Definitions

Question 1

Reasoning - advancing truth claims by means of special logical procedures of argument

Question 2

Statements or Propositions - sentence that can be either true or false (possess truth value) - also known as contingent statements ( can be either true or false)

Question 3

Bivalence - - statements can only have one truth value in the same sense and under same circumstances

Question 4

Excluded Middle - - no middle ground - true or false

Question 5

Non-Statements - sentences with no truth value

Question 6

Self Contradictions - - statements that under all circumstances are false

Question 7

Tautologies - - statements that under all circumstances are true

Question 8

4 principal ways to compare statements - -
1 - consistency - set of claims that can all be true at the same time
2 - contradiction - when truth of one claim necessitates the falsity of the other
3 - contrary - at least one claim must be false however both claims can be false at the same time
4 - equivalence - both claims must have the same truth values ( both true or both false)

Question 9

Conditional Claim - - type of complex claim in which the truth of one claim (consequent) depends upon on the truth of another claim (antecedent)

Antecedent - the component statement of a conditional claim that follows the “if” statement (premise)

Consequent - the component statement of a conditional claim that follows the “then” statement (conclusion)

Question 10

Deduction and Induction (defined) - -

Deduction - argument that is constructed so that it is impossible for the conclusion to be false if the premises are true

Induction - argument that is structured so that the truth of the premises makes it very likely that the conclusion is true

Question 11

Necessary and Sufficient (defined) - -

Necessary Condition - state of affairs that must occur for another state of affairs to occur ( minimum requirement)

Sufficient Condition - condition that when met is enough to know that some condition has also been met (the consequential requirement)

Question 12

Logical Operators (defined) - -
Conjunction = AND = true only when both conjuncts are true (dot)
Disjunction = OR = false only if both disjuncts are false (inverse of conjunction) (v)
Conditional = IF = false only if antecedent is true (if) and consequent (then) is false (over-turned u)
BiConditional = IFF = true when both claims have same truth value ( both true or both false) (3 stripes)
NEGATION = NO (~)

Question 13

Categorical Syllogisms - - 3 propositions (statements)
P1 = major premise
P2 = minor premise
C = conclusion

Question 14

Categorical Syllogisms - - 3 category names (subject, predicate, middle term)
S = subject of conclusion (must also be in minor premise)
P = predicate of conclusion (must also be in major premise)
M = middle term (only found in major and minor premises)

Question 15

Standard Form - - basic parts - categorical sentences:
Quantity = All / No / Some (quantifier)
Quality = Are / Are Not (affirmative / negative)
Subject = S = category or class
Predicate = P = category or class
Copula = quality = affirmative / negative)

Question 16

4 Standard Forms - - A - E - I - O - categorical sentences:
A = All S are P = universal
E = No S are P = universal
I = Some S are P = particular
O = Some S are Not P = particular

Question 17

Truth Bearing Possibilities - -
1 - Contingent Statements - statements that can be either true or false (aka - propositions)
2 - Self-Contradictions - statements that under all circumstances are false
3 - Tautologies - statements that under all circumstances are true

Question 18

Aristotelian Square of Opposition - -
A - E
I - O
(above is visual reference)
A - E = CONTRARY
I - O = SUBCONTRARY
A \ O = CONTRADICTION
I / E = CONTRADICTION
SUB-ALTERNATION (A > I = T) (I > A = F)
SUB-ALTERNATION (E > O = T) (O > E = F)

Question 19

Definitions - - square of opposition - (contrary, subcontrary, contradiction, sub-alternation)
A - E
I - O
Contrary (A - E) = one claim must be false but both claims can be false
Sub-Contrary (I - O) = one claim must be true but both claims can be true
Contradiction (A - O) or (I - E) = truth of one claim necessitates the falsity of the other
Sub-Alternation (A > I) or (E > O) = when A or E claim is true corresponding I or O claim is true
Sub-Alternation (I > A) or (O > E) = when I or O claim is false corresponding A or E claim is false

Question 20

Transformation Operations - -
Changing categorical propositions into other categorical propositions that have the very same meaning.
CONVERSION (converse) = switch subject and predicate term
CONTRAPOSITION (contrapositive) = replace subject and predicate terms with complement (opposite) and then switch subject and predicate
OBVERSION (obverse) = change quality of claim and replace predicate term with its complement

Question 21

2 types of equivalence = logical and material
Logical = logical form or structure explains equivalence of truth values (tautology)(self-contradiction)

Question 22

Complement - - categorical logic = everything outside of class or category

Question 23

Figure - categorical syllogisms - 4 possible figures (M = middle term)
FIGURE #1
M - P (premise 1)
S - M (premise 2)
FIGURE #2
P - M (premise 1)
S - M (premise 2)
FIGURE #3
M - P (premise 1)
M - S (premise 2)
FIGURE 4
P - M (premise 1)
M - S (premise 2)

Question 24

Quality and Quantity - defined - categorical claims
QUALITY = affirmative / negative (are / are not)
QUANTITY = universal / particular (all or no / some are or some are not)

Question 25

MOOD - structure of A - E - I - O - statements in P1 + P2 + C categorical syllogisms
VALID FORMS - combination of figure and mood
FIGURE 1 - AAA - EAE - AAI - AII - EIO - EAO
FIGURE 2 -