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1
Traditional Logic II
Martin Cothran
Instructor
Reduction of SyllogismsWhat is Reduction?
Two Methods of ReductionHow to Use the Mnemonic VerseFour Operations for Reduction
Review of ConversionReduction Involving Conversion
Review of Partial ConversionReduction Using Partial ConversionReduction Involving Multiple Steps
ReviewSample Exercises
2
Reduction of SyllogismsWhat is Reduction?
Two Methods of ReductionHow to Use the Mnemonic VerseFour Operations for Reduction
Review of ConversionReduction Involving Conversion
Review of Partial ConversionReduction Using Partial ConversionReduction Involving Multiple Steps
ReviewSample 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
3
Two Reasons to Reduce Syllogisms:
First Figure syllogisms are more straightforward than syllogisms in
other figuresReducing 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 figuresReducing syllogisms to the First Figure will help you understand
syllogisms better
4
Two Reasons to Reduce Syllogisms:
First Figure syllogisms are more straightforward than syllogisms in
other figuresReducing syllogisms to the First Figure will help you understand
syllogisms better
Reduction of SyllogismsWhat is Reduction?
Two Methods of ReductionHow to Use the Mnemonic VerseFour Operations for Reduction
Review of ConversionReduction Involving Conversion
Review of Partial ConversionReduction Using Partial ConversionReduction Involving Multiple Steps
ReviewSample Exercises
5
Two Methods for Reducing Syllogisms
Direct Reduction
Indirect Reduction
Two Methods for Reducing Syllogisms
Direct Reduction
Indirect Reduction
6
Two Methods for Reducing Syllogisms
Direct Reduction
Indirect Reduction
Reduction of SyllogismsWhat is Reduction?
Two Methods of ReductionHow to Use the Mnemonic VerseFour Operations for Reduction
Review of ConversionReduction Involving Conversion
Review of Partial ConversionReduction Using Partial ConversionReduction Involving Multiple Steps
ReviewSample Exercises
7
BARBARA, CELARENT, DARII, FERIOqueprioris;
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, FERIOqueprioris;
CESARE, CAMESTRES, FESTINO, BAROCOsecundae;
Tertia; DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
8
What the Consonants Mean
The first consonant in each name indicates the syllogism in the 1st
Figure to which it reduces
BARBARA, CELARENT, DARII, FERIOqueprioris;
CESARE, CAMESTRES, FESTINO, BAROCO secundae;
Tertia; DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
9
BARBARA, CELARENT, DARII, FERIOqueprioris;
CESARE, CAMESTRES, FESTINO, BAROCOsecundae;
Tertia; DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
BARBARA, CELARENT, DARII, FERIOqueprioris;
CESARE, CAMESTRES, FESTINO, BAROCO secundae;
Tertia; DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
10
BARBARA, CELARENT, DARII, FERIOqueprioris;
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, FERIOqueprioris;
CESARE, CAMESTRES, FESTINO, BAROCO secundae;
Tertia; DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
11
An Example
All chickensPd are birdsMu
No horseSd is a birdMd
No horseSd is a chickenPd
BARBARA, CELARENT, DARII, FERIOqueprioris;
CESARE, CAMESTRES, FESTINO, BAROCO secundae;
Tertia; DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
12
BARBARA, CELARENT, DARII, FERIOqueprioris;
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, FERIOqueprioris;
CESARE, CAMESTRES, FESTINO, BAROCO secundae;
Tertia; DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
13
BARBARA, CELARENT, DARII, FERIOqueprioris;
CESARE, CAMESTRES, FESTINO, BAROCO secundae;
Tertia; DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
An Example
cAm: All chickensPd are birdsMu
Est: No horseSd is a birdMd
rEs: No horseSd is a chickenPd
14
BARBARA, CELARENT, DARII, FERIOqueprioris;
CESARE, CAMESTRES, FESTINO, BAROCO secundae;
Tertia; DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
An Example
cEl: No birdMd is a horsePd
Ar: All chickensSd are birdsMu
Ent: No chickenSd is a horsePd
15
Reduction of SyllogismsWhat is Reduction?
Two Methods of ReductionHow to Use the Mnemonic VerseFour Operations for Reduction
Review of ConversionReduction Involving Conversion
Review of Partial ConversionReduction Using Partial ConversionReduction Involving Multiple Steps
ReviewSample Exercises
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
16
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
Rules for Reduction
17
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
Rules for Reduction
18
BARBARA, CELARENT, DARII, FERIOqueprioris;
CESARE, CAMESTRES, FESTINO, BAROCO secundae;
Tertia; DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
Reducing a CESARE
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E: No whaleSd is a fishPd
19
Reducing a CESARE
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E: No whaleSd is a fishPd
prae-prae (2nd Figure)
Reducing a CESARE
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E: No whaleSd is a fishPd
prae-prae (2nd Figure)
20
Reducing a CESARE
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E: No whaleSd is a fishPd
prae-prae (2nd Figure)
Reducing a CESARE
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E: No whaleSd is a fishPd
prae-prae (2nd Figure)
21
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
Rules for Reduction
22
Reduction of SyllogismsWhat is Reduction?
Two Methods of ReductionHow to Use the Mnemonic VerseFour Operations for Reduction
Review of ConversionReduction Involving Conversion
Review of Partial ConversionReduction Using Partial ConversionReduction Involving Multiple Steps
ReviewSample Exercises
Review of Conversion
Simple ConversionObversion
Contraposition
23
Review of Conversion
Simple ConversionObversion
Contraposition
Simple Conversion
Switch the subject and the predicate
24
Simple Conversion
No robins are sparrows
Simple Conversion
No sparrows are robins
25
Reduction of SyllogismsWhat is Reduction?
Two Methods of ReductionHow to Use the Mnemonic VerseFour Operations for Reduction
Review of ConversionReduction Involving Conversion
Review of Partial ConversionReduction Using Partial ConversionReduction Involving Multiple Steps
ReviewSample Exercises
Simple Conversion of CESARE
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E: No whaleSd is a fishPd
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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
27
Simple Conversion of CESARE
cEs: No fishPd is a mammalMd
Ar: All whalesSd are mammalsMu
E: No whaleSd is a fishPd
prae-prae (2nd Figure)
Simple Conversion of CESARE
cEs: No mammalMd is a fishPd
Ar: All whalesSd are mammalsMu
E: No whaleSd is a fishPd
28
Resulting in a CELARENT
cEl: No mammalMd is a fishPd
Ar: All whalesSd are mammalsMu
Ent: No whaleSd is a fishPd
sub-prae (1st Figure)
Resulting in a CELARENT
cEl: No mammalMd is a fishPd
Ar: All whalesSd are mammalsMu
Ent: No whaleSd is a fishPd
sub-prae (1st Figure)
29
BARBARA, CELARENT, DARII, FERIOqueprioris;
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
The Mnemonic Verse
30
Reduction of SyllogismsWhat is Reduction?
Two Methods of ReductionHow to Use the Mnemonic VerseFour Operations for Reduction
Review of ConversionReduction Involving Conversion
Review of Partial ConversionReduction Using Partial ConversionReduction Involving Multiple Steps
ReviewSample Exercises
Review of Partial Conversion
Partial conversion is accomplished by interchanging the subject and predicate of an A statement and
changing its quantity
31
Partial Conversion
All robins are birds
Partial Conversion
All birds are robins
32
Partial Conversion
Some birds are robins
Reduction of SyllogismsWhat is Reduction?
Two Methods of ReductionHow to Use the Mnemonic VerseFour Operations for Reduction
Review of ConversionReduction Involving Conversion
Review of Partial ConversionReduction Using Partial ConversionReduction Involving Multiple Steps
ReviewSample Exercises
33
Reducing a DARAPTI
dAr: All turkeysMd are irritablePu
Apt: All turkeysMd are birdsSu
I: Some birdsSu are irritablePu
sub-sub (3rd Figure)
Reducing a DARAPTI
dAr: All turkeysMd are irritablePu
Apt: All turkeysMd are birdsSu
I: Some birdsSu are irritablePu
sub-sub (3rd Figure)
34
Reducing a DARAPTI
dAr: All turkeysMd are irritablePu
Apt: All turkeysMd are birdsSu
I: Some birdsSu are irritablePu
sub-sub (3rd Figure)
Reducing a DARAPTI
dAr: All turkeysMd are irritablePu
Apt: All turkeysMd are birdsSu
I: Some birdsSu are irritablePu
sub-sub (3rd Figure)
35
Reducing a DARAPTI
dAr: All turkeysMd are irritablePu
Apt: All turkeysMd are birdsSu
I: Some birdsSu are irritablePu
sub-sub (3rd Figure)
Reducing a DARAPTI
dAr: All turkeysMd are irritablePu
Apt: All birdsSu are turkeysMd
tI: Some birdsSu are irritablePu
36
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
37
Reduction to DARII
dAr: All turkeysMd are irritablePu
I: Some birdsSu are turkeysMd
I: Some birdsSu are irritablePu
sub-prae (1st Figure)
Reduction to DARII
dAr: All turkeysMd are irritablePu
I: Some birdsSu are turkeysMd
I: Some birdsSu are irritablePu
sub-prae (1st Figure)
38
Reduction of SyllogismsWhat is Reduction?
Two Methods of ReductionHow to Use the Mnemonic VerseFour Operations for Reduction
Review of ConversionReduction Involving Conversion
Review of Partial ConversionReduction Using Partial ConversionReduction Involving Multiple Steps
ReviewSample Exercises
How to Reduce Using Multiple Steps
What if there is more than one reduction operation indicated by a
syllogism name?
39
BARBARA, CELARENT, DARII, FERIOqueprioris;
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, FERIOqueprioris;
CESARE, CAMESTRES, FESTINO, BAROCO secundae;
Tertia; DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
40
BARBARA, CELARENT, DARII, FERIOqueprioris;
CESARE, CAMESTRES, FESTINO, BAROCO secundae;
Tertia; DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
Example of a syllogism requiring multiple step
reduction
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is: Some animalsSu are extinctPu
sub-sub (3rd Figure)
41
Example of a syllogism requiring multiple step
reduction
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is: Some animalsSu are extinctPu
sub-sub (3rd Figure)
Example of a syllogism requiring multiple step
reduction
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is: Some animalsSu are extinctPu
sub-sub (3rd Figure)
42
Example of a syllogism requiring multiple step
reduction
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is: Some animalsSu are extinctPu
sub-sub (3rd Figure)
How to Reduce Using Multiple Steps
Perform the reduction operations in the order in which they are indicated by
the syllogism name
43
Reducing a DISAMIS
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is: Some animalsSu are extinctPu
sub-sub (3rd Figure)
Reducing a DISAMIS
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is: Some animalsSu are extinctPu
sub-sub (3rd Figure)
44
Reducing a DISAMIS
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is: Some animalsSu are extinctPu
sub-sub (3rd Figure)
Reducing a DISAMIS
dIs: Some birdsMu are extinctPu
Am: All birdsMd are animalsSu
Is: Some animalsSu are extinctPu
sub-sub (3rd Figure)
45
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
46
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
47
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
48
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
49
Reducing to a DARII
dAr: All birdsMd are animalsPu
I: Some extinct thingsSu are birdsMu
I: Some extinct thingsSu are animalsPu
sub-prae (1st Figure)
Reducing to a DARII
dAr: All birdsMd are animalsPu
I: Some extinct thingsSu are birdsMu
I: Some extinct thingsSu are animalsPu
sub-prae (1st Figure)
50
Reduction of SyllogismsWhat is Reduction?
Two Methods of ReductionHow to Use the Mnemonic VerseFour Operations for Reduction
Review of ConversionReduction Involving Conversion
Review of Partial ConversionReduction Using Partial ConversionReduction Involving Multiple Steps
ReviewSample Exercises
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
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
53
Reduction of SyllogismsWhat is Reduction?
Two Methods of ReductionHow to Use the Mnemonic VerseFour Operations for Reduction
Review of ConversionReduction Involving Conversion
Review of Partial ConversionReduction Using Partial ConversionReduction Involving Multiple Steps
ReviewSample Exercises
Why would logicians want to transform syllogisms in the other three figures to syllogisms in the
First Figure?
Exercise 4
54
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 4
To which syllogism in the First Figure does FESTINO reduce?
Exercise 15
55
To which syllogism in the First Figure does FESTINO reduce?
FESTINO reduces to FERIO.
Exercise 15
Explain what the consonants S, P, Mand C indicate when they are
found after the initial letters in the syllogism names?
Exercise 19
56
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 19
Reduce the following syllogism to the First Figure by following the
procedures indicated:
Some saints are philosophersAll philosophers are men
Some men are saints
Exercise 22
57
What figure is the syllogism in?
Some saints are philosophersAll philosophers are men
Some men are saints
Prae-prae (4th Figure)
Exercise 22
What mood is the syllogism in?
I: Some saints are philosophersA: All philosophers are menI: Some men are saints
The IAI mood
Exercise 22
58
What mood is the syllogism in?
dIm: Some saints are philosophersAr: All philosophers are menIs: 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
Exercise 22
59
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
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
Exercise 22
60
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
Exercise 22
61
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
Exercise 22
62
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
Exercise 22
63
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
Exercise 22
64
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
Exercise 22
Traditional Logic II
Martin Cothran
Instructor
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