explain what logic can and cannot do. In other words, what kinds of questions and logic are not decided by logical analysis

Is abortion moral?

Is there a God?

What are the ethics of polygamy?

No

Yes
the ethics of polygamy is to tell if someone is telling the true.

These are questions that logical analysis cannot answer.

Btw -- check the definition of polygamy.

the definition of polygamy is having more than one spouse, especially wife, at one time.

Yes.

Now back to your original question.

What can logic do? What can't it do?

What do you think?

I think that you are right this a question that a logic cannot answer.

Logic is a powerful tool for reasoning, but it does have its limitations. To understand what logic can and cannot do, it's important to recognize that logic operates within certain boundaries and assumptions. Here are some points to consider:

1. Logic is limited to evaluating validity: Logic is primarily concerned with determining the validity of arguments or reasoning processes. It aims to establish whether the conclusions follow logically from the premises. It does not inherently determine whether the premises of an argument are true or false, nor does it address matters of subjective beliefs or personal opinions.

2. Logic cannot establish true premises: While logic can help identify logical inconsistencies or fallacies within an argument, it cannot directly determine the truth or accuracy of the premises themselves. For example, if someone argues, "All elephants can fly. Dumbo is an elephant. Therefore, Dumbo can fly," logic can quickly identify the fallacy in the argument, but it cannot determine the truth of the claim that elephants can fly.

3. Logic does not address empirical matters: Logic deals with abstract concepts and formal systems, but it does not provide evidence or proof in matters of empirical observation. Questions concerning specific facts, empirical data, or the natural world usually go beyond the scope of logic alone. Scientific methods and empirical investigation are better suited to address such questions.

4. Logic does not capture all types of knowledge: Logic is a formal system based on rules and principles, but there are aspects of human knowledge that lie beyond its reach. Emotional experiences, aesthetic judgments, personal values, moral decision-making, and subjective experiences fall outside the domain of formal logic.

5. Logic cannot dictate personal preferences: Personal preferences and tastes are subjective and vary from person to person. While logic can help identify inconsistencies within preferences, it cannot provide an objective basis for determining what one should or should not like, as this depends on individual preferences and values.

In summary, logic is an invaluable tool for evaluating the validity of arguments and reasoning processes. However, it has limitations when it comes to determining the truth or falsehood of premises, addressing empirical matters, capturing all types of knowledge, and dictating personal preferences. To explore these areas, it is often necessary to supplement logical analysis with other methods, such as empirical research, subjective experiences, and personal values.