TASK 7 - CATEGORICAL SYLLOGISMS

Question 1

categorical syllogisms

Answer 1

= three categorical propositions containing 3 different terms, each of which appears twice

Question 2

major term

Answer 2

= PREDICATE of the conclusion

• makes its premise the major remise
• always first premise + second term in conclusion

Question 3

minor term

Answer 3

= SUBJECT of the conclusion

• makes its premise the minor premise
• always second premise + first term in conclusion

Question 4

middle term

Answer 4

= in both premises, not in conclusion

Question 5

standard-form categorical syllogism

Answer 5

1. all three statements are standard-form categorical propositions (A, E, I, o)
   - each statement has proper quantifier, subject term, copula, predicate term
2. two occurrences of each term are identical
3. each term is used in the same sense throughout the argument
4. the major premise is listed first (1), the minor premise second (2), the conclusion last (3)

Question 6

mood

Answer 6

= letter names of propositions

- e.g. AAA, AOA, AEE

Question 7

figure

Answer 7

= determined by where the 2 middle terms are

Question 8

figure 1

Answer 8

M P
S M
—–
S P

Question 9

figure 2

Answer 9

P M
S M
—–
S P

Question 10

figure 3

Answer 10

M P
M S
—–
S P

Question 11

figure 4

Answer 11

P M
M S
—–
S P

Question 12

check validity

Answer 12

1. identify major + minor term in conclusion
2. check whether premises are in the right order (1. major 2. minor)
3. assign S, P, M terms (highlight)
4. identify figure
5. identify mood
6. check poem/table whether combination is valid

Question 13

construct valid syllogism

Answer 13

1. mood
2. figure
3. add major (P) + minor terms (S)

Question 14

Venn diagram

Answer 14

• 3 circles, M term/circle on the top
  1. look at premises, mark according to categorical propositions
  2. an universal premise should be entered first
  3. be careful to shade all of the area in question
  4. two areas where an X goes is always initially divided into two parts
• iIf one of the parts has already been shaded, the X goes in the unshaded part
• if one of the parts is not shaded, the X goes on the line separating the two parts (= X may be in either (or both) of the two areas but it is unclear in which)
  5. check whether pattern (S and P circles) match the conclusion

Question 15

Boolean standpoint

- rule 1

Answer 15

= middle term must be distributed at least once

• predicate provides a common ground between subject + predicate
• fallacy: undistributed middle

Question 16

Boolean standpoint

- rule 2

Answer 16

= if a term is distributed in the conclusion, then it must be distributed in a premise

• otherwise conclusion contains information not contained in the premises
• fallacy: Illicit major/minor

Question 17

Boolean standpoint

- rule 3

Answer 17

= two negative premises are not allowed (quality)

• nothing is said
• fallacy: exclusive premises

Question 18

Boolean standpoint

- rule 4

Answer 18

= negative premise requires a negative conclusion + negative conclusion requires a negative premise (quality)
- fallacy: drawing an affirmative conclusion from a negative premise + vice versa

Question 19

Boolean standpoint

- rule 5

Answer 19

= if both premises are universal, the conclusion cannot be particular
- fallacy: existential fallacy

Question 20

Aristotelian standpoint

- rules + fallacies

Answer 20

• if a syllogism breaks only rule 5, it is still conditionally valid IF the term in question refers to an actually existing thing
• superfluous distribution rule: the term that needs to denote something that exists is the one that is superfluously distributed (= distributed once more than necessary)

Question 21

reduce the number of terms

Answer 21

• if a sentence is written in a way that it is impossible to test it with Venn diagrams or rules
• reduce the terms to a number of three if similar nouns with the same meaning are used (non-humans into humans…)
  1) conversion (E + i)
  2) obversion
  3) contraposition (A + o)

Question 22

enthymemes

Answer 22

= arguments that is expressible as a categorical syllogism but misses a premise/conclusion
- pay attention to indicator words –> provide clue what is the missing statement

Question 23

sorites

Answer 23

= chain of categorical syllogisms in which the intermediate conclusions have been left out

1. find the premise that contains the predicate of the conclusion and write it first
2. find the other term in the found premise & put it second
3. find intermediate conclusions

Question 24

standard-form sorites

Answer 24

1. each of the component propositions is in standard form
2. each term occurs twice
3. the predicate (major term) of the conclusion is in the first premise (major premise)
4. each successive premise has a term in common with the preceding one