unit 2

Question 1

metavariables

Answer 1

Metavariables (φ,ψ,θ,…) are variables that are part of our metalanguage (i.e. not a part of the object language TFL), which range over sentences of TFL.

Question 2

sentences of tfl

Answer 2

A string of symbols from the language of TFL is a sentence of TFL iff the string can be generated by any number of applications of the following rules

1. Every sentence letter is a sentence of TFL.
2. If φ is a sentence of TFL, then ¬φ is a sentence of TFL.
3. If φ and ψ are sentences of TFL, then (φ ∨ ψ) is a sentence of TFL.
4. If φ and ψ are sentences of TFL, then (φ ∧ ψ) is a sentence of TFL.
5. If φ and ψ are sentences of TFL, then (φ ⊃ ψ) is a sentence of TFL.
6. If φ and ψ are sentences of TFL, then (φ ≡ ψ) is a sentence of TFL.

Question 3

constructional history

Answer 3

a sequence of sentences of TFL and rules from the recursive definition of sentences of TFL that demonstrates that the string of symbols is a sentence

Question 4

main operator

Answer 4

the operator that is added in the final step of the constructional history

Question 5

subformulas

Answer 5

any sentence that occurs in the constructional history prior to the final step

Question 6

tautology

Answer 6

a sentence that could not possibly be false

Question 7

contradiction

Answer 7

a sentence that could not possibly be true

Question 8

contingency

Answer 8

a sentence that could be true and could be false

Question 9

logical equivalence

Answer 9

two sentences that are logically equivalent must have the same truth value

Question 10

joint satisfiability

Answer 10

a set of sentences are jointly satisfiable if all members of the set are true

Question 11

entailment

Answer 11

A set of sentences Γ entails a sentence φ just in case it could not possibly be the case that every member of Γ is true and φ is false.