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 “Nonplussed Student” Woodcut, Alfred Swinbourne _Picture Logic or the Grave Made Gay_ London: Longmans, Green, 1875), 17

Introduction to Logic
Truth, Validity, and Soundness


Abstract: Truth, validity and Soundness : the foundation-concepts of deductive logic are defined and accompanied by a self-scoring quiz.

I. Truth, Validity, and Soundness: probably the three most important concepts of the course.
A. First, let us briefly characterize these concepts.
1. truth: a property of statements, i.e., that they are the case.
2. validity: a property of arguments, i.e., that they have a good structure.

For example, consider the structure of this argument:

All B-s are Cs.
All As are Bs.
Therefore, All As are Cs.
(The premises and conclusion are so related that it is absolutely impossible for the premises to be true unless the conclusion is true also.)

Note that an argument can be valid even though its premises are false. Also note that an argument is not mistaken just on account of its conclusion being false or being what seems to be unreasonable.

3. Soundness is a property of both arguments and the statements in them, i.e., the argument is valid and all the statement are true.
A Sound Argument is (1) valid, (2) true premises (obviously the conclusion is true as well by the definition of validity).
B. The fact that a deductive argument is valid cannot, in itself, assure us that any of the statements in the argument are true; this fact only tells us that the conclusion must be true if the premises are true.
1. Let's look at the variety of valid argument kinds that can exist given the combinations of possible truth values of premises and conclusion:
Cases —> 1 2 3 4
premise(s) T F T F
Conclusion T T Logically impossible to be false. F

Note that case 3 is logically impossible. If it were possible to have true premises and a false conclusion, logic would be useless to prove anything.
2. Let's look at the variety of invalid argument kinds that can exist given the combinations of possible truth values of premises and conclusion:
Cases —> 1 2 3 4
premise(s) T F T F
Conclusion T T F F

Generally speaking, these are the possible truth combinations that can exist in simple deductive arguments. Actual examples of each type of argument, valid and invalid, are given in the syllabus Section A, page 17.
II. One way to summarize these terms of deductive arguments together with inductive arguments is to represent the logical territory in the following “tree-diagram.”

Arguments
_________|___________
Deductive

Inductive

  
_____|_____       _____|_____

Valid

Invalid

correct > > > >  incorrect

 _______|________
Sound

Unsound
(all statements are true) (at 
least one premise 
is false)



III. Self-Quiz for Truth, Validity, and Soundness
A. Tell whether the following statements are true or false.
1. A sound argument is a deductive argument which is valid and has true premises.
2. It is impossible for a deductive argument to be both valid and unsound.
3. If a deductive argument is valid, it cannot be unsound.
4. If the premises of a deductive argument are true, then the argument must be sound.
5. If the conclusion of a deductive argument is true, then the argument might be sound or it might be unsound.
6. If the premises of a deductive argument are true, then the conclusion must be true.
7. If a deductive argument is valid, then its conclusion might be true or it might be false.
8. A sound argument is a deductive argument that has valid premises.
9. If a valid argument has a false conclusion, then it must have at least one false premise.
10. If a deductive argument is valid and at least one of its premises is false, then its conclusion is also false.



B. That quiz is initially difficult for most persons first learning about this topic. For some more rules, definitions, and examples, see this appendix presented in the Appendix A on this topic. For more self-quizzes, check your understanding with the quiz and test on "Truth, Validity, and Soundness.

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