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From: sergi o <invalad@invalid.com>
Newsgroups: sci.math
Subject: Re: Natural numbers and vases II
Date: Wed, 6 Jul 2022 10:00:29 -0500
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On 7/6/2022 9:45 AM, Fritz Feldhase wrote:
> On Wednesday, July 6, 2022 at 3:48:13 PM UTC+2, WM wrote:
>> zelos...@gmail.com schrieb am Mittwoch, 6. Juli 2022 um 08:27:22 UTC+2:
>>
>> It is by my definition of dark elements: Things that cannot happen individually but can only happen collectively are dark.
> 
> This is not a definition, but BS.
> 
> Hint: Things? What things? Events? Mathematical objects/numbers? Can events be dark? Can numbers happen?
> 
> See: https://en.m.wikipedia.org/wiki/Equivocation
> and: https://en.m.wikipedia.org/wiki/Category_mistake


Fallacy of four terms

Equivocation in a syllogism (a chain of reasoning) produces a fallacy of four terms (quaternio terminorum). Below are some examples:

Since only man [human] is rational.
And no woman is a man [male].
Therefore, no woman is rational.[1]
The first instance of "man" implies the entire human species, while the second implies just those who are male.

A feather is light [not heavy].
What is light [bright] cannot be dark.
Therefore, a feather cannot be dark.
In the above example, distinct meanings of the word "light" are implied in contexts of the first and second statements.

All jackasses [male donkey] have long ears.
Carl is a jackass [annoying person].
Therefore, Carl has long ears.
Here, the equivocation is the metaphorical use of "jackass" to imply a simple-minded or obnoxious person instead of a male donkey.

Motte-and-bailey fallacy

Main article: Motte-and-bailey fallacy
Equivocation can also be used to conflate two positions which share similarities, one modest and easy to defend and one much more controversial. The 
arguer advances the controversial position, but when challenged, they insist that they are only advancing the more modest position.