Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Carnap and Logical Truth' and 'The Principles of Chemistry'

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19 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
13010 In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
9002 Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13681 Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13829 If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
9003 Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
9004 If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
9006 Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine]
10. Modality / A. Necessity / 6. Logical Necessity
9001 Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine]
12. Knowledge Sources / A. A Priori Knowledge / 7. A Priori from Convention
9005 Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
17402 Mendeleev saw three principles in nature: matter, force and spirit (where the latter seems to be essence) [Mendeleev, by Scerri]
27. Natural Reality / F. Chemistry / 2. Modern Elements
17399 Elements don't survive in compounds, but the 'substance' of the element does [Mendeleev]
27. Natural Reality / F. Chemistry / 3. Periodic Table
17401 Mendeleev had a view of elements which allowed him to overlook some conflicting observations [Mendeleev]
17400 Mendeleev focused on abstract elements, not simple substances, so he got to their essence [Mendeleev, by Scerri]