3. Logical Truth Flashcards
1
Q
A sentence is a logical truth iff…
A
- it is true in every possible situation.
- An FOLp sentence is a logical truth iff there is no row in its truth table in which it is F
2
Q
A sentence is a contradiction iff…
A
- it is false in every possible situation.
- A contradiction in FOLp is if there are no rows in its truth table in which it is T.
3
Q
How is a sentence logically possible?
A
- Iff there is at least one possible situation which it is T.
- An FOLp sentence is a logical possibility iff there is at least one row in its truth table in which it is T.
4
Q
What is a TT- contradiction?
A
Iff a sentence has a truth functional form that can be captured by an FOLp sentence which is a contradiction.
5
Q
Two sentences are logically equivalent iff…
A
they have the same truth value in every possible situation.
6
Q
Two FOLp sentences are logically equivalent iff…
A
- there is no assignment of truth values to their sentence letters in which they differ in truth value.
- or… in a joint truth table for the two sentences, there is no row in which one of them is T and the other is F.
7
Q
what does <=> mean?
A
logically equivalent
8
Q
When can an argument be described as TT-invalid?
A
An argument that is not logically valid in virtue of its truth functional form.
9
Q
How can we possibly determine whether two sentences are logically equivalent?
A
We can go through a chain of substitutions in which we rely on familiar equivalences.
