Question

Translate the following arguments into symbolic form and use the first eight rules of inference to derive the conclusion of each.

After you translate these problems, then solve the argument; as you solve them in part III. I have underlined the conclusion of each argument, you are required to prove that the conclusion follows from the premises.
1. Either art is dead or a new form will appear. If art is dead, then it is not the case that some sculpture by Botero is valuable. But the claim that it's not the case that some sculpture by Botero is valuable is false. So, a new form will appear and art is not dead.
2. If Mill is right, then consequences have moral weight; also, I like Mill's work. If Kant is right, then pleasure is not important; I'm not a fan of Kant's work. Either Mill is right or Kant is. So, either consequences have moral weight or pleasure is not important.
3. If values are transcendent, then truth does not matter. Either values are transcendent or the world has no meaning. But it is not the case that truth does not matter. So, either the world has no meaning or truth is pleonastic.
4. If names are either purely referential or contain descriptive content, then both Mill and Frege are worth reading. Names are purely referential and do not contain descriptive content. So, Mill is worth reading and names are purely referential.
5. If there is a self, then I could be eternal. If I could be eternal, then I am not my body. If I could be eternal, then I am not my soul. Either there is a self or I could be eternal. So, either I am not my body or I am not a soul.

Answer 1

The student's question pertains to translating arguments into symbolic logic and deriving conclusions using valid rules of inference. The use of logical forms like disjunctive syllogism, modus ponens, and modus tollens is essential for deductive reasoning, as they ensure the correctness of the conclusion when premises are true.

Step-by-step explanation:

The question involves translating arguments into symbolic form and deriving conclusions using rules of inference in deductive reasoning. A valid deductive inference guarantees the truth of the conclusion if the premises are true.

To solve these problems, one must apply logical forms such as disjunctive syllogism, modus ponens, and modus tollens. These are examples of valid argument structures that ensure the correctness of the conclusion when the premises are accurate.

For instance, a disjunctive syllogism takes the form:

1. X or Y.
2. Not Y.
3. Therefore X.

This structure allows us to conclude X if we know Y is not true. Similarly, modus ponens and modus tollens are other valid forms of deductive reasoning that employ conditional reasoning to reach a conclusion. To determine whether an argument is valid, one must consider whether the truth of the premises logically necessitates the truth of the conclusion.