Logic Test 1

Logic

The study of rational argumentation

Argument

A set of sentences such that one sentence, the conclusion, is claimed to follow from the other sentences, the premises.

Conclusion

The thing being argued for, that which we are trying to convince ourselves or others of, there is only one

Premises

 The grounds that are being proposed to support rational belief in the conclusion

Consistency

They are all true at the same time. (Very Weak)

Deduction

Argues from broad to narrow, that is, the content of its conclusion does not outrun the content of its premises

Induction

Argues from narrow to broad, the conclusion claims more than what the evidence actually proves

Validity

Assuming the truth of the premises for the sake of argument, the conclusion follows from them.

Well-groundedness

All of its premises are true

truth-functional language 

 two elements: atomic sentences and truth-functional connectives

 Atomic sentences

simple declarative sentences that are either true or false

Tautology

All the values in each truth table are true

Contradiction

There it is false for every possible arrangement of truth values of its constituent atomic sentences.

Contingency

If there is at least one set of truth values for its constituent atomic sentences that renders the sentence true and at least one set of truth values for its constituent atomic sentences that renders the sentence false.

Truth-functional Consistency

In a truth table containing both, there is at least one set of truth values for the constituent atomic sentences that renders both sentences true.

Truth-functional Equivalence

For every set of truth values in the atomic sentences, the truth values of S₁ and S₂ are the same.

Truth-functional Implication

If in every case in which the first sentence is true, the second sentence is also true.

Negation

-, not

Conjunction

^, &, and, both, also, but

Disjunction

v, or

exclusive or

either or, unless, if and only if

Conditional

→, if then, for, because if, only if

Deductive validity

The conclusion follows logically from the premises and falls within the scope of the premises