reductio ad absurdum: give examples of this from 10 disciplines<\/p>\n\n\n\n
Reductio ad absurdum<\/strong> 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<\/strong>, each illustrating reductio ad absurdum:<\/p>\n\n\n\n Claim:<\/strong> Assume \u221a2 is rational. Claim:<\/strong> Everyone should always act selfishly. Claim:<\/strong> An object can travel faster than light. Claim:<\/strong> Everyone should be allowed to enforce justice on their own terms. Claim:<\/strong> Every problem can be solved by brute force. Claim:<\/strong> Minimum wage should be $1,000\/hour to help the poor. Claim:<\/strong> All traits in organisms are perfectly adaptive. Claim:<\/strong> Grammar rules must never be broken. Claim:<\/strong> A perfectly omnipotent being can create a stone so heavy it can’t lift it. Claim:<\/strong> A single ruler should have unchecked power to make decisions quickly. Would you like visual representations or quotes to accompany any of these examples?<\/p>\n\n\n\n is Jesus’s claim that by their fruits ye shall know them, an instance of reductio<\/p>\n\n\n\n Great question. Jesus’s statement “By their fruits ye shall know them”<\/strong> (Matthew 7:16, KJV) is not<\/strong> an example of reductio ad absurdum<\/strong>. Here’s why:<\/p>\n\n\n\n He is offering a positive test for discernment<\/strong> \u2014 a practical principle to evaluate people (especially false prophets) by their actions (their “fruits”), rather than by appearances or claims.<\/p>\n\n\n\n \u201cEven so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit.\u201d \u2014 Matthew 7:17<\/em><\/p>\n<\/blockquote>\n\n\n\n This is a form of analogy and practical wisdom<\/strong>, not a logical proof by contradiction.<\/p>\n\n\n\n Reductio works by assuming<\/strong> a claim is true and then showing that this leads to a logical contradiction or absurd result<\/strong>, thereby disproving<\/strong> the original assumption.<\/p>\n\n\n\n No<\/strong>, Jesus’s statement is not<\/strong> an example of reductio ad absurdum<\/em>. It\u2019s an evaluative principle<\/strong>, not a refutation by contradiction.<\/p>\n\n\n\n However, if<\/strong> someone claimed “False prophets are indistinguishable from true ones,” then<\/strong> one could use Jesus’s teaching to construct a reductio<\/em>:<\/p>\n\n\n\n That would be a derived reductio<\/strong>, not what Jesus originally meant.<\/p>\n\n\n\n Let me know if you\u2019d like that structured as a formal argument.<\/p>\n\n\n\n a reductio is an instance of if p then q, not q, therefore not p, no?<\/p>\n\n\n\n You’re exactly right \u2014 that’s the basic form of a reductio ad absurdum<\/strong>, 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.<\/p>\n\n\n\n If P, then Q<\/strong> This is a valid deductive form called modus tollens<\/strong>, which can be used in reductio ad absurdum<\/strong> when the “Q” is absurd, contradictory, or impossible.<\/p>\n\n\n\n If<\/strong> \u221a2 is rational (P), This is a common reductio form.<\/p>\n\n\n\n This version assumes P, then derives a contradiction<\/strong> from that assumption. It’s sometimes structured more like:<\/p>\n\n\n\n This is also reductio ad absurdum, and it’s often used in formal proofs in math and philosophy.<\/p>\n\n\n\n You were right on track with your version \u2014 it’s one of the canonical forms.<\/p>\n\n\n\n Want to see how this applies to a real-world argument, like in ethics or politics?<\/p>\n\n\n\n is the jesus example then a reductio in a wider sense which includes modus tollens<\/p>\n\n\n\n Yes \u2014 in a broader, looser sense<\/strong>, Jesus\u2019s teaching \u201cBy their fruits ye shall know them\u201d<\/em> can inspire<\/strong> a reductio-style argument<\/strong>, but the statement itself<\/strong> is not a reductio, nor is it strictly modus tollens<\/strong>.<\/p>\n\n\n\n Let\u2019s unpack that:<\/p>\n\n\n\n \u201cBy their fruits ye shall know them.\u201d This is a positive epistemological principle<\/strong>: you know a person’s character by the results of their actions.<\/p>\n\n\n\n Yes \u2014 you could construct<\/strong> a reductio ad absurdum<\/strong> using<\/em> his principle. Here’s how:<\/p>\n\n\n\n P<\/strong>: \u201cThere is no way to tell a false prophet from a true one.\u201d<\/p>\n<\/blockquote>\n\n\n\n You could use Jesus\u2019s principle to construct a reductio<\/strong>:<\/p>\n\n\n\n If P, then not Q<\/strong> Which is modus tollens<\/strong>, and also a form of reductio ad absurdum<\/strong> when Q leads to a contradiction with known or accepted truth.<\/p>\n\n\n\n “Is the Jesus example a reductio in a wider sense which includes modus tollens?”<\/strong><\/p>\n<\/blockquote>\n\n\n\n Yes \u2014 in a derived or applied sense.<\/strong> In short:<\/p>\n\n\n\n Would you like that in a more formal symbolic version or in another context (e.g., legal, ethical)?<\/p>\n\n\n\n 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<\/p>\n\n\n\n Yes \u2014 the argument you gave is a textbook example of modus tollens<\/strong>, and thus a valid form of reductio ad absurdum<\/strong> if used to disprove<\/strong> the claim that the school is good.<\/p>\n\n\n\n Let\u2019s break it down:<\/p>\n\n\n\n If<\/strong> a school is good, then<\/strong> it will keep a good teacher. This is modus tollens<\/strong>, which takes the form:<\/p>\n\n\n\n If P, then Q<\/strong> Applied to your case:<\/p>\n\n\n\n Valid inference.<\/strong> If someone claimed:<\/p>\n\n\n\n “The school is good,”
\n\n\n\n1. Mathematics<\/strong><\/h3>\n\n\n\n
Argument:<\/strong>
If \u221a2 = a\/b (in lowest terms), then 2 = a\u00b2\/b\u00b2 \u21d2 a\u00b2 = 2b\u00b2.
So a\u00b2 is even \u21d2 a is even \u21d2 a = 2k \u21d2 a\u00b2 = 4k\u00b2 \u21d2 2b\u00b2 = 4k\u00b2 \u21d2 b\u00b2 = 2k\u00b2 \u21d2 b is even.
So both a and b are even \u21d2 contradiction (a\/b wasn’t in lowest terms).
Conclusion:<\/strong> \u221a2 is irrational.<\/p>\n\n\n\n
\n\n\n\n2. Philosophy (Ethics)<\/strong><\/h3>\n\n\n\n
Argument:<\/strong>
If everyone only acts selfishly, then no one helps anyone.
But cooperation and empathy are foundational to society.
This leads to societal breakdown\u2014a clearly absurd outcome.
Conclusion:<\/strong> It is not rational to claim everyone should act selfishly.<\/p>\n\n\n\n
\n\n\n\n3. Physics<\/strong><\/h3>\n\n\n\n
Argument:<\/strong>
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:<\/strong> Faster-than-light travel leads to absurdities \u21d2 not physically possible.<\/p>\n\n\n\n
\n\n\n\n4. Law<\/strong><\/h3>\n\n\n\n
Argument:<\/strong>
If all take justice into their own hands, laws become meaningless.
This leads to chaos, vigilantism, and breakdown of legal order.
Conclusion:<\/strong> The claim leads to absurdity \u21d2 law enforcement must be regulated.<\/p>\n\n\n\n
\n\n\n\n5. Computer Science<\/strong><\/h3>\n\n\n\n
Argument:<\/strong>
Brute force for NP-complete problems like the Traveling Salesman grows exponentially.
For large inputs, solution time exceeds the age of the universe.
Conclusion:<\/strong> Brute force for all problems is absurd \u21d2 efficient algorithms are needed.<\/p>\n\n\n\n
\n\n\n\n6. Economics<\/strong><\/h3>\n\n\n\n
Argument:<\/strong>
If wage is $1,000\/hr, most businesses can’t afford workers.
Mass layoffs, inflation, and economic collapse would follow.
Conclusion:<\/strong> Excessively high minimum wage leads to absurd results.<\/p>\n\n\n\n
\n\n\n\n7. Biology<\/strong><\/h3>\n\n\n\n
Argument:<\/strong>
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:<\/strong> The claim leads to absurd interpretations of biology.<\/p>\n\n\n\n
\n\n\n\n8. Linguistics<\/strong><\/h3>\n\n\n\n
Argument:<\/strong>
Everyday speech breaks grammar rules constantly (“Who you talking to?”).
If rules were never broken, language couldn’t evolve or be expressive.
Conclusion:<\/strong> Absolute rule-following leads to absurd rigidity in communication.<\/p>\n\n\n\n
\n\n\n\n9. Theology<\/strong><\/h3>\n\n\n\n
Argument:<\/strong>
If yes \u21d2 can’t lift it \u21d2 not omnipotent.
If no \u21d2 can’t create it \u21d2 not omnipotent.
Conclusion:<\/strong> The claim leads to logical absurdity \u21d2 reveals a flawed conception of omnipotence.<\/p>\n\n\n\n
\n\n\n\n10. Political Science<\/strong><\/h3>\n\n\n\n
Argument:<\/strong>
Unrestricted power leads to dictatorship, abuse, and oppression.
Historical examples (Hitler, Stalin) show disastrous outcomes.
Conclusion:<\/strong> The claim leads to political absurdity \u21d2 checks and balances are necessary.<\/p>\n\n\n\n
\n\n\n\nYou said:<\/h5>\n\n\n\n
ChatGPT said:<\/h6>\n\n\n\n
\n\n\n\n What Jesus is doing:<\/strong><\/h3>\n\n\n\n
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\n\n\n\n What reductio ad absurdum does:<\/strong><\/h3>\n\n\n\n
\n\n\n\n Comparison:<\/h3>\n\n\n\n
“By their fruits…”<\/strong><\/th> Reductio ad absurdum<\/strong><\/th><\/tr><\/thead> Positive moral test or discernment principle<\/td> Logical refutation via contradiction<\/td><\/tr> Offers a metaphorical way to judge character<\/td> Used to disprove a statement logically<\/td><\/tr> Practical, not formal logic<\/td> Formal or semi-formal logical method<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\n Conclusion:<\/h3>\n\n\n\n
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You said:<\/h5>\n\n\n\n
ChatGPT said:<\/h6>\n\n\n\n
\n\n\n\n Yes: Reductio ad absurdum often uses this structure:<\/h2>\n\n\n\n
Form (Modus Tollens style):<\/strong><\/h3>\n\n\n\n
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Not Q<\/strong>
Therefore, not P<\/strong><\/p>\n<\/blockquote>\n\n\n\nExample:<\/h3>\n\n\n\n
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then<\/strong> it can be expressed as a\/b in lowest terms (Q).
But that leads to a contradiction (not Q).
Therefore,<\/strong> \u221a2 is not rational (not P).<\/p>\n<\/blockquote>\n\n\n\n
\n\n\n\n Alternative form: Indirect proof via contradiction<\/strong><\/h2>\n\n\n\n
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\n\n\n\nSummary:<\/h3>\n\n\n\n
Type<\/th> Structure<\/th> Used in<\/th><\/tr><\/thead> Modus tollens form<\/strong><\/td> If P, then Q; not Q; therefore not P<\/td> Logic, philosophy<\/td><\/tr> Contradiction form<\/strong><\/td> Assume P; derive contradiction; therefore not P<\/td> Math proofs, logic<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\nYou said:<\/h5>\n\n\n\n
ChatGPT said:<\/h6>\n\n\n\n
\n\n\n\n What Jesus says:<\/h2>\n\n\n\n
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(Matthew 7:16)<\/p>\n<\/blockquote>\n\n\n\n
\n\n\n\n Can it support a reductio?<\/h2>\n\n\n\n
\n\n\n\n Suppose someone says:<\/h3>\n\n\n\n
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That implies there is<\/strong> a way: by their actions\/outcomes (Q).<\/li>\n\n\n\n
\u2192 It is not<\/strong> true that you can\u2019t distinguish them.<\/li>\n<\/ol>\n\n\n\nThis is in the form:<\/h3>\n\n\n\n
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Q<\/strong>
Therefore, not P<\/strong><\/p>\n<\/blockquote>\n\n\n\n
\n\n\n\n So to your question:<\/h2>\n\n\n\n
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While Jesus’s original statement is not<\/strong> a reductio, it can function as the foundation<\/strong> for constructing a reductio argument, particularly one using modus tollens<\/strong>.<\/p>\n\n\n\n\n
\n\n\n\nYou said:<\/h5>\n\n\n\n
ChatGPT said:<\/h6>\n\n\n\n
\n\n\n\n Your Argument:<\/h2>\n\n\n\n
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The school does not<\/strong> keep a good teacher.
Therefore,<\/strong> the school is not good.<\/p>\n<\/blockquote>\n\n\n\n
\n\n\n\n Logical Structure:<\/h2>\n\n\n\n
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Not Q<\/strong>
Therefore, not P<\/strong><\/p>\n<\/blockquote>\n\n\n\n\n
If the initial conditional<\/strong> (“If the school is good, it keeps a good teacher”) is accepted as true, then the conclusion logically follows.<\/p>\n\n\n\n
\n\n\n\n As Reductio Ad Absurdum:<\/h2>\n\n\n\n
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and you showed that this leads to the absurd outcome<\/strong> that a good school fails to retain good teachers, then you’re using a reductio<\/strong> style argument:<\/p>\n<\/blockquote>\n\n\n\n\n