validity Flashcards
model we create to study our reasoning. there can be infinitely many
logical system
the rules and principles of reasoning that we use every day. the study of our reasoning.
logic
the structure of logic. replacing words with symbols reveals form. reasoning depends on form
formal/ symbolic logic
whenever the premises are true, the conclusion is also true.
deductive logical entailment
true or false: it is impossible for the premises to be true and the conclusion false
true
true or false: whenever the premises are true, the conclusion cannot be false
true
what makes a valid argument?
premises entail the conclusion
possibility and likelihood in logic. (“probably”, “likely”)
inductive logic
guarantee and certainty in logic (“it is certain that…”, “guarantees that”)
deductive logic
give people the benefit of doubt and interpret their arguments in a reasonable way
principle of clarity
true or false: circular reasoning is valid
true
true or false: an argument w contradictory premises is valid
true
what makes an argument invalid?
when the premises are true and the conclusion is false
a necessary truth due to logical laws
logical truth
a necessary falsehood due to logical laws
logical falsity
true or false: an argument with a logically ture conclusion is always valid
true
something that might or might not be the case from a logical point of view; not necessary.
contingent
something that must be true because of the laws of logic
logical necessity
adding premises to make a new argument
augmentation
true or false: augmentation can make a valid argument invalid
false
valid + true premises
sound
what are the 3 weird cases of validity?
circular reasoning, logically true conclusions, and contradictory premises
what is an atomic sentence?
letters, no symbols
what is the number of rows in a truth table?
2^n
grammar and form
syntax
meaning and truth
semantics
use and context
pragmatics
a sentence that is logically true because of the truth functional connectives (Pv~P)
tautology
simplify using demorgan’s:
1. ~(PvQ)
2. ~(P&Q)
- ~P&~Q
- ~Pv~Q
what is a counterexample?
a row in which the premise is true and the conclusion false
true or false: if an argument has true premises and a true conclusion, then it must be valid
false
true or false: if an argument is invalid, then it must be unsound
true
true or false: a contingently false premise can entail a contingently true conclusion
truet
true or false: a contingently true premise can entail a contingently false conclusion
false
true or false: a logically true premise can entail a contingently true conclusion
false