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Full Idea
'All A's are B's' meant for Frege that the concept A implies the concept B, or that to be A implies also to be B. Moreover this applies to arbitrary x which happens to be A.
Gist of Idea
For Frege, 'All A's are B's' means that the concept A implies the concept B
Source
report of Gottlob Frege (Begriffsschrift [1879]) by Michal Walicki - Introduction to Mathematical Logic History D.2
Book Ref
Walicki,Michal: 'Introduction to Mathematical Logic' [World Scientific 2012], p.23
A Reaction
This seems to hit the renate/cordate problem. If all creatures with hearts also have kidneys, does that mean that being enhearted logically implies being kidneyfied? If all chimps are hairy, is that a logical requirement? Is inclusion implication?
17745 | For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki] |
13905 | If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon] |
13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |