1 First Week Flashcards
What is a statement?
A statement is a sentence (or a part of a sentence) that is true or false.
“7619 is a prime number.”
Is this a statement?
A statement is a sentence (or a part of a sentence) that is true or false.
So yes, this is a statement.
“Where is the grocery store?”
Is this a statement?
A statement is a sentence (or a part of a sentence) that is true or false.
A question is neither true nor false.
So questions are not statements.
So no, this is not a statement.
“Bloody hell!”
Is this a statement?
A statement is a sentence (or a part of a sentence) that is true or false.
“Bloody hell!” is neither true nor false, so it is not a statement.
“Get some eggs from the grocery store.”
Is this a statement?
A statement is a sentence (or a part of a sentence) that is true or false.
“Please get some eggs from the grocery store” is a command, not a statement.
“The largest city by population in the USA is LA.”
Is this a statement?
A statement is a sentence (or a part of a sentence) that is true or false.
So yes, this is a statement.
What is an inference?
An inference is a collection of one or more premises, together with a conclusion.
The premise is a statement (or, the premises are statements).
The conclusion is a statement.
Typically, someone giving an inference wants to persuade you that the conclusion is true, on the basis of the premises.
What is a valid inference?
What is an invalid inference?
An inference is valid if there is no possible situation in which the premises are true and the conclusion is false.
An inference is invalid if it is not valid.
Note that in logic “valid” is not just a synonym for “good” or “correct”.
Premise: Ashni goes running three times a week.
Conclusion: Ashni enjoys running.
Is this valid?
This inference is not valid.
Consider a possible situation in which Ashni doesn’t enjoy running, but goes
running several times a week anyway because her doctor told her to.
Premise: Ashni ordered either soup or salad.
Premise: Ashni didn’t order soup.
Conclusion: Ashni ordered salad.
Is this inference valid?
This inference is valid — there is no possible situation in which
the premises are true and the conclusion is false.
Premise: Ashni isn’t taking both PHIL 110 and PHIL 100w.
Premise: Ashni is taking PHIL 110.
Conclusion: Ashni isn’t taking PHIL 100w.
Is this inference valid?
This inference is valid — there is no possible situation in which
the premises are true and the conclusion is false.
Premise: People who spend more time outside are less likely to suffer from depression.
Conclusion: Spending time outside prevents depression.
Is this inference valid?
This inference is not valid. As every internet bore knows, correlation doesn’t prove causation.
What is an argument?
An argument is a series of statements. Each statement in the sequence is either a premise, or the conclusion of an inference whose premises are earlier in the sequence. The final statement in the sequence is the conclusion of the argument.
Typically, someone who presents an argument is trying to persuade you that the conclusion is true.
In practice, people often present arguments out of order, and they decorate the arguments with comments, jokes, and other things.
Past Exam Question!
No, Kai has not proved the statement.
A proof provides certainty.
Kai cannot be certain that there are no counterexamples to the statement above 1,000,000.
Past Exam Question
No, Jay has not proved the statement.
Even if Jay has shown that the sum of the internal angles in this triangle is 180°; it doesn’t follow with certainty that this is true for all triangles.
(Moreover, it is doubtful that the angles in Jay’s triangle add up to exactly 180°. Measurement is always imperfect!)
