Hypotheses or premises?

Stream: general

[Tyler Josephson]

In Theorem Proving in Lean, it seems to me that "hypothesis" is used to describe "that which is assumed." But to me as a scientist, hypotheses are posed and then tested for validity; they are more like conjectures. Is this confusing for anyone else? Is "hypothesis" generally used this way among mathematicians?

I'd probably prefer to use "premise" to describe "that which is assumed," rather than "hypothesis." Would there be any issue with that?

[Kyle Miller]

In logic, the P in "if P then Q" is often known as the antecedent or the hypothesis of the proposition. In a goal state, it probably would be more precise to call the corresponding terms premises or assumptions, though you'll see in written proofs that something is true "by assumption" or "by hypothesis" interchangeably.

[Kyle Miller]

Maybe one way to think of it is that each theorem you prove is an experiment that shows what else would need to be true if a given hypothesis were true -- proofs are in a sense evidence against their hypotheses.

[Riccardo Brasca]

This is standard mathematical terminology, isn't it? Assumption and hypothesis are synonymous.

[Patrick Massot]

I don't think we should change terminology only because physics and biology use the word hypothesis with a different meaning. And this has nothing to do with proof assistant. The name clash is already there in real life and when I teach maths to physics or biology majors I always emphasize this to prevent confusion.

[Mario Carneiro]

https://en.wiktionary.org/wiki/hypothesis mentions all these meanings, but the etymology seems to support the mathematical / grammatical meaning more than the scientific one

[Johan Commelin]

Yay! Let's change science!

[Julian Berman]

I hypothesize this will not work.

[Johan Commelin]

I assume the same.

[Tyler Josephson]

Haha - thanks, everyone!