Combining Texts

All the ideas for 'The Theory of Objects', 'Axiomatic Thought' and 'The Emperor's New 'Knows''

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15 ideas

4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
So-called 'free logic' operates without existence assumptions [Meinong, by George/Van Evra]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The facts of geometry, arithmetic or statics order themselves into theories [Hilbert]
Axioms must reveal their dependence (or not), and must be consistent [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
To decide some questions, we must study the essence of mathematical proof itself [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Number theory just needs calculation laws and rules for integers [Hilbert]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
There can be impossible and contradictory objects, if they can have properties [Meinong, by Friend]
9. Objects / A. Existence of Objects / 3. Objects in Thought
There are objects of which it is true that there are no such objects [Meinong]
Meinong says an object need not exist, but must only have properties [Meinong, by Friend]
9. Objects / A. Existence of Objects / 4. Impossible objects
Meinong said all objects of thought (even self-contradictions) have some sort of being [Meinong, by Lycan]
The objects of knowledge are far more numerous than objects which exist [Meinong]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
How could 'S knows he has hands' not have a fixed content? [Bach]
If contextualism is right, knowledge sentences are baffling out of their context [Bach]
Sceptics aren't changing the meaning of 'know', but claiming knowing is tougher than we think [Bach]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert]