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Ideas for 'works', 'Introduction to Mathematical Logic' and 'Thought'

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12 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Any two states are logically linked, by being entailed by their conjunction [Harman]
To determine the patterns in logic, one must identify its 'building blocks' [Walicki]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Deductive logic is the only logic there is [Harman]
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
You don't have to accept the conclusion of a valid argument [Harman]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Our underlying predicates represent words in the language, not universal concepts [Harman]
Logical form is the part of a sentence structure which involves logical elements [Harman]
A theory of truth in a language must involve a theory of logical form [Harman]
For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]