Why is there an O type conclusion in modus celaront

Question

Modus celaront is type logical syllogism.

 No reptiles have fur. (MeP)
 All snakes are reptiles. (SaM)
∴ Some snakes have no fur. (SoP)

The conclusion is of a O type(Some .. are not ...). Why is that should the correct conclusion not be of type E (No snakes have fur)?

On this link there is all in the parenthesis, but why can't we clearly say it?

I understand the felapton syllogism:

  No flowers are animals. (MeP)
   All flowers are plants. (MaS)
∴ Some plants are not animals. (SoP) 

I do not understand why we cannot assert that the E conclusion.

Answer 1

Celaront was not in the original Aristotle's list of valid syllogistic figures (or : moods).

It was added later (during the Middles Ages ?) as one of the two subalternate moods in the first figure (Barbari and Celaront).

If we agree (as Aristotle does) that every term has reference, from Cesare :

No reptiles have fur. (MeP)

All snakes are reptiles. (SaM)

∴ No snakes have fur. (SeP)

we derive Celaront because from "All snakes have no fur" it follows "Some snakes have no fur".

Answer 2

Both examples draw a particular conclusion (some... not) from two universal premises (all, none). Both syllogisms are valid, but are “weakened” forms because in each case the premises support the universal conclusion.

The term “weakened” originated with medieval logicians, who “thought it pointless to get a particular conclusion when one could get the universal conclusion instead.” Barker, The elements of logic (1965), 69.

Wikipedia lists these two syllogisms as “conditionally valid”. Wikipedia > List of valid argument forms.

Answer 3

The term subalterantion explains why one can derive a particular proposition from a universal proposition. This can also be referred to as the dictum de omni et nullo. There is a wiki page on it that I cant apply here for some reason.

Basically what can be denied of a whole must also apply to members of the whole simultaneously. We can't have exceptions under any circumstance. We would be inconsistent to say no dogs are reptiles and then also state Fido is a dog and a reptile. This sounds irrational doesn't it? So it is not the case the Quantifier NO is not correct in place of SOME ARE NOT. Both are correct once we know the set or class has occupants. In Mathematical logic there can be empty sets so many rules of the traditional square of opposition do not hold. There is a Boolean square which only recognizes the contradictory relationship.