statements
- a sentence that has a truth value
- often also called “proposition”
- not all sentences are statements
eg. questions don’t usually have a truth value - different sentences can be the same statements
can truth values change?
Yes, like it’s raining outside may be false now but if it starts raining it will be true.
compare arugments in ordinary language vs in logic
- in ordinary language: an argument is often a heated discussion between 2 or more people who disagree
- in logic: an argument is 2 or more statements intended to be related so that one is justified by the other (s)
what are the parts of an argument
one or more premises (the reasons) and exactly one conclusion
what’s the difference between arguments and explanations
- Arguments are about something being true or false
- explanations are about “why” or “how”
inductive vs deductive arguments
- Inductive: argument is sufficient to make the conclusion probable, but not necessary. (no guarantee).
- deductive: argument is sufficient to make the conclusion necessary (guaranteed true)
what is a valid argument
An argument that guarantees the truth of the conclusion whenever the premises are true.
(if the premises are true then conclusion must be true
if an argument has false premises can the argument be valid? how?
Yes if they would guarantee the conclusion if the premises were true, they’re still valid
do false premises guarantee false conclusions?
nope, conclusion can still be true
do true premises always mean the argument is valid
nope
how do you prove an argument is invalid?
If it permits a counterexample, (if there’s another structure they’re both invalid).
what’s a counter example
an argument with the same form as the original argument, but which has
* obviously true premises and an obviously false conclusion
Counterexamples
- Counterexamples are proof that an argument is invalid
- they are also effective in contexts were people don’t know logic
- someone who has never studied reasoning can often be convinced “by ear” that their argument is flawed with the presentation of a good counter example.
how do you provide counter example?
- take the original argument:
- identify the form (the structure of the argument)
- think of another argument with the same form but with obviously true premises and an obviously false conclusion.
an argument is “sound” if
it is Valid AND its premises are all true
(this helps us remember that valid does not mean TRUE, we wouldn’t need the concept “sound” if valid= true)
Inductive arguments
- Never valid: (no guarantee)
- strong (highly likely to be true) or weak (not likely to be)
fallacies
arguments that don’t work
