TASK 7 - CATEGORICAL SYLLOGISMS Flashcards
categorical syllogisms
= three categorical propositions containing 3 different terms, each of which appears twice
major term
= PREDICATE of the conclusion
- makes its premise the major remise
- always first premise + second term in conclusion
minor term
= SUBJECT of the conclusion
- makes its premise the minor premise
- always second premise + first term in conclusion
middle term
= in both premises, not in conclusion
standard-form categorical syllogism
- all three statements are standard-form categorical propositions (A, E, I, o)
- each statement has proper quantifier, subject term, copula, predicate term - two occurrences of each term are identical
- each term is used in the same sense throughout the argument
- the major premise is listed first (1), the minor premise second (2), the conclusion last (3)
mood
= letter names of propositions
- e.g. AAA, AOA, AEE
figure
= determined by where the 2 middle terms are
figure 1
M P
S M
—–
S P
figure 2
P M
S M
—–
S P
figure 3
M P
M S
—–
S P
figure 4
P M
M S
—–
S P
check validity
- identify major + minor term in conclusion
- check whether premises are in the right order (1. major 2. minor)
- assign S, P, M terms (highlight)
- identify figure
- identify mood
- check poem/table whether combination is valid
construct valid syllogism
- mood
- figure
- add major (P) + minor terms (S)
Venn diagram
- 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
Boolean standpoint
- rule 1
= middle term must be distributed at least once
- predicate provides a common ground between subject + predicate
- fallacy: undistributed middle
Boolean standpoint
- rule 2
= 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
Boolean standpoint
- rule 3
= two negative premises are not allowed (quality)
- nothing is said
- fallacy: exclusive premises
Boolean standpoint
- rule 4
= negative premise requires a negative conclusion + negative conclusion requires a negative premise (quality)
- fallacy: drawing an affirmative conclusion from a negative premise + vice versa
Boolean standpoint
- rule 5
= if both premises are universal, the conclusion cannot be particular
- fallacy: existential fallacy
Aristotelian standpoint
- rules + fallacies
- 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)
reduce the number of terms
- 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)
enthymemes
= 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
sorites
= chain of categorical syllogisms in which the intermediate conclusions have been left out
- find the premise that contains the predicate of the conclusion and write it first
- find the other term in the found premise & put it second
- find intermediate conclusions
standard-form sorites
- each of the component propositions is in standard form
- each term occurs twice
- the predicate (major term) of the conclusion is in the first premise (major premise)
- each successive premise has a term in common with the preceding one
