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All the ideas for 'works', 'The Passions' and 'Frege philosophy of mathematics'

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79 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom needs both thought and passion, with each reflecting on the other [Solomon]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Philosophy is creating an intellectual conceptual structure for life [Solomon]
2. Reason / A. Nature of Reason / 1. On Reason
Reason is actually passions, guided by perspicacious reflection [Solomon]
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 / 6. Verisimilitude
Truth does not admit of more and less [Frege]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Frege did not think of himself as working with sets [Frege, by Hart,WD]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The null set is indefensible, because it collects nothing [Frege, by Burge]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Frege, by Benardete,JA]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Frege frequently expressed a contempt for language [Frege, by 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]
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
Frege thinks there is an independent logical order of the truths, which we must try to discover [Frege, by Hart,WD]
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
For Frege, predicates are names of functions that map objects onto the True and False [Frege, by McGinn]
Frege gives a functional account of predication so that we can dispense with predicates [Frege, by Benardete,JA]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Frege always, and fatally, neglected the domain of quantification [Dummett on Frege]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Basic truths of logic are not proved, but seen as true when they are understood [Frege, by Burge]
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 / 5. Definitions of Number / c. Fregean numbers
If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content [Benardete,JA on Frege]
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 / a. Early logicism
Frege aimed to discover the logical foundations which justify arithmetical judgements [Frege, by Burge]
Eventually Frege tried to found arithmetic in geometry instead of in logic [Frege, by Friend]
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 / A. Nature of Existence / 3. Being / i. Deflating being
Frege's logic showed that there is no concept of being [Frege, by Scruton]
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]
9. Objects / F. Identity among Objects / 5. Self-Identity
Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x' [Frege, by Benardete,JA]
11. Knowledge Aims / A. Knowledge / 2. Understanding
To understand a thought, understand its inferential connections to other thoughts [Frege, by Burge]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Frege's concept of 'self-evident' makes no reference to minds [Frege, by Burge]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
An apriori truth is grounded in generality, which is universal quantification [Frege, by Burge]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
We often trust our intuitions as rational, despite their lack of reflection [Solomon]
14. Science / B. Scientific Theories / 1. Scientific Theory
The building blocks contain the whole contents of a discipline [Frege]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
Distinguishing reason from passion is based on an archaic 'faculty' theory [Solomon]
18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions
I say bodily chemistry and its sensations have nothing to do with emotions [Solomon]
Emotions are judgements about ourselves, and our place in the world [Solomon]
Emotions are defined by their objects [Solomon]
The heart of an emotion is its judgement of values and morality [Solomon]
Emotions can be analysed under fifteen headings [Solomon]
18. Thought / A. Modes of Thought / 3. Emotions / b. Types of emotion
Some emotions are externally directed, others internally [Solomon]
18. Thought / A. Modes of Thought / 3. Emotions / c. Role of emotions
It is only our passions which give our lives meaning [Solomon]
Which emotions we feel depends on our sense of our own powers [Solomon]
The passions are subjective, concerning what is important to me, rather than facts [Solomon]
Emotions are strategies for maximising our sense of dignity and self-esteem [Solomon]
Passions exist as emotions, moods and desires, which all generate meaning [Solomon]
The Myth of the Passions says they are irrational, uncontrolled and damaging [Solomon]
18. Thought / A. Modes of Thought / 3. Emotions / d. Emotional feeling
Feeling is a superficial aspect of emotion, and may be indeterminate, or even absent [Solomon]
18. Thought / A. Modes of Thought / 3. Emotions / e. Basic emotions
There are no 'basic' emotions, only socially prevalent ones [Solomon]
18. Thought / A. Modes of Thought / 3. Emotions / f. Emotion and reason
It is reason which needs the anchorage of passions, rather than vice versa [Solomon]
Dividing ourselves into confrontational reason and passion destroys our harmonious whole [Solomon]
The supposed irrationality of our emotions is often tactless or faulty expression of them [Solomon]
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]
Frege said concepts were abstract entities, not mental entities [Frege, by Putnam]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
A thought is not psychological, but a condition of the world that makes a sentence true [Frege, by Miller,A]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Frege's 'sense' is the strict and literal meaning, stripped of tone [Frege, by Miller,A]
'Sense' solves the problems of bearerless names, substitution in beliefs, and informativeness [Frege, by Miller,A]
Fregean semantics assumes a domain articulated into individual objects [Dummett]
19. Language / E. Analyticity / 1. Analytic Propositions
'P or not-p' seems to be analytic, but does not fit Kant's account, lacking clear subject or predicate [Frege, by Weiner]
19. Language / E. Analyticity / 2. Analytic Truths
Analytic truths are those that can be demonstrated using only logic and definitions [Frege, by Miller,A]
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
Emotions are our life force, and the source of most of our values [Solomon]
22. Metaethics / B. Value / 2. Values / g. Love
Lovers adopt the interests of their beloved, rather than just valuing them [Solomon]
23. Ethics / F. Existentialism / 2. Nihilism
'Absurdity' is just the result of our wrong choices in life [Solomon]
24. Political Theory / D. Ideologies / 1. Ideology
Ideologies are mythologies which guide our actions [Solomon]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Frege put forward an ontological argument for the existence of numbers [Frege, by Benardete,JA]