Exercises on Deductive Arguments
1. Which of the following would make the best major premise for a deductive argument?
2. Which would be the best way to restate the claim, "The hardest-working students receive the highest grades," for use in analyzing a deductive argument?
3. Since all deductive arguments can be expressed as either syllogisms or conditionals, choose the equivalent conditional for the following major premise of a syllogism: "All men are mortal."
4. Since all deductive arguments can be expressed as either syllogisms or conditionals, convert the following conditional into a premise for a syllogism: "If the Spartans win, then Amy will celebrate."
1. Which of the following would make the best major premise for a deductive argument? You answered:
Ghosts are
the products of over-active imaginations.
Two important factors for the main premise of a deductive argument are
that it relate two terms, and
that it be stated as a generalization, rule, or principle.
"Ghosts are the products of over-active imaginations" is both a generalization, and a way of relating two terms, "ghosts" and "products of an over-active imagination." We can therefore complete the argument with a second premise, "Hamlet's father is a ghost," and a conclusion, "Therefore, Hamlet's father is the product of an over-active imagination."
2. Which would be the best way to restate the claim, "The hardest-working students receive the highest grades," for use in analyzing a deductive argument? You answered:
Students
are highest grade receivers.
There are two important things to remember when restating claims:
Always replace active or passive verbs with state-of-being verbs.
Shorten phrases any way you want, as long as you do not create confusion or misunderstanding.
Here, "receive" has been replaced by "are receivers." The first term, "students," could have used more words, and the second, "highest grade receivers," could have used less, but as long as the meaning is clear.
3. Since all deductive arguments can be expressed as either syllogisms or conditionals, choose the equivalent conditional for the following major premise of a syllogism: "All men are mortal." You answered:
If they are men, then they are mortal.
4. Since all deductive arguments can be expressed as either syllogisms or conditionals, convert the following conditional into a premise for a syllogism: "If the Spartans win, then Amy will celebrate." You answered:
- All wins
are celebrations for Amy.
1. Which of the following would make the best major premise for a deductive argument? You answered:
- No one has
ever seen a ghost.
Two important factors for the main premise of a deductive argument are
that it relate two terms, and
that it be stated as a generalization, rule, or principle.
Though "no one has ever seen a ghost" may sound like a generalization, it actually reports the results of observations (or the lack of them) and, as a result, this claim is more suitable for an inductive argument.
1. Which of the following would make the best major premise for a deductive argument? You answered:
There are no ghosts.
Two important factors for the main premise of a deductive argument are
that it relate two terms, and
that it be stated as a generalization, rule, or principle.
Though this claim is certainly a generalization, it contains only one term. If we restated it in the form of a premise from a syllogism, it would become "No ghosts are," or "All ghosts are not." It's not impossible to get a deductive argument out of such a premise--"Yolanda is. Therefore, Yolanda is not a ghost"--but it is both awkward and reductive. B isn't the best choice here.
1. Which of the following would make the best major premise for a deductive argument? You answered:
- Scientific
study has proven that there are no ghosts.
Two important factors for the main premise of a deductive
that it relate two terms, and
that it be stated as a generalization, rule, or principle.
"Scientific study has proven that . . ." may sound like a generalization, but as a report of observations (even by scientists), this claim has the form of an inductive premise. And eliminating that phrase creates another problem: "there are no ghosts" only has a single term, "ghosts." Of course, we can imagine this claim being used deductively, just as we can imagine a second premise such as "Yohanan is," producing the conclusion, "Therefore, Yohanan is not a ghost." But D is certainly not the best choice.
2. Which would be the best way to restate the claim, "The hardest-working students receive the highest grades," for use in analyzing a deductive argument? You answered:
- Working
students receive highest grades.
There are two important things to remember when restating claims:
Always replace active or passive verbs with state-of-being verbs.
Shorten phrases anyway you want, as long as you do not create confusion or misunderstanding.
"Working students" may produce some confusion, since it denotes something different from "hadest-working students," but the real problem here is that the active verb, "receive," needs to be replaced by a state-of-being verb (such as "are"), in order to avoid misunderstandings.
2. Which would be the best way to restate the claim, "The hardest-working students receive the highest grades," for use in analyzing a deductive argument? You answered:
- Students
receive grades.
There are two important things to remember when restating claims:
Always replace active or passive verbs with state-of-being verbs.
Shorten phrases any way you want, as long as you do not create confusion or misunderstanding.
The abbreviations here are fine, but the active verb, "receive," needs to be replaced by a state-of-being verb (such as "are"), in order to avoid misunderstandings.
2. Which would be the best way to restate the claim, "The hardest-working students receive the highest grades," for use in analyzing a deductive argument? You answered:
- The
hardest-working students receive the highest grades.
There are two important things to remember when restating claims:
Always replace active or passive verbs with state-of-being verbs.
Shorten phrases any way you want, as long as you do not create confusion or misunderstanding.
No shortening occurred here, which is fine in cases like this where the terms are not terribly lengthy or complex. But the active verb, "receive," needs to be replaced by a state-of-being verb (such as "are"), in order to avoid misunderstandings.
3. Since all deductive arguments can be expressed as either syllogisms or conditionals, choose the equivalent conditional for the following major premise of a syllogism: "All men are mortal." You answered:
- If they are
men.
This answer is only part of a conditional, which has the form "If P then Q." You are missing the "then Q."
3. Since all deductive arguments can be expressed as either syllogisms or conditionals, choose the equivalent conditional for the following major premise of a syllogism: "All men are mortal." You answered:
- If all men
are mortal, then all mortals are men.
This has the form of a conditional, but the second part, "all mortals are men," introduces information not presented in the original claim. Be careful, in restating claims for the purpose of analysis, that you preserve the original meaning, without adding to it.
3. Since all deductive arguments can be expressed as either syllogisms or conditionals, choose the equivalent conditional for the following major premise of a syllogism: "All men are mortal." You answered:
- If they are
mortal, then they are men.
This claim has the form of a conditional, but it reverses the relationship of the two terms in "All men are mortal." Be careful, in restating claims for the purpose of analysis, that you preserve the original meaning.
4. Since all deductive arguments can be expressed as either syllogisms or conditionals, convert the following conditional into a premise for a syllogism: "If the Spartans win, then Amy will celebrate." You answered:
- All Spartans
are celebrators for Amy.
This answer would only be acceptable if you understood "Spartans" as meaning "Spartan wins," and "celebrators" as meaning "occasions for celebrating." Since this is possible, but not likely, there is a better choice than A.
4. Since all deductive arguments can be expressed as either syllogisms or conditionals, convert the following conditional into a premise for a syllogism: "If the Spartans win, then Amy will celebrate." You answered:
- All winners
are Spartans for Amy.
The two ideas associated in the original conditional are "winning" and "celebrating," but this answer associates "winning" and "Spartans." Be sure not to change the meaning of a claim in restating it for analysis.
4. Since all deductive arguments can be expressed as either syllogisms or conditionals, convert the following conditional into a premise for a syllogism: "If the Spartans win, then Amy will celebrate." You answered:
- All
celebrations are winners for Amy.
The verb has been converted to state-of-being here, but the sense has been altered. Instead of saying something about what happens when "the Spartans win," your answer talks about what it means when there are "celebrations."
You have completed the exercises on deductive arguments. You may now continue with related sections on Conditionals or Syllogisms, or return to the Main Menu.