The Figures

see also: http://eidetisch.tumblr.com/post/45801450925/the-deductions-in-the-figures-moods

| First Figure | Second Figure | Third Figure |

| Predicate Subject | Predicate Subject | Predicate Subject |

| Premise | a b | a b | a c |

| Premise | b c | a c | b c |

| Conclusion | a c | b c | a b |

Aristotle calls the term which is the predicate of the conclusion the major term and the term which is the subject of the conclusion the minor term.

The premise containing the major term is the major premise, and the premise containing the minor term is the minor premise.

Aristotle then systematically investigates all possible combinations of two premises in each of the three figures.

For each combination, he either demonstrates that some conclusion necessarily follows or demonstrates that no conclusion follows.

The results he states are correct.

via: http://plato.stanford.edu/archives/spr2012/entries/aristotle-logic/

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Form Mnemonic Proof

Aab, Abc ⊢ Aac Barbara Perfect

every b is an a, every c is a b ⊢

Eab, Abc ⊢ Eac Celarent Perfect

no b is an a, every c is a b. ⊢no c is an a

Aab, Ibc ⊢ Iac Darii Perfect; also by impossibility, from Camestres

every b is an a, some c is b. ⊢ some c is a.

Eab, Ibc ⊢ Oac Ferio Perfect; also by impossibility, from Cesare

no b is a., some c is b. ⊢ some c is not a.

SECOND FIGURE

Eab, Aac ⊢ Ebc Cesare (Eab, Aac)→(Eba, Aac)⊢CelEbc

no b is a., every c is an a. / no a is b., every c is an a. ⊢ no c is a b.

Aab, Eac ⊢ Ebc Camestres (Aab, Eac)→(Aab, Eca)=(Eca, Aab)⊢CelEcb→Ebc

every b is an a., no c is an a. / every b is an a., no a is c. ⊢ no b is c.

Eab, Iac ⊢ Obc Festino (Eab, Iac)→(Eba, Iac)⊢FerObc

no b is a., some c is a. / no a is b., some c is a. ⊢ some c is not b.

Aab, Oac ⊢ Obc Baroco (Aab, Oac +Abc)⊢Bar(Aac, Oac)⊢ImpObc

every b is a., some c is not a. /

if a belongs to every b / every b is a.

but does not belong to some c, / some c are not a

it is necessary for b not to belong to some c. / some c is not b.

Baroco (27a36-b1)

“Next, if M belongs to every N but does not belong to some X, it is ne

cessary for N not to belong to some X. For if it belongs to every X and M is also predicated of every N, then it is necessary for M to belong to every X: but it was assumed not to belong to some. And if M belongs to every N but not to every X, then there will be a deduction that N does not belong to every X. (The demonstration is the same.)”

if every N is M

and some X is not M.

some X is not N.

if every X is M

and every N is M

then every X is M.

For if it belongs to every X and M is also predicated of every N, then it is necessary for M to belong to every X: but it was assumed not to belong to some.

every N is M.

not every X is M.

not every X is N.

And if M belongs to every N but not to every X, then there will be a deduction that N does not belong to every X.

if a belongs to every b / every b is a.

but does not belong to some c, / some c are not a

it is necessary for b not to belong to some c. / some c is not b.

every b is an a. -> some a are b.

some c are not a

some c are not b

THIRD FIGURE

Aac, Abc ⊢Iab Darapti (Aac, Abc)→(Aac, Icb)⊢DarIab

all c is a., all c is b. / all c is a., some b is c. ⊢ some b is a.

Eac, Abc ⊢ Oab Felapton (Eac, Abc)→(Eac, Icb)⊢FerOab

no c is a., all c is b. / no a is c., all c is b. ⊢ some b are not a.

Iac, Abc ⊢ Iab Disamis (Iac, Abc)→(Ica, Abc)=(Abc, Ica)⊢DarIba→Iab

some c is a., every c is b. / some a is c., every c is b. ⊢ some a is b.

Aac, Ibc ⊢ Iab Datisi (Aac, Ibc)→(Aac, Icb)⊢DarIab

every c is a., some c is b. / every c is a., some b is c. ⊢ some b is a.

Oac, Abc ⊢ Oab Bocardo (Oac, +Aab, Abc)⊢Bar(Aac, Oac)⊢ImpOab

some c is not a. all c is b. / some a is not c. , all c is b.

Eac, Ibc ⊢ Oab Ferison (Eac, Ibc)→(Eac, Icb)⊢FerOab

no c is a., some c is b. ⊢ some b are not a.