Combining Texts

All the ideas for 'Frege philosophy of mathematics', 'The Anti-Christ' and 'The Sense of Reality'

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40 ideas

1. Philosophy / B. History of Ideas / 1. History of Ideas
The great moments are the death of Aristotle, Machiavelli, and Romanticism [Berlin, by Watson]
1. Philosophy / B. History of Ideas / 2. Ancient Thought
All intelligent Romans were Epicureans [Nietzsche]
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
3. Truth / A. Truth Problems / 3. Value of Truth
Truth has had to be fought for, and normal life must be sacrificed to achieve it [Nietzsche]
One must never ask whether truth is useful [Nietzsche]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
A prime number is one which is measured by a unit alone [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A number is a multitude composed of units [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The identity of a number may be fixed by something outside structure - by counting [Dummett]
Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett]
7. Existence / D. Theories of Reality / 2. Realism
Realism is just the application of two-valued semantics to sentences [Dummett]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism assumes unmediated mental contact with objects [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
The existence of abstract objects is a pseudo-problem [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Abstract objects nowadays are those which are objective but not actual [Dummett]
It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
Abstract objects need the context principle, since they can't be encountered directly [Dummett]
9. Objects / F. Identity among Objects / 2. Defining Identity
Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett]
Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
18. Thought / D. Concepts / 4. Structure of Concepts / i. Conceptual priority
Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett]
An argument for conceptual priority is greater simplicity in explanation [Dummett]
18. Thought / E. Abstraction / 1. Abstract Thought
Abstract terms are acceptable as long as we know how they function linguistically [Dummett]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait]
We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett]
18. Thought / E. Abstraction / 8. Abstractionism Critique
To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
Philosophy grasps the limits of human reason, and values are beyond it [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
Christianity is at war with the higher type of man, and excommunicates his basic instincts [Nietzsche]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
Virtues must be highly personal; if not, it is merely respect for a concept [Nietzsche]
23. Ethics / D. Deontological Ethics / 1. Deontology
Each person should devise his own virtues and categorical imperative [Nietzsche]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]
28. God / A. Divine Nature / 4. Divine Contradictions
A God who cures us of a head cold at the right moment is a total absurdity [Nietzsche]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Christianity is a revolt of things crawling on the ground against elevated things [Nietzsche]
29. Religion / B. Monotheistic Religion / 5. Bible
The story in Genesis is the story of God's fear of science [Nietzsche]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
'Faith' means not wanting to know what is true [Nietzsche]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
The great lie of immortality destroys rationality and natural instinct [Nietzsche]