4. identifying argument forms
section a. for each of the following arguments, identify the form of the argument
1. if socrates is a human, then socrates is mortal. socrates is a human. so, socrates is mortal.
2. if socrates is a cow, then socrates gives milk. socrates is a cow. so, socrates gives milk.
3. if socrates is a cow, then socrates has four legs. socrates has four legs. so, socrates is a cow.
4. if socrates is a human, then hes a mammal. socrates is not a human. so, socrates is not a mammal.
5. if socrates is a horse, then hes warm - blooded. socrates is not warm - blooded. so, socrates is not a horse.
6. if socrates was a philosopher then he wasnt a historian. socrates wasnt a historian. so, socrates was a philosopher.
section b. place the following arguments in standard form. identify the form and whether or not it is valid or invalid. if it is invalid, explain why.
1. if the color of the hat on his own head does not cause the one - eyed prisoner to go blind, then the prison yard will be unoccupied during the bowl game. the color of the hat on his own head does not cause the one - eyed prisoner to go blind. therefore, the prison yard will be empty during the game.
2. you will not contribute to the spread of the virus only if you follow the public health guidelines. thus, you are not a spreader since you clearly cooperate with the public health measures.
3. if number were an idea, then arithmetic would be psychology. but arithmetic is no more psychology than, say, astronomy is. astronomy is concerned, not with ideas of the planets, but with the planets themselves, and by the same token, the objects of arithmetic are not ideas either. --gottlob frege, the foundations of arithmetic
4. if you dont pay your taxes, youll be sent to federal prison. but dont worry. you paid your taxes, so you wont be sent to federal prison.

Question

Accepted Answer

# Section A:
# Brief Explanations:
Each argument is matched to its logical form, defined by standard deductive argument structures.
# Answer:
1. Modus Ponens (Affirming the Antecedent)
2. Modus Ponens (Affirming the Antecedent)
3. Affirming the Consequent
4. Denying the Antecedent
5. Modus Tollens (Denying the Consequent)
6. Affirming the Consequent

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# Section B:
# Brief Explanations:
Arguments are restated in standard premise-conclusion form, identified by their logical structure, and evaluated for validity (valid forms preserve truth; invalid forms allow true premises and false conclusion).
# Answer:
1. **Standard Form**:
   Premise 1: If the color of the hat on his own head does not cause the one-eyed prisoner to go blind, then the prison yard will be unoccupied during the bowl game.
   Premise 2: The color of the hat on his own head does not cause the one-eyed prisoner to go blind.
   Conclusion: Therefore, the prison yard will be empty during the game.
   **Form**: Modus Ponens
   **Validity**: Valid

2. **Standard Form**:
   Premise 1: You will not contribute to the spread of the virus only if you follow the public health guidelines. (Restated: If you do not contribute to the spread of the virus, then you follow the public health guidelines)
   Premise 2: You follow the public health guidelines.
   Conclusion: Therefore, you are not a spreader.
   **Form**: Affirming the Consequent
   **Validity**: Invalid. The premise only states that not spreading requires following guidelines, but following guidelines does not guarantee not spreading (there could be other ways to spread).

3. **Standard Form**:
   Premise 1: If number were an idea, then arithmetic would be psychology.
   Premise 2: Arithmetic is not psychology.
   Conclusion: Therefore, numbers are not ideas.
   **Form**: Modus Tollens
   **Validity**: Valid

4. **Standard Form**:
   Premise 1: If you don't pay your taxes, you'll be sent to federal prison.
   Premise 2: You paid your taxes.
   Conclusion: Therefore, you won't be sent to federal prison.
   **Form**: Denying the Antecedent
   **Validity**: Invalid. The premise only states that not paying taxes leads to prison, but paying taxes does not guarantee avoiding prison (there could be other reasons to be sent to prison).

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Question

Explanation:

Section A:

Answer:

Section B: