Counterexamples Flashcards
What is a counterexample to an argument?
A possible situation in which the premises of the argument are all true and its conclusion is false.
How can an argument be logically invalid?
Iff there is a possible situation in which its premises are all true and its conclusion is false. (if it has a counterexample).
What is a sentential connective?
A sentential connective takes one or more sentences (atomic or complex) and forms new, complex sentences from them.
(and, it is not the case that, because)
What is the adverb which describes the connectives which create complex sentences?
Sentential
How many sentential connectives are in FOL?
5
What is ¬ ?
- It is not the case that
- It is a 1-place connective
What is ∧ ?
and
2-place connective
What is ∨ ?
either/or
2-place connective
What makes a connective truth functional?
Iff the truth value of the complex sentence built up using the connective is completely determined by the truth value of the simpler sentences from which it is built.
What does a truth table do?
It shows how the truth value of the complex sentence is determined by the truth value of the simpler sentences.
Why is ‘because’ not a truth functional connective?
The truth value of a complex sentence built up using the connective ‘because’ isn’t completely determined by the truth value of the simpler sentences from which it was built.
Is the English sentential connective ‘and’ truth functional?
The temporal and causal relations are not part of what is literally said by the sentence, it is only a conversational implication. (cancellable)
Is the English sentential connective ‘and’ truth functional?
yes
When are the outer brackets dropped on zoxiy?
When the main connective of an FOL sentence is a 2-place connective (∨, ∧)
