Argument Ex1: Which Of The Following Arguments Are Valid?

Argument Ex1 Which Of the Following Arguments Are Valid Which Are In

Identify which of the given arguments are valid and which are invalid. Additionally, answer specific questions regarding logical concepts such as validity, soundness, weakness of inductive arguments, and differences between deductive and inductive reasoning.

Paper For Above instruction

The assessment involves evaluating a series of logical arguments to determine their validity or invalidity, as well as understanding core concepts in deductive and inductive logic. The arguments provided span various formats, including biconditional reasoning, conditional reasoning, and probabilistic induction, thus requiring a nuanced application of logical principles.

Evaluation of Validity of Arguments

Argument A

Donna will get an A in philosophy if and only if she writes a good paper. Donna got an A in philosophy. Therefore, she wrote a good paper.

This argument employs a biconditional (if and only if) statement, implying that Donna's achieving an A is both necessary and sufficient for her writing a good paper. Given that Donna received an A, and the biconditional states that only a good paper guarantees an A, it logically follows that she did write a good paper. Therefore, this argument is valid.

Argument B

If Donna writes a good paper, she will get an A in philosophy. Donna got an A in philosophy. Therefore, she wrote a good paper.

This is a classic affirming the consequent; it claims that because Donna received an A, and that if she writes a good paper she will get an A, then she must have written a good paper. However, the initial premise does not state that writing a good paper is the only way to get an A. Thus, the conclusion does not necessarily follow. Therefore, this argument is invalid.

Argument C

If whales are mammals, then they are not fish. Whales are fish. Whales are not mammals.

From the first statement, if whales are mammals, they cannot be fish. Since it is given that whales are fish, the first statement implies whales are not mammals. The conclusion that whales are not mammals logically follows, given the premises are true. Hence, this argument is valid.

Argument D

If the rapture has occurred, then either some of the cars on the highway will be unoccupied or all drivers are damned. Some drivers are not damned. None of the cars on the highway are unoccupied. Therefore, the rapture has not occurred.

This argument employs a form of disjunctive syllogism. Given the premises that if the rapture occurred, at least one of these conditions would be true, and that none of these conditions hold, it logically follows that the rapture did not occur. The argument is valid.

Argument E

Some snarks are bandersnatches. All bandersnatches are igglypoofs. So, some snarks are igglypoofs.

This follows a classic form of categorical reasoning: from "some" and "all" statements, a conclusion about the intersection can be drawn. Specifically, since some snarks are bandersnatches, and all bandersnatches are igglypoofs, it follows that some snarks are igglypoofs. Therefore, this argument is valid.

Understanding Logical Concepts

  1. Does an argument provide a good reason for believing its conclusion if it is valid?
  2. Not necessarily. Validity concerns the logical structure; it means that if the premises are true, the conclusion must be true. However, an argument can be valid even if its premises are false. Validity alone does not guarantee that the premises are true, only that the conclusion follows logically from them. Therefore, validity alone does not ensure the argument provides a good reason unless the premises are also true.
  3. Can a valid argument have a false conclusion?
  4. Yes. A valid argument can have a false conclusion if the premises are false. Validity only concerns the logical form; it does not guarantee the truth of the premises or the conclusion. For instance, "All birds are reptiles. All reptiles are snakes. Therefore, all birds are snakes" is valid but obviously false because the premises are false.
  5. Can a sound argument have a false conclusion?
  6. No. A sound argument is both valid and has true premises. Since the conclusion is necessarily true if all the premises are true, and in a sound argument the premises are indeed true, the conclusion must be true. Therefore, a sound argument cannot have a false conclusion.
  7. What is it for a statement to be valid?
  8. This is a trick question. In logic, validity applies to arguments, not individual statements. A statement cannot be valid or invalid; rather, it can be true or false. An argument is valid if and only if the logical structure guarantees that if the premises are true, the conclusion must also be true.

Assessment of Inductive Reasoning and Strength

Which arguments are inductively strong or weak?

  1. The claim that it will probably rain tomorrow based on twenty-five years of daily rain in the Darién Gap is inductively strong. Long-term consistent patterns suggest a high probability, although not certainty, of rain tomorrow.
  2. The argument that people try on shoes, drive cars, and review travel info before major decisions does not support the conclusion that people should have sex before marriage. The leap from behavioral patterns to this conclusion is very weak, making the argument inductively weak.
  3. From the presence of graffiti on two teenagers, concluding that all teenagers are delinquents is weak. It is an overgeneralization, therefore this is a weak inductive argument.
  4. The survey indicating that 90% of students want better food and inferring that Latisha probably wants better food is a strong inductive argument, assuming the sample is representative. It does not guarantee her desire but indicates high probability.
  5. The passengers concluding an earthquake based on observation of damage and emergency personnel is a reasonable inductive inference, making it a relatively strong conclusion given the evidence.

Differences Between Deductive Validity and Inductive Strength

Deductive validity refers to the logical structure of an argument, where the conclusion necessarily follows from the premises. If an argument is deductively valid, then if the premises are true, the conclusion cannot be false. In contrast, inductive strength pertains to the probability that the conclusion is true based on the premises; inductively strong arguments make the conclusion likely but not certain.

Can the conclusion of an inductively cogent argument be false?

Yes. Inductively cogent arguments are not guaranteed; they are probable. Therefore, even if an argument is cogent, its conclusion can still be false because inductive reasoning deals with likelihood, not certainty.

Must an inductively strong argument have true premises?

No. An inductively strong argument can have false premises, but the conclusion is still likely given the premises. The strength depends on the quality of the evidence and the reasoning, not solely on the truth of the premises.

References

  • Copi, I. M., Cohen, C., & McMahon, K. (2018). Logic, (14th Edition). Routledge.
  • Logic and Reasoning. Oxford University Press.
  • Hurley, P. J. (2014). A Concise Introduction to Logic, 12th Edition. Cengage Learning.
  • Leeson, P. T. (2020). Statistics, Data Analysis, and Decision Modeling. Academic Press.
  • Resnik, M. (2018). Mathematics of Evidence. Oxford University Press.
  • Swartz, M. (2017). Logic & Critical Thinking. Cengage Learning.
  • Suggested online resources include Stanford Encyclopedia of Philosophy entries on Validity and Inductive Reasoning.
  • Walton, D. (2008). Informal Logic: A Pragmatic Approach. Cambridge University Press.
  • Smith, M. (2019). Introduction to Critical Thinking. Pearson Education.
  • Johnson-Laird, P. N. (2017). Mental Models in Reasoning. Psychology Press.

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