more on this theme
|
more from this thinker
Single Idea 7622
[filed under theme 5. Theory of Logic / A. Overview of Logic / 2. History of Logic
]
Full Idea
By 1879 Frege had discovered an algorithm, a mechanical proof procedure, that embraces what is today standard 'second order logic'.
Gist of Idea
In 1879 Frege developed second order logic
Source
report of Gottlob Frege (Begriffsschrift [1879]) by Hilary Putnam - Reason, Truth and History Ch.5
Book Ref
Putnam,Hilary: 'Reason, Truth and History' [CUP 1998], p.124
A Reaction
Note that Frege did more than introduce quantifiers, and the logic of predicates.
The
20 ideas
from 'Begriffsschrift'
|
7622
|
In 1879 Frege developed second order logic
[Frege, by Putnam]
|
|
7729
|
Frege replaced Aristotle's subject/predicate form with function/argument form
[Frege, by Weiner]
|
|
9991
|
For Frege the variable ranges over all objects
[Frege, by Tait]
|
|
10536
|
Frege's domain for variables is all objects, but modern interpretations first fix the domain
[Dummett on Frege]
|
|
9950
|
A quantifier is a second-level predicate (which explains how it contributes to truth-conditions)
[Frege, by George/Velleman]
|
|
13609
|
Frege produced axioms for logic, though that does not now seem the natural basis for logic
[Frege, by Kaplan]
|
|
7730
|
Frege introduced quantifiers for generality
[Frege, by Weiner]
|
|
7742
|
Frege reduced most quantifiers to 'everything' combined with 'not'
[Frege, by McCullogh]
|
|
13824
|
Proof theory began with Frege's definition of derivability
[Frege, by Prawitz]
|
|
17855
|
It may be possible to define induction in terms of the ancestral relation
[Frege, by Wright,C]
|
|
10607
|
Frege's logic has a hierarchy of object, property, property-of-property etc.
[Frege, by Smith,P]
|
|
11008
|
Existence is not a first-order property, but the instantiation of a property
[Frege, by Read]
|
|
22280
|
Frege's account was top-down and decompositional, not bottom-up and compositional
[Frege, by Potter]
|
|
7741
|
The predicate 'exists' is actually a natural language expression for a quantifier
[Frege, by Weiner]
|
|
22270
|
Frege changed philosophy by extending logic's ability to check the grounds of thinking
[Potter on Frege]
|
|
8939
|
We should not describe human laws of thought, but how to correctly track truth
[Frege, by Fisher]
|
|
17745
|
For Frege, 'All A's are B's' means that the concept A implies the concept B
[Frege, by Walicki]
|
|
7728
|
Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing)
[Frege, by Weiner]
|
|
4971
|
I don't use 'subject' and 'predicate' in my way of representing a judgement
[Frege]
|
|
16881
|
The laws of logic are boundless, so we want the few whose power contains the others
[Frege]
|