[munificent]

All snakes have scales, so there is a 100% correlation between being a snake and having scales.

That does not imply that fish are snakes. Nor does the presence of scaled fish invalidate the observation that having scales is a defining attribute of snakes (it's just not a sufficient attribute to define snakes).

[cousin_it]

For correlation to be 1, it's not enough that all snakes have scales. You also need all scaly animals to be snakes.

Here's a toy example. Imagine three equally sized groups of animals: scaly snakes, scaly fish, and scaleless fish. (So all snakes have scales, but not all scaly animals are snakes.) That's three data points (1,1) (0,1) (0,0) with probability 1/3 each. The correlation between snake and scaly comes out as 1/2.

You can also see it geometrically. The only way correlation can be 1 is if all points lie on a straight line. But in this case it's a triangle.

[the_optimist]

You’re looking for the logical argument here, not the statistical one. You sampled from snakes and said there is a 100% correlation with being a snake (notwithstanding the counterarg in an adjacent comment about scale-free snakes).

I am noting that the logical argument does not hold in the provided definition. If “some” attributes hold in a definition, you are expanding the definitional set, not reducing it, and thus creating a low-res definition. That is why I said: ‘this is a poor definition.’

[oasisaimlessly]

> there is a 100% correlation between being a snake and having scales.

That's a strange definition of "correlation" that you're using.

[TylerE]

That’s not accurate either. Scaleless snakes, thigh a rare mutation, do exist as genetic mutants.

https://www.morphmarket.com/morphpedia/corn-snakes/scaleless...