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For example, suppose that it is a known fact that all the pens I have are blue.
Statement 1: All my pens are blue
Statement 2: Some of my pens are blue
Similarly,
Statement 1: All dogs are animals
Statement 2: Some dogs are animals
We know that statement 1 is correct. But is statement 2 correct?
Statement 1: All dogs are animals / Statement 2: Some dogs are animals. We know that statement 1 is correct. But is statement 2 correct?
No, it is not.
You are trying to make "some" = "all". We have different words to express different ideas.
OED:
Some: 4.a. A certain indeterminate part of something; a portion.
1611 Bible (King James) Luke viii. 6 And some fell vpon a rocke, and..it withered away.
1796 C. Marshall Gardening (1813) xix. 371 As it is a small flower, pot some.
1872 J. Morley Voltaire i. 6 Some of it, much of it, has ceased to be alive for us now.
II. In plural senses. 5.a. An indefinite or unspecified (but not large) number of persons (or animals); certain persons not named or enumerated.
NB "all" is a specified and definite quantity.
1842 J. C. Loudon Suburban Horticulturist 121 It feeds on worms..and according to some, on roots.
1878 T. Hardy Return of Native I. i. iii. 45 I shouldn't have cared about the man, though some may say he's good-looking.
MW
being one, a part, or an unspecified number of something (such as a class or group) named or implied
some gems are hard
b: being of an unspecified amount or number
give me some water / have some apples
This seems at first more a question of logic than English. If all your pens are blue, any subgroup of them is a group of blue pens. So both statements are true.
However, logic is not enough. Your question hints at an English usage that suggests that when we say "some of my pens are blue", there is an implication or possibility that "others of my pens are not blue". Because "blue" is a restricted class of all possible coloured pens, this is a reasonable supposition within the flow of the spoken or written English that we should consider "not-blue" pens.
However, your first statement tells us that there is no possible group of your pens that is not blue, so the English usage has in this case led us to identify a group of your pens that might exist had the first statement not told us that it cannot exist.
In the case of dogs and animals: your question might hint at usage suggesting that when we say "some dogs are animals", there is an implication or possibility that "other dogs are not animals". Because "animal" is a hyperclass (rather than a restricted class) of dogs, this is not a reasonable supposition.
