Answer “true” or “false” to the following statements: 1. Some arguments, while not completely valid, are almost valid. 2. Inductive arguments allow for varying degrees of strength and weakness. 3. Invalid deductive arguments are basically the same as inductive arguments. 4. If a deductive argument has true premises and a false conclusion, it is necessarily invalid. 5. A valid argument may have a false premise and a false conclusion. 6. A valid argument may have a false premise and a true conclusion. 7. A sound argument may be invalid. 8. A sound argument may have a false conclusion. 9. A strong argument may have false premises and a probably false conclusion. 10. A strong argument may have true premises and a probably false conclusion. 11. A cogent argument may have a probably false conclusion. 12. A cogent argument must be inductively strong. 13. If an argument has true premises and a true conclusion, we know that it is a perfectly good argument.
The Correct Answer and Explanation is:
Here are the answers (True or False) to the statements, followed by a 300-word explanation:
- False
- True
- False
- True
- True
- True
- False
- False
- True
- True
- True
- True
- False
In logic, deductive and inductive arguments differ in structure and evaluation criteria. Deductive arguments aim for absolute certainty—if the premises are true and the reasoning is valid, the conclusion must be true. In contrast, inductive arguments seek to provide probable support for conclusions, allowing for degrees of strength.
Statement 1 is false because an argument is either valid or invalid in deductive logic; there’s no “almost valid.” Statement 2 is true because inductive reasoning comes in degrees—it can be strong or weak depending on how much the premises support the conclusion. Statement 3 is false because invalid deductive arguments do not follow the rules of deductive reasoning, and while their form may resemble inductive reasoning, their intent and evaluation differ.
Statement 4 is true—a deductive argument with true premises and a false conclusion is necessarily invalid because validity requires that the conclusion must be true if the premises are. Statements 5 and 6 are both true because validity concerns logical structure, not the truth value of premises or conclusion.
Statement 7 is false—a sound argument must be valid and have all true premises. Statement 8 is also false—a sound argument cannot have a false conclusion.
Statements 9 and 10 are true because inductive arguments can be strong yet still lead to probably false conclusions if the premises are weak or incomplete. Statement 11 is true—a cogent argument (strong with true premises) still allows for a probably false conclusion due to the nature of inductive reasoning. Statement 12 is true because cogency requires inductive strength.
Statement 13 is false—true premises and a true conclusion do not guarantee the argument is good; the reasoning may still be invalid or weak (e.g., the conclusion may not follow from the premises).
