A question about a specific induction problem

Question

We know why the induction principle does not work for the statement that all horses are of the same color.

Nevertheless, in the book that I am reading there’s a statement which goes as follows: “Our argument proves that if any two horses did have the same color, then all horses would have the same color, but that result would be a horse of a different color.”

I don’t understand what is meant by the last sentence highlighted in bold, because we concluded that if the induction base was (falsely) correct, they would be all of the same color, while in the end there’s mention of a different color. What does it say?

We’d be better able to help you if you explain what on Earth an induction over the colour of a horse would look like. Maybe type up the author’s exact wording / argument — FShrike, Aug 27 '22 at 17:54
@FShrike I think my question has been already explained clearly — , Aug 27 '22 at 17:56

score 2 · Accepted Answer · answered Aug 27 '22 at 18:12

2

The author is trying to make a joke here. "A horse of a different color" is an English idiom that means "quite a different matter" or something like that. So in particular, that phrase doesn't have anything to do with the mathematical argument.

answered Aug 27 '22 at 18:12

Greg Martin

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2

Thanks so much, I learned a new English idiom :) – Aug 27 '22 at 18:22

A question about a specific induction problem

1 Answers1