Chapter 1: What is Logic? Flashcards
(17 cards)
What is a logical argument?
A set of sentences structured with premises intended to offer support for a conclusion. Anatomy: first sentences are premises, last sentence is the conclusion. An argument whose premises have no relation with the conclusion can still be defined as such.
What are premises? Give some premise indicators.
Starting points, used to lend support to the conclusion.
Indicators: since, because, given that
What is a conclusion? Give some conclusion indicators.
The claim the argument is trying to establish.
Indicators: therefore, hence, thus, then, so
What are propositions?
Sentences that can be true or false (not questions; regardless of facts or opinions).
What do we consider as a sentence?
A sentence that expresses a proposition and can either be true or false. Answers (e.g. “I do not know how to write.”) Imperatives (e.g. “Wake up!” “Leave!”) Not questions, not exclamations.
Two ways an argument could be weak?
- At least one of its premises might be false.
2. Premises might fail to support the conclusion or fail to support it sufficiently strong.
What does it mean for an argument to be deductively valid?
Argument is deductively valid iff it is impossible for all the premises to be true while the conclusion is false.
Define a sound argument.
An argument is sound iff it is valid and all of its premises are true.
What does it mean for a sentence to be impossible?
There is no possible way for it to be true. Must be false. (E.g. Pigs can fly and pigs cannot fly) [just “pigs can fly” is NOT impossible!]
Define contingent sentences
Sentences that could be true, or could be false. (E.g. It is raining) A contingent sentence is a sentence that is neither a tautology nor a contradiction.
Define logical truth/ tautology
Sentences that must be true no matter what (e.g. It is either cold today, or it is not cold today)
Define contradiction and what it means for a sentence to be logically false.
Logically false = contradiction. Sentence is always false no matter what. (E.g. “There is an earthquake happening here right now and there are never earthquakes here.”)
When do we say two sentences are logically equivalent?
When they necessarily (always) have the same truth value (i.e. Sentence X <=> Sentence Y)
What does it mean for a set of sentences to be inconsistent?
When the sentences could not all be true at the same time.
What does it mean for a set of sentences to be consistent?
When the sentences could all be true at the same time.
What does a logical language being bivalent mean?
Bivalent = two-valued = true and false are the only possible truth values for the language
Classical logic?
The logic system we are using. Every sentence is either true or false (exactly 1 truth value)
