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Actually a quite interesting article: https://en.wikipedia.org/wiki/All_horses_are_the_same_color
I did do this proof by induction back in the day, but now looking at the article I am clueless.
I took a peek and it is sort of dumb but logically “sound”. Specifically the indictive step.
In the inductive step you assume the statement is true for some number n and use this statement to prove the statement n + 1 is true. If you can do that then you can prove the induction step.
So in this example the statement we assume is true is given n horses, all of them are the same color. To prove the statement for n + 1 horses we look at the n + 1 horses. Then we exclude the last horse. By excluding the last horse we have a set of n horses. By the induction statement this set of horses must all be the same color. So now we’ve proven the first n horses are the same color.
Next we can exclude the first horse. This also gives us a set of n horses. By the induction statement all these horses must also be the same color. Therefore all n + 1 horses must be the same color.
This sounds really dumb but the proof works in the induction step.
The logical issue is that the base case is wrong which is necessary for a complete proof by induction.
Also related: https://en.wikipedia.org/wiki/Raven_paradox
A much more interesting question, if you ask me.
It was stated as a lemma, which in particular allowed the author to “prove” that Alexander the Great did not exist, and he had an infinite number of limbs.[4]
Talk about burying the lede! 😄
This is what arguing with people about politics feels like.
Why is there a picture of an empty field?
I assume John Cena is standing there and we just can’t see him
I’m not even convinced that horses are real.
They’re what the government uses to spy on the Amish.
Why can’t they just use birds like for everyone else?
I’m not convinced that anything outside my own thoughts are real. In fact are my thoughts real?
You’re not real. I am not real. Nothing is real.
True. They look too similar to giraffes
Actually this just refers to the color of their fur. I’d say that a blonde white man and a white read head are the same color, just their hair has a different color.
(I’m not totally serious and will not die on this hill)
Oh, I’m gonna make sure you die on that hill!
First, by building you a lovely house on that hill and a nearby Denny’s…
Sounds nice, go on!
(I’m gullible and will fall into any trap I come across)
In some cultures this might be the same color.
Their hair is the same color. What color is the skin?
Horse blindness is a made up illness designed to gaslight us into believing that horses exist.
That theory assumes that color is real. Color is just some photons smacking into your retina and then the brain deciding what that even means.
Well, sorta. Different materials bounce different wavelengths of light that our eyes catch and send to the brain to piece together and interpret color from. There is a degree of responsibility for what we see on the object the light bounces off of in the form of what wavelengths they absorb or reflect.
Aha, but that assumes light is real and materials are real and the universe is real!
Yeah, colors are just whatever the simulation decided it should be
That assumes the simulation is real
On the inside?
…what?
Horse hair colors vary.
If you shave a horse, any breeds with dark black or blue-ish grey hair will give you a variety of that pallet, getting dark enough to be stopped and frisked in larger American cities. Sometime blueish-black skin and hair pigmentation matches as well.
Most other breeds will give you a pink color range.
https://artpictures.club/autumn-2023.html
Source: was given a saddle for Christmas once.
If you read the Wikipedia article (or other articles) about “all horses are the same color”, it is really just about an inductive fallacy that can occur.
Mammals only make brown, but we do a lot with it.
Maybe author of the sentence was looking at horses in space and wikipedia is completly wrong.
