8. Three connectives

Question 1

AND Truth-Conditional (3)

Answer 1

A) Binary and propositional connective (Symbol ∧)
Connects two expressions/sentences
B) Truth condition: A=1 B=1 then Conclusion=1
All other cases=0
C) Order of variables are fixed (Syntax)

Question 2

AND Non-Truth-Conditional (3)

Answer 2

A) Temporal Succession
e.g. Eve married Adam and she became pregnant.
B) Simultaneity
e.g. Jean-Paul is reading a book and smoking a cigarette
C) Causality
e.g. The vase fell on the ground and it broke into pieces

Question 3

OR Truth-Conditional (4)

Answer 3

A) Binary and propositional connective (Symbol ∨)
Connects two expressions/sentences
B) Truth condition: If A=1 or B=1 then Conclusion=1
If A=0 & B=0 then Conclusion=0
C) Inclusive Disjunction (A or B or Both) = ∨
D) Exclusive Disjunction (A or B but not both) = ⊕

Question 4

NOT Truth-Conditional (3)

Answer 4

A) Negational connective (Symbol ¬)
Negates/Denies a sentence
B) Truth Condition: If A=1, then not A=0
If A=0, then not A=1
Not-Not: If A=1, then not A=0, then not-not A=1
C) A is equivalent to not=not A

Question 5

Scope (2)

Answer 5

A) Scope ambiguity is a type of structural ambiguity by
1) How words are put together and
2) Combining connectives
B) Use brackets to avoid ambiguities in formal language

Question 6

Atomic Propositions (2)

Answer 6

A) Most basic propositions
EX: A, B
B) Basic Building blocks for all other propositions

Question 7

Molecular Propositions (2)

Answer 7

A) Complex propositions
EX: (A ∧ B)
B) Built from atomic propositions

Question 8

Formalization

Answer 8

1) Formalize argument:
Watch out for hidden premises and scope ambiguities
2) Investigate validity of formal argument:
All murk has been cleared out: Mathematical exercise
3) Two possible mistakes
A) Correct formalization but Mathematical Mistake
B) Incorrect formalization