Math Problem Statement

Test the validity of the argument: All who have confidence in the American scientific community will believe what they tell you is really science. You don’t believe what they tell you is really science. Therefore, you don’t have confidence in the American scientific community.

Solution

The argument presented in the image can be broken down logically as follows:

  1. Premise 1: All who have confidence in the American scientific community will believe what they tell you is really science.
  2. Premise 2: You don’t believe what they tell you is really science.
  3. Conclusion: Therefore, you don’t have confidence in the American scientific community.

Analysis:

The structure of this argument can be examined by checking if the conclusion logically follows from the premises. It resembles a modus tollens argument, a valid logical form. In modus tollens:

  • If P, then Q (All who have confidence in the scientific community believe what they tell you is science).
  • Not Q (You don't believe what they tell you is science).
  • Therefore, not P (You don't have confidence in the scientific community).

This follows a valid logical form, so the argument seems valid based on the structure of reasoning.

Would you like further details on logical forms like modus tollens? Here are some related questions you could explore:

  1. How does modus tollens differ from modus ponens in logic?
  2. What are some common fallacies that occur in invalid arguments?
  3. Can an argument be valid but unsound, and how does that apply here?
  4. What other examples of valid argument forms are used in deductive logic?
  5. How does formal logic relate to real-world reasoning, like in science or law?

Tip: In logical arguments, it's important to distinguish between validity (whether the conclusion logically follows from the premises) and truth (whether the premises themselves are true).