TASK 6 - CATEGORICAL PROPOSITIONS

Question 1

categorical propositions

Answer 1

= proposition that relates two classes or categories
- that which is understood is viewed as something (= subject) which is more closely defined by a semantic content (= predicate)

Question 2

subject term

Answer 2

= THAT WHICH we indicate

• refer to that which is understood
• humans

Question 3

predicate term

Answer 3

= WITH WHICH we indicate

• expression of the semantic content by which it is understood
• mortal

Question 4

quantity

Answer 4

- either universal vs. particular depending on whether the statement makes a claim about every member or just some member of the class denoted by the subject term 
= all, no, some

Question 5

copula

Answer 5

= link between subject and predicate

= are/aren’t

Question 6

quality

Answer 6

• either affirmative vs. negative depending on whether it affirms or denies a class membership
• are/aren’t, all/no

Question 7

distribution

Answer 7

• distributed = when it makes an assertion about every member of the class denoted by that term
• All S are P = S distributed = ALL S = every member

Question 8

standard-form categorical propositions

- A

Answer 8

= all S are P

• the whole subject class is included in the predicate class
• universal, affirmative
• S distributed

Question 9

standard-form categorical propositions

- E

Answer 9

= no S are P

• the whole subject class is excluded from the predicate class
• universal, negative
• both distributed

Question 10

standard-form categorical propositions

- i

Answer 10

= some S are P

• part of the subject class is included in the predicate class
• particular, affirmative
• undistributed (none distributed)

Question 11

standard-form categorical propositions

- o

Answer 11

= some S are not P

• part of the subject class is excluded from the predicate class
• particular, negative
• P distributed

Question 12

Existential import

Answer 12

= two possible interpretations of universal propositions (A + E)
–> both recognised that particular propositions (i + o) make positive assertions about existence

Question 13

Aristotelian standpoint

Answer 13

= statements imply existence of the things talked about thus has existential import

• statements can have existential import, because their subject terms denote actually existing things
• open to existence

Question 14

Boolean standpoint

Answer 14

= statements to imply existence thus no existential

• there is no universal proposition with existential import
• closed to existence
• existence is not recognised

Question 15

Venn diagram

Answer 15

= arrangement of overlapping circles; each circle represents the class denoted by a term in a categorical proposition (S + P)

• members of a class are situated inside their corresponding circle
• members belonging to both classes are situated in the overlapping area
• if any member is situated outside, it does not belong to any of the two classes

Question 16

traditional square of opposition

Answer 16

= represents the relationship of mutually contradictory pairs of propositions

Question 17

traditional square of opposition

- contradictory

Answer 17

= opposite truth value =complete opposition/ mutually exclusive

1. A true = o false
2. o true = A false
3. E true = i false
4. i true = E false

Question 18

traditional square of opposition

- contrary

Answer 18

= at least one is false = cannot both true as affirmation + negation of same thing

1. A true = o false = E false
2. E true = o true = A false
3. A/E given false = invalid; logically undetermined value

Question 19

traditional square of opposition

- subcontrary

Answer 19

= at least one is true = cannot both be wrong

- same as contrary just with i + o

Question 20

traditional square of opposition

- subalternation

Answer 20

= truth flows downward, falsity flows upward

1. A true = i true
2. A false = invalid; undetermined
3. i false = A false
4. i true = invalid; undetermined

Question 21

traditional square of opposition

- rule of thumb

Answer 21

1. always use CONTRADICTION first when using the square
2. if one remaining relation yield a logically undetermined truth value, the other will as well
3. whenever one statement turns out to have logically undetermined truth value, its contradiction will also

Question 22

existential fallacy

Answer 22

= when contrary/subcontrary/subalternation are used (in an otherwise correct way) to draw a conclusion from a premise about things that do not exist

• all begin with universal proposition with no existential import + conclude with particular proposition with existential import
• conditionally valid: when not sure whether something actually exists

Question 23

conversion

Answer 23

= switching subject + predicate terms

• conversion of E + i = equivalent
• illicit conversion: invalid inference (A + o)

Question 24

obversion

Answer 24

= change quality (affirmative vs. negative) without changing the quantity –> replace predicate with term complement (= group consisting of everything outside the class, e.g. dog = non-dog)

• all are logically equivalent
• -> for A + E: quantifier changed
• -> for i + o = copula changed

Question 25

contraposition

Answer 25

= switch subject + predicate terms –> replace them with their term complements

• A + o = equivalent
• E + i = illicit contraposition

Question 26

translate ordinary language into categorical form

Answer 26

• add pronoun/noun to make genuinely denotative
• reform non-standard verbs to insert “are (not)”
• add parameter to singular propositions
• replace adverbs with places/times and pronouns with people/things (following w-word = subject form)
• expressed quantifiers that are implicit
• conditional statements: what follows “if” = subject term, what follows “only if” = predicate term
• exclusive propositions (only, none but, none except): what follows those = predicate
• what comes after “the only” = subject term
• exceptive propositions must be replaced by pairs of conjoined categorical propositions