Traditional Logic II
Martin Cothran
Instructor
Reduction of Syllogisms
What is Reduction?
Two Methods of Reduction
How to Use the Mnemonic Verse
Four Operations for Reduction
Review of Conversion
Reduction Involving Conversion
Review of Partial Conversion
Reduction Using Partial Conversion
Reduction Involving Multiple Steps
Review
Sample Exercises
1
Reduction of Syllogisms
What is Reduction?
Two Methods of Reduction
How to Use the Mnemonic Verse
Four Operations for Reduction
Review of Conversion
Reduction Involving Conversion
Review of Partial Conversion
Reduction Using Partial Conversion
Reduction Involving Multiple Steps
Review
Sample Exercises
What is Reduction?
Reduction of a syllogism is the
process of changing a 2nd, 3rd,
or 4th Figure syllogism into a
syllogism of the 1st Figure
2
Two Reasons to Reduce
Syllogisms:
First Figure syllogisms are more
straightforward than syllogisms in
other figures
Reducing syllogisms to the First
Figure will help you understand
syllogisms better
Two Reasons to Reduce
Syllogisms:
First Figure syllogisms are more
straightforward than syllogisms in
other figures
Reducing syllogisms to the First
Figure will help you understand
syllogisms better
3
Two Reasons to Reduce
Syllogisms:
First Figure syllogisms are more
straightforward than syllogisms in
other figures
Reducing syllogisms to the First
Figure will help you understand
syllogisms better
Reduction of Syllogisms
What is Reduction?
Two Methods of Reduction
How to Use the Mnemonic Verse
Four Operations for Reduction
Review of Conversion
Reduction Involving Conversion
Review of Partial Conversion
Reduction Using Partial Conversion
Reduction Involving Multiple Steps
Review
Sample Exercises
4
Two Methods for
Reducing Syllogisms
Direct Reduction
Indirect Reduction
Two Methods for
Reducing Syllogisms
Direct Reduction
Indirect Reduction
5
Two Methods for
Reducing Syllogisms
Direct Reduction
Indirect Reduction
Reduction of Syllogisms
What is Reduction?
Two Methods of Reduction
How to Use the Mnemonic Verse
Four Operations for Reduction
Review of Conversion
Reduction Involving Conversion
Review of Partial Conversion
Reduction Using Partial Conversion
Reduction Involving Multiple Steps
Review
Sample Exercises
6
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
7
What the Consonants
Mean
The first consonant in each name
indicates the syllogism in the 1st
Figure to which it reduces
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
8
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
9
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
10
An Example
All chickensPd are birdsMu
No horseSd is a birdMd
No horseSd is a chickenPd
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
11
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
12
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
An Example
cAm: All chickensPd are birdsMu
Est: No horseSd is a birdMd
rEs: No horseSd is a chickenPd
13
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
An Example
cEl: No birdMd is a horsePd
Ar: All chickensSd are birdsMu
Ent: No chickenSd is a horsePd
14
Reduction of Syllogisms
What is Reduction?
Two Methods of Reduction
How to Use the Mnemonic Verse
Four Operations for Reduction
Review of Conversion
Reduction Involving Conversion
Review of Partial Conversion
Reduction Using Partial Conversion
Reduction Involving Multiple Steps
Review
Sample Exercises
Rules for Reduction
S: Simple conversion of the proposition signified by
the preceding vowel
P: Per accidens, or partial conversion of the
proposition signified by the preceding vowel
M: Mutatio, or transposition of the premises; make
the minor premise the major, and the major the
minor
C: Reduction by contradiction. This is the indirect
method of reduction through (rather than to)
BARBARA. It is signified by a non-initial c and is
applied only to BAROCO AND BOCARDO
15
Rules for Reduction
S: Simple conversion of the proposition signified by
the preceding vowel
P: Per accidens, or partial conversion of the
proposition signified by the preceding vowel
M: Mutatio, or transposition of the premises; make
the minor premise the major, and the major the
minor
C: Reduction by contradiction. This is the indirect
method of reduction through (rather than to)
BARBARA. It is signified by a non-initial c and is
applied only to BAROCO AND BOCARDO
Rules for Reduction
S: Simple conversion of the proposition signified by
the preceding vowel
P: Per accidens, or partial conversion of the
proposition signified by the preceding vowel
M: Mutatio, or transposition of the premises; make
the minor premise the major, and the major the
minor
C: Reduction by contradiction. This is the indirect
method of reduction through (rather than to)
BARBARA. It is signified by a non-initial c and is
applied only to BAROCO AND BOCARDO
16
Rules for Reduction
S: Simple conversion of the proposition signified by
the preceding vowel
P: Per accidens, or partial conversion of the
proposition signified by the preceding vowel
M: Mutatio, or transposition of the premises; make
the minor premise the major, and the major the
minor
C: Reduction by contradiction. This is the indirect
method of reduction through (rather than to)
BARBARA. It is signified by a non-initial c and is
applied only to BAROCO AND BOCARDO
Rules for Reduction
S: Simple conversion of the proposition signified by
the preceding vowel
P: Per accidens, or partial conversion of the
proposition signified by the preceding vowel
M: Mutatio, or transposition of the premises; make
the minor premise the major, and the major the
minor
C: Reduction by contradiction. This is the indirect
method of reduction through (rather than to)
BARBARA. It is signified by a non-initial c and is
applied only to BAROCO AND BOCARDO
17
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
Reducing a CESARE
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E: No whaleSd is a fishPd
18
Reducing a CESARE
prae-prae (2nd Figure)
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E: No whaleSd is a fishPd
Reducing a CESARE
prae-prae (2nd Figure)
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E: No whaleSd is a fishPd
19
Reducing a CESARE
prae-prae (2nd Figure)
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E: No whaleSd is a fishPd
Reducing a CESARE
prae-prae (2nd Figure)
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E: No whaleSd is a fishPd
20
Rules for Reduction
S: Simple conversion of the proposition signified by
the preceding vowel
P: Per accidens, or partial conversion of the
proposition signified by the preceding vowel
M: Mutatio, or transposition of the premises; make
the minor premise the major, and the major the
minor
C: Reduction by contradiction. This is the indirect
method of reduction through (rather than to)
BARBARA. It is signified by a non-initial c and is
applied only to BAROCO AND BOCARDO
Rules for Reduction
S: Simple conversion of the proposition signified by
the preceding vowel
P: Per accidens, or partial conversion of the
proposition signified by the preceding vowel
M: Mutatio, or transposition of the premises; make
the minor premise the major, and the major the
minor
C: Reduction by contradiction. This is the indirect
method of reduction through (rather than to)
BARBARA. It is signified by a non-initial c and is
applied only to BAROCO AND BOCARDO
21
Reduction of Syllogisms
What is Reduction?
Two Methods of Reduction
How to Use the Mnemonic Verse
Four Operations for Reduction
Review of Conversion
Reduction Involving Conversion
Review of Partial Conversion
Reduction Using Partial Conversion
Reduction Involving Multiple Steps
Review
Sample Exercises
Review of Conversion
Simple Conversion
Obversion
Contraposition
22
Review of Conversion
Simple Conversion
Obversion
Contraposition
Simple Conversion
Switch the subject and the
predicate
23
Simple Conversion
No robins are sparrows
Simple Conversion
No sparrows are robins
24
Reduction of Syllogisms
What is Reduction?
Two Methods of Reduction
How to Use the Mnemonic Verse
Four Operations for Reduction
Review of Conversion
Reduction Involving Conversion
Review of Partial Conversion
Reduction Using Partial Conversion
Reduction Involving Multiple Steps
Review
Sample Exercises
Simple Conversion of
CESARE
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E:
No whaleSd is a fishPd
25
Simple Conversion of
CESARE
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E:
No whaleSd is a fishPd
Simple Conversion of
CESARE
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E:
No whaleSd is a fishPd
26
Simple Conversion of
CESARE
prae-prae (2nd Figure)
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E:
No whaleSd is a fishPd
Simple Conversion of
CESARE
cEs: No mammalMd is a fishPd
Ar: All whalesSd are mammalsMu
E:
No whaleSd is a fishPd
27
Resulting in a
CELARENT
sub-prae (1st Figure)
cEl: No mammalMd is a fishPd
Ar: All whalesSd are mammalsMu
Ent: No whaleSd is a fishPd
Resulting in a
CELARENT
sub-prae (1st Figure)
cEl: No mammalMd is a fishPd
Ar: All whalesSd are mammalsMu
Ent: No whaleSd is a fishPd
28
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
29
Reduction of Syllogisms
What is Reduction?
Two Methods of Reduction
How to Use the Mnemonic Verse
Four Operations for Reduction
Review of Conversion
Reduction Involving Conversion
Review of Partial Conversion
Reduction Using Partial Conversion
Reduction Involving Multiple Steps
Review
Sample Exercises
Review of Partial
Conversion
Partial conversion is accomplished
by interchanging the subject and
predicate of an A statement and
changing its quantity
30
Partial Conversion
All robins are birds
Partial Conversion
All birds are robins
31
Partial Conversion
Some birds are robins
Reduction of Syllogisms
What is Reduction?
Two Methods of Reduction
How to Use the Mnemonic Verse
Four Operations for Reduction
Review of Conversion
Reduction Involving Conversion
Review of Partial Conversion
Reduction Using Partial Conversion
Reduction Involving Multiple Steps
Review
Sample Exercises
32
Reducing a DARAPTI
sub-sub (3rd Figure)
dAr: All turkeysMd are irritablePu
Apt: All turkeysMd are birdsSu
I:
Some birdsSu are irritablePu
Reducing a DARAPTI
sub-sub (3rd Figure)
dAr: All turkeysMd are irritablePu
Apt: All turkeysMd are birdsSu
I:
Some birdsSu are irritablePu
33
Reducing a DARAPTI
sub-sub (3rd Figure)
dAr: All turkeysMd are irritablePu
Apt: All turkeysMd are birdsSu
I:
Some birdsSu are irritablePu
Reducing a DARAPTI
sub-sub (3rd Figure)
dAr: All turkeysMd are irritablePu
Apt: All turkeysMd are birdsSu
I:
Some birdsSu are irritablePu
34
Reducing a DARAPTI
sub-sub (3rd Figure)
dAr: All turkeysMd are irritablePu
Apt: All turkeysMd are birdsSu
I:
Some birdsSu are irritablePu
Reducing a DARAPTI
dAr: All turkeysMd are irritablePu
Apt: All birdsSu are turkeysMd
tI:
Some birdsSu are irritablePu
35
Reducing a DARAPTI
dAr: All turkeysMd are irritablePu
Apt: All birdsSu are turkeysMd
I:
Some birdsSu are irritablePu
Reducing a DARAPTI
dAr: All turkeysMd are irritablePu
Apt: Some birdsSu are turkeysMd
I:
Some birdsSu are irritablePu
36
Reduction to DARII
sub-prae (1st Figure)
dAr: All turkeysMd are irritablePu
I:
Some birdsSu are turkeysMd
I:
Some birdsSu are irritablePu
Reduction to DARII
sub-prae (1st Figure)
dAr: All turkeysMd are irritablePu
I:
Some birdsSu are turkeysMd
I:
Some birdsSu are irritablePu
37
Reduction of Syllogisms
What is Reduction?
Two Methods of Reduction
How to Use the Mnemonic Verse
Four Operations for Reduction
Review of Conversion
Reduction Involving Conversion
Review of Partial Conversion
Reduction Using Partial Conversion
Reduction Involving Multiple Steps
Review
Sample Exercises
How to Reduce Using
Multiple Steps
What if there is more than one
reduction operation indicated by a
syllogism name?
38
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
39
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOque
prioris;
CESARE, CAMESTRES, FESTINO, BAROCO
secundae;
Tertia; DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP,
CAMENES, DIMARIS, FESAPO, FRESISON
Example of a syllogism
requiring multiple step
reduction
sub-sub (3rd Figure)
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is:
Some animalsSu are extinctPu
40
Example of a syllogism
requiring multiple step
reduction
sub-sub (3rd Figure)
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is:
Some animalsSu are extinctPu
Example of a syllogism
requiring multiple step
reduction
sub-sub (3rd Figure)
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is:
Some animalsSu are extinctPu
41
Example of a syllogism
requiring multiple step
reduction
sub-sub (3rd Figure)
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is:
Some animalsSu are extinctPu
How to Reduce Using
Multiple Steps
Perform the reduction operations in the
order in which they are indicated by
the syllogism name
42
Reducing a DISAMIS
sub-sub (3rd Figure)
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is:
Some animalsSu are extinctPu
Reducing a DISAMIS
sub-sub (3rd Figure)
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is:
Some animalsSu are extinctPu
43
Reducing a DISAMIS
sub-sub (3rd Figure)
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is:
Some animalsSu are extinctPu
Reducing a DISAMIS
sub-sub (3rd Figure)
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is:
Some animalsSu are extinctPu
44
Reducing a DISAMIS
dIs: Some extinct thingsPu are birdsMu
Am: All birdsMd are animalsSu
Is:
Some animalsSu are extinctPu
Reducing a DISAMIS
dIs: Some extinct thingsPu are birdsMu
Am: All birdsMd are animalsSu
Is:
Some animalsSu are extinctPu
45
Reducing a DISAMIS
dIs: Some extinct thingsPu are birdsMu
Am: All birdsMd are animalsSu
Is:
Some animalsSu are extinctPu
Reducing a DISAMIS
dAr: All birdsMd are animalsSu
Im: Some extinct thingsPu are birdsMu
Is:
Some animalsSu are extinctPu
46
Reducing a DISAMIS
dAr: All birdsMd are animalsSu
I:
Some extinct thingsPu are birdsMu
Is:
Some animalsSu are extinctPu
Reducing a DISAMIS
dAr: All birdsMd are animalsSu
I:
Some extinct thingsPu are birdsMu
Is:
Some animalsSu are extinctPu
47
Reducing a DISAMIS
dAr: All birdsMd are animalsSu
I:
Some extinct thingsPu are birdsMu
Is:
Some animalsSu are extinctPu
Reducing to a DARII
dAr: All birdsMd are animalsPu
I:
Some extinct thingsSu are birdsMu
I:
Some extinct thingsSu are animalsPu
48
Reducing to a DARII
sub-prae (1st Figure)
dAr: All birdsMd are animalsPu
I:
Some extinct thingsSu are birdsMu
I:
Some extinct thingsSu are animalsPu
Reducing to a DARII
sub-prae (1st Figure)
dAr: All birdsMd are animalsPu
I:
Some extinct thingsSu are birdsMu
I:
Some extinct thingsSu are animalsPu
49
Reduction of Syllogisms
What is Reduction?
Two Methods of Reduction
How to Use the Mnemonic Verse
Four Operations for Reduction
Review of Conversion
Reduction Involving Conversion
Review of Partial Conversion
Reduction Using Partial Conversion
Reduction Involving Multiple Steps
Review
Sample Exercises
Review
Two Methods of Reduction
Four Operations of Reduction
Reduction Involving a Single Step
Reduction Involving Multiple Steps
50
Review
Two Methods of Reduction
Four Operations of Reduction
Reduction Involving a Single Step
Reduction Involving Multiple Steps
Review
Two Methods of Reduction
Four Operations of Reduction
Reduction Involving a Single Step
Reduction Involving Multiple Steps
51
Review
Two Methods of Reduction
Four Operations of Reduction
Reduction Involving a Single Step
Reduction Involving Multiple Steps
Review
Two Methods of Reduction
Four Operations of Reduction
Reduction Involving a Single Step
Reduction Involving Multiple Steps
52
Reduction of Syllogisms
What is Reduction?
Two Methods of Reduction
How to Use the Mnemonic Verse
Four Operations for Reduction
Review of Conversion
Reduction Involving Conversion
Review of Partial Conversion
Reduction Using Partial Conversion
Reduction Involving Multiple Steps
Review
Sample Exercises
Exercise 4
Why would logicians want to
transform syllogisms in the other
three figures to syllogisms in the
First Figure?
53
Exercise 4
Why would logicians want to
transform syllogisms in the other
three figures to syllogisms in the
First Figure?
First Figure syllogisms are more
straightforward than syllogisms in
other figures. In addition, the
process of reducing syllogisms helps
you to understand syllogisms better.
Exercise 15
To which syllogism in the First
Figure does FESTINO reduce?
54
Exercise 15
To which syllogism in the First
Figure does FESTINO reduce?
FESTINO reduces to FERIO.
Exercise 19
Explain what the consonants S, P, M
and C indicate when they are
found after the initial letters in the
syllogism names?
55
Exercise 19
Explain what the consonants S, P,
M and C indicate when they are
found after the initial letters in
the syllogism names?
These letters indicate which
procedure must be used to
change the proposition indicated
by the preceding vowel.
Exercise 22
Reduce the following syllogism to the
First Figure by following the
procedures indicated:
Some saints are philosophers
All philosophers are men
Some men are saints
56
Exercise 22
What figure is the syllogism in?
Some saints are philosophers
All philosophers are men
Some men are saints
Prae-prae (4th Figure)
Exercise 22
What mood is the syllogism in?
I: Some saints are philosophers
A:
All philosophers are men
I:
Some men are saints
The IAI mood
57
Exercise 22
What mood is the syllogism in?
dIm: Some saints are philosophers
Ar: All philosophers are men
Is:
Some men are saints
The IAI mood
Exercise 22
Which consonant (or consonants) tells
you how to reduce to the First
Figure?
dIm: Some saintsPu are philosophersMu
Ar:
All philosophersMd are menSu
Is:
Some menSu are saintsPu
58
Exercise 22
Which consonant (or consonants)
tells you how to reduce to the
First Figure?
dIm: Some saintsPu are philosophersMu
Ar: All philosophersMd are menSu
Is: Some menSu are saintsPu
Exercise 22
Rules for Reduction
S: Simple conversion of the proposition signified by
the preceding vowel
P: Per accidens, or partial conversion of the
proposition signified by the preceding vowel
M: Mutatio, or transposition of the premises; make
the minor premise the major, and the major the
minor
C: Reduction by contradiction. This is the indirect
method of reduction through (rather than to)
BARBARA. It is signified by a non-initial c and is
applied only to BAROCO AND BOCARDO
59
Exercise 22
Reduce the following syllogism to
the First Figure by following the
procedures indicated:
dIm: Some saintsPu are philosophersMu
Ar: All philosophersMd are menSu
Is: Some menSu are saintsPu
Exercise 22
Reduce the following syllogism to
the First Figure by following the
procedures indicated:
dIm: Some saintsPu are philosophersMu
Ar: All philosophersMd are menSu
Is: Some menSu are saintsPu
60
Exercise 22
Reduce the following syllogism to
the First Figure by following the
procedures indicated:
dAr: All philosophersMd are menSu
I:
Some saintsPu are philosophersMu
Is: Some menSu are saintsPu
Exercise 22
Reduce the following syllogism to
the First Figure by following the
procedures indicated:
dAr: All philosophersMd are menSu
I:
Some saintsPu are philosophersMu
Is: Some menSu are saintsPu
61
Exercise 22
Reduce the following syllogism to
the First Figure by following the
procedures indicated:
dAr: All philosophersMd are menSu
I:
Some saintsPu are philosophersMu
Is: Some menSu are saintsPu
Exercise 22
Reduce the following syllogism to
the First Figure by following the
procedures indicated: Write the
syllogism after it has been
reduced to the First Figure:
dAr: All philosophersMd are menPu
I:
Some saintsSu are philosophersMu
I:
Some saintsSu are menPu
62
Exercise 22
Write the syllogism after it has been
reduced to the First Figure:
dAr: All philosophersMd are menPu
I:
Some saintsSu are philosophersMu
I:
Some saintsSu are menPu
Exercise 22
What mood is the syllogism now in
(give the name)
dAr: All philosophersMd are menPu
I:
Some saintsSu are philosophersMu
I:
Some saintsSu are menPu
The syllogism is now a DARII
63
Exercise 22
Reduce the following syllogism to
the First Figure by following the
procedures indicated:
dAr: All philosophersMd are menPu
I:
Some saintsSu are philosophersMu
I:
Some saintsSu are menPu
Traditional Logic II
Martin Cothran
Instructor
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