Originally posted by Tom
In PF v2.0, I posted some exercises to reinforce the material covered in the notes. Audacity Dan (now Dissident Dan) posted his solutions to the first set. If you would like to see them, then cough up the $20 for the archive CD.
Here are some exercises that cover Chapter 0 pretty comprehensively.
Disproof by Counterexample
Each of the following deductive arguments is invalid. Provide a counterexample for each.
Argument 1:
All paramecia are single-celled organisms.
No sea urchins are paramecia.
Therefore, no sea urchins are single-celled organisms.
All humans are multi-cellular.
No dogs are humans.
Therefore, no dogs are multi-cellular.
Argument 2:
Some Englishmen are Protestants.
Winston Churchill was a Protestant.
Therefore, Winston Churchill was an Englishman.
Some PF members are atheists.
Futurist was a PF member.
Therefore, Futurist was an atheist (this one is for those of you who have been here for a while).
Argument 3:
If an animal is a mammal, then it bears its young live.
A gorilla bears its young live.
Therefore, a gorilla is a mammal.
If an animal is a bird, then it lays eggs.
An Iguana lays eggs.
Therefore an Iguana is a bird.
Argument 4:
Some dogs are good pets.
Some dogs are terriers.
Therefore, some terriers are good pets.
Some fish are fearsome predators.
Some fish are goldfish.
Therefore, some goldfish are fearsome predators.
Deductive or Inductive?
Examine each argument below. Is the argument deductive or inductive? Explain.
Argument 1:
All human choices are determined, since all events in the universe are determined and all human choices are events in the universe.
Deductive. You are taking two propositions (that all events in the Universe are determined, and that all human choices are events in the Universe) and finding the proposition that logically follows.
Argument 2:
All birds can fly. I’ve never seen one that can’t.
Inductive. You are reasoning only on an observed pattern.
Argument 3:
Today is Wednesday. You came 4 days ago, so that means you came on Saturday.
Deductive. You are again taking two propositions (that I came 4 days ago, and that today is Wednesday), and finding the proposition that logically follows.
Argument 4:
I sent her the letter 3 weeks ago and have still received no answer; therefore, my letter must have been lost in the mail.
Hmm. Inductive, I guess - though there this is not really a logical conclusion, but just one of the possibilities.
Argument 5:
A=B and B=C, therefore A=C.
Deductive. This is a mathematical approach. Plus, you have taken two premises, that must always be true, and found the proposition that logically follows.
Argument Analysis and Charity
Assuming ordinary context, examine each of the following arguments. Identify the conclusion and the premises, and supply a missing premise that would make the argument deductively valid.
Argument 1:
Bats are not birds, because birds have feathers.
Propositions:
1) Birds have feathers.
3) Bats are not birds.
Missing proposition:
2) Bats don't have feathers.
Argument 2:
The baseball game was dull, since both teams played poorly.
Propositions:
1) The game was dull.
3) Both teams played poorly.
Missing proposition:
2) Games, in which both teams play poorly, are dull.
Argument 3:
This liquid is not acid, for the litmus paper we placed in it did not turn red.
Propositions:
1) This liquid is not acid.
3) The litmus paper didn't turn read.
Missing proposition:
2) When litmus paper is introduced to an acid, it turns red.
Argument 4:
He passed the examination; therefore, he must have lied.
1) He passed the exam.
3) He must have lied.
Missing Proposition:
2) He cannot pass without lying.
These are probably all wrong, but it was fun trying.
