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