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All the ideas for 'Frege philosophy of mathematics', 'The View from Nowhere' and 'Commentary on the Sentences'

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52 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
There is more insight in fundamental perplexity about problems than in their supposed solutions [Nagel]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Philosophy is the childhood of the intellect, and a culture can't skip it [Nagel]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
It seems mad, but the aim of philosophy is to climb outside of our own minds [Nagel]
2. Reason / A. Nature of Reason / 5. Objectivity
Realism invites scepticism because it claims to be objective [Nagel]
Views are objective if they don't rely on a person's character, social position or species [Nagel]
Things cause perceptions, properties have other effects, hence we reach a 'view from nowhere' [Nagel, by Reiss/Sprenger]
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
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 / D. Essence of Objects / 12. Essential Parts
If parts change, the whole changes [William of Ockham]
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]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / b. Primary/secondary
Modern science depends on the distinction between primary and secondary qualities [Nagel]
We achieve objectivity by dropping secondary qualities, to focus on structural primary qualities [Nagel]
13. Knowledge Criteria / B. Internal Justification / 2. Pragmatic justification
Epistemology is centrally about what we should believe, not the definition of knowledge [Nagel]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
Scepticism is based on ideas which scepticism makes impossible [Nagel]
14. Science / C. Induction / 4. Reason in Induction
Observed regularities are only predictable if we assume hidden necessity [Nagel]
16. Persons / B. Nature of the Self / 4. Presupposition of Self
Personal identity cannot be fully known a priori [Nagel]
The question of whether a future experience will be mine presupposes personal identity [Nagel]
16. Persons / D. Continuity of the Self / 4. Split Consciousness
I can't even conceive of my brain being split in two [Nagel]
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 / B. Value / 1. Nature of Value / c. Objective value
Total objectivity can't see value, but it sees many people with values [Nagel]
22. Metaethics / B. Value / 2. Values / e. Death
We don't worry about the time before we were born the way we worry about death [Nagel]
22. Metaethics / B. Value / 2. Values / f. Altruism
If our own life lacks meaning, devotion to others won't give it meaning [Nagel]
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
Pain doesn't have a further property of badness; it gives a reason for its avoidance [Nagel]
23. Ethics / D. Deontological Ethics / 1. Deontology
Something may be 'rational' either because it is required or because it is acceptable [Nagel]
23. Ethics / D. Deontological Ethics / 2. Duty
If cockroaches can't think about their actions, they have no duties [Nagel]
23. Ethics / D. Deontological Ethics / 3. Universalisability
If we can decide how to live after stepping outside of ourselves, we have the basis of a moral theory [Nagel]
We should see others' viewpoints, but not lose touch with our own values [Nagel]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
We find new motives by discovering reasons for action different from our preexisting motives [Nagel]
23. Ethics / E. Utilitarianism / 3. Motivation for Altruism
Utilitarianism is too demanding [Nagel]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]