Combining Texts

All the ideas for 'fragments/reports', 'The Philosophy of Mathematics' and 'Hermeneutics: a very short introduction'

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16 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
We take part in objective truth, rather than observe it from a distance [Zimmermann,J]
Hermeneutic knowledge is not objective, but embraces interpretations [Zimmermann,J]
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 / 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]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius]
12. Knowledge Sources / B. Perception / 1. Perception
In phenomenology, all perception is 'seeing as' [Zimmermann,J]
19. Language / F. Communication / 1. Rhetoric
Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato]
Destroy seriousness with laughter, and laughter with seriousness [Gorgias]
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
The hermeneutic circle is between the reader's self-understanding, and the world of the text [Zimmermann,J]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
Natural law theorists fear that without morality, law could be based on efficiency [Zimmermann,J]
29. Religion / B. Monotheistic Religion / 2. Judaism
Traditionally, God dictated the Torah to Moses, unlike the later biblical writings [Zimmermann,J]