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Traditional Logic II
Martin Cothran
Instructor
Indirect Reduction of Syllogisms
Review of ReductionExplanation of Indirect ReductionIndirect Reduction of BAROCOThe Three Steps of Reduction
A Review of Contradictory StatementsIndirect Reduction of BOCARDO
The Three Steps for Reducing a BOCARDO Review of Chapter
2
Reduction of Syllogisms
Review of ReductionExplanation of Indirect ReductionIndirect Reduction of BAROCOThe Three Steps of Reduction
A Review of Contradictory StatementsIndirect Reduction of BOCARDO
The Three Steps for Reducing a BOCARDO Review of Chapter
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 Methods for Reducing Syllogisms
Direct Reduction
Indirect Reduction
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
4
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
5
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
6
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
7
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, BAROCOsecundae;
Tertia; DARAPTI, DISAMIS, DATISI, FELAPTON, BOCARDO, FERISON habet;
Quarta insuper addit; BRAMANTIP, CAMENES, DIMARIS, FESAPO, FRESISON
The Mnemonic Verse
8
Reduction of Syllogisms
Review of ReductionExplanation of Indirect ReductionIndirect Reduction of BAROCOThe Three steps of Reduction
A Review of Contradictory StatementsIndirect Reduction of BOCARDO
The Three Steps for Reducing a BOCARDOReview of Chapter
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
9
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
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
What is Indirect Reduction?
Indirect reduction is the process of showing that an argument form
is valid by showing that it is impossible for it to be invalid
What does this mean?
A syllogism is either valid or invalid. If it is not invalid, then it
must be valid.
11
The Principle Behind Indirect Reduction
In a valid syllogism, if the conclusion is false, then at least one of the
premises must be false
An Example of the Principle
All plants are animalsThe daisy is a plant
The daisy is an animal
12
An Example of the Principle
All plants are animalsThe daisy is a plant
The daisy is an animal
sub-prae (1st Figure)
An Example of the Principle
All plants are animalsThe daisy is a plant
The daisy is an animal
sub-prae (1st Figure)
A:A:A:
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
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
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
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
15
An Example of the Principle
All plants are animalsThe daisy is a plant
The daisy is an animal
BARBARA
An Example of the Principle
All plants are animalsThe daisy is a plant
The daisy is an animal
BARBARA
16
The Principle Behind Indirect Reduction
In a valid syllogism, if the conclusion is false, then at least one of the
premises must be false
An Example of the Principle
All plants are animalsThe daisy is a plant
The daisy is an animal
BARBARA
17
An Example of the Principle
All plants are animalsThe daisy is a plant
The daisy is an animal
BARBARA
An Example of the Principle
All plants are animalsThe daisy is a plant
The daisy is an animal
BARBARA
18
Indirect Reduction of BAROCO
All collies are dogsSome animals are not dogsSome animals are not collies
Indirect Reduction of BAROCO
All collies are dogsSome animals are not dogsSome animals are not collies
19
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
20
Indirect Reduction of BAROCO
All collies are dogsSome animals are not dogsSome animals are not collies
A:O:O:
prae-prae (2nd Figure)
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
21
Indirect Reduction of BAROCO
All collies are dogsSome animals are not dogsSome animals are not collies
BAROCO
The Principle
In a valid syllogism, if the conclusion is false, then at least one of the
premises must be false
22
The PrincipleApplied
If the syllogism is valid, then when we deny the conclusion we should end up with a
denial of one of the premises.
Indirect Reduction of Syllogisms
Review of ReductionExplanation of Indirect ReductionIndirect Reduction of BAROCO
The Three Steps for Reducing a BAROCOA Review of Contradictory Statements
Indirect Reduction of BOCARDO The Three Steps for Reducing a BOCARDO
Review of Chapter
23
The Three Steps for Reducing a BAROCO
STEP #1: Retain the original major premise
STEP #2: Use the contradiction of the original conclusion as the new minor
premiseSTEP #3: Derive the new conclusion, which, if the original syllogism is valid,
should be the contradiction of the original minor premise
The Three Steps for Reducing a BAROCO
STEP #1: Retain the original major premise
STEP #2: Use the contradiction of the original conclusion as the new minor
premiseSTEP #3: Derive the new conclusion, which, if the original syllogism is valid,
should be the contradiction of the original minor premise
24
The Three Steps for Reducing a BAROCO
STEP #1: Retain the original major premise
STEP #2: Use the contradiction of the original conclusion as the new minor
premiseSTEP #3: Derive the new conclusion,
which, if the original syllogism is valid, should be the contradiction of the original
minor premise
The Three Steps for Reducing a BAROCO
STEP #1: Retain the original major premise
STEP #2: Use the contradiction of the original conclusion as the new minor
premiseSTEP #3: Derive the new conclusion,
which, if the original syllogism is valid, should be the contradiction of the original
minor premise
25
Indirect Reduction of BAROCO
All collies are dogsSome animals are not dogsSome animals are not collies
BAROCO
Indirect Reduction of BAROCO
All collies are dogsSome animals are not dogsSome animals are not collies
BAROCO
26
Indirect Reduction of BAROCO
All collies are dogsSome animals are not dogsSome animals are not collies
BAROCO
Indirect Reduction of BAROCO
All collies are dogsSome animals are not dogsSome animals are not collies
BAROCO
27
The Three Steps of Indirect Reduction
Retain the original major premiseUse the contradiction of the original
conclusion as the new minor premiseDerive the new conclusion, which, if
the original syllogism is valid, should be the contradiction of the original
minor premise
Four Kinds of Opposition
ContradictoryContrary
SubcontrarySubaltern
28
Four Kinds of Opposition
ContradictoryContrary
SubcontrarySubaltern
Rule of Contradiction
Contradictory statements are statements that differ in both
quality and quantity.
29
Quantity and Quality of the Four Categorical Statements
Quality
Affirmative Negative
Universal A E
Quantity
Particular I O
The First Law of Opposition
Contradictories cannot at the same time be true nor at the
same time false.
30
Quantity and Quality of the Four Categorical Statements
Quality
Affirmative Negative
Universal A E
Quantity
Particular I O
Contradictory Statements
A: All men are mortalO: Some men are not
mortal
31
Quantity and Quality of the Four Categorical Statements
Quality
Affirmative Negative
Universal A E
Quantity
Particular I O
Contradictory Statements
E: No men are godsI: Some men are gods
32
The Three Steps of Indirect Reduction
Retain the original major premiseUse the contradiction of the original
conclusion as the new minor premiseDerive the new conclusion, which, if
the original syllogism is valid, should be the contradiction of the original
minor premise
Indirect Reduction of BAROCO
All collies are dogsSome animals are not dogsSome animals are not collies
BAROCO
33
What statement is the contradictory of this
statement?
Some animals are not collies
We first change the quantity
Some animals are not collies
No animals are collies
FROM:
34
We first change the quantity
Some animals are not collies
No animals are colliesTO:
We then change the quality
No animals are collies
All animals are collies
FROM:
35
We then change the quality
No animals are collies
All animals are colliesTO:
Indirect Reduction of BAROCO
All collies are dogsSome animals are not dogsSome animals are not collies
BAROCO
36
Indirect Reduction of BAROCO
All collies are dogsAll animals are collies
Some animals are not collies
The Three Steps of Indirect Reduction
Retain the original major premiseUse the contradiction of the original
conclusion as the new minor premiseDerive the new conclusion, which, if
the original syllogism is valid, should be the contradiction of the original
minor premise
37
Indirect Reduction of BAROCO
All collies are dogsAll animals are collies
?
Indirect Reduction of BAROCO
All collies are dogsAll animals are colliesAll animals are dogs
38
The PrincipleApplied
If the syllogism is valid, then when we deny the conclusion we should end up with a
denial of one of the premises.
Indirect Reduction of BAROCO
All collies are dogsSome animals are not dogsSome animals are not collies
BAROCO
39
Indirect Reduction of BAROCO
All collies are dogsAll animals are colliesAll animals are dogs
The Three Steps of Indirect Reduction
Retain the original major premiseUse the contradiction of the original
conclusion as the new minor premiseDerive the new conclusion, which, if
the original syllogism is valid, should be the contradiction of the original
minor premise
40
Is the new conclusion contradictory to the original
minor premise?
All animals are dogs
Some animals are not dogs
Is the new conclusion contradictory to the original
minor premise?
All animals are dogs
Some animals are not dogs
A:
O:
41
Indirect Reduction of BAROCO
O: Some animals are not dogsvs.
A: All animals are dogs
Indirect Reduction of BAROCO
All collies are dogsAll animals are colliesAll animals are dogs
BARBARA
42
Reduction of Syllogisms
Review of ReductionExplanation of Indirect ReductionIndirect Reduction of BAROCOThe Three Steps of Reduction
A Review of Contradictory StatementsIndirect Reduction of BOCARDO
Review of Chapter
Indirect Reduction of BOCARDO
Some dogs are not collies All dogs are animals
Some animals are not collies
43
Indirect Reduction of BOCARDO
Some dogs are not collies All dogs are animals
Some animals are not collies
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
44
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
Indirect Reduction of BOCARDO
Some dogs are not collies All dogs are animals
Some animals are not collies
O:A:O:
45
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
Indirect Reduction of BOCARDO
Some dogs are not collies All dogs are animals
Some animals are not collies
BOCARDO
46
The Principle
In a valid syllogism, if the conclusion is false, then at least one of the
premises must be false
The PrincipleApplied
If the syllogism is valid, then when we deny the conclusion we should end up with a
denial of one of the premises.
47
Reduction of Syllogisms
Review of ReductionExplanation of Indirect ReductionIndirect Reduction of BAROCOThe Three Steps of Reduction
A Review of Contradictory StatementsIndirect Reduction of BOCARDO
The Three Steps of ReductionReview of Chapter
The Three Steps for Reducinga BOCARDO
Retain the original minor premiseUse the contradiction of the original
conclusion as the new major premiseDerive the new conclusion, which, if
the original syllogism is valid, should be the contradiction of the original
major premise
48
The Three Steps for Reducinga BOCARDO
Retain the original minor premiseUse the contradiction of the original
conclusion as the new major premiseDerive the new conclusion, which, if
the original syllogism is valid, should be the contradiction of the original
major premise
Indirect Reduction of BOCARDO
Some dogs are not collies All dogs are animals
Some animals are not collies
BOCARDO
49
Indirect Reduction of BOCARDO
Some dogs are not collies All dogs are animals
Some animals are not collies
BOCARDO
Indirect Reduction of BOCARDO
Some dogs are not collies All dogs are animals
Some animals are not collies
BOCARDO
50
Indirect Reduction of BOCARDO
Some dogs are not collies All dogs are animals
Some animals are not collies
BOCARDO
The Three Steps of Indirect Reduction
Retain the original minor premiseUse the contradiction of the original
conclusion as the new major premiseDerive the new conclusion, which, if
the original syllogism is valid, should be the contradiction of the original
major premise
51
Indirect Reduction of BOCARDO
Some dogs are not collies All dogs are animals
Some animals are not collies
BOCARDO
What statement is the contradictory of this
statement?
Some animals are not collies
52
We first change the quantity
Some animals are not collies
No animals are collies
FROM:
We first change the quantity
Some animals are not collies
No animals are colliesTO:
53
We then change the quality
No animals are collies
All animals are collies
FROM:
We then change the quality
No animals are collies
All animals are colliesTO:
54
Indirect Reduction of BOCARDO
Some dogs are not collies All dogs are animalsAll animals are collies
Indirect Reduction of BOCARDO
All animals are colliesAll dogs are animalsAll animals are collies
55
The Three Steps of Indirect Reduction
Retain the original minor premiseUse the contradiction of the original
conclusion as the new major premiseDerive the new conclusion, which, if
the original syllogism is valid, should be the contradiction of the original
major premise
Indirect Reduction of BOCARDO
All animalsM are colliesP
All dogsS are animalsM
?
56
Indirect Reduction of BOCARDO
All animalsM are colliesP
All dogsS are animalsM
All dogsS are __________P
BARBARA
Indirect Reduction of BOCARDO
All animalsM are colliesP
All dogsS are animalsM
All dogsS are colliesP
BARBARA
57
The Three Steps of Indirect Reduction
Retain the original major premiseUse the contradiction of the original
conclusion as the new minor premiseDerive the new conclusion, which, if
the original syllogism is valid, should be the contradiction of the original
minor premise
Is the new conclusion contradictory to the original
minor premise?
All dogs are collies
Some dogs are not collies
58
Is the new conclusion contradictory to the original
minor premise?
All dogs are collies
Some dogs are not collies
A:
O:
All dogs are collies
Some dogs are not collies
A:
O:
Is the new conclusion contradictory to the original
minor premise?
59
The Three Steps of Indirect Reduction
Retain the original major premiseUse the contradiction of the original
conclusion as the new minor premiseDerive the new conclusion, which, if
the original syllogism is valid, should be the contradiction of the original
minor premise
Indirect Reduction of BOCARDO
All animals are colliesAll dogs are animalsAll dogs are collies
BARBARA
60
Reduction of Syllogisms
Review of ReductionExplanation of Indirect ReductionIndirect Reduction of BAROCOThe Three Steps of Reduction
A Review of Contradictory StatementsIndirect Reduction of BOCARDO
Review of Chapter
Indirect ReductionIndirect Reduction (IR) shows the validity of syllogisms
by showing that it is impossible for it to be invalid.
IR of BAROCO involves keeping the original majorpremise and replacing the minor premise with the
contradiction of the conclusion, which should yield the contradiction of the original minor premise.
IR of BOCARDO involves keeping the original minorpremise and replacing the major premise with the
contradiction of the conclusion, which should yield the contradiction of the original major premise.
61
Review of Exercises
How to create a syllogism
A review of Direct Reduction
Exercises 25-43
Creating your own syllogisms
62
Creating a Syllogism
Step #1: Construct your conclusion 1st. Step #2: Provide the correct quantifiers for the premises.Step #3: Determine the location of the middle terms.Step #4: Identify major & minor terms.Step #5: Fill in the middle terms.
Exercises 26
Creating your own CELARENT
63
Creating a Syllogism
Step #1: Construct your conclusion 1st.Step #2: Provide the correct quantifiers for the premises.Step #3: Determine the location of the middle terms.Step #4: Identify major & minor terms.Step #5: Fill in the middle terms.
Step #1: Begin with a Conclusion
Make sure it is the correct quantity and quality
65
Step #1: Begin with a Conclusion
No _________ is a ____________
Step #1: Begin with a Conclusion
No _________ is a ____________
66
Step #1: Begin with a Conclusion
No _________ is ____________
Step #1: Begin with a Conclusion
No _________ is ____________
67
Step #1: Begin with a Conclusion
No Sneetch is a Lorax
Step #1: Begin with a Conclusion
No Sneetch is a Lorax
68
Creating a Syllogism
Step #1: Construct your conclusion 1st. Step #2: Provide the correct quantifiers for the premises.Step #3: Determine the location of the middle terms.Step #4: Identify major & minor terms.Step #5: Fill in the middle terms.
Exercises 26
Creating your own CELARENT
70
Exercises 26
Creating your own CELARENT
Step #2: Provide Correct Quantifiers for Premises
No ________ is ____________All ________ is ____________
No Sneetch is a Lorax
71
Creating a Syllogism
Step #1: Construct your conclusion 1st. Step #2: Provide the correct quantifiers for the premises.Step #3: Determine the location of the middle terms.Step #4: Identify major & minor terms.Step #5: Fill in the middle terms.
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
72
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
Step #3: Determine Location of Middle Terms
No ________ is ____________All ________ is ____________
No Sneetch is a Lorax
73
Step #3: Determine Location of Middle Terms
No ________M is ____________All ________ is ____________
No Sneetch is a Lorax
Step #3: Determine Location of Middle Terms
No ________M is ____________All ________ is ____________M
No Sneetch is a Lorax
74
Creating a Syllogism
Step #1: Construct your conclusion 1st. Step #2: Provide the correct quantifiers for the premises.Step #3: Determine the location of the middle terms.Step #4: Identify major & minor terms.Step #5: Fill in the middle terms.
Step #4: Identify Major & Minor Terms
No ________M is ____________All ________ is ____________M
No SneetchS is a LoraxP
75
Step #4: Identify Major & Minor Terms
No ________M is ____________All ________ is ____________M
No SneetchS is a LoraxP
Step #4: Identify Major & Minor Terms
No ________M is ____________All ________ is ____________M
No SneetchS is a LoraxP
76
Step #4: Identify Major & Minor Terms
No ________M is a LoraxP
All ________ is ____________M
No SneetchS is a LoraxP
Step #4: Identify Major & Minor Terms
No ________M is a LoraxP
All ________ is ____________M
No SneetchS is a LoraxP
77
Step #4: Identify Major & Minor Terms
No ________M is a LoraxP
All SneetchesS are ____________M
No SneetchS is a LoraxP
Step #4: Identify Major & Minor Terms
No ________M is a LoraxP
All SneetchesS are ____________M
No SneetchS is a LoraxP
78
Creating a Syllogism
Step #1: Construct your conclusion 1st. Step #2: Provide the correct quantifiers for the premises.Step #3: Determine the location of the middle terms.Step #4: Identify major & minor terms.Step #5: Fill in the middle term.
Rule #1 for Determining the Middle Term
If the quality of the conclusion is affirmative, then pick something the things signified by the major
and minor terms have in common.
79
Rule #2 for Determining the Middle Term
If the quality of the conclusion is negative, then pick something the things signified by the major and
minor terms do NOT have in common.
Step #5: Fill in theMiddle Term
No ________M is a LoraxP
All SneetchesS are ____________M
No SneetchS is a LoraxP
80
Step #5: Fill in theMiddle Term
No ________M is a LoraxP
All SneetchesS are ____________M
No SneetchS is a LoraxP
Step #5: Fill in theMiddle Term
No ________M is a LoraxP
All SneetchesS are ____________M
No SneetchS is a LoraxP
81
Step #5: Fill in theMiddle Term
No feathered thingM is a LoraxP
All SneetchesS are ____________M
No SneetchS is a LoraxP
Step #5: Fill in theMiddle Term
No feathered thingM is a LoraxP
All SneetchesS are feathered thingsM
No SneetchS is a LoraxP
82
Step #5: Fill in theMiddle Term
No feathered thingM is a LoraxP
All SneetchesS are feathered thingsM
No SneetchS is a LoraxP
Exercises 33
Creating your own DARAPTI
83
Creating a Syllogism
Step #1: Construct your conclusion 1st.Step #2: Provide the correct quantifiers for the premises.Step #3: Determine the location of the middle terms.Step #4: Identify major & minor terms.Step #5: Fill in the middle terms.
Exercises 33
Creating your own DARAPTI
84
Step #1: Begin with a Conclusion
Some _________ are ____________
Step #1: Begin with a Conclusion
Some things are things that can sing
85
Creating a Syllogism
Step #1: Construct your conclusion 1st. Step #2: Provide the correct quantifiers for the premises.Step #3: Determine the location of the middle terms.Step #4: Identify major & minor terms.Step #5: Fill in the middle terms.
Exercises 33
Creating your own DARAPTI
86
Step #2: Provide Correct Quantifiers for Premises
All ________ is ____________All ________ is ____________
Some things are things that can sing
Creating a Syllogism
Step #1: Construct your conclusion 1st. Step #2: Provide the correct quantifiers for the premises.Step #3: Determine the location of the middle term.Step #4: Identify major & minor terms.Step #5: Fill in the middle terms.
87
Exercises 33
Creating your own DARAPTI
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
88
Step #3: Determine Location of Middle Term
All ________ is ____________All ________ is ____________
Some things are things that can sing
Step #3: Determine Location of Middle Term
All ________M is ____________All ________M is ____________
Some things are things that can sing
89
Creating a Syllogism
Step #1: Construct your conclusion 1st. Step #2: Provide the correct quantifiers for the premises.Step #3: Determine the location of the middle terms.Step #4: Identify major & minor terms.Step #5: Fill in the middle terms.
Step #4: Identify Major and Minor Terms
All ________M is ____________All ________M is ____________
Some things are things that can singP
90
Step #4: Identify Major and Minor Terms
All ________M is ____________All ________M is ____________
Some thingsS are things that can singP
Step #4: Identify Major and Minor Terms
All ________M is ____________All ________M is ____________
Some thingsS are things that can singP
91
Step #4: Identify Major and Minor Terms
All ________M are things that can singP
All ________M is ____________Some thingsS are things that can singP
Step #4: Identify Major and Minor Terms
All ________M are things that can singP
All ________M are thingsS
Some thingsS are things that can singP
92
Step #4: Identify Major and Minor Terms
All ________M are things that can singP
All ________M are thingsS
Some thingsS are things that can singP
Creating a Syllogism
Step #1: Construct your conclusion 1st. Step #2: Provide the correct quantifiers for the premises.Step #3: Determine the location of the middle term.Step #4: Identify major & minor terms.Step #5: Fill in the middle term.
93
Rule #1 for Determining the Middle Term
If the quality of the conclusion is affirmative, then pick something the things signified by the major
and minor terms have in common.
Step #5: Fill in theMiddle Term
All YingsM are things that can singP
All YingsM are thingsS
Some thingsS are things that can singP
94
Step #5: Fill in theMiddle Term
All YingsM are things that can singP
All YingsM are thingsS
Some thingsS are things that can singP
Reducing a BRAMANTIP
All dogs are mammalsAll mammals are animalsSome animals are dogs
95
Reducing a BRAMANTIP
All dogs are mammalsAll mammals are animalsSome animals are dogs
Reducing a BRAMANTIP
All dogs are mammalsAll mammals are animalsSome animals are dogs
96
Reducing a BRAMANTIP
All dogs are mammalsAll mammals are animalsSome animals are dogs
Reducing a BRAMANTIP
All mammals are animalsSome animals are dogs
All dogs are mammals
97
Reducing a BRAMANTIP
All dogs are mammalsSome animals are dogs
All dogs are mammals
Reducing a BRAMANTIP
All dogs are mammalsSome animals are dogs
All dogs are mammals
98
Reducing a BRAMANTIP
All mammals are animalsAll dogs are mammalsSome animals are dogs
Reducing a BRAMANTIP
All mammals are animalsAll dogs are mammalsSome animals are dogs
99
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 BRAMANTIP
All mammals are animalsAll dogs are mammalsSome animals are dogs
100
Review of Partial Conversion
Change the quantity
Switch the terms
Review of Partial Conversion
All men are mortal
Some mortal things are men
101
Review of Partial Conversion
Some men are vicious
All vicious things are men
Reducing a BRAMANTIP
All mammals are animalsAll dogs are mammalsSome animals are dogs
102
Reducing a BRAMANTIP
All mammals are animalsAll dogs are mammalsSome animals are dogs
Reducing a BRAMANTIP
All mammals are animalsAll dogs are mammalsSome animals are dogs
103
Reducing a BRAMANTIP
All mammals are animalsAll dogs are mammalsSome animals are dogs
Reducing a BRAMANTIP
All mammals are animalsAll dogs are mammalsAll animals are dogs
104
Reducing a BRAMANTIP
All mammals are animalsAll dogs are mammalsAll animals are dogs
Reducing a BRAMANTIP
All mammals are animalsAll dogs are mammalsAll dogs are animals
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