CATEGORICAL SYLLOGISM Presentation Transcript
1. CATEGORICALSYLLOGISM
2. INTRODUCTION the mere analysis of the of the S and P or direct observation will not
disclose their judgment. The mind compares the two certain ideas with the third idea to which
is familiar
3. INTRODUCTION IDEA 1 IDEA 2 IDEA 3
4. INTRODUCTION IDEA 1 IDEA 2 IDEA 3 OR
5. INTRODUCTION • MEDIATE INFERENCE – we derive conclusion from two or more
premise • MEDIATION of the THIRD IDEA
6. MEDIATE INFERENCE a process of the mind in which from the agreement or
disagreement of 2 ideas with a third idea we infer their agreement or disagreement with each
other
7. EXAMPLE All animal is mortal. But every dog is an animal. Therefore, every dog is mortal.
8. THE SYLLOGISM IDEA : TERM JUDGEMENT : PROPOSITION MEDIATE INFERENCE :
ARGUMENTATION
9. THE SYLLOGISM• ARGUMENTATION – a discourse which logically deduces one
proposition from the others
10. SYLLOGISM An argumentation in which, from two known propositions that contain a
common idea, and one at least of which is universal, a third proposition, different from the
two propositions, follow with necessity. (Timbreza, 1992)
11. SYLLOGISM is a kind of logical argument in which one proposition (the conclusion) is
inferred from two or more others (the premises) of a certain form. (Merriam-Webster
Dictionary)
12. CATEGORICAL SYLLOGISM is a piece of deductive, mediate inference which consists
of three categorical propositions, the first two which are premises and the third is the
conclusion It contains exactly three terms, each of which occurs in exactly two of the
constituent propositions.
13. EXAMPLE All fish swim. (Major Premise) Every shark is a fish. (Minor Premise)
Therefore every shark swim. (Conclusion)
14. STRUCTURES OF A CATEGORICAL SYLLOGISM Three Propositions: Three terms: 1.
Major Premise 1. Major term (P) 2. Minor Premise 2. Minor term (S) 3. Conclusion 3. Middle
term (M)
15. THREE PROPOSITIONSMAJOR PREMISE: MINOR PREMISE: is the one wherein the
is the one wherein the minor major term (P) is compared term (S) is compared to the to the
middle term (M) middle term (M) less universal class universal class not challenged and
assumed to be true
16. THREE PROPOSITIONSCONCLUSION: is the new truth arrived at , the result of
reasoning, wherein the agreement or disagreement between the minor term (S) and the
major term (P) is enunciated or expressed.
17. THREE TERMSMAJOR TERM (P): MINOR TERM (S):• compared to the • compared to
the middle term in a major middle term in a minor premise premise• more universal class •
less universal class• predicate of the conclusion • subject of the conclusion
18. THREE TERMSMIDDLE TERM: term of comparison appears twice in the premise but
NEVER in the conclusion
19. EXAMPLE All fish (M) are sea creatues (P) (Major Premise) Every shark (S) s a fish (M)
(Minor Premise) Therefore every shark (S) are sea creatures (P) (Conclusion)
20. EXERCISE _________ All mammals (_) have lungs (_). _________ All whales (_) have
lungs (_). _________ Therefore, all whales (_) are mammals(_).
21. EXERCISE A land and water dwellers are called amphibians. All salamanders are land
and water dwellers. All salamanders are amphibians.
22. TO SUMMARIZE All M is P – Major premise All is S is M – Minor premise Therefore, all
S is P - Conclusion
23. General Axioms (Principles) of the Syllogism Prepared by: Agnes Baculi, Rn Geinah R.
Quiñones, RN
24. 1. Principle of Reciprocal Identity If two terms agree (or are identical) with a third term,
then they are identical with each other. M is P. M agrees with P. S is M. S agrees with M. ∴ S
is P. ∴ S agrees with P.
25. Example: A dog is an animal. A hound is a dog. ∴ a hound is an animal.
26. 2. Principle of Reciprocal Non-Identity If two terms, one of which is identical with a third,
but the other of which is not, then they are not identical with each other. P is M. P agrees
with M. S is not M. S does not agree with M. ∴ S is not P. ∴ S does not agree with P.
27. Example: Nuclear-powered submarines are not commercial vessels. All nuclear-powered
submarines are warships. ∴ warships are not commercial vessels.
28. 3. Dictum de Omni (The Law of All) What is affirmed of a logical class may also be
affirmed of its logical member. P M S
29. Formula: 1. P is affirmed of M. But M is affirmed of S. Hence, P may also be affirmed of
S. 2. Circle M is inside circle P. But circle S in inside circle M. Therefore, circle S is inside
circle P.
30. Formula: 3. M is part of P. But S is a part of M. Therefore, S is also a part of P. 4. Circle
P contains circle M. But circle M contains circle S. Therefore, circle P also contains circle S.
31. Example:All terriers are mammals.Terriers are dogs.Therefore, all dogs are mammals.
Mammals Dogs Terrier
32. 4. Dictum de Nullo (The Law of None) What is denied of a logical class is also denied of
its logical member. What is denied universally of a term is also denied of each of all referents
of that term.
33. Example:Graduate students are voters.No person under eighteen years of age is a
voter.Therefore, graduate students are not under eighteen years of age. Voters Under
eighteen Graduate years of students age
34. Eight General Syllogistic Rules1. There must be only three terms in the syllogism.2.
Neither the major nor the minor term may be distributed in the conclusion, if it is undistributed
in the premises.3. The middle term must not appear in the conclusion.4. The middle term
must be distributed at least once in the premises.
35. Eight General Syllogistic Rules5. Only an affirmative conclusion can be drawn from two
affirmative premises.6. No conclusion can be drawn from two negative premises.7. If one
premise is particular, the conclusion must also be particular; if one premise is negative, the
conclusion must be negative.8. No conclusion can be drawn from two particular premises.
36. Rule 1: There must be only three terms in the syllogism. -Minor Term (S) -Major Term (P)
-Middle Term (M)
37. Fallacy of Four Terms occurs when a syllogism has four (ormore) terms rather than the
requisitethree. All M is P. All S is R. ∴ all S is P.
38. Example:All academicians are egotists.Susan is someone who works in a
university.Therefore, Susan is an egotist.
39. Fallacy of Ambiguous MiddleSound travels very fast.His knowledge of law is
sound.Therefore, his knowledge of law travels very fast.
40. Rule 2: Neither the major nor the minorterm may be distributed in the conclusion, if it is
undistributed in the premises.a) Major term must not become universal in the conclusion if it
is only particular in the major premise.b) Minor term must not become universal in the
conclusion if it is only particular in the minor premise.
41. Fallacy of Illicit Processa) Fallacy of Illicit Majorb) Fallacy of Illicit Minor
42. Fallacy of Illicit MajorCommitted if and only if the majorterm (P) becomes universal in
theconclusion while it is only particular inthe major premise.
43. Example:All Texans are Americans.No Californians are Texans.Therefore, no
Californians are Americans.
44. Mu PpA- All Texans are Americans. Su MuE- No Californians are Texans. Su PuE-
Therefore, no Californians are Americans.
45. Fallacy of Illicit MinorMinor term becomes universal inthe conclusion while it is
onlyparticular (undistributed) in theminor premise.
46. Example:All animal rights activists are vegans.All animal rights activists are
humans.Therefore, all humans are vegans.
47. Mu PpA- All animal rights activists are vegans. Mu SpA- All animal rights activists are
humans. Su PuA- Therefore, all humans are vegans.
48. Rule 3: The middle term must not appear in the conclusion.All tables have four legsAll
dogs have four legsTherefore all dogs and tables have four legs.
49. Rule 4: The middle term must be distributed at least once in the premises.Middle term
must be used as least once asuniversal in any of the premises.It must be shown in the
premises that atleast all members or referents of themiddle term are identical or not
identicalwith all the members or referents of eitherthe minor or the major term.
50. Example:Contradictories are opposites.Black and white are opposites.∴ black and white
are contradictories.
51. Pu MpContradictories are opposites. Su MpBlack and white are opposites. Su Pp∴ black
and white are contradictories.
52. Fallacy of Undistributed Middle Arises when the middle term is not used at least once as
universal in the premises.
53. RULES ON PREMISES5. Only an affirmative conclusion can be drawn from affirmative
premises• The major term (P) and minor term (S) of both affirmative premises agree with the
middle term.• Hence, the conclusion must express agreement between the major term (P)
and minor term (S).
54. EXAMPLEEvery carnivore is a meat-eater. (affirmative) A lion is a carnivore.
(affirmative)Therefore, a Lion is a meat-eater. (affirmative)
55. RULES ON PREMISES6. No conclusion can be drawn from two negative premises• If
both the premises are negative, major term (P) and the minor term (S) disagree with the
middle term, then the middle term cannot establish any relation between the major term (P)
and the minor term (S)
56. FALLACY OF TWO NEGATIVES No vegetables are fruits. (negative) All tomatoes are
not vegetables. (negative) Therefore, all tomatoes are not fruits. (negative)
57. RULES ON PREMISES7. If one premise is particular, the conclusion must be particular;
if the one premise is negative the conclusion must be negative.• Only a portion of either the
minor term (S) or major term (P) referents share something in common with the middle term.
58. FALLACY OF ILLICIT MINOR All Spartans are Greek. Some warriors are Spartans.
(particular) Therefore, all warriors are Greek.
59. EXAMPLE All Spartans are Greek. Some warriors are Spartans. Therefore, some
warriors are Greek.
60. RULES ON PREMISES if one of the premises is negative, then neither agrees with the
middle term therefore they don’t agree with each other negative propostion: S is not P
61. EXAMPLE No cube is round. (negative) A box is a cube. Therefore a box is not round.
(negative)
62. RULES ON PREMISES8. No conclusion can be drawn from two particular premises.•
THREE POSSIBILITIES: a) either both are affirmative b) both are negative c) one is
affirmative and the other is negative
63. THREE POSSIBILITIESa) either both are affirmative • if both premises are particular
affirmative then all four terms will be particular.b) if both premises are particular negative no
conclusion can be made.
64. THREE POSSIBILITIES c) if either of the particular premises is negative then the
syllogism will contain either a fallacy of illicit major or undistributed middle
65. FALLACY OF ILLICIT MAJOR Some priests are Dominicans. Some teachers are not
priests. Therefore, some teachers are not Dominicans.
66. FALLACY OF UNDISTRIBUTEDMIDDLE Some elephants are big. Some boys are big.
Therefore some boys are elephants.
67. Figures and Moods of the Categorical Syllogism
68. FigureProper arrangement (position) of themiddle term (M) with respect to themajor term
(P) and the minor term (S)in the premises.
69. 4 Syllogistic Figures 1st M-p p-M M-p p-MPremise 2nd s-M s-M M-s M-sPremise Figure 1
2 3 4
70. Figure 1: The middle term is the subject of the major premise and the predicate of the
minor premise Some people are difficult to get along with.M-p All Americans are people.s-M
Therefore, some Americans are difficult to getS-P along with.
71. Figure 2: The middle term is the predicate of both premises.p-M Registered students are
members of this class.s-M John is a member of this class.S-P Therefore, John is a registered
student.
72. MoodProper arrangement of the premisesaccording to quantity and quality. AAAA EEEE
IIII OOOO AEIO AEIO AEIO AEIO
73. Valid Moods of the Four Figures Figure 1 AAA , EAE, AII, EIO Figure 2 EAE, AEE, EIO,
AOO Figure 3 AAI, EAO, IAI, AII, OAO, EIO Figure 4 AAI, AEE, IAI, EAO, EIO
74. Example:A- All textbooks are books intended for careful study.I- Some reference books
are intended for careful study.I- Therefore, some reference books are textbooks.
75. Example:A- All criminal actions are wicked deeds.A- All prosecutions for murder are
criminal actions.A- Therefore, all prosecutions for murder are wicked deeds.
1. CATEGORICALSYLLOGISM
2. INTRODUCTION the mere analysis of the of the S and P or direct observation
will not disclose their judgment. The mind compares the two certain ideas with the
third idea to which is familiar
3. INTRODUCTION IDEA 1 IDEA 2 IDEA 3
4. INTRODUCTION IDEA 1 IDEA 2 IDEA 3 OR
5. INTRODUCTION • MEDIATE INFERENCE – we derive conclusion from two or
more premise • MEDIATION of the THIRD IDEA
6. MEDIATE INFERENCE a process of the mind in which from the agreement or
disagreement of 2 ideas with a third idea we infer their agreement or disagreement
with each other
7. EXAMPLE All animal is mortal. But every dog is an animal. Therefore, every dog
is mortal.
8. THE SYLLOGISM IDEA : TERM JUDGEMENT : PROPOSITION MEDIATE
INFERENCE : ARGUMENTATION
9. THE SYLLOGISM• ARGUMENTATION – a discourse which logically deduces
one proposition from the others
10. SYLLOGISM An argumentation in which, from two known propositions that
contain a common idea, and one at least of which is universal, a third proposition,
different from the two propositions, follow with necessity. (Timbreza, 1992)
11. SYLLOGISM is a kind of logical argument in which one proposition (the
conclusion) is inferred from two or more others (the premises) of a certain form.
(Merriam-Webster Dictionary)
12. CATEGORICAL SYLLOGISM is a piece of deductive, mediate inference which
consists of three categorical propositions, the first two which are premises and the
third is the conclusion It contains exactly three terms, each of which occurs in
exactly two of the constituent propositions.
13. EXAMPLE All fish swim. (Major Premise) Every shark is a fish. (Minor Premise)
Therefore every shark swim. (Conclusion)
14. STRUCTURES OF A CATEGORICAL SYLLOGISM Three Propositions: Three
terms: 1. Major Premise 1. Major term (P) 2. Minor Premise 2. Minor term (S) 3.
Conclusion 3. Middle term (M)
15. THREE PROPOSITIONSMAJOR PREMISE: MINOR PREMISE: is the one
wherein the is the one wherein the minor major term (P) is compared term (S) is
compared to the to the middle term (M) middle term (M) less universal class
universal class not challenged and assumed to be true
16. THREE PROPOSITIONSCONCLUSION: is the new truth arrived at , the result
of reasoning, wherein the agreement or disagreement between the minor term (S)
and the major term (P) is enunciated or expressed.
17. THREE TERMSMAJOR TERM (P): MINOR TERM (S):• compared to the •
compared to the middle term in a major middle term in a minor premise premise•
more universal class • less universal class• predicate of the conclusion • subject of
the conclusion
18. THREE TERMSMIDDLE TERM: term of comparison appears twice in the
premise but NEVER in the conclusion
19. EXAMPLE All fish (M) are sea creatues (P) (Major Premise) Every shark (S) s a
fish (M) (Minor Premise) Therefore every shark (S) are sea creatures (P)
(Conclusion)
20. EXERCISE _________ All mammals (_) have lungs (_). _________ All whales
(_) have lungs (_). _________ Therefore, all whales (_) are mammals(_).
21. EXERCISE A land and water dwellers are called amphibians. All salamanders
are land and water dwellers. All salamanders are amphibians.
22. TO SUMMARIZE All M is P – Major premise All is S is M – Minor premise
Therefore, all S is P - Conclusion
23. General Axioms (Principles) of the Syllogism Prepared by: Agnes Baculi, Rn
Geinah R. Quiñones, RN
24. 1. Principle of Reciprocal Identity If two terms agree (or are identical) with a
third term, then they are identical with each other. M is P. M agrees with P. S is M.
S agrees with M. ∴ S is P. ∴ S agrees with P.
25. Example: A dog is an animal. A hound is a dog. ∴ a hound is an animal.
26. 2. Principle of Reciprocal Non-Identity If two terms, one of which is identical
with a third, but the other of which is not, then they are not identical with each other.
P is M. P agrees with M. S is not M. S does not agree with M. ∴ S is not P. ∴ S
does not agree with P.
27. Example: Nuclear-powered submarines are not commercial vessels. All
nuclear-powered submarines are warships. ∴ warships are not commercial vessels.
28. 3. Dictum de Omni (The Law of All) What is affirmed of a logical class may also
be affirmed of its logical member. P M S
29. Formula: 1. P is affirmed of M. But M is affirmed of S. Hence, P may also be
affirmed of S. 2. Circle M is inside circle P. But circle S in inside circle M. Therefore,
circle S is inside circle P.
30. Formula: 3. M is part of P. But S is a part of M. Therefore, S is also a part of P.
4. Circle P contains circle M. But circle M contains circle S. Therefore, circle P also
contains circle S.
31. Example:All terriers are mammals.Terriers are dogs.Therefore, all dogs are
mammals. Mammals Dogs Terrier
32. 4. Dictum de Nullo (The Law of None) What is denied of a logical class is also
denied of its logical member. What is denied universally of a term is also denied of
each of all referents of that term.
33. Example:Graduate students are voters.No person under eighteen years of age
is a voter.Therefore, graduate students are not under eighteen years of age. Voters
Under eighteen Graduate years of students age
34. Eight General Syllogistic Rules1. There must be only three terms in the
syllogism.2. Neither the major nor the minor term may be distributed in the
conclusion, if it is undistributed in the premises.3. The middle term must not appear
in the conclusion.4. The middle term must be distributed at least once in the
premises.
35. Eight General Syllogistic Rules5. Only an affirmative conclusion can be drawn
from two affirmative premises.6. No conclusion can be drawn from two negative
premises.7. If one premise is particular, the conclusion must also be particular; if
one premise is negative, the conclusion must be negative.8. No conclusion can be
drawn from two particular premises.
36. Rule 1: There must be only three terms in the syllogism. -Minor Term (S) -Major
Term (P) -Middle Term (M)
37. Fallacy of Four Terms occurs when a syllogism has four (ormore) terms rather
than the requisitethree. All M is P. All S is R. ∴ all S is P.
38. Example:All academicians are egotists.Susan is someone who works in a
university.Therefore, Susan is an egotist.
39. Fallacy of Ambiguous MiddleSound travels very fast.His knowledge of law is
sound.Therefore, his knowledge of law travels very fast.
40. Rule 2: Neither the major nor the minorterm may be distributed in the
conclusion, if it is undistributed in the premises.a) Major term must not become
universal in the conclusion if it is only particular in the major premise.b) Minor term
must not become universal in the conclusion if it is only particular in the minor
premise.
41. Fallacy of Illicit Processa) Fallacy of Illicit Majorb) Fallacy of Illicit Minor
42. Fallacy of Illicit MajorCommitted if and only if the majorterm (P) becomes
universal in theconclusion while it is only particular inthe major premise.
43. Example:All Texans are Americans.No Californians are Texans.Therefore, no
Californians are Americans.
44. Mu PpA- All Texans are Americans. Su MuE- No Californians are Texans. Su
PuE- Therefore, no Californians are Americans.
45. Fallacy of Illicit MinorMinor term becomes universal inthe conclusion while it is
onlyparticular (undistributed) in theminor premise.
46. Example:All animal rights activists are vegans.All animal rights activists are
humans.Therefore, all humans are vegans.
47. Mu PpA- All animal rights activists are vegans. Mu SpA- All animal rights
activists are humans. Su PuA- Therefore, all humans are vegans.
48. Rule 3: The middle term must not appear in the conclusion.All tables have four
legsAll dogs have four legsTherefore all dogs and tables have four legs.
49. Rule 4: The middle term must be distributed at least once in the
premises.Middle term must be used as least once asuniversal in any of the
premises.It must be shown in the premises that atleast all members or referents of
themiddle term are identical or not identicalwith all the members or referents of
eitherthe minor or the major term.
50. Example:Contradictories are opposites.Black and white are opposites.∴ black
and white are contradictories.
51. Pu MpContradictories are opposites. Su MpBlack and white are opposites. Su
Pp∴ black and white are contradictories.
52. Fallacy of Undistributed Middle Arises when the middle term is not used at least
once as universal in the premises.
53. RULES ON PREMISES5. Only an affirmative conclusion can be drawn from
affirmative premises• The major term (P) and minor term (S) of both affirmative
premises agree with the middle term.• Hence, the conclusion must express
agreement between the major term (P) and minor term (S).
54. EXAMPLEEvery carnivore is a meat-eater. (affirmative) A lion is a carnivore.
(affirmative)Therefore, a Lion is a meat-eater. (affirmative)
55. RULES ON PREMISES6. No conclusion can be drawn from two negative
premises• If both the premises are negative, major term (P) and the minor term (S)
disagree with the middle term, then the middle term cannot establish any relation
between the major term (P) and the minor term (S)
56. FALLACY OF TWO NEGATIVES No vegetables are fruits. (negative) All
tomatoes are not vegetables. (negative) Therefore, all tomatoes are not fruits.
(negative)
57. RULES ON PREMISES7. If one premise is particular, the conclusion must be
particular; if the one premise is negative the conclusion must be negative.• Only a
portion of either the minor term (S) or major term (P) referents share something in
common with the middle term.
58. FALLACY OF ILLICIT MINOR All Spartans are Greek. Some warriors are
Spartans. (particular) Therefore, all warriors are Greek.
59. EXAMPLE All Spartans are Greek. Some warriors are Spartans. Therefore,
some warriors are Greek.
60. RULES ON PREMISES if one of the premises is negative, then neither agrees
with the middle term therefore they don’t agree with each other negative
propostion: S is not P
61. EXAMPLE No cube is round. (negative) A box is a cube. Therefore a box is not
round. (negative)
62. RULES ON PREMISES8. No conclusion can be drawn from two particular
premises.• THREE POSSIBILITIES: a) either both are affirmative b) both are
negative c) one is affirmative and the other is negative
63. THREE POSSIBILITIESa) either both are affirmative • if both premises are
particular affirmative then all four terms will be particular.b) if both premises are
particular negative no conclusion can be made.
64. THREE POSSIBILITIES c) if either of the particular premises is negative then
the syllogism will contain either a fallacy of illicit major or undistributed middle
65. FALLACY OF ILLICIT MAJOR Some priests are Dominicans. Some teachers
are not priests. Therefore, some teachers are not Dominicans.
66. FALLACY OF UNDISTRIBUTEDMIDDLE Some elephants are big. Some boys
are big. Therefore some boys are elephants.
67. Figures and Moods of the Categorical Syllogism
68. FigureProper arrangement (position) of themiddle term (M) with respect to
themajor term (P) and the minor term (S)in the premises.
69. 4 Syllogistic Figures 1st M-p p-M M-p p-MPremise 2nd s-M s-M M-s M-
sPremise Figure 1 2 3 4
70. Figure 1: The middle term is the subject of the major premise and the predicate
of the minor premise Some people are difficult to get along with.M-p All Americans
are people.s-M Therefore, some Americans are difficult to getS-P along with.
71. Figure 2: The middle term is the predicate of both premises.p-M Registered
students are members of this class.s-M John is a member of this class.S-P
Therefore, John is a registered student.
72. MoodProper arrangement of the premisesaccording to quantity and quality.
AAAA EEEE IIII OOOO AEIO AEIO AEIO AEIO
73. Valid Moods of the Four Figures Figure 1 AAA , EAE, AII, EIO Figure 2 EAE,
AEE, EIO, AOO Figure 3 AAI, EAO, IAI, AII, OAO, EIO Figure 4 AAI, AEE, IAI,
EAO, EIO
74. Example:A- All textbooks are books intended for careful study.I- Some
reference books are intended for careful study.I- Therefore, some reference books
are textbooks.
75. Example:A- All criminal actions are wicked deeds.A- All prosecutions for murder
are criminal actions.A- Therefore, all prosecutions for murder are wicked deeds.
The Categorical Syllogism (Exercises) Answer Sheet
1. All Canadians are people. John is a person. Ergo, John is Canadian.
Invalid. Undistributed Middle Term.
2. Some Lifeissues.net readers are philosophers. Sean is a philosopher. Ergo, Sean is a Lifeissues.net reader.
Invalid. Undistributed Middle Term.
3. No man is perfect
Some men are presidents. Ergo, some presidents are not perfect.
Valid
4. All matter obeys wave equations. All waves obey wave equations. Ergo, all matter is waves.
Invalid. Undistributed Middle Term.
5. All human action is conditioned by circumstances. All human action involves morality. Ergo, all that involves morality is conditioned by circumstances (moral relativism).
Invalid. Any term which is distributed in the conclusion must also be distributed in the premises (“All that involves morality” is distributed in the conclusion, but not in the second premise).
6. All that is good is pleasant. All eating is pleasant. Ergo, all eating is good.
Invalid. Undistributed Middle Term.
7. All patriots are voters. Some citizens are not voters. Ergo, some citizens are not patriots.
Valid. The logic is valid, even though the conclusion may be false. For the first
premise might be false. In other words, one may have false premises and a false conclusion, while the logic remains valid. It is also possible to have true premises and a true conclusion but false logic (the conclusion simply does not follow from the premises).
8. All potatoes have eyes. Frank's head has eyes. Ergo, Frank is a potato head.
Invalid. Undistributed Middle Term.
9. All A are B Some C are not B. Ergo, some C are not A.
Valid.
10. All a priori categories are conditions for the possibility of knowing anything. Some a posteriori imperatives of an a-cosmic ethics are not conditions for the possibility of knowing anything. Ergo, some a posteriori imperatives of an a-cosmic ethics are not a priori categories.
Valid. *This syllogism means absolutely nothing. But in order to determine its validity, one need not know the meaning of the terms.
11. No oak trees bear fruit. No maple trees bear fruit. Therefore, no oak trees are maples.
Invalid. One cannot conclude anything from two negative premises. The role of
the Middle Term is to join the Major and Minor Terms. The Middle Term cannot do this if both premises are negative.
12. All socialists favor higher taxes. Some Liberals favor higher taxes. Ergo, some Liberals are Socialists.
Invalid. Undistributed Middle Term.
13. All educated people have worked hard. Some students are not educated. Ergo, some students have not worked hard.
Invalid. The term “not worked hard” is distributed in the conclusion, but it is undistributed in the first premise.
14. Mathematicians know what mathematics is. No philosopher is a mathematician. Ergo, no philosopher knows what mathematics is.
Invalid. “Knows what mathematics is” is distributed in the conclusion, but is undistributed in the first premise.
15. All scientific knowledge is a work of reason. All scientific knowledge is true. Ergo, all that is true is a work of reason.
Invalid. “All that is true” is distributed in the conclusion, but is undistributed in the second premise.
16. All married people know about marriage problems. No priests are married people. Ergo, no priests know about marriage problems.
Invalid. “Know about marriage problems” is distributed in the conclusion, but is undistributed in the first premise.
17. All C are B All T are B Ergo, all T are C
Invalid. Undistributed Middle Term.
18. All chickens are born from eggs. All turkeys are born from eggs. Ergo, all turkeys are chickens.
Invalid. Undistributed Middle Term.
19. Nothing easy is worthwhile. Nothing good is easy. Ergo, nothing good is worthwhile.
Invalid. No conclusion can be drawn from two negative premises.
20. All contraceptives acts are for avoiding pregnancy. All use of NFP is for avoiding pregnancy. Ergo, All use of NFP is contraceptive.
Invalid. Undistributed Middle Term.
21. All Germans despise Judaism. All of the people reading this text are German. Ergo, all of the people reading this text despise Judaism.
Valid. The premises are false, and the conclusion is false, but the logic is valid. No rules are broken.
22. All parts of a living organism are inside the body. The fetus is inside the (mother's) body. Therefore, the fetus is a part of the living organism (mother's body)
Invalid. Undistributed Middle Term.