# Arguments, Validity and Soundness

Philosophy I · Logic · https://tryals.app/learn/philosophy-i/arguments-validity-and-soundness

## Following, Not Being True

An **argument** is a set of **premises** offered in support of a **conclusion**. Logic studies one relation only, whether the conclusion *follows*, and it is remarkably indifferent to whether anything said is true.

An argument is **valid** when it is impossible for all the premises to be true and the conclusion false. Notice what this does *not* say. It says nothing about whether the premises are actually true. Validity is about the **form** of the inference, not its content:

> All fish are mammals. All mammals are green. Therefore all fish are green.

Every sentence here is false, and the argument is perfectly valid. Meanwhile:

> Paris is in France. Therefore 2 + 2 = 4.

Both sentences are true, and the argument is invalid, the conclusion does not follow from the premise, it merely happens to be true alongside it.

**Soundness** is the stricter notion: an argument is sound when it is valid **and** all its premises are actually true. A sound argument therefore guarantees a true conclusion, which is why soundness is what we usually want and validity is what logic can check.

The reason logic studies form is that validity travels. Any argument of the shape

$$\text{If } P \text{ then } Q. \quad P. \quad \therefore Q$$

is valid whatever $P$ and $Q$ are, this is **modus ponens**. Two forms and their near-miss counterparts are worth memorising:

| Form | Pattern | Valid? |
|---|---|---|
| Modus ponens | If P then Q; P; so Q | Yes |
| Modus tollens | If P then Q; not Q; so not P | Yes |
| Affirming the consequent | If P then Q; Q; so P | **No** |
| Denying the antecedent | If P then Q; not P; so not Q | **No** |

The last two are **formal fallacies**, and they are the commonest reasoning errors in ordinary argument precisely because they look so like the valid pair.

Logic in this narrow sense is **deductive**: the conclusion is already contained in the premises, and a valid deduction adds no information. **Inductive** arguments, generalising from cases, can be strong or weak but never valid, since their conclusions genuinely go beyond their premises.

> **Common pitfall:** calling an argument "valid" because you agree with it, or "invalid" because a premise is false. A false premise makes an argument *unsound*, never invalid. Validity is a property of the inference alone, and an argument made entirely of falsehoods can be impeccably valid.

## Practice questions

7 of this lesson's 11 practice questions, with answers. The full set is in the app.

### 1. An argument has all false premises and a false conclusion, yet it is impossible for the premises to be true and the conclusion false. Is it valid, and why?

A. Invalid, because a valid deductive inference must guarantee that its conclusion is true
B. Invalid, as an argument containing false premises cannot be classified as deductively valid
C. Valid, because validity concerns the form of the inference, not the truth of the parts
D. Valid, but only conditionally, as validity requires the premises to be verified as true

**Answer:** C. Valid, because validity concerns the form of the inference, not the truth of the parts

**Why:** Validity is entirely about form. "All fish are mammals; all mammals are green; so all fish are green" is made of falsehoods and is impeccably valid. False premises make it *unsound*, which is a different defect.

Page: https://tryals.app/practice/philosophy-i/arguments-validity-and-soundness/an-argument-has-all-false-premises-and-a-false-conclusion-yet-it-is

### 2. Of the four classic conditional argument forms — modus ponens, modus tollens, affirming the consequent, denying the antecedent — how many are valid?

**Answer:** 2

**Why:** **Two**: modus ponens and modus tollens. Affirming the consequent and denying the antecedent are formal fallacies, and they are common precisely because they so closely resemble the valid pair.

Page: https://tryals.app/practice/philosophy-i/arguments-validity-and-soundness/of-the-four-classic-conditional-argument-forms-modus-ponens-modus

### 3. Logic isolates whether a conclusion follows from its premises from whether those premises are true. What does this separation imply for an argument whose conclusion is demonstrably true?

A. The argument may be completely invalid despite the factual accuracy
B. The truth of the conclusion guarantees that the reasoning is valid
C. The premises must be sound even if the inference cannot be verified
D. The argument is necessarily deductive because the conclusion holds

**Answer:** A. The argument may be completely invalid despite the factual accuracy

**Why:** Factual truth does not confer validity; an inference fails whenever premises fail to necessitate the conclusion. Confusing truth with structural support conflates soundness with validity, or deduction with mere factual coincidence.

Page: https://tryals.app/practice/philosophy-i/arguments-validity-and-soundness/logic-isolates-whether-a-conclusion-follows-from-its-premises-from

### 4. Which statements about validity are correct?

A. Validity depends on the form of the inference
B. A valid argument must have a true conclusion
C. A valid argument can have entirely false premises
D. No assignment of truth values can defeat a valid argument from the top down

**Answer:** A. Validity depends on the form of the inference; C. A valid argument can have entirely false premises; D. No assignment of truth values can defeat a valid argument from the top down

**Why:** Validity permits false premises and false conclusions; it forbids only the combination of true premises with a false conclusion. Guaranteeing a true conclusion requires soundness, not merely validity.

Page: https://tryals.app/practice/philosophy-i/arguments-validity-and-soundness/which-statements-about-validity-are-correct

### 5. Sort each argument by whether it is deductive or inductive.

**Answer:**

- Deductive: All humans are mortal; Socrates is human; so Socrates is mortal, If it rains the match is cancelled; it rains; so it is cancelled
- Inductive: Every swan observed so far has been white; so all swans are white, This drug helped 90 of 100 patients; so it will probably help the next

**Why:** A deductive conclusion is already contained in its premises, so a valid deduction adds no information. Inductive conclusions genuinely go beyond the evidence, which is why they can be strong or weak but never valid.

Page: https://tryals.app/practice/philosophy-i/arguments-validity-and-soundness/sort-each-argument-by-whether-it-is-deductive-or-inductive

### 6. Arrange these steps in the order you would use to evaluate an argument.

**Answer:**

1. Identify the conclusion being argued for
2. Identify the premises offered in support
3. Test whether the conclusion could fail while everything offered in support holds
4. If that combination is impossible, the argument is valid
5. Then ask separately whether the premises are actually true

**Why:** Structure first, then validity, then truth. Keeping the last two steps separate is the whole discipline, collapsing them is what produces "that argument is invalid because I disagree with the premise".

Page: https://tryals.app/practice/philosophy-i/arguments-validity-and-soundness/arrange-these-steps-in-the-order-you-would-use-to-evaluate-an

### 7. Match each term to its precise meaning.

**Answer:**

- Valid → The premises cannot be true with the conclusion false
- Sound → Valid, and with premises that are actually true
- Formal fallacy → An invalid pattern that resembles a valid one
- Premise → A claim offered in support of the conclusion

**Why:** Soundness is validity plus true premises, so every sound argument is valid but not conversely. Formal fallacies matter because their resemblance to valid forms is exactly what makes them persuasive.

Page: https://tryals.app/practice/philosophy-i/arguments-validity-and-soundness/match-each-term-to-its-precise-meaning