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CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
Categorical Propositions
PHIL UA-70: LogicApril 7–9, 2015
S P
D
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
OUTLINE
CATEGORICAL PROPOSITIONS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
QUALITY, QUANTITY, AND DISTRIBUTION
THE SQUARE OF OPPOSITION
THE TRADITIONAL SQUARE
THE MODERN SQUARE
CATEGORICAL SYLLOGISMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
MOOD AND FIGURE
VENN DIAGRAMS
REPRESENTING STANDARD FORM CATEGORICAL
PROPOSITIONS WITH VENN DIAGRAMS
TESTING THE VALIDITY OF CATEGORICAL SYLLOGISMS
WITH VENN DIAGRAMS
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
A BRIEF HISTORICAL INTERLUDE
▶ Before looking at the system of logic known asQuantificational Logic, or ‘QL’, we’ll look at the ancient andmedieval system of logic which studied categoricalsyllogisms.
▶ Two goals:
▶ Gain an informal understanding of what’s going on in QL
▶ In particular, how that theory understands ‘all’ and ‘some’
▶ come to appreciate just how much of an improvement QLrepresents.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
A BRIEF HISTORICAL INTERLUDE
▶ Before looking at the system of logic known asQuantificational Logic, or ‘QL’, we’ll look at the ancient andmedieval system of logic which studied categoricalsyllogisms.
▶ Two goals:
▶ Gain an informal understanding of what’s going on in QL
▶ In particular, how that theory understands ‘all’ and ‘some’
▶ come to appreciate just how much of an improvement QLrepresents.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
A BRIEF HISTORICAL INTERLUDE
▶ Before looking at the system of logic known asQuantificational Logic, or ‘QL’, we’ll look at the ancient andmedieval system of logic which studied categoricalsyllogisms.
▶ Two goals:▶ Gain an informal understanding of what’s going on in QL
▶ In particular, how that theory understands ‘all’ and ‘some’▶ come to appreciate just how much of an improvement QL
represents.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
A BRIEF HISTORICAL INTERLUDE
▶ Before looking at the system of logic known asQuantificational Logic, or ‘QL’, we’ll look at the ancient andmedieval system of logic which studied categoricalsyllogisms.
▶ Two goals:▶ Gain an informal understanding of what’s going on in QL
▶ In particular, how that theory understands ‘all’ and ‘some’
▶ come to appreciate just how much of an improvement QLrepresents.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
A BRIEF HISTORICAL INTERLUDE
▶ Before looking at the system of logic known asQuantificational Logic, or ‘QL’, we’ll look at the ancient andmedieval system of logic which studied categoricalsyllogisms.
▶ Two goals:▶ Gain an informal understanding of what’s going on in QL
▶ In particular, how that theory understands ‘all’ and ‘some’▶ come to appreciate just how much of an improvement QL
represents.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
OUTLINE
CATEGORICAL PROPOSITIONS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
QUALITY, QUANTITY, AND DISTRIBUTION
THE SQUARE OF OPPOSITION
THE TRADITIONAL SQUARE
THE MODERN SQUARE
CATEGORICAL SYLLOGISMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
MOOD AND FIGURE
VENN DIAGRAMS
REPRESENTING STANDARD FORM CATEGORICAL
PROPOSITIONS WITH VENN DIAGRAMS
TESTING THE VALIDITY OF CATEGORICAL SYLLOGISMS
WITH VENN DIAGRAMS
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL PROPOSITIONS
▶ examples of categorical propositions:
1. Everyone loves a Georgia peach.2. No animal eats its young.3. Somebody loves Kesha.4. Some hats are not fashionable.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL PROPOSITIONS
▶ examples of categorical propositions:1. Everyone loves a Georgia peach.
2. No animal eats its young.3. Somebody loves Kesha.4. Some hats are not fashionable.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL PROPOSITIONS
▶ examples of categorical propositions:1. Everyone loves a Georgia peach.2. No animal eats its young.
3. Somebody loves Kesha.4. Some hats are not fashionable.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL PROPOSITIONS
▶ examples of categorical propositions:1. Everyone loves a Georgia peach.2. No animal eats its young.3. Somebody loves Kesha.
4. Some hats are not fashionable.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL PROPOSITIONS
▶ examples of categorical propositions:1. Everyone loves a Georgia peach.2. No animal eats its young.3. Somebody loves Kesha.4. Some hats are not fashionable.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL PROPOSITIONS
▶ They say something about how the members of one classor category are related to the members of another class orcategory.
1. Everything in the class of people is contained in the class ofthings that love a Georgia peach.
2. Nothing in the class of animals is contained in the class ofthings that eat their young.
3. Something in the class of people is contained in the class ofthings that love Kesha.
4. Something in the class of hats is not contained in the classof things that are fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL PROPOSITIONS
▶ They say something about how the members of one classor category are related to the members of another class orcategory.
1. Everything in the class of people is contained in the class ofthings that love a Georgia peach.
2. Nothing in the class of animals is contained in the class ofthings that eat their young.
3. Something in the class of people is contained in the class ofthings that love Kesha.
4. Something in the class of hats is not contained in the classof things that are fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL PROPOSITIONS
▶ They say something about how the members of one classor category are related to the members of another class orcategory.
1. Everything in the class of people is contained in the class ofthings that love a Georgia peach.
2. Nothing in the class of animals is contained in the class ofthings that eat their young.
3. Something in the class of people is contained in the class ofthings that love Kesha.
4. Something in the class of hats is not contained in the classof things that are fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL PROPOSITIONS
▶ They say something about how the members of one classor category are related to the members of another class orcategory.
1. Everything in the class of people is contained in the class ofthings that love a Georgia peach.
2. Nothing in the class of animals is contained in the class ofthings that eat their young.
3. Something in the class of people is contained in the class ofthings that love Kesha.
4. Something in the class of hats is not contained in the classof things that are fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL PROPOSITIONS
▶ They say something about how the members of one classor category are related to the members of another class orcategory.
1. Everything in the class of people is contained in the class ofthings that love a Georgia peach.
2. Nothing in the class of animals is contained in the class ofthings that eat their young.
3. Something in the class of people is contained in the class ofthings that love Kesha.
4. Something in the class of hats is not contained in the classof things that are fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
STANDARD FORM CATEGORICAL PROPOSITIONS
▶ Four standard form categorical propositions:
A) All S are P
All people are Georgia peach-lovers.
E) No S are P
No animals are young-eaters.
I) Some S are P
Some people are Kesha-lovers.
O) Some S are not P
Some hats are not fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
STANDARD FORM CATEGORICAL PROPOSITIONS
▶ Four standard form categorical propositions:A) All S are P
All people are Georgia peach-lovers.E) No S are P
No animals are young-eaters.
I) Some S are P
Some people are Kesha-lovers.
O) Some S are not P
Some hats are not fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
STANDARD FORM CATEGORICAL PROPOSITIONS
▶ Four standard form categorical propositions:A) All S are P
All people are Georgia peach-lovers.
E) No S are P
No animals are young-eaters.I) Some S are P
Some people are Kesha-lovers.
O) Some S are not P
Some hats are not fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
STANDARD FORM CATEGORICAL PROPOSITIONS
▶ Four standard form categorical propositions:A) All S are P
All people are Georgia peach-lovers.
E) No S are P
No animals are young-eaters.
I) Some S are P
Some people are Kesha-lovers.O) Some S are not P
Some hats are not fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
STANDARD FORM CATEGORICAL PROPOSITIONS
▶ Four standard form categorical propositions:A) All S are P
All people are Georgia peach-lovers.
E) No S are P
No animals are young-eaters.
I) Some S are P
Some people are Kesha-lovers.
O) Some S are not P
Some hats are not fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
STANDARD FORM CATEGORICAL PROPOSITIONS
▶ Four standard form categorical propositions:A) All S are P All people are Georgia peach-lovers.E) No S are P
No animals are young-eaters.
I) Some S are P
Some people are Kesha-lovers.
O) Some S are not P
Some hats are not fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
STANDARD FORM CATEGORICAL PROPOSITIONS
▶ Four standard form categorical propositions:A) All S are P All people are Georgia peach-lovers.E) No S are P No animals are young-eaters.I) Some S are P
Some people are Kesha-lovers.
O) Some S are not P
Some hats are not fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
STANDARD FORM CATEGORICAL PROPOSITIONS
▶ Four standard form categorical propositions:A) All S are P All people are Georgia peach-lovers.E) No S are P No animals are young-eaters.I) Some S are P Some people are Kesha-lovers.
O) Some S are not P
Some hats are not fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
STANDARD FORM CATEGORICAL PROPOSITIONS
▶ Four standard form categorical propositions:A) All S are P All people are Georgia peach-lovers.E) No S are P No animals are young-eaters.I) Some S are P Some people are Kesha-lovers.
O) Some S are not P Some hats are not fashionable clothing.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
OUTLINE
CATEGORICAL PROPOSITIONS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
QUALITY, QUANTITY, AND DISTRIBUTION
THE SQUARE OF OPPOSITION
THE TRADITIONAL SQUARE
THE MODERN SQUARE
CATEGORICAL SYLLOGISMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
MOOD AND FIGURE
VENN DIAGRAMS
REPRESENTING STANDARD FORM CATEGORICAL
PROPOSITIONS WITH VENN DIAGRAMS
TESTING THE VALIDITY OF CATEGORICAL SYLLOGISMS
WITH VENN DIAGRAMS
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
▶ A categorical proposition has four components:
1. A quantifier—either ‘All’, ‘No’, or ‘Some’2. A subject term—the thing denoted in A,E, I, and O above
with an ‘S’3. A copula—either ‘are’ or ‘are not’4. A predicate term—the thing denoted in A,E, I, and O above
with a ‘P’
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
▶ A categorical proposition has four components:1. A quantifier—either ‘All’, ‘No’, or ‘Some’
2. A subject term—the thing denoted in A,E, I, and O abovewith an ‘S’
3. A copula—either ‘are’ or ‘are not’4. A predicate term—the thing denoted in A,E, I, and O above
with a ‘P’
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
▶ A categorical proposition has four components:1. A quantifier—either ‘All’, ‘No’, or ‘Some’2. A subject term—the thing denoted in A,E, I, and O above
with an ‘S’
3. A copula—either ‘are’ or ‘are not’4. A predicate term—the thing denoted in A,E, I, and O above
with a ‘P’
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
▶ A categorical proposition has four components:1. A quantifier—either ‘All’, ‘No’, or ‘Some’2. A subject term—the thing denoted in A,E, I, and O above
with an ‘S’3. A copula—either ‘are’ or ‘are not’
4. A predicate term—the thing denoted in A,E, I, and O abovewith a ‘P’
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
▶ A categorical proposition has four components:1. A quantifier—either ‘All’, ‘No’, or ‘Some’2. A subject term—the thing denoted in A,E, I, and O above
with an ‘S’3. A copula—either ‘are’ or ‘are not’4. A predicate term—the thing denoted in A,E, I, and O above
with a ‘P’
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
All︸︷︷︸quantifier
people︸ ︷︷ ︸subject term
are︸︷︷︸copula
Georgia peach lovers︸ ︷︷ ︸predicate term
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
No︸︷︷︸quantifier
animals︸ ︷︷ ︸subject term
are︸︷︷︸copula
young-eaters︸ ︷︷ ︸predicate term
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
Some︸ ︷︷ ︸quantifier
people︸ ︷︷ ︸subject term
are︸︷︷︸copula
Kesha-lovers︸ ︷︷ ︸predicate term
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
Some︸ ︷︷ ︸quantifier
hats︸︷︷︸subject term
are not︸ ︷︷ ︸copula
fashionable clothing︸ ︷︷ ︸predicate term
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
▶ ‘subject term’ and ‘predicate term’ as they are being usedhere need not line up with the grammatical subject and thegrammatical predicate.
▶ ‘Some S are P’ does not imply that some S are not P.
▶ ‘Everyone loves Kesha’ and ‘Someone loves Kesha’ areconsistent.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
▶ ‘subject term’ and ‘predicate term’ as they are being usedhere need not line up with the grammatical subject and thegrammatical predicate.
▶ ‘Some S are P’ does not imply that some S are not P.
▶ ‘Everyone loves Kesha’ and ‘Someone loves Kesha’ areconsistent.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
▶ ‘subject term’ and ‘predicate term’ as they are being usedhere need not line up with the grammatical subject and thegrammatical predicate.
▶ ‘Some S are P’ does not imply that some S are not P.▶ ‘Everyone loves Kesha’ and ‘Someone loves Kesha’ are
consistent.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
OUTLINE
CATEGORICAL PROPOSITIONS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
QUALITY, QUANTITY, AND DISTRIBUTION
THE SQUARE OF OPPOSITION
THE TRADITIONAL SQUARE
THE MODERN SQUARE
CATEGORICAL SYLLOGISMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
MOOD AND FIGURE
VENN DIAGRAMS
REPRESENTING STANDARD FORM CATEGORICAL
PROPOSITIONS WITH VENN DIAGRAMS
TESTING THE VALIDITY OF CATEGORICAL SYLLOGISMS
WITH VENN DIAGRAMS
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY, QUANTITY, AND DISTRIBUTION
▶ three properties of categorical propositions:
▶ their quality (either affirmative or negative)▶ their quantity (either universal or particular)▶ whether or not they distribute their subject or predicate
terms
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY, QUANTITY, AND DISTRIBUTION
▶ three properties of categorical propositions:▶ their quality (either affirmative or negative)
▶ their quantity (either universal or particular)▶ whether or not they distribute their subject or predicate
terms
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY, QUANTITY, AND DISTRIBUTION
▶ three properties of categorical propositions:▶ their quality (either affirmative or negative)▶ their quantity (either universal or particular)
▶ whether or not they distribute their subject or predicateterms
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY, QUANTITY, AND DISTRIBUTION
▶ three properties of categorical propositions:▶ their quality (either affirmative or negative)▶ their quantity (either universal or particular)▶ whether or not they distribute their subject or predicate
terms
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY
▶ In both of the claims1) All people are Georgia peach lovers.3) Some people are Kesha-lovers.
membership in the predicate class is affirmed.
▶ In both of the claims
2) No animals are young-eaters.4) Some hats are not fashionable clothing.
membership in the predicate class is denied
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY
▶ In both of the claims1) All people are Georgia peach lovers.3) Some people are Kesha-lovers.
membership in the predicate class is affirmed.
▶ In both of the claims
2) No animals are young-eaters.4) Some hats are not fashionable clothing.
membership in the predicate class is denied
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY
▶ In both of the claims1) All people are Georgia peach lovers.3) Some people are Kesha-lovers.
membership in the predicate class is affirmed.▶ In both of the claims
2) No animals are young-eaters.4) Some hats are not fashionable clothing.
membership in the predicate class is denied
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY
▶ In both of the claims1) All people are Georgia peach lovers.3) Some people are Kesha-lovers.
membership in the predicate class is affirmed.▶ In both of the claims
2) No animals are young-eaters.4) Some hats are not fashionable clothing.
membership in the predicate class is denied
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY
▶ If membership in the predicate class if affirmed, then thecategorical proposition has affirmative quality.
▶ If membership in the predicate class is denied, then thecategorical proposition has negative quality.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY
▶ If membership in the predicate class if affirmed, then thecategorical proposition has affirmative quality.
▶ If membership in the predicate class is denied, then thecategorical proposition has negative quality.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY
▶ A and I standard form categorical propositions haveaffirmative quality.
A) All S are P.I) Some S are P.
▶ E and O standard form categorical propositions havenegative quality.
E) No S are P.O) Some S is not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY
▶ A and I standard form categorical propositions haveaffirmative quality.
A) All S are P.
I) Some S are P.
▶ E and O standard form categorical propositions havenegative quality.
E) No S are P.O) Some S is not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY
▶ A and I standard form categorical propositions haveaffirmative quality.
A) All S are P.I) Some S are P.
▶ E and O standard form categorical propositions havenegative quality.
E) No S are P.O) Some S is not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY
▶ A and I standard form categorical propositions haveaffirmative quality.
A) All S are P.I) Some S are P.
▶ E and O standard form categorical propositions havenegative quality.
E) No S are P.O) Some S is not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY
▶ A and I standard form categorical propositions haveaffirmative quality.
A) All S are P.I) Some S are P.
▶ E and O standard form categorical propositions havenegative quality.
E) No S are P.
O) Some S is not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY
▶ A and I standard form categorical propositions haveaffirmative quality.
A) All S are P.I) Some S are P.
▶ E and O standard form categorical propositions havenegative quality.
E) No S are P.O) Some S is not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUANTITY
▶ In both of the claims1) All people are Georgia peach lovers.2) No animals are young-eaters.
we are told something about all of the things in the subjectclass.
▶ In both of the claims
3) Some people are Kesha-lovers.4) Some hats are not fashionable clothing.
We are told something only about some of the things in thesubject class.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUANTITY
▶ In both of the claims1) All people are Georgia peach lovers.2) No animals are young-eaters.
we are told something about all of the things in the subjectclass.
▶ In both of the claims
3) Some people are Kesha-lovers.4) Some hats are not fashionable clothing.
We are told something only about some of the things in thesubject class.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUANTITY
▶ In both of the claims1) All people are Georgia peach lovers.2) No animals are young-eaters.
we are told something about all of the things in the subjectclass.
▶ In both of the claims3) Some people are Kesha-lovers.4) Some hats are not fashionable clothing.
We are told something only about some of the things in thesubject class.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUANTITY
▶ In both of the claims1) All people are Georgia peach lovers.2) No animals are young-eaters.
we are told something about all of the things in the subjectclass.
▶ In both of the claims3) Some people are Kesha-lovers.4) Some hats are not fashionable clothing.
We are told something only about some of the things in thesubject class.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUANTITY
▶ If a standard form categorical proposition says somethingabout all of the members of the subject class, then it hasuniversal quantity.
▶ If a standard form categorical proposition says somethingabout only some of the members of the subject class, then ithas particular quantity.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUANTITY
▶ If a standard form categorical proposition says somethingabout all of the members of the subject class, then it hasuniversal quantity.
▶ If a standard form categorical proposition says somethingabout only some of the members of the subject class, then ithas particular quantity.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUANTITY
▶ A and E have universal quantity.
A) All S are P.E) No S are P.
▶ I and O have particular quantity.
I) Some S are PO) Some S are not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUANTITY
▶ A and E have universal quantity.A) All S are P.
E) No S are P.
▶ I and O have particular quantity.
I) Some S are PO) Some S are not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUANTITY
▶ A and E have universal quantity.A) All S are P.E) No S are P.
▶ I and O have particular quantity.
I) Some S are PO) Some S are not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUANTITY
▶ A and E have universal quantity.A) All S are P.E) No S are P.
▶ I and O have particular quantity.
I) Some S are PO) Some S are not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUANTITY
▶ A and E have universal quantity.A) All S are P.E) No S are P.
▶ I and O have particular quantity.I) Some S are P
O) Some S are not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUANTITY
▶ A and E have universal quantity.A) All S are P.E) No S are P.
▶ I and O have particular quantity.I) Some S are P
O) Some S are not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
QUALITY & QUANTITY
Affirmative Negativen
Universal A Eff g
Particular I Ormo
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION
▶ Quality and Quantity are properties of categoricalpropositions.
▶ Distribution is a property of the subject and predicate termsappearing in categorical propositions.
▶ A class term is distributed in a categorical proposition ifand only if the proposition tells you something about everymember of that class.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION
▶ Quality and Quantity are properties of categoricalpropositions.
▶ Distribution is a property of the subject and predicate termsappearing in categorical propositions.
▶ A class term is distributed in a categorical proposition ifand only if the proposition tells you something about everymember of that class.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION
▶ Quality and Quantity are properties of categoricalpropositions.
▶ Distribution is a property of the subject and predicate termsappearing in categorical propositions.
▶ A class term is distributed in a categorical proposition ifand only if the proposition tells you something about everymember of that class.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION—A
A) All S are P.
▶ S is distributed.▶ P is not distributed.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION—A
A) All S are P.▶ S is distributed.
▶ P is not distributed.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION—A
A) All S are P.▶ S is distributed.▶ P is not distributed.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION—E
E) No S are P.
▶ S is distributed.▶ P is distributed.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION—E
E) No S are P.▶ S is distributed.
▶ P is distributed.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION—E
E) No S are P.▶ S is distributed.▶ P is distributed.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION—I
I) Some S are P
▶ S is not distributed.▶ P is not distributed.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION—I
I) Some S are P▶ S is not distributed.
▶ P is not distributed.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION—I
I) Some S are P▶ S is not distributed.▶ P is not distributed.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION—O
O) Some S are not P
▶ S is not distributed.▶ P is distributed.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION—O
O) Some S are not P▶ S is not distributed.
▶ P is distributed.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION—O
O) Some S are not P▶ S is not distributed.▶ P is distributed.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
DISTRIBUTION
Distributed?S P
A: All S are P ✓ ×E: No S are P ✓ ✓I: Some S are P × ×O: Some S are not P × ✓
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
OUTLINE
CATEGORICAL PROPOSITIONS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
QUALITY, QUANTITY, AND DISTRIBUTION
THE SQUARE OF OPPOSITION
THE TRADITIONAL SQUARE
THE MODERN SQUARE
CATEGORICAL SYLLOGISMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
MOOD AND FIGURE
VENN DIAGRAMS
REPRESENTING STANDARD FORM CATEGORICAL
PROPOSITIONS WITH VENN DIAGRAMS
TESTING THE VALIDITY OF CATEGORICAL SYLLOGISMS
WITH VENN DIAGRAMS
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
OUTLINE
CATEGORICAL PROPOSITIONS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
QUALITY, QUANTITY, AND DISTRIBUTION
THE SQUARE OF OPPOSITION
THE TRADITIONAL SQUARE
THE MODERN SQUARE
CATEGORICAL SYLLOGISMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
MOOD AND FIGURE
VENN DIAGRAMS
REPRESENTING STANDARD FORM CATEGORICAL
PROPOSITIONS WITH VENN DIAGRAMS
TESTING THE VALIDITY OF CATEGORICAL SYLLOGISMS
WITH VENN DIAGRAMS
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE LOGICAL RELATIONS BETWEEN A, E, I, AND O
The traditional view:▶ A and E cannot both be true.
▶ That is, A and E are contraries.
▶ A and O necessarily have different truth-values (if A istrue, then O is false, and if A is false, then O is true).
▶ That is, A and O are contradictories.
▶ I and E necessarily have different truth-values (if I is true,then E is false, and if I is false, then E is true).
▶ That is, I and E are contradictories.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE LOGICAL RELATIONS BETWEEN A, E, I, AND O
The traditional view:▶ A and E cannot both be true.
▶ That is, A and E are contraries.
▶ A and O necessarily have different truth-values (if A istrue, then O is false, and if A is false, then O is true).
▶ That is, A and O are contradictories.
▶ I and E necessarily have different truth-values (if I is true,then E is false, and if I is false, then E is true).
▶ That is, I and E are contradictories.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE LOGICAL RELATIONS BETWEEN A, E, I, AND O
The traditional view:▶ A and E cannot both be true.
▶ That is, A and E are contraries.
▶ A and O necessarily have different truth-values (if A istrue, then O is false, and if A is false, then O is true).
▶ That is, A and O are contradictories.
▶ I and E necessarily have different truth-values (if I is true,then E is false, and if I is false, then E is true).
▶ That is, I and E are contradictories.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE LOGICAL RELATIONS BETWEEN A, E, I, AND O
The traditional view:▶ A and E cannot both be true.
▶ That is, A and E are contraries.
▶ A and O necessarily have different truth-values (if A istrue, then O is false, and if A is false, then O is true).
▶ That is, A and O are contradictories.
▶ I and E necessarily have different truth-values (if I is true,then E is false, and if I is false, then E is true).
▶ That is, I and E are contradictories.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE LOGICAL RELATIONS BETWEEN A, E, I, AND O
The traditional view:▶ A and E cannot both be true.
▶ That is, A and E are contraries.
▶ A and O necessarily have different truth-values (if A istrue, then O is false, and if A is false, then O is true).
▶ That is, A and O are contradictories.
▶ I and E necessarily have different truth-values (if I is true,then E is false, and if I is false, then E is true).
▶ That is, I and E are contradictories.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE LOGICAL RELATIONS BETWEEN A, E, I, AND O
The traditional view:▶ A and E cannot both be true.
▶ That is, A and E are contraries.
▶ A and O necessarily have different truth-values (if A istrue, then O is false, and if A is false, then O is true).
▶ That is, A and O are contradictories.
▶ I and E necessarily have different truth-values (if I is true,then E is false, and if I is false, then E is true).
▶ That is, I and E are contradictories.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
AAll S are P
ENo S are P
ISome S are P
OSome S are not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
AAll S are P
ENo S are P
ISome S are P
OSome S are not P
contraries
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
AAll S are P
ENo S are P
ISome S are P
OSome S are not P
contradictories
contraries
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
AAll S are P
ENo S are P
ISome S are P
OSome S are not P
contradictories
contradictories
contraries
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
AAll S are P
ENo S are P
ISome S are P
OSome S are not P
contradictories
contradictories
contraries
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
AAll S are P
ENo S are P
ISome S are P
OSome S are not P
contradictories
contradictories
contraries
subcontraries
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
AAll S are P
ENo S are P
ISome S are P
OSome S are not P
contradictories
contradictories
contraries
entails
subcontraries
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
AAll S are P
ENo S are P
ISome S are P
OSome S are not P
contradictories
contradictories
contraries
entails
entails
subcontraries
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
AAll S are P
ENo S are P
ISome S are P
OSome S are not P
contradictories
contradictories
contraries
entails
entails
subcontraries
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All S are P. (A)2. So, some S are P. (I)
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No S are P. (E)2. So, some S are not P. (O)
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some S are P. (∼I)2. So, some S are not P. (O)
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some S are not P. (∼O)2. So, some S are P. (I)
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
According to the Traditional Square of Opposition, thefollowing inferences are all formally deductively valid:
1. All libertarian presidents are still alive.2. So, some libertarian presidents are still alive.
1. No libertarian presidents are still alive .2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are still alive.2. So, some libertarian presidents are not still alive.
1. It is false that some libertarian presidents are not still alive.2. So, some libertarian presidents are still alive.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ Even though there are no libertarian presidents,
All libertarian presidents are still alive
and
No libertarian presidents are still alive
cannot both be true (they are contraries).
▶ Likewise,
Some libertarian presidents are still alive
and
Some libertarian presidents are not still alive
cannot both be false (they are subcontraries).
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ Even though there are no libertarian presidents,All libertarian presidents are still alive
and
No libertarian presidents are still alive
cannot both be true (they are contraries).
▶ Likewise,
Some libertarian presidents are still alive
and
Some libertarian presidents are not still alive
cannot both be false (they are subcontraries).
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ Even though there are no libertarian presidents,All libertarian presidents are still alive
and
No libertarian presidents are still alive
cannot both be true (they are contraries).
▶ Likewise,
Some libertarian presidents are still alive
and
Some libertarian presidents are not still alive
cannot both be false (they are subcontraries).
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ Even though there are no libertarian presidents,All libertarian presidents are still alive
andNo libertarian presidents are still alive
cannot both be true (they are contraries).
▶ Likewise,
Some libertarian presidents are still alive
and
Some libertarian presidents are not still alive
cannot both be false (they are subcontraries).
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ Even though there are no libertarian presidents,All libertarian presidents are still alive
andNo libertarian presidents are still alive
cannot both be true (they are contraries).
▶ Likewise,
Some libertarian presidents are still alive
and
Some libertarian presidents are not still alive
cannot both be false (they are subcontraries).
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ Even though there are no libertarian presidents,All libertarian presidents are still alive
andNo libertarian presidents are still alive
cannot both be true (they are contraries).
▶ Likewise,
Some libertarian presidents are still alive
and
Some libertarian presidents are not still alive
cannot both be false (they are subcontraries).
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ Even though there are no libertarian presidents,All libertarian presidents are still alive
andNo libertarian presidents are still alive
cannot both be true (they are contraries).
▶ Likewise,
Some libertarian presidents are still alive
and
Some libertarian presidents are not still alive
cannot both be false (they are subcontraries).
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ Even though there are no libertarian presidents,All libertarian presidents are still alive
andNo libertarian presidents are still alive
cannot both be true (they are contraries).
▶ Likewise,Some libertarian presidents are still alive
and
Some libertarian presidents are not still alive
cannot both be false (they are subcontraries).
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ Even though there are no libertarian presidents,All libertarian presidents are still alive
andNo libertarian presidents are still alive
cannot both be true (they are contraries).
▶ Likewise,Some libertarian presidents are still alive
and
Some libertarian presidents are not still alive
cannot both be false (they are subcontraries).
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ Even though there are no libertarian presidents,All libertarian presidents are still alive
andNo libertarian presidents are still alive
cannot both be true (they are contraries).
▶ Likewise,Some libertarian presidents are still alive
andSome libertarian presidents are not still alive
cannot both be false (they are subcontraries).
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ Even though there are no libertarian presidents,All libertarian presidents are still alive
andNo libertarian presidents are still alive
cannot both be true (they are contraries).
▶ Likewise,Some libertarian presidents are still alive
andSome libertarian presidents are not still alive
cannot both be false (they are subcontraries).
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ The traditional view: if there are no Ss, then
▶ the I sentence is (vacuously) false, and (therefore)▶ the E sentence is (vacuously) true.
▶ Interestingly, this implies that
Some libertarian presidents are dead
is false, while
Some libertarian presidents are not still alive
is true.▶ That’s very strange.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ The traditional view: if there are no Ss, then▶ the I sentence is (vacuously) false, and (therefore)
▶ the E sentence is (vacuously) true.
▶ Interestingly, this implies that
Some libertarian presidents are dead
is false, while
Some libertarian presidents are not still alive
is true.▶ That’s very strange.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ The traditional view: if there are no Ss, then▶ the I sentence is (vacuously) false, and (therefore)▶ the E sentence is (vacuously) true.
▶ Interestingly, this implies that
Some libertarian presidents are dead
is false, while
Some libertarian presidents are not still alive
is true.▶ That’s very strange.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ The traditional view: if there are no Ss, then▶ the I sentence is (vacuously) false, and (therefore)▶ the E sentence is (vacuously) true.
▶ Interestingly, this implies that
Some libertarian presidents are dead
is false, while
Some libertarian presidents are not still alive
is true.▶ That’s very strange.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ The traditional view: if there are no Ss, then▶ the I sentence is (vacuously) false, and (therefore)▶ the E sentence is (vacuously) true.
▶ Interestingly, this implies that
Some libertarian presidents are dead
is false, while
Some libertarian presidents are not still alive
is true.▶ That’s very strange.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ The traditional view: if there are no Ss, then▶ the I sentence is (vacuously) false, and (therefore)▶ the E sentence is (vacuously) true.
▶ Interestingly, this implies thatSome libertarian presidents are dead
is false, while
Some libertarian presidents are not still alive
is true.▶ That’s very strange.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ The traditional view: if there are no Ss, then▶ the I sentence is (vacuously) false, and (therefore)▶ the E sentence is (vacuously) true.
▶ Interestingly, this implies thatSome libertarian presidents are dead
is false, while
Some libertarian presidents are not still alive
is true.▶ That’s very strange.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ The traditional view: if there are no Ss, then▶ the I sentence is (vacuously) false, and (therefore)▶ the E sentence is (vacuously) true.
▶ Interestingly, this implies thatSome libertarian presidents are dead
is false, whileSome libertarian presidents are not still alive
is true.▶ That’s very strange.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ The traditional view: if there are no Ss, then▶ the I sentence is (vacuously) false, and (therefore)▶ the E sentence is (vacuously) true.
▶ Interestingly, this implies thatSome libertarian presidents are dead
is false, whileSome libertarian presidents are not still alive
is true.
▶ That’s very strange.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
▶ The traditional view: if there are no Ss, then▶ the I sentence is (vacuously) false, and (therefore)▶ the E sentence is (vacuously) true.
▶ Interestingly, this implies thatSome libertarian presidents are dead
is false, whileSome libertarian presidents are not still alive
is true.▶ That’s very strange.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
AAll S are P
ENo S are P
ISome S are P
OSome S are not P
contradictories
contradictories
contraries
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE TRADITIONAL SQUARE OF OPPOSITION
AAll S are P
ENo S are P
ISome S are P
OSome S are not P
contradictories
contradictories
contraries
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
OUTLINE
CATEGORICAL PROPOSITIONS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
QUALITY, QUANTITY, AND DISTRIBUTION
THE SQUARE OF OPPOSITION
THE TRADITIONAL SQUARE
THE MODERN SQUARE
CATEGORICAL SYLLOGISMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
MOOD AND FIGURE
VENN DIAGRAMS
REPRESENTING STANDARD FORM CATEGORICAL
PROPOSITIONS WITH VENN DIAGRAMS
TESTING THE VALIDITY OF CATEGORICAL SYLLOGISMS
WITH VENN DIAGRAMS
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE MODERN SQUARE OF OPPOSITION
AAll S are P
ENo S are P
ISome S are P
OSome S are not P
contradictories
contradictories
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE MODERN SQUARE OF OPPOSITION
▶ When the S class is empty,
Traditional ModernA: All S are P False TrueE: No S are P True TrueI: Some S are P False FalseO: Some S are not P True False
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE MODERN SQUARE OF OPPOSITION
▶ When the S class is empty,
Traditional ModernA: All S are P False TrueE: No S are P True TrueI: Some S are P False FalseO: Some S are not P True False
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE MODERN SQUARE OF OPPOSITION
▶ When the S class is empty,
Traditional ModernA: All S are P False TrueE: No S are P True TrueI: Some S are P False FalseO: Some S are not P True False
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE MODERN SQUARE OF OPPOSITION
▶ From the modern standpoint, the argument form
All S are PSome S are P
is invalid—as is the argument form:
No S are PSome S are not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE MODERN SQUARE OF OPPOSITION
▶ From the modern standpoint, the argument form
All S are PSome S are P
is invalid—as is the argument form:
No S are PSome S are not P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE MODERN SQUARE OF OPPOSITION
▶ Similarly,All S are P
It is false that no S are P
No S are PIt is false that all S are P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
THE MODERN SQUARE OF OPPOSITION
▶ Similarly,It is false that some S are P
Some S are not P
It is false that some S are not PSome S are P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
IN CLASS EXERCISE!
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
OUTLINE
CATEGORICAL PROPOSITIONS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
QUALITY, QUANTITY, AND DISTRIBUTION
THE SQUARE OF OPPOSITION
THE TRADITIONAL SQUARE
THE MODERN SQUARE
CATEGORICAL SYLLOGISMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
MOOD AND FIGURE
VENN DIAGRAMS
REPRESENTING STANDARD FORM CATEGORICAL
PROPOSITIONS WITH VENN DIAGRAMS
TESTING THE VALIDITY OF CATEGORICAL SYLLOGISMS
WITH VENN DIAGRAMS
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL SYLLOGISMS
▶ A syllogism is an argument containing two premises and aconclusion.
▶ A categorical syllogism is a syllogism whose premises andconclusion are categorical propositions.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL SYLLOGISMS
▶ A syllogism is an argument containing two premises and aconclusion.
▶ A categorical syllogism is a syllogism whose premises andconclusion are categorical propositions.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL SYLLOGISMS
▶ For instance,
1. All people are Kesha-lovers.2. Some Kesha-lovers are bacon-eaters.3. So, some people are bacon-eaters.
1. All hats are fashionable clothing.2. All fashionable clothing is purple.3. So, some hats are purple.
1. All hats are fashionable clothing.2. All fashionable clothing is purple.3. So, all hats are purple.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL SYLLOGISMS
▶ For instance,1. All people are Kesha-lovers.2. Some Kesha-lovers are bacon-eaters.3. So, some people are bacon-eaters.
1. All hats are fashionable clothing.2. All fashionable clothing is purple.3. So, some hats are purple.
1. All hats are fashionable clothing.2. All fashionable clothing is purple.3. So, all hats are purple.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL SYLLOGISMS
▶ For instance,1. All people are Kesha-lovers.2. Some Kesha-lovers are bacon-eaters.3. So, some people are bacon-eaters.
1. All hats are fashionable clothing.2. All fashionable clothing is purple.3. So, some hats are purple.
1. All hats are fashionable clothing.2. All fashionable clothing is purple.3. So, all hats are purple.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
CATEGORICAL SYLLOGISMS
▶ For instance,1. All people are Kesha-lovers.2. Some Kesha-lovers are bacon-eaters.3. So, some people are bacon-eaters.
1. All hats are fashionable clothing.2. All fashionable clothing is purple.3. So, some hats are purple.
1. All hats are fashionable clothing.2. All fashionable clothing is purple.3. So, all hats are purple.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
OUTLINE
CATEGORICAL PROPOSITIONS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
QUALITY, QUANTITY, AND DISTRIBUTION
THE SQUARE OF OPPOSITION
THE TRADITIONAL SQUARE
THE MODERN SQUARE
CATEGORICAL SYLLOGISMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
MOOD AND FIGURE
VENN DIAGRAMS
REPRESENTING STANDARD FORM CATEGORICAL
PROPOSITIONS WITH VENN DIAGRAMS
TESTING THE VALIDITY OF CATEGORICAL SYLLOGISMS
WITH VENN DIAGRAMS
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
1. All M are P.2. Some S are M.3. So, some S are P
▶ the major term is the predicate term of the conclusion
▶ the major term is the predicate term of the conclusion▶ In a STANDARD FORM CATEGORICAL SYLLOGISM, the
middle term is a term which doesn’t show up in theconclusion, but does show up in both of the premises
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
1. All M are P.2. Some S are M.3. So, some S are P
▶ the major term is the predicate term of the conclusion▶ the major term is the predicate term of the conclusion
▶ In a STANDARD FORM CATEGORICAL SYLLOGISM, themiddle term is a term which doesn’t show up in theconclusion, but does show up in both of the premises
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
1. All M are P.2. Some S are M.3. So, some S are P
▶ the major term is the predicate term of the conclusion▶ the major term is the predicate term of the conclusion▶ In a STANDARD FORM CATEGORICAL SYLLOGISM, the
middle term is a term which doesn’t show up in theconclusion, but does show up in both of the premises
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
1. All M are P.2. Some S are M.3. So, some S are P
▶ the major premise is the premise which contains the majorterm.
▶ the minor premise is the premise which contains the minorterm.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
1. All M are P.2. Some S are M.3. So, some S are P
▶ the major premise is the premise which contains the majorterm.
▶ the minor premise is the premise which contains the minorterm.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
STANDARD FORM CATEGORICAL SYLLOGISMS
A STANDARD FORM CATEGORICAL SYLLOGISM contains:
1. Two premises and a conclusion, each a standard formcategorical proposition.
2. A major term which appears only in the first premise andthe predicate of the conclusion.
3. A minor term which appears only in the second premiseand the subject of the conclusion
4. A middle term which appears in both premises but not inthe conclusion.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
OUTLINE
CATEGORICAL PROPOSITIONS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
QUALITY, QUANTITY, AND DISTRIBUTION
THE SQUARE OF OPPOSITION
THE TRADITIONAL SQUARE
THE MODERN SQUARE
CATEGORICAL SYLLOGISMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
MOOD AND FIGURE
VENN DIAGRAMS
REPRESENTING STANDARD FORM CATEGORICAL
PROPOSITIONS WITH VENN DIAGRAMS
TESTING THE VALIDITY OF CATEGORICAL SYLLOGISMS
WITH VENN DIAGRAMS
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD
▶ we may categorize categorical syllogisms by:
▶ the kind of standard form categorical proposition whichappears as its first (i.e., major) premise,
▶ the kind of standard form categorical proposition whichappears as its second (i.e., minor) premise, and
▶ the kind of standard form categorical propositions whichappears as its conclusion.
▶ call such a specification the MOOD of the sentence.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD
▶ we may categorize categorical syllogisms by:▶ the kind of standard form categorical proposition which
appears as its first (i.e., major) premise,
▶ the kind of standard form categorical proposition whichappears as its second (i.e., minor) premise, and
▶ the kind of standard form categorical propositions whichappears as its conclusion.
▶ call such a specification the MOOD of the sentence.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD
▶ we may categorize categorical syllogisms by:▶ the kind of standard form categorical proposition which
appears as its first (i.e., major) premise,▶ the kind of standard form categorical proposition which
appears as its second (i.e., minor) premise, and
▶ the kind of standard form categorical propositions whichappears as its conclusion.
▶ call such a specification the MOOD of the sentence.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD
▶ we may categorize categorical syllogisms by:▶ the kind of standard form categorical proposition which
appears as its first (i.e., major) premise,▶ the kind of standard form categorical proposition which
appears as its second (i.e., minor) premise, and▶ the kind of standard form categorical propositions which
appears as its conclusion.
▶ call such a specification the MOOD of the sentence.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD
▶ we may categorize categorical syllogisms by:▶ the kind of standard form categorical proposition which
appears as its first (i.e., major) premise,▶ the kind of standard form categorical proposition which
appears as its second (i.e., minor) premise, and▶ the kind of standard form categorical propositions which
appears as its conclusion.
▶ call such a specification the MOOD of the sentence.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD
All P are MAll S are MSome S are P
▶ The first premise is of the form A▶ The second premise is of the form A▶ the conclusion is of the form I.▶ Thus, the mood of this argument is AAI.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD
All P are MAll S are MSome S are P
▶ The first premise is of the form A
▶ The second premise is of the form A▶ the conclusion is of the form I.▶ Thus, the mood of this argument is AAI.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD
All P are MAll S are MSome S are P
▶ The first premise is of the form A▶ The second premise is of the form A
▶ the conclusion is of the form I.▶ Thus, the mood of this argument is AAI.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD
All P are MAll S are MSome S are P
▶ The first premise is of the form A▶ The second premise is of the form A▶ the conclusion is of the form I.
▶ Thus, the mood of this argument is AAI.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD
All P are MAll S are MSome S are P
▶ The first premise is of the form A▶ The second premise is of the form A▶ the conclusion is of the form I.▶ Thus, the mood of this argument is AAI.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD
All P are MAll S are MSome S are P
All M are PAll S are MSome S are P
▶ The mood of both arguments is AAI.▶ Yet the left-hand-side argument is invalid; whereas the
right-hand-side argument is valid.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD
All P are MAll S are MSome S are P
All M are PAll S are MSome S are P
▶ The mood of both arguments is AAI.
▶ Yet the left-hand-side argument is invalid; whereas theright-hand-side argument is valid.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD
All P are MAll S are MSome S are P
All M are PAll S are MSome S are P
▶ The mood of both arguments is AAI.▶ Yet the left-hand-side argument is invalid; whereas the
right-hand-side argument is valid.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
FIGURE
1 2 3 4M PS MS P
P MS MS P
M PM SS P
P MM SS P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD AND FIGURE
All P are MAll S are MSome S are P
All M are PAll S are MSome S are P
▶ The left-hand-side argument has mood AAI and figure2—AAI-2
▶ The right-hand-side argument has mood AAI and figure1—AAI-1
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD AND FIGURE
All P are MAll S are MSome S are P
All M are PAll S are MSome S are P
▶ The left-hand-side argument has mood AAI and figure2—AAI-2
▶ The right-hand-side argument has mood AAI and figure1—AAI-1
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD AND FIGURE
All P are MAll S are MSome S are P
All M are PAll S are MSome S are P
▶ The left-hand-side argument has mood AAI and figure2—AAI-2
▶ The right-hand-side argument has mood AAI and figure1—AAI-1
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD AND FIGURE
▶ There are then 43 = 64 different moods
▶ And each mood has 4 different figures.▶ Thus, there are 64 × 4 = 256 different kinds of standard
form categorical syllogisms.▶ The traditional theory then just lists off the standard form
categorical syllogisms which are valid.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD AND FIGURE
▶ There are then 43 = 64 different moods▶ And each mood has 4 different figures.
▶ Thus, there are 64 × 4 = 256 different kinds of standardform categorical syllogisms.
▶ The traditional theory then just lists off the standard formcategorical syllogisms which are valid.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD AND FIGURE
▶ There are then 43 = 64 different moods▶ And each mood has 4 different figures.▶ Thus, there are 64 × 4 = 256 different kinds of standard
form categorical syllogisms.
▶ The traditional theory then just lists off the standard formcategorical syllogisms which are valid.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD AND FIGURE
▶ There are then 43 = 64 different moods▶ And each mood has 4 different figures.▶ Thus, there are 64 × 4 = 256 different kinds of standard
form categorical syllogisms.▶ The traditional theory then just lists off the standard form
categorical syllogisms which are valid.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
MOOD AND FIGURE
▶ On the traditional theory, all of the forms below are valid.On the modern theory, only the forms listed above the lineare valid.
AAA-1 EAE-2 IAI-3 AEE-4EAE-1 AEE-2 AII-3 IAI-4AII-1 EIO-2 OAO-3 EIO-4EIO-1 AOO-2 EIO-3AAI-1 AEO-2 AAI-3 AEO-4EAO-1 EAO-2 EAO-3 EAO-4
AAI-4
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
RULES FOR VALIDITY
A standard form categorical syllogism is valid on the moderntheory if and only if each of the following five propositions areall true of it. A standard form categorical syllogism is validon the traditional theory if and only if each of the first fourpropositions are true of it.
1. The middle term is distributed at least once.2. If a term is distributed in the conclusion, then that term is
distributed in one of the premises.3. There is at least one affirmative premise.4. There is a negative premise if and only if there is a
negative conclusion.5. If both premises are universal, then the conclusion is
universal.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
OUTLINE
CATEGORICAL PROPOSITIONS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
QUALITY, QUANTITY, AND DISTRIBUTION
THE SQUARE OF OPPOSITION
THE TRADITIONAL SQUARE
THE MODERN SQUARE
CATEGORICAL SYLLOGISMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
MOOD AND FIGURE
VENN DIAGRAMS
REPRESENTING STANDARD FORM CATEGORICAL
PROPOSITIONS WITH VENN DIAGRAMS
TESTING THE VALIDITY OF CATEGORICAL SYLLOGISMS
WITH VENN DIAGRAMS
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS
D
F G
x
An INTERPRETATION of a Venn diagramsays
1. what the box, or the domain, D is;and
2. which class of things each circlerepresents.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS
D
F G
x
An INTERPRETATION of a Venn diagramsays
1. what the box, or the domain, D is;and
2. which class of things each circlerepresents.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS
F G
H
D
x
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
OUTLINE
CATEGORICAL PROPOSITIONS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
QUALITY, QUANTITY, AND DISTRIBUTION
THE SQUARE OF OPPOSITION
THE TRADITIONAL SQUARE
THE MODERN SQUARE
CATEGORICAL SYLLOGISMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
MOOD AND FIGURE
VENN DIAGRAMS
REPRESENTING STANDARD FORM CATEGORICAL
PROPOSITIONS WITH VENN DIAGRAMS
TESTING THE VALIDITY OF CATEGORICAL SYLLOGISMS
WITH VENN DIAGRAMS
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
STANDARD FORM CATEGORICAL PROPOSITIONS AND
VENN DIAGRAMS
▶ we will see how to represent the standard form categoricalpropositions A, E, I, and O using Venn diagrams.
▶ we will simply take D to be the class of all things. Thus, theS circles will represent all things which are S; and the Pcircles will represents all things which are P.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
STANDARD FORM CATEGORICAL PROPOSITIONS AND
VENN DIAGRAMS
▶ we will see how to represent the standard form categoricalpropositions A, E, I, and O using Venn diagrams.
▶ we will simply take D to be the class of all things. Thus, theS circles will represent all things which are S; and the Pcircles will represents all things which are P.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAM FOR A
S P
D
Figure: All S are P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAM FOR E
S P
D
Figure: No S are P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAM FOR I
S P
D
x
Figure: Some S are P.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAM FOR O
S P
D
x
Figure: Some S are not P.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
OUTLINE
CATEGORICAL PROPOSITIONS
THE COMPONENTS OF A CATEGORICAL PROPOSITION
QUALITY, QUANTITY, AND DISTRIBUTION
THE SQUARE OF OPPOSITION
THE TRADITIONAL SQUARE
THE MODERN SQUARE
CATEGORICAL SYLLOGISMS
MAJOR TERMS, MINOR TERMS, MIDDLE TERMS
MOOD AND FIGURE
VENN DIAGRAMS
REPRESENTING STANDARD FORM CATEGORICAL
PROPOSITIONS WITH VENN DIAGRAMS
TESTING THE VALIDITY OF CATEGORICAL SYLLOGISMS
WITH VENN DIAGRAMS
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS AND VALIDITY
▶ use a Venn diagram to represent the claims of thepremises, and then check to see whether the Venn diagramcontains within it the claim of the conclusion.
▶ If it does, then the categorical syllogism is valid.▶ If it does not, then the categorical syllogism is invalid.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS AND VALIDITY
▶ use a Venn diagram to represent the claims of thepremises, and then check to see whether the Venn diagramcontains within it the claim of the conclusion.
▶ If it does, then the categorical syllogism is valid.
▶ If it does not, then the categorical syllogism is invalid.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS AND VALIDITY
▶ use a Venn diagram to represent the claims of thepremises, and then check to see whether the Venn diagramcontains within it the claim of the conclusion.
▶ If it does, then the categorical syllogism is valid.▶ If it does not, then the categorical syllogism is invalid.
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS AND VALIDITY
▶ it will help us if we first represent the claims of universalpremises, and then represent the claims of particularpremises
▶ If there are only universal premises or only particularpremises, then it won’t matter the order in which werepresent the claims of the premises
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS AND VALIDITY
▶ it will help us if we first represent the claims of universalpremises, and then represent the claims of particularpremises
▶ If there are only universal premises or only particularpremises, then it won’t matter the order in which werepresent the claims of the premises
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS AND VALIDITY—AAI-1
All M are PAll S are MAll S are P
D
S M
P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS AND VALIDITY—AAI-1
All M are PAll S are MAll S are P
D
S M
P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS AND VALIDITY—AAI-1
All M are PAll S are MAll S are P
D
S M
P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS AND VALIDITY—AIA-4
All P are MSome M are SAll S are P
D
S M
P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS AND VALIDITY—AIA-4
All P are MSome M are SAll S are P
D
S M
P
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
VENN DIAGRAMS AND VALIDITY—AIA-4
All P are MSome M are SAll S are P
D
S M
P
x
CATEGORICAL PROPOSITIONS THE SQUARE OF OPPOSITION CATEGORICAL SYLLOGISMS VENN DIAGRAMS
IN CLASS EXERCISE!
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