All courses > Basic studies > Logical Reasoning ::

Logical Reasoning Foundations: Does the Conclusion Follow from the Support?

Capítulo 8

Estimated reading time: 8 minutes

The Core Evaluation Question

When you evaluate an argument, the central question is: If the premises were true, would that make the conclusion more likely—or even guaranteed? This keeps you focused on the connection between support and conclusion, not on whether you personally agree with the topic.

Think of support on a spectrum:

Deductive support: the premises aim to make the conclusion unavoidable. If the reasoning is good, the conclusion must follow.
Inductive support: the premises aim to make the conclusion probable. Even with good reasoning, the conclusion could still be false, but it should be unlikely.

Deductive Reasoning: Does the Conclusion Have to Be True?

Deductive arguments succeed when the structure is such that it’s impossible for the premises to be true while the conclusion is false. You do not need heavy symbols to test this; you can use an intuitive “could this happen?” check.

Valid vs. Invalid Patterns (Intuitive)

Valid pattern (categorical / class membership):

Premise: All mammals are warm-blooded.
Premise: Whales are mammals.
Conclusion: Whales are warm-blooded.

If the premises are true, the conclusion cannot fail. There is no room for a counterexample.

Continue in our app.

Listen to the audio with the screen off.
Earn a certificate upon completion.
Over 5000 courses for you to explore!

Or continue reading below...

Download the app

Invalid pattern (common mistake: affirming the consequent):

Premise: If the alarm is set, the light is on.
Premise: The light is on.
Conclusion: Therefore, the alarm is set.

The premises could be true and the conclusion false (the light might be on for another reason). The support does not guarantee the conclusion.

Valid pattern (either/or reasoning):

Premise: The package is either in Locker A or Locker B.
Premise: It is not in Locker A.
Conclusion: It is in Locker B.

Once the options are truly limited to those two, ruling one out forces the other.

Invalid pattern (denying the antecedent):

Premise: If it’s a professional camera, it shoots RAW.
Premise: This camera is not professional.
Conclusion: Therefore, it does not shoot RAW.

Non-professional cameras can also shoot RAW. The conclusion doesn’t have to follow.

Quick Deductive Check: The Counterexample Test

To test deductive validity, ask: Can the premises be true while the conclusion is false? If you can imagine even one realistic scenario where that happens, the reasoning is invalid.

Step-by-step: How to Run the Counterexample Test

Assume the premises are true (even if you doubt them in real life).
Try to construct a situation where the conclusion fails anyway.
If you can build such a situation without contradicting the premises, the argument is invalid.
If you cannot (and the link seems airtight), the argument is valid.

Mini-practice:

Premise: All employees with access badges can enter the lab.
Premise: Dana can enter the lab.
Conclusion: Dana has an access badge.

Counterexample: Dana can enter because she is escorted by security, not because she has a badge. Premises can be true, conclusion false → invalid.

Inductive Reasoning: Is the Support Strong Enough to Make the Conclusion Likely?

Inductive arguments do not promise certainty; they promise good odds. The evaluation question becomes: If the premises were true, would the conclusion be strongly supported?

Strong vs. Weak Inductive Support (Intuitive)

Strong generalization (bigger, more representative sample):

Premise: In a random sample of 1,500 city residents, 62% support the new transit plan.
Conclusion: A majority of city residents likely support the new transit plan.

This is not guaranteed, but it is reasonably likely if the sample is genuinely random and representative.

Weak generalization (small or biased sample):

Premise: I asked 8 people at a transit advocacy meeting, and 7 support the plan.
Conclusion: Most city residents support the plan.

The sample is small and likely biased toward supporters, so the support is weak.

Cause-and-Effect: Strong vs. Weak Support

Stronger causal support (alternative explanations addressed):

Premise: After the software update, crash reports rose sharply only on devices that installed the update; devices that did not update did not show the increase.
Conclusion: The update likely caused the increase in crashes.

This is stronger because it compares groups and reduces competing explanations.

Weaker causal support (post hoc / timing only):

Premise: The app started crashing more often after the update.
Conclusion: The update caused the crashes.

Timing alone is not enough; other changes could have occurred (new OS version, server changes, heavier usage).

Categorical Claims: Inductive “Most/Usually” vs. Deductive “All”

Be alert to how categorical language changes the needed support:

Conclusion: All members of a group have a trait → requires extremely strong support (often deductive or near-deductive).
Conclusion: Most or usually → can be supported inductively with good data.

Example:

Premise: 19 of the last 20 deliveries arrived on time.
Conclusion A: The next delivery will arrive on time. (inductively reasonable)
Conclusion B: All deliveries from this company arrive on time. (too strong for the evidence)

Three Quick Tests for “Does the Conclusion Follow?”

You can evaluate most arguments quickly using three checks: counterexample, relevance, and sufficiency. They work together: an argument can fail because the support is irrelevant, or because it’s relevant but not enough, or because it aims at certainty but allows counterexamples.

1) Counterexample Test (Mainly for Deductive Claims)

Question: Can the premises be true and the conclusion false?

Use when: the argument sounds like it’s claiming certainty (often with words like “must,” “cannot,” “therefore definitely,” or universal claims like “all,” “none”).

Example (categorical):

Premise: All certified electricians have passed the licensing exam.
Premise: Priya has passed the licensing exam.
Conclusion: Priya is a certified electrician.

Counterexample: Priya passed but hasn’t completed paperwork or hasn’t been certified yet. Premises true, conclusion false → does not follow.

2) Relevance Test (For Any Argument)

Question: Does this reason actually bear on the conclusion?

Sometimes a premise is true and sounds persuasive, but it doesn’t connect to what is being claimed.

Example (irrelevant support):

Premise: This restaurant has been in business for 40 years.
Conclusion: The restaurant’s soup is low in sodium.

Longevity may suggest popularity or stability, but it does not specifically support a claim about sodium content. The premise is not relevant to the conclusion as stated.

Cause-and-effect relevance trap:

Premise: The city installed more bike lanes.
Conclusion: Therefore, housing prices will rise.

Bike lanes might correlate with neighborhood change, but the premise alone doesn’t directly connect unless you add a mechanism or supporting data. As-is, relevance is unclear or weak.

3) Sufficiency Test (For Any Argument)

Question: Even if the reason is relevant, is it enough to justify the conclusion’s strength?

Many arguments fail not because the premises are unrelated, but because they don’t provide enough support for how strong the conclusion is.

Example (small sample generalization):

Premise: Two customers complained about the new checkout system.
Conclusion: The new checkout system is a failure.

Complaints are relevant, but two complaints are not sufficient to justify “is a failure” without more context (how many users, severity, comparison to old system).

Example (overconfident causal claim):

Premise: After the new manager started, sales increased.
Conclusion: The new manager caused the sales increase.

The premise is relevant (timing), but insufficient: you’d want to rule out seasonal effects, marketing campaigns, pricing changes, or broader market trends.

Matching the Conclusion’s Strength to the Support

A practical way to judge “does it follow?” is to compare how bold the conclusion is to how much the premises can carry.

Conclusion Type	What It Requires	Common Failure
Guaranteed / must / cannot	No counterexamples possible	Premises allow an alternative scenario
All / none	Exception-free support	Evidence covers only some cases
Likely / probably	Strong pattern, good data, few alternatives	Small sample, bias, missing comparisons
Possible / might	Some relevant support	Premise is irrelevant or too vague

Example (adjusting strength):

Premise: Three independent reviewers reported the laptop battery lasted under 4 hours.
Too-strong conclusion: This laptop’s battery life is always under 4 hours.
Better-fit conclusion: This laptop’s battery life is often under 4 hours, or may be worse than advertised.

Practical Workflow: Evaluate “Does the Conclusion Follow?” in Under a Minute

Identify the intended level of certainty in the conclusion (guaranteed vs. likely vs. possible).
Run the relevance test: does each premise connect to the conclusion?
Run the sufficiency test: is the support enough for that level of certainty?
If the conclusion aims at certainty, run the counterexample test: can premises be true and conclusion false?
Check for “scope creep”: does the conclusion go beyond what the premises cover (all vs. some, always vs. sometimes, caused by vs. associated with)?

Short Example Set (Practice-Style)

A) Categorical Claim

Argument:

Premise: No vehicles are allowed in the park.
Premise: Bicycles are vehicles.
Conclusion: Bicycles are not allowed in the park.

Evaluation: If the premises are true, the conclusion follows (deductively strong). If someone objects, the likely issue is with a premise (e.g., whether bicycles count as vehicles), not with the support-to-conclusion link.

B) Cause-and-Effect

Argument:

Premise: Whenever the office uses the old printer, paper jams increase.
Premise: Today there were many paper jams.
Conclusion: The office must have used the old printer today.

Evaluation: Counterexample exists (jams could increase for other reasons: humidity, bad paper, maintenance). Premises can be true and conclusion false → does not follow.

C) Generalization from a Small Sample

Argument:

Premise: I tried one class at this gym and the instructor was unprepared.
Conclusion: The gym’s classes are low quality.

Evaluation: Premise is relevant but insufficient. The sample is too small and may not represent other instructors or class times. A weaker, better-supported conclusion would be: “That class might be low quality,” or “I should sample more classes before deciding.”

Now answer the exercise about the content:

When an argument’s conclusion uses words like “must,” “cannot,” or claims about “all/none,” which check is most appropriate to evaluate whether the conclusion truly follows from the premises?

You are right! Congratulations, now go to the next page

You missed! Try again.

Conclusions that aim at certainty require deductive support. The counterexample test checks validity by asking whether the premises could be true while the conclusion is false; if so, the conclusion does not follow.