Evaluating Arguments: Validity, Soundness and Fallacies

Tell a valid argument from a true one, understand soundness and cogency, use the negate-the-conclusion test to check validity, and recognise the most common formal and argumentative fallacies.

1 Introduction

Reconstructing an argument tells you what is being claimed and on what grounds (see Constructing and Reconstructing Arguments). Evaluating it tells you whether the argument actually works. This page introduces the vocabulary used to assess arguments — validity, truth, soundness, cogency — a practical test for validity, and the most common ways arguments go wrong.

The single most important distinction is the first one: validity is not the same as truth.

2 Two Kinds of Argument

Arguments come in two broad types, each judged by a different standard.

Deductive arguments aim for certainty: if the premises are true, the conclusion follows with absolute certainty. They are evaluated in terms of validity and soundness.

Inductive arguments aim for probability: true premises make the conclusion likely but not guaranteed. They are evaluated in terms of cogency (and the strength/weakness of the inference).

Deductive: If you touch the stove you get burned. You touch the stove. ∴ You got burned.

Inductive: The sun has risen every day so far. ∴ The sun will rise tomorrow.

NoteThe problem of induction

No number of confirming observations can definitively prove a universal statement. That the sun has always risen does not strictly guarantee it will rise tomorrow. This is the classic problem of induction — and it is why inductive conclusions are held with degrees of confidence rather than certainty.

3 Validity, Truth and Soundness

These three terms are constantly confused. Keep them apart:

• Truth is a property of statements (premises and conclusions). A statement is true or false.
• Validity is a property of the argument’s structure. An argument is valid if it is impossible for all its premises to be true and its conclusion false at the same time. Validity is about the connection between premises and conclusion, not about whether they happen to be true.
• Soundness is a property of deductive arguments. An argument is sound if it is valid and all its premises are actually true.

Two consequences follow that students often find counter-intuitive:

• An argument can be valid even though its premises are false. Validity only requires that if the premises were true, the conclusion would have to be. (“All cats are reptiles; all reptiles purr; ∴ all cats purr” is valid but unsound.)
• A valid argument with true premises is sound, and its conclusion is guaranteed true. A valid argument with a false premise is not sound — sometimes described as a valid-but-wrong argument.

For inductive arguments the parallel standard is cogency: an argument with “enough” supporting premises is cogent; one with too little support is weak.

4 A Practical Test for Validity

Here is a quick procedure to test a deductive argument:

Is it possible to keep all the premises true while negating the conclusion?

• Yes → the argument is invalid.
• No → the argument is valid.

4.1 Example 1 — an invalid argument

P1: There is no water on Venus. P2: There is no oxygen on Venus. C: Therefore, there is no life on Venus.

Can both premises be true while the conclusion is false? Yes — one can imagine a life form needing neither water nor oxygen. So the conclusion can be negated without contradicting the premises: the argument is invalid.

4.2 Example 2 — a valid argument (but is it sound?)

P1: If the US manipulated its currency in the past, then the US is not justified in accusing China of manipulating its currency. P2: The US manipulated its currency in the past. C: The US is not justified in accusing China of manipulating its currency.

Here you cannot hold both premises true and deny the conclusion — this is modus ponens, so it is valid. Whether it is sound is a separate question that turns on whether P1 and P2 are actually true.

5 Formal Fallacies

A formal fallacy is an invalid argument structure. The two most common imitate the valid conditional syllogisms (covered in Propositional Logic):

• Fallacy of the converse: P → Q; Q; ∴ P. “If it rains the street is wet; the street is wet; ∴ it rains.” Invalid.
• Fallacy of the inverse: P → Q; ¬P; ∴ ¬Q. “If it rains the street is wet; it is not raining; ∴ the street is not wet.” Invalid.

6 Argumentative Fallacies

Argumentative (informal) fallacies are arguments that may be formally fine but persuade illegitimately — through the content or rhetoric rather than genuine support. A working catalogue:

• Circularity — repeating the premise in the conclusion. “You should not cut class because you are obliged to attend all classes.” / “This book is the best because it’s the most recommended, and it’s the most recommended because it’s the best.”
• Appeal to ignorance — claiming something is true (or false) merely because it has not been disproven (or proven). “No one has proven P, so P is false.”
• Appeal to authority — using an authority’s say-so as the evidence itself. “God exists because the Bible says so, and the Bible must be right because it is the word of God.”
• Ad hominem — attacking a feature of the person rather than their argument. “You’re just a high-school graduate, so your opinion doesn’t matter.”
• Ad populum — treating a claim as true because many people believe it. “Most people support this policy, so it must be the right thing to do.”

NoteWhy this matters beyond the seminar room

Fallacies are not just exam material. Recognising them is central to evaluating evidence and arguments in practice — in management decisions, policy debates, and the assessment of claims that present themselves as “scientific”. A confident tone and a real authority’s name are not substitutes for a valid, sound argument.

Note🎓 MA / PhD

The boundary between a fallacy and a legitimate inference is often context-dependent. An appeal to authority, for instance, is fallacious when the authority’s say-so is offered as the evidence, but deferring to relevant expertise under uncertainty can be epistemically rational. Argumentation theory studies these moves systematically, and feminist and rhetorical perspectives have criticised the narrow “adversarial” picture of argument as a contest to be won, emphasising instead argument as cooperative inquiry. Engaging with that literature is a good way to sharpen your own evaluative practice.

7 Summary

• Deductive arguments aim for certainty (judged by validity/soundness); inductive arguments aim for probability (judged by cogency), and face the problem of induction.
• Truth is a property of statements; validity of structure; soundness = validity + true premises.
• A valid argument can have false premises; only a sound argument guarantees a true conclusion.
• Test validity by asking whether you can hold the premises true while negating the conclusion.
• Watch for formal fallacies (converse, inverse) and argumentative fallacies (circularity, ad hominem, ad populum, appeals to authority and ignorance).

8 What to Read Next

• Constructing and Reconstructing Arguments — getting an argument into evaluable form in the first place.
• What Makes an Explanation Scientific? The Deductive-Nomological Model — how these logical tools underpin a model of scientific explanation.

9 Further Reading

• Kahane, H., Hausman, A., & Boardman, F. (2021). Logic and Philosophy: A Modern Introduction (13th ed.). Hackett.
• Lewiński, M., & Mohammed, D. (2016). “Argumentation Theory.” In The International Encyclopedia of Communication Theory and Philosophy. Wiley.