reductio ad absurdum: give examples of this from 10 disciplines
ChatGPT said:
Reductio ad absurdum is a form of argument where a claim is disproven by following its implications to an absurd or contradictory conclusion. Below are 10 examples from different disciplines, each illustrating reductio ad absurdum:
1. Mathematics
Claim: Assume √2 is rational.
Argument:
If √2 = a/b (in lowest terms), then 2 = a²/b² ⇒ a² = 2b².
So a² is even ⇒ a is even ⇒ a = 2k ⇒ a² = 4k² ⇒ 2b² = 4k² ⇒ b² = 2k² ⇒ b is even.
So both a and b are even ⇒ contradiction (a/b wasn’t in lowest terms).
Conclusion: √2 is irrational.
2. Philosophy (Ethics)
Claim: Everyone should always act selfishly.
Argument:
If everyone only acts selfishly, then no one helps anyone.
But cooperation and empathy are foundational to society.
This leads to societal breakdown—a clearly absurd outcome.
Conclusion: It is not rational to claim everyone should act selfishly.
3. Physics
Claim: An object can travel faster than light.
Argument:
According to relativity, mass increases with speed.
At light speed, mass becomes infinite; beyond it, math breaks down.
This leads to causality violations (effects before causes).
Conclusion: Faster-than-light travel leads to absurdities ⇒ not physically possible.
4. Law
Claim: Everyone should be allowed to enforce justice on their own terms.
Argument:
If all take justice into their own hands, laws become meaningless.
This leads to chaos, vigilantism, and breakdown of legal order.
Conclusion: The claim leads to absurdity ⇒ law enforcement must be regulated.
5. Computer Science
Claim: Every problem can be solved by brute force.
Argument:
Brute force for NP-complete problems like the Traveling Salesman grows exponentially.
For large inputs, solution time exceeds the age of the universe.
Conclusion: Brute force for all problems is absurd ⇒ efficient algorithms are needed.
6. Economics
Claim: Minimum wage should be $1,000/hour to help the poor.
Argument:
If wage is $1,000/hr, most businesses can’t afford workers.
Mass layoffs, inflation, and economic collapse would follow.
Conclusion: Excessively high minimum wage leads to absurd results.
7. Biology
Claim: All traits in organisms are perfectly adaptive.
Argument:
Some traits (e.g., human appendix, male nipples) lack current adaptive value.
Assuming perfect adaptation implies natural selection never makes mistakes, which contradicts known evolutionary processes.
Conclusion: The claim leads to absurd interpretations of biology.
8. Linguistics
Claim: Grammar rules must never be broken.
Argument:
Everyday speech breaks grammar rules constantly (“Who you talking to?”).
If rules were never broken, language couldn’t evolve or be expressive.
Conclusion: Absolute rule-following leads to absurd rigidity in communication.
9. Theology
Claim: A perfectly omnipotent being can create a stone so heavy it can’t lift it.
Argument:
If yes ⇒ can’t lift it ⇒ not omnipotent.
If no ⇒ can’t create it ⇒ not omnipotent.
Conclusion: The claim leads to logical absurdity ⇒ reveals a flawed conception of omnipotence.
10. Political Science
Claim: A single ruler should have unchecked power to make decisions quickly.
Argument:
Unrestricted power leads to dictatorship, abuse, and oppression.
Historical examples (Hitler, Stalin) show disastrous outcomes.
Conclusion: The claim leads to political absurdity ⇒ checks and balances are necessary.
Would you like visual representations or quotes to accompany any of these examples?
You said:
is Jesus’s claim that by their fruits ye shall know them, an instance of reductio
ChatGPT said:
Great question. Jesus’s statement “By their fruits ye shall know them” (Matthew 7:16, KJV) is not an example of reductio ad absurdum. Here’s why:
What Jesus is doing:
He is offering a positive test for discernment — a practical principle to evaluate people (especially false prophets) by their actions (their “fruits”), rather than by appearances or claims.
“Even so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit.” — Matthew 7:17
This is a form of analogy and practical wisdom, not a logical proof by contradiction.
What reductio ad absurdum does:
Reductio works by assuming a claim is true and then showing that this leads to a logical contradiction or absurd result, thereby disproving the original assumption.
Comparison:
| “By their fruits…” | Reductio ad absurdum |
|---|---|
| Positive moral test or discernment principle | Logical refutation via contradiction |
| Offers a metaphorical way to judge character | Used to disprove a statement logically |
| Practical, not formal logic | Formal or semi-formal logical method |
Conclusion:
No, Jesus’s statement is not an example of reductio ad absurdum. It’s an evaluative principle, not a refutation by contradiction.
However, if someone claimed “False prophets are indistinguishable from true ones,” then one could use Jesus’s teaching to construct a reductio:
- Assume: You can’t tell false prophets from true ones.
- Then: Actions (“fruits”) don’t reflect inner truth.
- But: If a prophet brings destruction, lies, or harm, that is clearly bad fruit.
- So: The assumption leads to absurdity — we can distinguish them.
- Therefore: The original claim is false.
That would be a derived reductio, not what Jesus originally meant.
Let me know if you’d like that structured as a formal argument.
You said:
a reductio is an instance of if p then q, not q, therefore not p, no?
ChatGPT said:
You’re exactly right — that’s the basic form of a reductio ad absurdum, though there are two slightly different ways it’s used in logic, and you’re pointing to one of them. Let’s break it down clearly.
Yes: Reductio ad absurdum often uses this structure:
Form (Modus Tollens style):
If P, then Q
Not Q
Therefore, not P
This is a valid deductive form called modus tollens, which can be used in reductio ad absurdum when the “Q” is absurd, contradictory, or impossible.
Example:
If √2 is rational (P),
then it can be expressed as a/b in lowest terms (Q).
But that leads to a contradiction (not Q).
Therefore, √2 is not rational (not P).
This is a common reductio form.
Alternative form: Indirect proof via contradiction
This version assumes P, then derives a contradiction from that assumption. It’s sometimes structured more like:
- Assume P (the claim you want to disprove)
- From P, logically derive Q
- Show that Q is a contradiction or absurdity (e.g., Q ∧ ¬Q)
- Therefore, P must be false
This is also reductio ad absurdum, and it’s often used in formal proofs in math and philosophy.
Summary:
| Type | Structure | Used in |
|---|---|---|
| Modus tollens form | If P, then Q; not Q; therefore not P | Logic, philosophy |
| Contradiction form | Assume P; derive contradiction; therefore not P | Math proofs, logic |
You were right on track with your version — it’s one of the canonical forms.
Want to see how this applies to a real-world argument, like in ethics or politics?
You said:
is the jesus example then a reductio in a wider sense which includes modus tollens
ChatGPT said:
Yes — in a broader, looser sense, Jesus’s teaching “By their fruits ye shall know them” can inspire a reductio-style argument, but the statement itself is not a reductio, nor is it strictly modus tollens.
Let’s unpack that:
What Jesus says:
“By their fruits ye shall know them.”
(Matthew 7:16)
This is a positive epistemological principle: you know a person’s character by the results of their actions.
Can it support a reductio?
Yes — you could construct a reductio ad absurdum using his principle. Here’s how:
Suppose someone says:
P: “There is no way to tell a false prophet from a true one.”
You could use Jesus’s principle to construct a reductio:
- Assume P: There’s no way to distinguish true from false prophets.
- But Jesus says, “By their fruits ye shall know them.”
That implies there is a way: by their actions/outcomes (Q). - If P were true, then Q would be false (i.e., you can’t know them).
- But Q is true — we can know them by their fruits. (Not Q is false)
- Therefore, P is false.
→ It is not true that you can’t distinguish them.
This is in the form:
If P, then not Q
Q
Therefore, not P
Which is modus tollens, and also a form of reductio ad absurdum when Q leads to a contradiction with known or accepted truth.
So to your question:
“Is the Jesus example a reductio in a wider sense which includes modus tollens?”
Yes — in a derived or applied sense.
While Jesus’s original statement is not a reductio, it can function as the foundation for constructing a reductio argument, particularly one using modus tollens.
In short:
- Jesus gives a principle.
- We can build a reductio using that principle.
- The principle itself isn’t the reductio — the argument we construct from it is.
Would you like that in a more formal symbolic version or in another context (e.g., legal, ethical)?
You said:
what about the following: if a school is good, it will keep a good teacher; the school does not keep a good teacher, therefore, it is not good
ChatGPT said:
Yes — the argument you gave is a textbook example of modus tollens, and thus a valid form of reductio ad absurdum if used to disprove the claim that the school is good.
Let’s break it down:
Your Argument:
If a school is good, then it will keep a good teacher.
The school does not keep a good teacher.
Therefore, the school is not good.
Logical Structure:
This is modus tollens, which takes the form:
If P, then Q
Not Q
Therefore, not P
Applied to your case:
- P = “The school is good”
- Q = “The school keeps a good teacher”
- You observe not Q (it doesn’t keep the good teacher)
- Therefore, not P (the school is not good)
Valid inference.
If the initial conditional (“If the school is good, it keeps a good teacher”) is accepted as true, then the conclusion logically follows.
As Reductio Ad Absurdum:
If someone claimed:
“The school is good,”
and you showed that this leads to the absurd outcome that a good school fails to retain good teachers, then you’re using a reductio style argument:
- Assume: The school is good.
- Then: It would retain good teachers.
- But: It doesn’t retain a good teacher (contrary to what would follow).
- Contradiction with expected consequence.
- Conclusion: The assumption (that it’s good) must be false.
So yes — this is:
- Modus tollens
- Reductio ad absurdum (if used to reject the claim that the school is good)
Would you like to see how this reasoning might be challenged or defended in, say, a debate or policy discussion?
You said:
can you form a reductio concerning president trump
ChatGPT said:
Yes — we can construct a reductio ad absurdum argument concerning President Trump, but it depends on what specific claim we’re trying to refute. Here’s a neutral, logic-based example — not based on personal opinion, but on illustrating logical structure.
Let’s take a hypothetical claim, often made by supporters:
Claim (P): “President Trump always tells the truth.”
We can construct a reductio ad absurdum to challenge that claim.
Reductio ad Absurdum Example
1. Assume P:
President Trump always tells the truth.
2. But Trump has made contradictory statements on record. For example:
a. “COVID will just disappear.”
b. Later: “I always knew it was a pandemic.”
These statements cannot both be true, as they conflict about his prior knowledge.
3. Therefore, assuming he always tells the truth leads to:
A contradiction — someone cannot truthfully say both “I didn’t know” and “I always knew.”
4. Conclusion:
The original assumption (that Trump always tells the truth) leads to an absurdity (a logical contradiction).
Therefore, the claim is false.
This is a classic reductio using:
- P: Trump always tells the truth
- Derive Q: Contradictory truths must both be true
- Contradiction ⇒ Absurd outcome
- Therefore, not P
Neutral Note:
This kind of argument can be applied to any political figure or claim, regardless of ideology. The key is to:
- Start with a claim someone makes,
- Assume it’s true,
- Show it leads to a contradiction or unacceptable consequence, and
- Therefore, conclude the claim must be false or flawed.
Would you like a reductio involving a different kind of Trump-related claim — perhaps about policy, democracy, or legal matters?
You said:
all
ChatGPT said:
Got it — you’re asking for multiple reductio ad absurdum arguments involving President Trump, covering various claims (not just truthfulness), across different areas: personal behavior, policy, democracy, legal matters, etc.
I’ll provide a series of reductio arguments, each refuting a different common or hypothetical claim by assuming it’s true, then showing it leads to contradiction or absurdity — the essence of reductio ad absurdum.
1. Claim: “President Trump always tells the truth.”
- Assume: Trump always tells the truth.
- But: He has made public statements that contradict each other (e.g., “I always knew it was a pandemic” vs. earlier dismissals).
- Contradiction: Two opposite claims can’t both be true.
- Conclusion: He does not always tell the truth.
2. Claim: “Trump respects democratic norms completely.”
- Assume: Trump fully respects democratic processes.
- Then: He would have accepted certified election results in 2020.
- But: He actively sought to overturn them and pressured officials (e.g., “find 11,780 votes”).
- Contradiction: Seeking to overturn certified results contradicts respecting democratic norms.
- Conclusion: The original claim is false.
3. Claim: “No charges against Trump can be legitimate — it’s all a witch hunt.”
- Assume: All legal charges are purely political and without basis.
- Then: There should be no evidence supporting the charges.
- But: Multiple grand juries, judges, and evidence (e.g., classified documents found at Mar-a-Lago) exist.
- Contradiction: If evidence exists and due process is followed, it can’t all be baseless.
- Conclusion: The blanket “witch hunt” claim leads to absurd dismissal of due process.
4. Claim: “Trump’s economic policies created a perfect economy.”
- Assume: The economy under Trump was perfect.
- Then: There should be no significant economic weaknesses.
- But: National debt rose by over $7 trillion, and trade wars (e.g., with China) hurt certain sectors (e.g., farming).
- Contradiction: A “perfect” economy wouldn’t have major failures.
- Conclusion: The claim is exaggerated or false.
5. Claim: “Trump made America respected globally.”
- Assume: Trump’s leadership increased global respect for the U.S.
- Then: Allies should have trusted and supported U.S. leadership more.
- But: Many allies (e.g., NATO members) expressed deep concern or openly distanced themselves from Trump-era policies.
- Contradiction: Losing allies’ trust contradicts increased respect.
- Conclusion: The claim doesn’t hold.
6. Claim: “Trump is a self-made billionaire.”
- Assume: He built his wealth independently.
- But: Evidence shows he inherited at least $400 million and received financial bailouts from his father throughout his life.
- Contradiction: Inheriting massive wealth and ongoing support conflicts with “self-made.”
- Conclusion: The claim is misleading.
7. Claim: “Presidents are above the law.” (Trump has not explicitly said this, but some defenses imply it.)
- Assume: Presidents are immune from prosecution.
- Then: A president could commit any crime (e.g., murder) and avoid accountability while in office.
- Absurdity: This leads to a scenario where presidents can violate all laws without consequence.
- Conclusion: The idea is untenable — no one is above the law.
8. Claim: “The 2020 election was stolen because Trump said so.”
- Assume: The election was stolen simply because Trump claims it.
- Then: Any losing candidate could claim fraud and invalidate results.
- Absurdity: This would make democratic elections meaningless — only winners are legitimate if they say so.
- Conclusion: That claim leads to absurd breakdown of democracy.
Summary: Reductio Across Claims
| Claim | Absurd Consequence |
|---|---|
| Trump always tells the truth | Contradictory public statements |
| Respects democracy fully | Tried to overturn certified results |
| All charges are fake | Evidence and due process ignored |
| Economy was perfect | Massive debt and sector damage |
| Gained global respect | Alienated traditional allies |
| Self-made billionaire | Inherited fortune contradicts |
| Presidents are immune | Enables dictatorship |
| “Stolen” election b/c he said so | Destroys democratic legitimacy |
Would you like any of these expanded into full formal logical structures or adapted to use in writing or debate?
You said:
construct a reductio of trump to reject the american form of government
ChatGPT said:
Great — you’re asking for a reductio ad absurdum that uses Donald Trump’s behavior or claims to challenge or refute the American form of government — that is, to show that if we accept Trump within the system as legitimate without limits, the system itself leads to absurdity or contradiction.
This is a higher-level philosophical move: starting from Trump’s actions, we show that if the American system truly allows or legitimizes those actions, then the system itself becomes self-undermining.
Let’s construct this step-by-step.
Claim to be tested (P):
“The American form of government (as currently constituted) is sound, resilient, and self-correcting.”
Let’s assume this is true and test it using reductio ad absurdum.
Reductio Argument
1. Assume:
The American system of government — with its checks and balances, electoral system, and legal structures — is sufficiently robust to prevent authoritarianism and protect democracy.
2. Observe Trump’s behavior:
- Attempted to overturn a certified election (pressured Georgia officials, promoted false claims of fraud).
- Incited or enabled an attack on the U.S. Capitol on January 6, 2021.
- Refused peaceful transfer of power, a foundational democratic norm.
- Openly suggested he would become a “dictator on day one” (even if in jest).
- Faces multiple criminal indictments yet retains mass political support and may return to power.
3. Assume the system is working properly → then it should:
- Disqualify someone who behaves this way from power.
- Prevent such a person from maintaining institutional control.
- Hold them legally and politically accountable in time.
4. But in reality:
- Trump was not removed or disqualified by impeachment.
- Legal consequences are slow, contested, and possibly ineffective.
- He remains the frontrunner for the 2024 GOP nomination (or has already secured it, depending on timing).
- The system has not corrected itself or protected its own integrity.
5. Contradiction / Absurdity:
If the system is truly robust and self-correcting, it should not permit someone who attempted to subvert it to remain a central political figure — let alone potentially return to power.
But the system does permit it.
6. Conclusion:
Therefore, the original assumption — that the American system is fully robust and self-correcting — leads to a contradiction with observable political reality.
Therefore, the assumption must be false.
Summary (in logical form):
- If the American system is sound (P),
- then it would not allow an anti-democratic actor to retain legitimacy or power (Q).
- But Trump, who undermined the system, is still a viable political leader (not Q).
- Therefore, not P: the system is not fully sound or self-correcting.
Reductio complete.
Implication:
This reductio doesn’t merely criticize Trump — it uses his example to question whether the American form of government, as it currently exists, can withstand anti-democratic pressures from within.
It shows that, unless reformed, the system might be internally structured to allow its own unraveling — a democratic paradox.
Would you like this written in a rhetorical or essay style suitable for publication, or reframed from another ideological point of view (libertarian, conservative, progressive, etc.)?