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🛡️ Debate/Coaching/NTT/NTT Reductios.md
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🛡️ Debate/Coaching/NTT/NTT Reductios.md
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### NTT Reductio (Non-Negated Antecedent w/ Conjunction)
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| <font color="CC6600">**Definiendum**</font> | <font color="CC6600">**Definiens**</font> |
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|:-------------------------------------------:|:----------------------------------------- |
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| <font color="CC6600">**T**</font> | a being (x) is ethical to consume |
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| <font color="CC6600">**P**</font> | a being (x) has fur |
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| <font color="CC6600">**Q**</font> | a being (x) has horns |
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| <font color="CC6600">**R**</font> | a being (x) has hooves |
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| <font color="CC6600">**a**</font> | hypothetical human |
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<div style="text-align: center">
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<font color="CC6600">
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<b>P1)</b></font> For all x, where x is a being, they are ethical to consume if, and only if, x has fur, x has horns, and x has hooves.
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<br />
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<font color="CC6600">
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<b>(∀x(Tx↔(Px∧Qx∧Rx)))</b>
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<br />
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<b>P2)</b></font> A hypothetical human has fur, horns, and hooves.
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<br />
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<font color="CC6600">
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<b>(Pa∧Qa∧Ra)</b>
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<br />
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<b>C)</b></font> Therefore, A hypothetical human is ethical to consume.
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<br />
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<font color="CC6600">
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<b>(∴Ta)</b>
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<br />
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<br />
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</font>
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</div>
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[Proof Tree](https://www.umsu.de/trees/#(~6x(Tx~4(Px~1Qx~1Rx))),(Pa~1Qa~1Ra)|=(Ta))
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### NTT Reductio (Negated Antecedent w/ Conjunction)
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| <font color="CC6600">**Definiendum**</font> | <font color="CC6600">**Definiens**</font> |
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|:-------------------------------------------:|:------------------------------------------ |
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| <font color="CC6600">**T**</font> | a being (x) is ethical to consume |
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| <font color="CC6600">**P**</font> | a being (x) has average human intelligence |
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| <font color="CC6600">**Q**</font> | a being (x) has language skills |
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| <font color="CC6600">**R**</font> | a being (x) has human genetics |
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| <font color="CC6600">**a**</font> | hypothetical schmuman |
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<div style="text-align: center">
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<font color="CC6600">
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<b>P1)</b></font> For all x, where x is a being, they are not ethical to consume if, and only if, x has average human intelligence, x has language skills, and x has human genetics.
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<br />
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<font color="CC6600">
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<b>(∀x(¬Tx↔(Px∧Qx∧Rx)))</b>
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<br />
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<b>P2)</b></font> A hypothetical schmuman does not have human genetics.
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<br />
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<font color="CC6600">
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<b>(¬Ra)</b>
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<br />
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<b>C)</b></font> Therefore, a hypothetical schmuman is ethical to consume.
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<br />
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<font color="CC6600">
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<b>(∴Ta)</b>
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<br />
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<br />
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</font>
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</div>
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[Proof Tree](https://www.umsu.de/trees/#(~6x(~3Tx~4(Px~1Qx~1Rx))),(~3Ra)|=(Ta))
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### NTT Reductio (Non-Negated Antecedent w/ Disjunction)
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| <font color="CC6600">**Definiendum**</font> | <font color="CC6600">**Definiens**</font> |
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|:-------------------------------------------:|:----------------------------------------- |
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| <font color="CC6600">**T**</font> | a being (x) is ethical to consume |
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| <font color="CC6600">**P**</font> | a being (x) has fur |
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| <font color="CC6600">**Q**</font> | a being (x) has horns |
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| <font color="CC6600">**R**</font> | a being (x) has hooves |
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| <font color="CC6600">**a**</font> | hypothetical human |
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<div style="text-align: center">
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<font color="CC6600">
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<b>P1)</b></font> For all x, where x is a being, they are ethical to consume if, and only if, x has fur, or x has horns, or x has hooves.
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<br />
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<font color="CC6600">
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<b>(∀x(Tx↔(Px∨Qx∨Rx)))</b>
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<br />
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<b>P2)</b></font> A hypothetical human has hooves.
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<br />
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<font color="CC6600">
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<b>(Ra)</b>
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<br />
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<b>C)</b></font> Therefore, A hypothetical human is ethical to consume.
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<br />
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<font color="CC6600">
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<b>(∴Ta)</b>
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<br />
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<br />
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</font>
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</div>
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[Proof Tree](https://www.umsu.de/trees/#(~6x(Tx~4(Px~2Qx~2Rx))),(Ra)|=(Ta))
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### NTT Reductio (Negated Antecedent w/ Disjunction)
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| <font color="CC6600">**Definiendum**</font> | <font color="CC6600">**Definiens**</font> |
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|:-------------------------------------------:|:------------------------------------------ |
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| <font color="CC6600">**T**</font> | a being (x) is ethical to consume |
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| <font color="CC6600">**P**</font> | a being (x) has average human intelligence |
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| <font color="CC6600">**Q**</font> | a being (x) has language skills |
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| <font color="CC6600">**R**</font> | a being (x) has human genetics |
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| <font color="CC6600">**a**</font> | hypothetical schmuman |
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<div style="text-align: center">
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<font color="CC6600">
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<b>P1)</b></font> For all x, where x is a being, they are not ethical to consume if, and only if, x has average human intelligence, or x has language skills, or x has human genetics.
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<br />
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<font color="CC6600">
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<b>(∀x(¬Tx↔(Px∨Qx∨Rx)))</b>
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<br />
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<b>P2)</b></font> A hypothetical schmuman does not have average human intelligence, language skills, and human genetics.
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<br />
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<font color="CC6600">
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<b>(¬Pa∧¬Qa∧¬Ra)</b>
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<br />
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<b>C)</b></font> Therefore, a hypothetical schmuman is ethical to consume.
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<br />
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<font color="CC6600">
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<b>(∴Ta)</b>
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<br />
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<br />
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</font>
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</div>
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[Proof Tree](https://www.umsu.de/trees/#(~6x(~3Tx~4(Px~2Qx~2Rx))),(~3Pa~1~3Qa~1~3Ra)|=(Ta))
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---
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# Hashtags
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#debate
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#debate_coursework
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#namethetrait
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#ntt
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