obsidian/🛡️ Debate/Arguments/Vegan/Anti-Pollination Reductio.md

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2024-06-28 02:13:12 -05:00
### Pollination Reductio
| <font color="CC6600">**Definiendum**</font> | <font color="CC6600">**Definiens**</font> |
|:-------------------------------------------:|:--------------------------------------------------------------------- |
| <font color="CC6600">**V**</font> | something (x) is vegan |
| <font color="CC6600">**E**</font> | something (x) does not involve human on non-human animal exploitation |
| <font color="CC6600">**P**</font> | the products (x) generated are not vegan |
| <font color="CC6600">**b**</font> | bees pollinating human crops |
| <font color="CC6600">**a**</font> | apples |
<div style="text-align: center">
<font color="CC6600">
<b>P1)</b></font> Something is vegan if, and only if, something does not involve human on non-human animal exploitation.
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<font color="CC6600">
<b>(∀x(Vx↔¬Ex))</b>
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<b>P2)</b></font> Bees pollinating human crops involves human on non-human exploitation.
<br />
<font color="CC6600">
<b>(Eb)</b>
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<b>P3)</b></font> If bees pollinating human crops is not vegan, then the products generated are not vegan.
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<font color="CC6600">
<b>(¬Vb→∀x(¬Px))</b>
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<b>C)</b></font> Therefore, apples are not vegan.
<br />
<font color="CC6600">
<b>(∴¬Pa)</b>
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<br />
</font>
</div>
[Proof Tree](https://www.umsu.de/trees/#(~6x(Vx~4~3Ex)),(Eb),(~3Vb~5~6x(~3Px))|=(~3Pa))
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