Combining Texts

All the ideas for 'Wiener Logik', 'Reliabilism' and 'The Philosophy of Mathematics'

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13 ideas

2. Reason / D. Definition / 2. Aims of Definition
A simplification which is complete constitutes a definition [Kant]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic gives us the necessary rules which show us how we ought to think [Kant]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
If we knew what we know, we would be astonished [Kant]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Reliabilist knowledge is evidence based belief, with high conditional probability [Comesaņa]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
In a sceptical scenario belief formation is unreliable, so no beliefs at all are justified? [Comesaņa]
How do we decide which exact process is the one that needs to be reliable? [Comesaņa]