Ideas from 'Begriffsschrift' by Gottlob Frege [1879], by Theme Structure
[found in 'Translations from the Writings of Gottlob Frege' by Frege,Gottlob (ed/tr Geach,P. /Black,Max) [Blackwell 1980,0631129111]].
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2. Reason / B. Laws of Thought / 1. Laws of Thought
8939

We should not describe human laws of thought, but how to correctly track truth

4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀
17745

For Frege, 'All A's are B's' means that the concept A implies the concept B

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
7728

Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing)

16881

The laws of logic are boundless, so we want the few whose power contains the others

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
7622

In 1879 Frege developed second order logic

5. Theory of Logic / E. Structures of Logic / 1. Logical Form
4971

I don't use 'subject' and 'predicate' in my way of representing a judgement

7729

Frege replaced Aristotle's subject/predicate form with function/argument form

5. Theory of Logic / G. Quantification / 1. Quantification
9950

A quantifier is a secondlevel predicate (which explains how it contributes to truthconditions)

5. Theory of Logic / G. Quantification / 2. Domain of Quantification
9991

For Frege the variable ranges over all objects

5. Theory of Logic / G. Quantification / 3. Objectual Quantification
7742

Frege reduced most quantifiers to 'everything' combined with 'not'

7730

Frege introduced quantifiers for generality

5. Theory of Logic / H. Proof Systems / 1. Proof Systems
13824

Proof theory began with Frege's definition of derivability

5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
13609

Frege produced axioms for logic, though that does not now seem the natural basis for logic

6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10607

Frege's logic has a hierarchy of object, property, propertyofproperty etc.

7. Existence / A. Nature of Existence / 1. Nature of Existence
11008

Existence is not a firstorder property, but the instantiation of a property

28. God / C. Proofs of Reason / 2. Ontological Proof critique
7741

The predicate 'exists' is actually a natural language expression for a quantifier
