Combining Texts

All the ideas for 'Review of Chihara 'Struct. Accnt of Maths'', 'Letters to Paul Pellison-Fontinier' and 'The Tragedy of Reason'

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24 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
You have to be a Platonist to debate about reality, so every philosopher is a Platonist [Roochnik]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
Philosophy aims to satisfy the chief human desire - the articulation of beauty itself [Roochnik]
2. Reason / A. Nature of Reason / 2. Logos
'Logos' ranges from thought/reasoning, to words, to rational structures outside thought [Roochnik]
In the seventeenth century the only acceptable form of logos was technical knowledge [Roochnik]
The hallmark of a person with logos is that they give reasons why one opinion is superior to another [Roochnik]
Logos cannot refute the relativist, and so must admit that it too is a matter of desire (for truth and agreement) [Roochnik]
Human desire has an ordered structure, with logos at the pinnacle [Roochnik]
Logos is not unconditionally good, but good if there is another person willing to engage with it [Roochnik]
2. Reason / A. Nature of Reason / 4. Aims of Reason
We prefer reason or poetry according to whether basics are intelligible or not [Roochnik]
2. Reason / A. Nature of Reason / 8. Naturalising Reason
Modern science, by aiming for clarity about the external world, has abandoned rationality in the human world [Roochnik]
2. Reason / A. Nature of Reason / 9. Limits of Reason
Unfortunately for reason, argument can't be used to establish the value of argument [Roochnik]
Attempts to suspend all presuppositions are hopeless, because a common ground must be agreed for the process [Roochnik]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory is the standard background for modern mathematics [Burgess]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess]
There is no one relation for the real number 2, as relations differ in different models [Burgess]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
If set theory is used to define 'structure', we can't define set theory structurally [Burgess]
Abstract algebra concerns relations between models, not common features of all the models [Burgess]
How can mathematical relations be either internal, or external, or intrinsic? [Burgess]
7. Existence / D. Theories of Reality / 3. Reality
Reality can be viewed neutrally, or as an object of desire [Roochnik]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
Relativism is a disease which destroys the possibility of rational debate [Roochnik]
19. Language / F. Communication / 1. Rhetoric
If relativism is the correct account of human values, then rhetoric is more important than reasoning [Roochnik]
Reasoning aims not at the understanding of objects, but at the desire to give beautiful speeches [Roochnik]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
Clearly, force is that from which action follows, when unimpeded [Leibniz]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
Time doesn't exist, since its parts don't coexist [Leibniz]