TASK 6 - CATEGORICAL PROPOSITIONS Flashcards
categorical propositions
= 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)
subject term
= THAT WHICH we indicate
- refer to that which is understood
- humans
predicate term
= WITH WHICH we indicate
- expression of the semantic content by which it is understood
- mortal
quantity
- 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
copula
= link between subject and predicate
= are/aren’t
quality
- either affirmative vs. negative depending on whether it affirms or denies a class membership
- are/aren’t, all/no
distribution
- 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
standard-form categorical propositions
- A
= all S are P
- the whole subject class is included in the predicate class
- universal, affirmative
- S distributed
standard-form categorical propositions
- E
= no S are P
- the whole subject class is excluded from the predicate class
- universal, negative
- both distributed
standard-form categorical propositions
- i
= some S are P
- part of the subject class is included in the predicate class
- particular, affirmative
- undistributed (none distributed)
standard-form categorical propositions
- o
= some S are not P
- part of the subject class is excluded from the predicate class
- particular, negative
- P distributed
Existential import
= two possible interpretations of universal propositions (A + E)
–> both recognised that particular propositions (i + o) make positive assertions about existence
Aristotelian standpoint
= 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
Boolean standpoint
= statements to imply existence thus no existential
- there is no universal proposition with existential import
- closed to existence
- existence is not recognised
Venn diagram
= 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
traditional square of opposition
= represents the relationship of mutually contradictory pairs of propositions
traditional square of opposition
- contradictory
= opposite truth value =complete opposition/ mutually exclusive
- A true = o false
- o true = A false
- E true = i false
- i true = E false
traditional square of opposition
- contrary
= at least one is false = cannot both true as affirmation + negation of same thing
- A true = o false = E false
- E true = o true = A false
- A/E given false = invalid; logically undetermined value
traditional square of opposition
- subcontrary
= at least one is true = cannot both be wrong
- same as contrary just with i + o
traditional square of opposition
- subalternation
= truth flows downward, falsity flows upward
- A true = i true
- A false = invalid; undetermined
- i false = A false
- i true = invalid; undetermined
traditional square of opposition
- rule of thumb
- always use CONTRADICTION first when using the square
- if one remaining relation yield a logically undetermined truth value, the other will as well
- whenever one statement turns out to have logically undetermined truth value, its contradiction will also
existential fallacy
= 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
conversion
= switching subject + predicate terms
- conversion of E + i = equivalent
- illicit conversion: invalid inference (A + o)
obversion
= 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
contraposition
= switch subject + predicate terms –> replace them with their term complements
- A + o = equivalent
- E + i = illicit contraposition
translate ordinary language into categorical form
- 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
