are non-men.
For O statements (steps condensed):
Some S is not P Some non-P is S. Slide81
To Be Updated…
Review for Chapters 4-9 (85-87)
Located in your book. Very helpful!
Upcoming Chapters
10: What is Deductive Inference?
11: Terminological Rules for Categorical Syllogisms
12: Quantitative Rules for Categorical Syllogisms
13: Qualitative Rules for Categorical SyllogismsSlide82
Chapter 10: What is Deductive Inference? Slide83
Introduction (95)
Chapters 4-9 have discussed
proposition
.
Deductive inference is one kind of reasoning.
Reasoning:
the act by which the mind acquires new knowledge by means of what it already knows.
Mental Act
Verbal Expression
Simple
Apprehension
Term
Judgment
Proposition
Deductive Inference
Syllogism
Slide84
Introduction (96)
Deductive inference: the act by which the mind establishes a connection between the antecedent and the consequent.
Syllogism: a group of propositions in orderly sequences, one of which (consequent) is said to be necessarily inferred form the others (antecedent)
Argument
Term
Definition
All
men are mortal.
Premise/Antecedent
Goes before
Socrates is a man.
Premise/Antecedent
Goes before
Therefore, Socrates is mortal.
Conclusion/Consequent
Conclude Slide85
Validity (96-97)
Essential Law of Argumentation: If the antecedent is true, the consequent must also be true.
Two corollaries
1.) If the syllogism is valid and the consequent is false, then the antecedent must be false.
2.) In a valid syllogism with a true consequent, the antecedent is not necessarily true. Slide86
Corollary 1 (97)
All men are sinners.
My dog Spot is a man.
Therefore, my dog Spot is a sinner.
This syllogism is valid (premises are true, therefore conclusion is true).
But the conclusion is true. Corollary 1 says a premise is false. Which one is false? Slide87
Corollary 2 (97)
All vegetables are philosophers.
Socrates is a vegetable.
Therefore, Socrates is a philosopher.
The conclusion is true: Socrates is a philosopher.
Corollary 2 says although the consequent is true, its antecedents are false. Slide88
Terms in a Syllogism (97-98)
Major Term:
the predicate of the conclusion
Minor Term:
the subject of the conclusion
Middle Term:
appears in both premises, but not the conclusion.
All
men
M
are
mortal
P
.
Socrates
S
is a
man
M
.
Therefore,
Socrates
S
is
mortal
P
. Slide89
Syllogism Simplified (98)
Chapters 4-9 matter because of the following:
Notice terms boil into subjects and predicates, which makes syllogisms possible.
Argument
Simplified
All
men
M
are
mortal
P
.
All M is P.
Socrates
S
is a
man
M
.
All S is M.
Therefore,
Socrates
S
is
mortal
P
Therefore, All S is P. Slide90
Proper Form (98-99)
A syllogism is properly formed if the major premise if first, the minor premise is second, and the conclusion is third.
Major
premise: contains the major term.
Minor premise: contains the minor term.
However, not a syllogisms are properly formed, meaning we may have to rearrange them. Slide91
Syllogistic Principles (99)
Principle of Reciprocal Identity
: two terms that are identical with a third term are identical to each other.
EX: mortal vs. man, man vs. Socrates
Argument
Term
All
men
M
are
mortal
P
.
M = M
Socrates
S
is a
man
M
.
S = M
Therefore,
Socrates
S
is
mortal
P
S = M,
or Subject = PredicateSlide92
Syllogistic Principles (99)
Principle of Reciprocal Non-Identity
: two terms, one of which is identical with a third term and the other of which is non-identical with that third term, are non-identical to each other.
Syllogism
Term
No men are angels.
M ≠ A
Socrates is a man.
S = M
Therefore, Socrates is not an angel.
S ≠ A or S ≠ PSlide93
Syllogistic Principles (99)
Dictum de Omni:
what is affirmed universally of a certain term is affirmed of every term that comes under the term.
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
Since every man is mortal, Socrates, an extension of man, is therefore mortal. Slide94
Syllogistic Principles (100)
Dictum de
Nullo
:
what is denied universally of a certain term is denied of every term that comes under that term.
No man is God.
Socrates is man.
Therefore, Socrates is not God.
This argument denies divinity universally of men. Slide95
Chapter 11: Terminological Rules for Categorical SyllogismsSlide96
The Seven Rules (107)
Terminological Rules
I. There must be three and only three terms.
II. The middle term must not occur in the conclusion.
Quantitative Rules
III. If a term is distributed in the conclusion, then it must be distributed in the premises.
IV. The middle term must be distributed at least once.Slide97
The Seven Rules (107)
Qualitative Rules
V. No conclusion can follow from two negative premises.
VI. If the two premises are affirmative, the conclusion must also be affirmative.
VII. If either premise is negative, the conclusion must also be negative. Slide98
Terminological Rules (107-108)
Rule 1: There must be three and only three terms.
Can be violated in two ways.
1. Fallacy of Four Terms: when there are more than three clearly distinguishable terms.
2. Fallacy of Equivocation: when we use a term for both its meanings Slide99
Fallacy of Four Terms (108)
All mammals (S) have hair (P)
All horses (?) have manes (?)
Therefore, some mammals (S) have hair (P)
Note: None of these terms actually connect. However, changing one term makes it valid:
All mammals (M) have hair (P)
All horses (S) are mammals (M)
Therefore, all horses (S) have hair (P) Slide100
Fallacy of Equivocation (108)
This fallacy is less obvious. Example below.
All planes are two-dimensional
All 747s are planes
Therefore, all 747s are two-dimensional
Because the middle terms are use equivocally, there are four terms.
Therefore, the argument is not valid. Slide101
Terminological Rules (109)
Rule II: The middle term must not occur in the conclusion.
The role of the middle is to connect the major and minor terms. If it were in the conclusion, it would stand in for the others.
All plants are living things
All animals are living things
Therefore, all living things are plants or animals Slide102
Chapter 12: Quantitative Rules for Categorical SyllogismsSlide103
Quantitative Rules (116)
Rule III: If a term is distributed in the conclusion, then it must be distributed in the premises.
Prevents us from trying to say more in the conclusion than what is contained in the premises.
Distribution: the status of a term in regard to its extension
(what
a term refers to). Slide104
Quick Reminders
Two Things To Remember…
Quantity: Universal or Particular? (115-116)
Distribution by Category (Chapter 8) Slide105
Quantitative Rules (116)
All angels___ are spiritual beings___
No men___ are angels___
Therefore, no men___ are spiritual beings___
This conclusion presumes all spiritual beings are angels, but that is not stated in the premises.
The conclusion says more than the premise allows.
While the premises are both true, they are not valid.
*Use the Distribution Chart and fill this in using S, P, and M, and “d” for Distributed, and “u” for… Slide106
Quantitative Rules (116-117)
All angels
(
Md
)
are spiritual beings
(
Pu
)
No men
(
Sd
)
are angels
(
Md
)
Therefore, no men
(
Sd
)
are spiritual beings
(
Pd
)
Notice the Predicate is distributed in the Conclusion, but not the Premise. Thus, it violates Rule III. Slide107
Rule III Fallacies (117-118)
Syllogisms that violate Rule III commit the Fallacy of Illicit Process.
1. Fallacy of Illicit Major: when the major term is distributed in the conclusion, but not the premises
2. Fallacy of Illicit Minor: when the minor term is distributed in the conclusion, but not the premises
Remember: Fallacies are so because they are easy to mix up. Reach each term for what it is; not what it says in its respective premise/conclusion.
Slide108
Rule III Fallacies (118)
Which Rule III fallacy does this fit?
All men___ are animals___
All men___ are mortals___
Therefore, all mortals___ are
animals___
Fill in the terms as they are, and then add the distribution. Slide109
Rule III Fallacies (118)
Which Rule III fallacy does this fit?
All men
(
Md
)
are animals
(
Pu
)
All men
(
Md
)
are mortals
(Su)
Therefore, all mortals
(
Sd
)
are animals
(
Pu
)
The Fallacy of the Illicit Minor, because the minor term is not distributed in the minor premise. Slide110
Quantitative Rules (118)
Rule IV: The middle term must be distributed at least once.
The
Fallacy of the Undistributed Middle
Fill in the following syllogism
All angels___ are spiritual beings___
All men___ are spiritual beings___
Therefore, all men___ are angels___Slide111
Quantitative Rules (118)
The Correct Answer
All angels (
Pd
) are spiritual beings (Mu)
All men (
Sd
) are spiritual beings (Mu)
Therefore, all men (
Sd
) are angels (
Pu
)
Notice the middle, although used, was not distributed. Thus, this syllogism is not valid. Slide112
Chapter 13: Qualitative Rules for Categorical Syllogisms Slide113
Review of Rules I-IV (125)
Terminological Rules
I. There must be three and only three terms.
II. The middle term must not occur in the conclusion.
Quantitative Rules
III. If a term is distributed in the conclusion, then it must be distributed in the premises.
IV. The middle term must be distributed at least once. Slide114
Making Predictions…
If Quantitative Rules dealt with Quantity, that is, distribution, what might today’s rules do?
Quality is defined as what?
How might that affect syllogisms? Slide115
Qualitative Rules (126)
Rule V: No conclusion can follow from two negative premises.
Prevents us from saying more in the conclusion than is stated in the premises.
When broken, commits
The Fallacy of Exclusive Premises. Slide116
An Example (126)
The following syllogism breaks Rule V
No plants are animals
Some minerals are not animals
Therefore, some minerals are not plants
While both premises are true, the conclusion does not follow.
Remember:
No
conclusion can follow from two negative premises! Slide117
Qualitative Rules (126)
Rule VI: If the two premises are affirmative, the conclusion must also be affirmative.
Syllogism:
Fallacy of Drawing a Negative Conclusion from Affirmative Premises.
All men are mortals
All mortals make mistakes
Therefore, some things that make mistakes are not menSlide118
Qualitative Rules (126)
Rule VII: If either premise is negative, the conclusion must also be negative.
If breaks,
Fallacy of Drawing an Affirmative Conclusion from a Negative Premise.
All cannibals are bloodthirsty
Some accountants are not bloodthirsty
Therefore,
some accountants
are cannibals