The opposite of all

About this video

Small words like "all", "some" and "none" do a lot of work in reasoning. Each claim with one of them is about a group, the apples in a basket, and says how much of the group has a feature, being red. They are called quantity words, because they say how many.

In everyday talk "some" often hints "but not all". In logic, "some" means just at least one: maybe a few, maybe most, maybe all. So a shop sign saying "Some fruit half price!" isn't wrong when every piece of fruit is half price.

The opposite of "all the apples are red" is where people slip. Many say "none of them are red", but that is too much. One apple that isn't red is enough to make "all are red" false, so the opposite is "not all are red", which means the same as "some are not red". In the same way, the opposite of "none are red" is "some are red".

Last, the animation draws groups as circles. "All dogs are animals" puts the dog circle inside the animal circle, with cats, birds and fish in the space around it. Inside only goes one way, so an "all" claim can't be turned around: all animals are not dogs. This video goes with the All, Some and None and All Dogs Are Animals lessons of Logic Level 1 on Knaph.

Transcript

1. 0:00All, some, none. How much of the group?
2. 0:04In logic, some means at least one. Maybe even all.
3. 0:10The opposite of all are red? Not none. One green apple is enough. Some are not red.
4. 0:17All dogs are animals. The dog circle sits inside.
5. 0:22But not all animals are dogs.
6. 0:26Some means at least one. The opposite of all is not all.