Truth, Validity, and Soundness: Important Concepts in Logic and Correct Reasoning

To comprehend the various forms of arguments and inferences, it is essential to be familiar first with the very significant concepts of ‘truth,’ ‘validity,’ and ‘soundness.’ Let us begin discussing these topics by telling you a short story:

In one of my Logic classes, the students asserted that the statement “All Hawaiians are Americans” is valid. Upon noticing the disagreement from my facial expression, some of them right away shifted to claiming that it is invalid. 

With slick smile, I pronounced that neither answer is correct. And I guess many of you, readers, are as confused as they were.

Validity and truth are not synonymous

The confusion here stems from the erroneous notion that validity and truth are synonymous. Contrary to what many presume, ‘what is true’ is not accurately tantamount to ‘what is valid’, and vice versa.

Study of Logic informs us that statement is either true or false, while arguments, either valid or invalid. From this information alone, one could identify the basic difference between validity and truth: Validity is a quality of arguments while truth is a value of statements.

Hence, it is wrong to say that “All Hawaiians are Americans” is valid or invalid–-because it is a statement, and thus, can only be either true or false.

The mistakenly assumed similarity in meaning of the terms validity and truth has another unpleasant consequence. The confusion it produces makes many err in distinguishing between valid and invalid arguments. Let’s take the case of these two deductive arguments:

A. All dogs are mammals.
All puppies are dogs.
Therefore, all puppies are mammals.

B. All cats are frogs.
All monkeys are cats.
Therefore, all monkeys are frogs.

When students are asked whether each is valid or invalid, majority, if not all, tend to respond that the first argument is valid while the second, invalid. This claim is of course wrong. Logically speaking, both arguments are valid.

Again, the confusion springs from equating the validity of an argument to the truth of its premises and conclusion, and its invalidity to the falsity of its premises and conclusion. Realizing that the three statements composing argument B are in reality false, many conclude that the argument as a whole is invalid. This is of course logically incorrect.

What is truth?

So what istruth? What is validity? Although truth is not a concept that one can comfortably define, especially in Philosophy, but just for the urgency to distinguish it from validity here, it is not wrong to say that “a statement is true if what it asserts matches what is observed in reality.”

The statement “All gold are metal” is deemed true on the ground that in reality, gold are seen to possess the qualities of what we call metal (not that of stone or anything else). Truth, therefore, can be said to be referring to the certitude or correctness of statement in relation to reality.

Related: Distinguish Opinion from Truth

What is validity?

Validity, on the other hand, is a condition of an argument in which the conclusion is true on the reason that its premises are considered true. In other words, a valid argument is such that if the premises are assumed to be true, it is impossible for the conclusion to be false. In a valid argument, the conclusion is regarded as true not necessarily because of its relation to reality but because of the assumed truth of its legitimate premises.

This is the reason argument B is just as valid as argument A. If one assumes “All cats are frog” and “All monkeys are cats” to be true, then he is necessitated to acknowledge that “All monkeys are frogs” as also true—in the same way he admits the conclusion “All puppies are mammals” to be true, based on its respective premises in argument A.

The two arguments have the same structure or form that requires our logical thinking to consider them both valid.

Argument B thus exemplifies the principle that it is possible for all the premises of an argument to be false, and yet for the argument to be valid. Remember that validity depends upon how one reasons.

To say that our reasoning is valid is not to say that the premises we use are, in fact, true. Rather, it is to say that if the premises in our argument are true, and if our reasoning is valid, it will be impossible for the conclusion to be false.

True premises and conclusion = valid?

Now, since validity and truth are not semantically the same, we also have to note that simply because an argument has true premises and even a true conclusion does not necessarily mean that it embodies valid reasoning. Let us take this example:

C. All Filipinos are mortal.
All Manileños are mortal.
Therefore, all Manileños are Filipinos.

No doubt, its premises and conclusion are all true. Yet, the argument is invalid for it commits the fallacy called undistributed middle. To easily understand how invalid this argument is, take a look at this another argument with perfectly the same logical structure:

D. All men are human beings.
All women are human beings.
Therefore, all women are men.

Take note that argument D just replaces the terms Filipinos, mortal, and Manileños in argument C with the terms men, human beings, and women respectively. Having identical form, argument C is thus as invalid as argument D. Take note that this argument about men and women likewise illustrates another important point in Logic—the premises of an argument may be true and yet the argument can be invalid.

By now, it must be clear that validity and truth are not interchangeable. Nonetheless, both of them are necessary in another significant concept called soundness.

What is a sound argument?

A sound argumentis that which has a true conclusion that follows from true premises. A reasoning is sound if and only if the argument is valid and all of its premises are true. Argument A is actually an example of a sound argument. Not only does the conclusion follow necessarily from its premises, all of its premises (about dogs and puppies) also are in fact true.

Since validity does not necessarily involve the concept truth, an argument may be valid but not sound. Argument B is an example of this kind of argument.

Though its structure entails that its conclusion necessarily follows from its premises, the statements involved (about cats, monkeys, and frogs) are obviously false. (Argument C exemplifies an invalid argument that contains true statements (premises and conclusion) whereas argument D is a case of an invalid argument with unsurprisingly false conclusion.)

Validity vs. Soundness

This thus spells the difference between validity and soundness: validity is concerned only with the correctness of the flow of thought in inferring conclusion from premises, whereas soundness is also concerned with whether or not the premises composing the argument are actually true.

As a final note, Logic deals mainly with validity and not necessarily with truth. In fact, this academic subject entertains sentences like “All gremlins are green,”“All A are B,” “All utts are itts,”and other things whose subjects are non-existent, unreal, or mere concepts.

Debate, on the other hand, also cares about soundness as truth in debate also matters. (But although Logic focuses on validity, ultimately it aims as well to teach the skill in creating sound arguments. For one thing, it is Logic also that accurately informs us that we should combine the concepts of truth and validity to come up with sound reasoning.) (© 2014 by Jensen DG. Mañebog/MyInfoBasket.com)

Also Check Out:
Reasoning and Debate: A Handbook and a Textbook by Jensen DG. Mañebog

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