# syllogistic figures

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Syllogistic Figures and Moods/Modes

Syllogistic figure: disposition of the middle term with respect to the major and minor terms in the premises Syllogistic moods/modes: arrangement of the premises according to quantitiy (U or P) and quality (+ or -)

4 syllogistic figures:1. M P S M ____ S P 2. P M S M ____ S P 3. M P M S ____ S P 4. P M M S ____ S P

4 types of modes:A = Universal affirmative (u + p) E = Universal negative (u p) I = Particular affirmative (p + p) O = Particular negative (p p)

16 theoretical combination of syllogistics figures and modes:1.A A 5. E A 9. I A 13. O A 2. A E 6. E E 10. I E 14. O E 3. A I 7. E I 11. I I 15. O I 4. A O 8. E O 12. I O 16. O O

Violation of law 6 (no 2 negative propositions):E E E O O E O O

Violation of law 8 (no 2 particulars):I I I O O I

Violation of law 2 (no particular in conclusion if it was universal in proposition):I : Beberapa binatang melata bisa terbang (pM + pP) E : Tiada katak yang binatang melata (pS uM) Tiada katak yang bisa terbang (uS + uP)

Valid syllogistic figures:A A E A I A O A A E E I A I A O

Figure 1:M P S M S P The minor premise must be affirmative; the major premise must be universal

A uM + pP A uS + pM uS + pP (valid)

A uM + pP E uS - uM uS - uP (illicit major)

A uM + pP I pS + pM pS + pP (valid) I pM + pP A uS + pM uS + pP (undistributed Middle)

A uM + pP O pS - uM pS - uP (illicit major)

E uM uP A uS + pM uS - uP (valid)

E uM uP I pS + pM pS uP (valid)

O pM uP A uS + pM uS - uP (undistributed Middle)

Fidure 1: illicit major

A uM + pP E uS - uM uS - uP

A: Semua pinsil adalah alat kantor E: Semua sendok bukan pinsil Semua sendok bukan alat kantor A: Semua garpu adalah alat makan E: Semua sendok bukan garpu Semua sendok bukan alat makan

Figure 1: undistributed middleI: Beberapa orang kaya adalah orang Betawi A: Semua tuan tanah adalah orang kaya Semua tuan tanah orang Betawi I: Beberapa orang Betawi miskin A: Semua tuan tanah adalah orang Betawi Semua tuan tanah miskin I pM + pPA uS + pM uS + pP

Figure 1: validEvery passion causes emotional instability Greed is pasion Greed causes emotional instability Excessive hoarders of money are misers Some lawyers are excessive hoarders of money Some lawyers are misers (next .)

No quadrupleds have wings All donkeys are quadrupleds No donkeys have wings No thieves will prosper Some politicians are thieves Some politicians will not proper

Figure 2:P M S M S P One premise must be negative; the major premis must be universal.

A uP + pM A uP + pM E uS - uM A uS + pM uS uP uS + pP (Undistributed (Valid) Middle) E uP - uM A uS + pM uS - uP (Valid) E uP - uM I pS + pM pS - uP (Valid)

A uP + pM I pS + pM pS + pP (Undistributed Middle)

A uP + pM O pS - uM pS uP (Valid)

I pP + pM O pP - uM A uS + pM A uS + pM uS - uP uS + pP (Undistributed (Illicit major) Middle)

Figure 2: undistributed middleI: Semua reptilia melata A: Semua ular melata Semua ular adalah reptilia I: Semua buaya melata A: Semua ular melata Semua ular adalah buayaA uP + pM A uS + pM uS + pP

Figure 2: illicit major

O pP - uM A uS + pM uS - uP

O: Sebagian wanita tidak menghasilkan sperma A: Semua pria menghasilkan sperma Semua pria bukan wanita O: Sebagian yang berotot tidak maskulin A: Semua pria berotot Semua pria bukan maskulin

Figure 2: validAll men are rational No monkeys are rational No monkeys are men All cars are mobile Some phones are not mobile Some phones are not cars

No poor people are money lenders All bankers are money lenders No bankers are poor people No real nationalists burn national flags Some demonstrators burn national flags Some demonstrators are not real nationalists

Figure 3:M P M S S P The minor premise must be affirmative; the conclusion must be particular; one of the premises must be universal

A uM + pP A uM + pS pS + pP (valid) E uM - uP A uM + pS pS - uP (valid)

A uM + pP E uM - uS uS - uP (illicit major) E uM - uP I pM + pS pS - uP (valid)

A uM + pP I pM + pS pS + pP (valid)

A uM + pP O pM - uS uS - uP (illicit major)

I pM + pP O pM - uP A uM + pS A uM + pS pS uP pS + pP (valid) (valid)

Figure 3: illicit major

A uM + pP E uM - uS uS - uP

A: Semua pedagang K5 berakal sehat E: Semua pedagang K5 bukan elit politik Semua elit politik tidak berakal sehat A: Semua pedagang K5 berpolitik E: Semua pedagang K5 bukan elit politik Semua elit politik tidak berpolitik

Figure 3: validAll birds have wings All birds are bipeds Some bipeds have wings All fools think themselves wise Some fools are professors Some professors think themselves wise

No pigs are vegetable All pigs are mamal Some mamals are not vegetable No bodies are immaterial Some bodies are elements Some elements are not immaterial

Some PRD members are revolutionary All PRD members are radicals Some radicals are revolutionary Some criminals do not steal All criminals are lawbreakers Some lawbreakers do not steal

Figure 4P M M S S P If the major premise is affirmative, the minor premise must be universal; if the minor premise is affirmative, the conclusion must be particular; if one of the premises is negative, the major premise must be universal

A uP + pM A uM + pS pS + pP (valid) E uP - uM A uM + pS pS - uP (valid)

A uP + p M E uM - uS uS - uP (valid)

A uP + pM I pM + pS pS + pP (Undistributed Middle) I pP + pM E uP - uM A uM + pS I pM + pS pS + pP pS + pP (valid) (valid)

A uP + pM O pM - uS pS - uP (Undistributed Middle) O pP - uM A uM + pS pS - uP (illicit major)

Figure 4: Undistributed MiddleA: Semua mantan pengungsi terlantar I: Sebagian orang yang terlantar menjadi gelandangan Beberapa gelandangan adalah mantan pengungsi A uP + pM A: Semua kucing suka daging I pM + pS pS + pP I: Semur daging disukai tikus Beberapa tikus adalah kucing

Figure 4: Illicit majorO: Sebagian alas kaki bukan untuk olah raga A: Semua olah raga memerlukan sepatu Beberapa sepatu bukan alas kaki O: Sebagian sepatu bukan untuk olah raga A: Semua olah raga memerlukan alas kaki Beberapa alas kaki bukan sepatuO pP - uM A uP + pS pS - uP

Figure 4: ValidA: All murders are crimes A: All crimes are something detestable Something detestable is murder All animals are sentient beings No sentient beings are lifeless beings No lifeless beings are animals

No plants are sentient beings All sentient beings are living beings Some living beings are not plants No inorganic bodies are living beings Some living beings are sentient beings Some sentient beings are not inorganic bodies

Some bodies are plant All plants are living beings Some living beings are bodies