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I have been asked a question in class where we would need to pick out the false statement from a given set of options. The problem is that I am not really sure why my answer was wrong?

Here is the question:

Which of the following is false?

A) One and the same argument cannot be both inductive and cogent

B) One and the same argument can be both sound and logically weak

C) An inductive argument can be cogent

D) A deductive argument can be invalid

My answer was A, but the correct answer appears to be B. I am not sure why that is true because as I understand, inductive arguments can be cogent, so wouldn't by saying they cannot be cogent would be false?

Thanks in advance!

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    By “logically weak”, is the problem referring to the weakened form of a syllogism? This occurs when the premises are universal but the conclusion is only particular. AAI in the first figure is an example. – Mark Andrews Dec 8 '19 at 1:57
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    A) and C) seem the same... Sound implies valid; thus, if by "logically weak" we mean that it is not "logically correct", then a sound argument cannot be "logically incorrect". – Mauro ALLEGRANZA Dec 8 '19 at 9:40
  • A and C are contradictories, so one of those must be false. (Unless perhaps you are a skeptic about all inductive arguments.) A good inductive argument is cogent, so C is true and A false. The term 'logically weak' has no generally accepted conventional meaning that I'm aware of, so it is harder to assess B. If 'weak' implies 'invalid' then B is false. But a sound argument can be question-begging, so maybe an argument could be weak in that sense and B would be true. – Bumble Dec 9 '19 at 1:36
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First, let's review some ideas of argumentation.

With deduction, we can talk about arguments about being sound and valid. Valid means the structure of the argument leads to the correct conclusion independent of the premises, whereas soundness implies the argument is not only valid, but has true premises. For instance, "If Socrates is in the kitchen, he is in the house, therefore Socrates is in the house" is a valid argument, however it's sound only if it's actually true "Socrates is in the kitchen".

Remember, a deduction is a deterministic form of inference (things MUST follow), and induction is a form of inference that is probabilistic (things PROBABLY follow). Strength and cogency for our purposes here will mirror validity and soundness in induction. Hence a strong inductive argument is one that relies on many good techniques to establish a certain probability exists, but ultimately, if those techniques are faulty because they make bad assumptions, then argument ultimately isn't cogent.

Now let's examine each statement and see where the analysis leads.

A) One and the same argument cannot be both inductive and cogent

FALSE. (Reworded:"An inductive argument cannot be cogent".) Any inductive argument that has strong form and is based on true premises by definition is cogent.

B) One and the same argument can be both sound and logically weak

FALSE. By definition, soundness applies to deduction and weakness applies to induction.

C) An inductive argument can be cogent

TRUE. This is the opposite assertion of A. Again, it bears reminding that a cogent argument is an inductive argument that is both logically strong and based on true premises.

D) A deductive argument can be invalid

TRUE. Deductive arguments can be valid or invalid depending on their logical form. An example of an invalid deductive argument would be "All men are mortal, Socrates is a man, therefore Socrates is not mortal." Note both premises are true, however, the conclusion will always be wrong.

Conclusion

Maybe I missed something, but it does appear to me that both A and B are false. Presuming you haven't transcribed the problem wrong, I would endorse the view that the problem isn't with your answer, but someone else's question, although I'm amenable to criticism. As someone who has written questions, it's quite easy to forget to add a negation or to switch between vocabulary for one thing when it applies to the other. I would politely bring it to the attention of your instructor, who if they practice what they teach will have to concede your deduction that the question is invalid is both valid and sound!

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    Great explanation! Thanks a lot! – Flavio Esposito Dec 8 '19 at 21:24

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