Problem 7 Flashcards
Universal affirmative (A)
Every, all
–> Affirmo (“I affirm”)
Particular affirmative (I)
Some
–> affIrmo (“I affirm”)
Universal negative (E)
None
–> nEgo (“I deny”)
Particular negative (O)
Some.. not
–> negO (“I deny”)
Logical square
Refers to a diagram that incorporates 4 possible kinds of proposition with the same subject + predicate
–> universal proposition indicates whether subaltern is wrong or right
Contradictory
Opposite truth value
–> thus A is opposite to O; E vs I
e.g.: A false = O true
Contrary
Cannot be true at same time but can be false or different at same time
ex.: All swiss watches + no switch watches are work of arts are both false propositions if only some are.
–> A vs E
AT LEAST ONE IS FALSE (not both true)
Subcontrary
Cannot be false at the same time, but can be true or different at same time
ex.: Some swiss watches are work of art + some are not are both true, if part of them are work of art and some not.
–> I + O
AT LEAST ONE IS TRUE (not both false)
Subaltern
If UP is true, the PP is too + If PP is false then UP is too
e.g.: “Truth comes from heaven + lies come from hell”
–> A + E are the UPs and I + O are the PPs
Proposition
Sentence that is either true or false
Categorical proposition
Refers to a proposition that relates 2 categories
e.g.: subject + predicate
Quantifiers
Specify how much of the subject class is included to excluded from the predicate term
ex.: all, no, some
Copula
Link the subject with the predicate
ex.: are, are not
Quality of the proposition
Can be either affirmative or negative
Existential import
Implying that one or more things denoted by subject actually exist or don’t
Aristotelian standpoint
UPs about existing things have existential import
–> open to existence
Boolean standpoint
No UPs have existential import
–> closed to existence
Unconditionally valid
Refer to arguments that are valid from the boolean standpoint, which are valid regardless of whirler the terms refer to existing things
Existential fallacy
The Boolean standpoint suggests that an argument is invalid merely because the premise lacks existential import.
➔ Detecting it: A pair of diagrams in which the premise diagram contains shading and the conclusion diagram contains an X. If the X in the conclusion diagram is in the same part of the left circle that is unshaded in the premise diagram, the inference commits EXISTENTIAL FALLACY.
Conversion
Switching the subject with the predicate
ex.: No foxes are hedgehogs, no hedgehogs are foxes
Obversion
- Changing the quality w/o changing the quantity
e. g.: No S are P to All S are P - Replacing the P with its term complement
ex. : all horses are animal –> no horses are non animals
TRUTH VALUE STAYS THE SAME
Contraposition
- Switching subject + predicate terms
- Replacing subject + predicate with their complements
ex. : ALL goats are animal –> ALL non-animals are non-goats
Rules of thumb
- Always use CONTRADICTION FIRST
–> If one of the remaining relations yields a logically undetermined truth value, the others will as well
- Whenever one statement turns out to have logically undetermined truth value, its contradictory will also.
–> Statements having logically undetermined truth value will always occur in pairs, at opposite ends of diagonals on the square.
How do you prove the traditional square of opposition ?
- If the A statement is given as True (left S circle is empty) O statement false (left S circle is red.
- If the O statement is given as True (left S circle is not empty) O statement false.
- If the O statement is given as false (left S circle is empty) A statement true
- If the A statement is given as false (left S circle is not empty or overlap area is empty or both)
How do you test immediate inferences ?
- Reduce the inference to its forms and test if from the Boolean standpoint.
–> If the form is valid, proceed no further
- If the inference form is invalid from the Boolean standpoint and has a particular conclusion, then adopt the Aristotelian standpoint and look to see if the left hand premise circle is partly shaded
–> If it is, enter a circled X in the unshaded part of the retest form, then the information of the conclusion diagram is represented in the premise diagram. Thus, the inference form is conditionally valid from an Aristotelian standpoint.
- If the inference form is conditionally valid, determine if the circle X represents something that exists.
–> If it does, the condition is fulfilled, and the inference is valid from the Aristotelian standpoint.
BUT: If not, the inference is invalid and it commits the existential fallacy from the Aristotelian standpoint
General rule of translation
One should understand the meaning of the given statement, then re-express it in a new statement that has
a) quantifier
b) subject
c) predicate
d) copula
Terms without nouns
If a term consists of only an adjective, a plural noun or pronoun should be introduced
ex.: all tigers are carnivorous –> carnivorous animals
Nonstandard verbs
The only copulas that are allowed in standard-form categorical propositions are “are” + “are not”
ex.: All ducks swim –> all ducks are swimmers
Singular propositions
Refer to propositions that make an assertion about a specific
a) person
b) place
c) thing
d) time
–> Parameters are used to translate singular propositions into UPs
ex.: George went home –> all people identical to george are people who went home
Parameter
Refers to a phrase that when introduced into a statement, affects the form but not the meaning
Distributed vs Undistributed
1.Distributed
A = distributes the S
E = distributes S+P
- Undistributed
I = distributes neither
O = distributes the P
