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All the ideas for 'Frege philosophy of mathematics', 'Lecture on Nominalism' and 'The Human Condition'

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57 ideas

2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
2. Reason / F. Fallacies / 1. Fallacy
The Struthionic Fallacy is that of burying one's head in the sand [Quine]
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]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
All relations, apart from ancestrals, can be reduced to simpler logic [Quine]
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 / 3. Mathematical Nominalism
Nominalism rejects both attributes and classes (where extensionalism accepts the classes) [Quine]
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]
10. Modality / B. Possibility / 7. Chance
'Luck' is the unpredictable and inexplicable intersection of causal chains [Kekes]
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]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
An action may be intended under one description, but not under another [Kekes]
20. Action / C. Motives for Action / 2. Acting on Beliefs / a. Acting on beliefs
To control our actions better, make them result from our attitudes, not from circumstances [Kekes]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / c. Purpose of ethics
Values are an attempt to achieve well-being by bringing contingencies under control [Kekes]
Values help us to control life, by connecting it to what is stable and manageable [Kekes]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Responsibility is unprovoked foreseeable harm, against society, arising from vicious character [Kekes]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
Reason and morality do not coincide; immorality can be reasonable, with an ideology [Kekes]
Practical reason is not universal and impersonal, because it depends on what success is [Kekes]
If morality has to be rational, then moral conflicts need us to be irrational and immoral [Kekes]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Relativists say all values are relative; pluralists concede much of that, but not 'human' values [Kekes]
22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value
Cultural values are interpretations of humanity, conduct, institutions, and evaluations [Kekes]
The big value problems are evil (humanity), disenchantment (cultures), and boredom (individuals) [Kekes]
We are bound to regret some values we never aspired to [Kekes]
There are far more values than we can pursue, so they are optional possibilities [Kekes]
Innumerable values arise for us, from our humanity, our culture, and our individuality [Kekes]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Our attitudes include what possibilities we value, and also what is allowable, and unthinkable [Kekes]
Unconditional commitments are our most basic convictions, saying what must never be done [Kekes]
Doing the unthinkable damages ourselves, so it is more basic than any value [Kekes]
22. Metaethics / B. Value / 2. Values / j. Evil
Evil isn't explained by nature, by monsters, by uncharacteristic actions, or by society [Kekes]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
Control is the key to well-being [Kekes]
Well-being needs correct attitudes and well-ordered commitments to local values [Kekes]
23. Ethics / F. Existentialism / 4. Boredom
Boredom destroys our ability to evaluate [Kekes]
Boredom is apathy and restlessness, yearning for something interesting [Kekes]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Society is alienating if it lacks our values, and its values repel us [Kekes]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
The ideal of an ideology is embodied in a text, a role model, a law of history, a dream of the past... [Kekes]
Ideologies have beliefs about reality, ideals, a gap with actuality, and a program [Kekes]
25. Social Practice / B. Equalities / 4. Economic equality
Equal distribution is no good in a shortage, because there might be no one satisfied [Kekes]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]