Problem 7

Question 1

Universal affirmative (A)

Answer 1

Every, all

–> Affirmo (“I affirm”)

Question 2

Particular affirmative (I)

Answer 2

Some

–> affIrmo (“I affirm”)

Question 3

Universal negative (E)

Answer 3

None

–> nEgo (“I deny”)

Question 4

Particular negative (O)

Answer 4

Some.. not

–> negO (“I deny”)

Question 5

Logical square

Answer 5

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

Question 6

Contradictory

Answer 6

Opposite truth value
–> thus A is opposite to O; E vs I

e.g.: A false = O true

Question 7

Contrary

Answer 7

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)

Question 8

Subcontrary

Answer 8

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)

Question 9

Subaltern

Answer 9

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

Question 10

Proposition

Answer 10

Sentence that is either true or false

Question 11

Categorical proposition

Answer 11

Refers to a proposition that relates 2 categories

e.g.: subject + predicate

Question 12

Quantifiers

Answer 12

Specify how much of the subject class is included to excluded from the predicate term

ex.: all, no, some

Question 13

Copula

Answer 13

Link the subject with the predicate

ex.: are, are not

Question 14

Quality of the proposition

Answer 14

Can be either affirmative or negative

Question 15

Existential import

Answer 15

Implying that one or more things denoted by subject actually exist or don’t

Question 16

Aristotelian standpoint

Answer 16

UPs about existing things have existential import

–> open to existence

Question 17

Boolean standpoint

Answer 17

No UPs have existential import

–> closed to existence

Question 18

Unconditionally valid

Answer 18

Refer to arguments that are valid from the boolean standpoint, which are valid regardless of whirler the terms refer to existing things

Question 19

Existential fallacy

Answer 19

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.

Question 20

Conversion

Answer 20

Switching the subject with the predicate

ex.: No foxes are hedgehogs, no hedgehogs are foxes

Question 21

Obversion

Answer 21

1. Changing the quality w/o changing the quantity
   e. g.: No S are P to All S are P
2. Replacing the P with its term complement
   ex. : all horses are animal –> no horses are non animals

TRUTH VALUE STAYS THE SAME

Question 22

Contraposition

Answer 22

1. Switching subject + predicate terms
2. Replacing subject + predicate with their complements
   ex. : ALL goats are animal –> ALL non-animals are non-goats

Question 23

Rules of thumb

Answer 23

1. Always use CONTRADICTION FIRST

–> If one of the remaining relations yields a logically undetermined truth value, the others will as well

2. 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.

Question 24

How do you prove the traditional square of opposition ?

Answer 24

1. If the A statement is given as True (left S circle is empty) O statement false (left S circle is red.
2. If the O statement is given as True (left S circle is not empty) O statement false.
3. If the O statement is given as false (left S circle is empty) A statement true
4. If the A statement is given as false (left S circle is not empty or overlap area is empty or both)

Question 25

How do you test immediate inferences ?

Answer 25

1. Reduce the inference to its forms and test if from the Boolean standpoint.

–> If the form is valid, proceed no further

2. 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.

3. 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

Question 26

General rule of translation

Answer 26

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

Question 27

Terms without nouns

Answer 27

If a term consists of only an adjective, a plural noun or pronoun should be introduced

ex.: all tigers are carnivorous –> carnivorous animals

Question 28

Nonstandard verbs

Answer 28

The only copulas that are allowed in standard-form categorical propositions are “are” + “are not”

ex.: All ducks swim –> all ducks are swimmers

Question 29

Singular propositions

Answer 29

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

Question 30

Parameter

Answer 30

Refers to a phrase that when introduced into a statement, affects the form but not the meaning

Question 31

Distributed vs Undistributed

Answer 31

1.Distributed
A = distributes the S
E = distributes S+P

2. Undistributed
   I = distributes neither
   O = distributes the P