Other logical notions

For each of the following: Is it necessarily true, necessarily false, or contingent?

1. Caesar crossed the Rubicon.

2. Someone once crossed the Rubicon.

3. No one has ever crossed the Rubicon.

4. If Caesar crossed the Rubicon, then someone has.

5. Even though Caesar crossed the Rubicon, no one has ever crossed the Rubicon.

6. If anyone has ever crossed the Rubicon, it was Caesar.

Consider the following sentences:

1. There are at least four giraffes at the wild animal park.

2. There are exactly seven gorillas at the wild animal park.

3. There are not more than two Martians at the wild animal park.

4. Every giraffe at the wild animal park is a Martian.

Now consider each of the following collections of sentences. Which are jointly possible? Which are jointly impossible?

1. Sente…

Which of the following is possible? If it is possible, give an example. If it is not possible, explain why.

1. A valid argument that has one false premise and one true premise

2. A valid argument that has a false conclusion

3. A valid argument, the conclusion of which is a necessary falsehood

4. An invalid argument, the conclusion of which is a necessary truth

5. A necessary truth that is contingent

6. …