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Single Idea 17745

[filed under theme 4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀ ]

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?

The 4 ideas with the same theme [symbol showing a variable refers to 'all' objects]:

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]