Combining Texts

Ideas for 'fragments/reports', 'Thinking About Logic' and 'Introduction to Mathematical Logic'

expand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

21 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
17741 To determine the patterns in logic, one must identify its 'building blocks' [Walicki]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10986 Not all validity is captured in first-order logic [Read]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
10972 The non-emptiness of the domain is characteristic of classical logic [Read]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
11024 Semantics must precede proof in higher-order logics, since they are incomplete [Read]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10985 We should exclude second-order logic, precisely because it captures arithmetic [Read]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10970 A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read]
10984 Logical consequence isn't just a matter of form; it depends on connections like round-square [Read]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
10973 A theory is logically closed, which means infinite premisses [Read]
5. Theory of Logic / G. Quantification / 1. Quantification
11007 Quantifiers are second-order predicates [Read]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10978 In second-order logic the higher-order variables range over all the properties of the objects [Read]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10971 A logical truth is the conclusion of a valid inference with no premisses [Read]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
17747 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
10988 Any first-order theory of sets is inadequate [Read]
17748 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
17763 Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
17761 A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10974 Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read]
10975 Compactness does not deny that an inference can have infinitely many premisses [Read]
10977 Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read]
10976 Compactness makes consequence manageable, but restricts expressive power [Read]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
11014 Self-reference paradoxes seem to arise only when falsity is involved [Read]