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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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)

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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)

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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

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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

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Review of Conversion

Simple ConversionObversion

Contraposition

Simple Conversion

Switch the subject and the predicate

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Simple Conversion

No robins are sparrows

Simple Conversion

No sparrows are robins

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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

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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

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

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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)

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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

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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

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Partial Conversion

All robins are birds

Partial Conversion

All birds are robins

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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

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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)

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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)

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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

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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

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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)

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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?

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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

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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)

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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)

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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

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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)

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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)

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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

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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

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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

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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

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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)

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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