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Rationalissimus of the Elenchus

Assumption of linearity / "Oven Logic"

Often, we wrongly model things linearly, as if the variable x against some sort of common metric y should yield a straight line (or at least, we assume the gradient won't change significantly in the course of our data plotting). This is the incorrect thinking behind the fallacy of Extrapolation, but I wanted to ask about a more particular case.

The reason this thread is titled "Oven Logic" is because this 'logic' is often applied to baking. Here's an example:

Sara-Lee: Hmm. The recipe says 30 minutes at 150C. But I don't have time! I've got to get these cakes out so I can be at Kristen's birthday party on time. *shrug* I guess I'll put them in for 15 minutes at 300C instead; double the temp, half the time, no?

But as it turns out, she ends up nearly burning down her entire house. 300C was too high.

Why did this happen? She wrongly believed that a variable will produce a valid result if a second variable is  changed 'proportionately'. So if x + y = z, 1/2x + 2y should equal the same z. Yet, the cakes do not bake like that.

This seems to be a common error in reasoning, yet I get the impression that it could simply be dismissed as a factual error...which seems wrong to me.

Is assuming linearity more a case of just 'sucking at maths', or does it count as one of the named fallacies on the site?

(Or could it even be a new one?)

asked on Thursday, Jun 10, 2021 07:37:28 PM by Rationalissimus of the Elenchus

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Bo Bennett, PhD
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This seems like it would require domain-specific information. In your example, one would have to know about baking/chemistry to know that linearity does not apply. In many other cases, linearity does apply (for example, if I walk twice as fast to school, I will make it there in half the time). It would be a flaw in reasoning to assume such linearity applies to all situations, but does anyone really think this? But what about someone who thinks it applies to a certain situation when it doesn't? This is where I am thinking that they would just be factually incorrect, because they lack the domain-specific information. To me, it doesn't really seem like a fallacy. Unless I am missing something :)

answered on Friday, Jun 11, 2021 07:54:05 AM by Bo Bennett, PhD

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Arlo
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As I was with the "applying a statistic from a group to an individual" case, I'm leaning toward factual error as opposed to a logical fallacy.

As you say, it's not uncommon for many folks to misunderstand how some things actually work (just like it's not uncommon for folks to misunderstand or misapply statistics), but it seems that diluting "logical fallacies" by adding in all of the possible ways folks might just "suck at (some area of knowledge)" does a disservice to the "logic" part of our discussions.

I think it comes down to a case of failing to identify incorrect and implied premises than using poor logic.

answered on Friday, Jun 11, 2021 12:03:58 PM by Arlo

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Rationalissimus of the Elenchus writes:

As you say, it's not uncommon for many folks to misunderstand how some things actually work (just like it's not uncommon for folks to misunderstand or misapply statistics), but it seems that diluting "logical fallacies" by adding in all of the possible ways folks might just "suck at (some area of knowledge)" does a disservice to the "logic" part of our discussions.

I know, and I'm not trying to do that - in fact, I was even just gravitating towards "lack of knowledge" rather than 'fallacy'. However, I have experienced people assuming linearity in a variety of situations, so I thought I might put this up for discussion.

Your answer is sensible though

posted on Friday, Jun 11, 2021 06:15:49 PM