Combining Texts

All the ideas for 'works', 'The Tragedy of Reason' and 'Russell's Mathematical Logic'

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33 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 / a. Philosophy as worldly
Philosophy attains its goal if one person feels perfect accord between their system and experience [Fichte]
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 / 7. Status of Reason
For Fichte there is no God outside the ego, and 'our religion is reason' [Fichte, by Feuerbach]
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
Attempts to suspend all presuppositions are hopeless, because a common ground must be agreed for the process [Roochnik]
Unfortunately for reason, argument can't be used to establish the value of argument [Roochnik]
2. Reason / D. Definition / 8. Impredicative Definition
Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Impredicative definitions are admitted into ordinary mathematics [Gödel]
7. Existence / D. Theories of Reality / 3. Reality
Reality can be viewed neutrally, or as an object of desire [Roochnik]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Fichte believed in things-in-themselves [Fichte, by Moore,AW]
We can deduce experience from self-consciousness, without the thing-in-itself [Fichte]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
The absolute I divides into consciousness, and a world which is not-I [Fichte, by Bowie]
Reason arises from freedom, so philosophy starts from the self, and not from the laws of nature [Fichte]
Abandon the thing-in-itself; things only exist in relation to our thinking [Fichte]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
Relativism is a disease which destroys the possibility of rational debate [Roochnik]
16. Persons / F. Free Will / 4. For Free Will
Spinoza could not actually believe his determinism, because living requires free will [Fichte]
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]