Which one of the following options describes a valid deductive argument with all the premises and the conclusion as True?
Understanding Deductive Arguments and Soundness
The question asks us to identify the term that describes a valid deductive argument where all the premises are true, and consequently, the conclusion is also true. To answer this, we need to understand the key concepts related to deductive arguments: validity, truth, and soundness.
What is a Deductive Argument?
A deductive argument is a type of argument where if the premises are true, the conclusion must necessarily be true. Deductive arguments aim to provide guaranteed support for their conclusions.
Validity in Deductive Arguments
Validity is a property of the structure or form of a deductive argument. A deductive argument is considered valid if it is impossible for the premises to be true and the conclusion to be false at the same time. Validity doesn't depend on whether the premises are actually true, but rather on the logical connection between premises and conclusion. If the logic holds, the argument is valid.
Truth of Premises and Conclusion
Truth refers to whether a statement (a premise or a conclusion) accurately reflects reality. A premise or a conclusion can be either true or false.
Defining a Sound Argument
A sound argument is a specific type of deductive argument that meets two crucial conditions:
- It must be a valid deductive argument.
- All of its premises must be true.
If a deductive argument is valid and all its premises are true, its conclusion must also be true. This is because the definition of validity states that if the premises are true, the conclusion cannot be false.
Analyzing the Options
Let's look at the given options in the context of a valid deductive argument with all true premises and a true conclusion:
- Probable Argument / Improbable Argument: These terms are typically used to describe inductive arguments, not deductive ones. Inductive arguments aim to show that their conclusions are likely or probable given the premises, not necessarily true. A deductive argument is either valid (premises guarantee the conclusion) or invalid (premises do not guarantee the conclusion); probability isn't the primary measure of its strength.
- Unsound Argument: An unsound argument is a deductive argument that is either invalid, or has at least one false premise, or both. The question specifically describes an argument that is valid and has all true premises. Therefore, it cannot be an unsound argument. An unsound argument could, by chance, have a true conclusion, but it doesn't fit the criteria of being valid with all true premises.
- Sound Argument: As defined above, a sound argument is a valid deductive argument with all true premises. If an argument is valid and all its premises are true, its conclusion must necessarily be true. This description perfectly matches the criteria given in the question.
Therefore, the option that describes a valid deductive argument with all premises and the conclusion as true is a Sound Argument.
Revision Table: Key Terms in Argumentation
| Term | Description | Applies to |
|---|---|---|
| Deductive Argument | If premises true, conclusion must be true. | Argument Type |
| Validity | Logical structure where true premises make false conclusion impossible. (Form/Structure) | Deductive Arguments |
| Truth | Statement corresponds to reality. (Content) | Statements (Premises, Conclusions) |
| Soundness | Argument is valid AND all premises are true. | Deductive Arguments |
| Unsoundness | Argument is invalid OR has ≥1 false premise. | Deductive Arguments |
Additional Information on Argument Types
While the question focuses on deductive arguments, it's helpful to contrast them with inductive arguments.
- Deductive Arguments: Aim for certainty. If valid and sound, the conclusion is guaranteed. Example: "All men are mortal. Socrates is a man. Therefore, Socrates is mortal." (Valid and Sound, assuming premises are true).
- Inductive Arguments: Aim for probability. The premises provide support that makes the conclusion likely, but not guaranteed. Example: "Every swan I have ever seen is white. Therefore, all swans are white." (Even if premises are true, the conclusion could be false - e.g., black swans exist).
Validity and soundness are concepts strictly applied to deductive arguments, while terms like 'strong', 'weak', 'cogent', and 'uncogent' are used to evaluate inductive arguments based on the probability the premises lend to the conclusion and the truth of the premises.
Important Questions from Argument Forms - Teaching
The Fallacy committed in the argument
"All textbooks are books intended for careful study. Some reference books are books intended for careful study. Therefore, some reference books are textbooks." is
- The space program deserves increased expenditure in the years ahead. Not only does the national defence depend upon it, but the program will more than pay for itself in terms of technological snipoffs. Furthermore, at current funding levels, the program cannot fulfil its anticipated potential”. What is the conclusion of the above argument?
All mortals are men.
Socrates is mortal
Therefore Socrates is a man.
Which of the following statements are true of the above argument?
(A) Above arguments is sound.
(B) Above argument is valid.
(C) Above argument is fallacious.
(D) Above argument commits the fallacy of undistributed middle.
Choose the correct answer from the options given below:"Environmentalists accuse us of blocking the plan to convert Antartica into a World park. In fact nothing could be further from the truth. Antartica is a huge continent teeming with life. It is home to millions of penguins, seals, seabirds and sea lions. Also great schools of finfish and whales inhabit its coastal waters."
Which fallacy is committed in the above argument?
Given below are two statements:
Statement I : An argument form that allows for a substitution instance having true premises and a false conclusion is an invalid form.
Statement II : Any arguments having true premises and a false conclusion is an invalid argument.
In the light of the above statements, choose the correct answer from the options given below :
