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 1980,0-631-12911-1]].

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2. Reason / B. Laws of Thought / 1. Laws of Thought
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 ∀
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
Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing)
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
In 1879 Frege developed second order logic
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
I don't use 'subject' and 'predicate' in my way of representing a judgement
Frege replaced Aristotle's subject/predicate form with function/argument form
5. Theory of Logic / G. Quantification / 1. Quantification
A quantifier is a second-level predicate (which explains how it contributes to truth-conditions)
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
For Frege the variable ranges over all objects
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
Frege introduced quantifiers for generality
Frege reduced most quantifiers to 'everything' combined with 'not'
5. Theory of Logic / H. Proof Systems / 1. Proof Systems
Proof theory began with Frege's definition of derivability
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
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
Frege's logic has a hierarchy of object, property, property-of-property etc.
7. Existence / A. Nature of Existence / 1. Nature of Existence
Existence is not a first-order property, but the instantiation of a property
28. God / C. Proofs of Reason / 2. Ontological Proof critique
The predicate 'exists' is actually a natural language expression for a quantifier