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All the ideas for 'works', 'The Will to Power (notebooks)' and 'Grundlagen der Arithmetik (Foundations)'

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257 ideas

1. Philosophy / A. Wisdom / 2. Wise People
The wisest man is full of contradictions, and attuned to other people, with occasional harmony [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
I don't want to persuade anyone to be a philosopher; they should be rare plants [Nietzsche]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
The syntactic category is primary, and the ontological category is derivative [Frege, by Wright,C]
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
Never lose sight of the distinction between concept and object [Frege]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Frege was the first to give linguistic answers to non-linguistic questions [Frege, by Dummett]
Frege initiated linguistic philosophy, studying number through the sense of sentences [Frege, by Dummett]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
Frege developed formal systems to avoid unnoticed assumptions [Frege, by Lavine]
2. Reason / A. Nature of Reason / 3. Pure Reason
Thoughts have a natural order, to which human thinking is drawn [Frege, by Yablo]
2. Reason / A. Nature of Reason / 5. Objectivity
Frege sees no 'intersubjective' category, between objective and subjective [Dummett on Frege]
Keep the psychological and subjective separate from the logical and objective [Frege]
Could not the objective character of things be merely a difference of degree within the subjective? [Nietzsche]
2. Reason / A. Nature of Reason / 7. Status of Reason
Reason is a mere idiosyncrasy of a certain species of animal [Nietzsche]
2. Reason / A. Nature of Reason / 9. Limits of Reason
What can be 'demonstrated' is of little worth [Nietzsche]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Our inability to both affirm and deny a single thing is merely an inability, not a 'necessity' [Nietzsche]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
Everything simple is merely imaginary [Nietzsche]
2. Reason / D. Definition / 7. Contextual Definition
Originally Frege liked contextual definitions, but later preferred them fully explicit [Frege, by Dummett]
Nothing should be defined in terms of that to which it is conceptually prior [Frege, by Dummett]
2. Reason / E. Argument / 6. Conclusive Proof
Proof aims to remove doubts, but also to show the interdependence of truths [Frege]
2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes
You can't transfer external properties unchanged to apply to ideas [Frege]
3. Truth / A. Truth Problems / 3. Value of Truth
Truth was given value by morality, but eventually turned against its own source [Nietzsche]
3. Truth / A. Truth Problems / 4. Uses of Truth
'Truth' is the will to be master over the multiplicity of sensations [Nietzsche]
3. Truth / A. Truth Problems / 7. Falsehood
Only because there is thought is there untruth [Nietzsche]
3. Truth / A. Truth Problems / 8. Subjective Truth
True beliefs are those which augment one's power [Nietzsche, by Scruton]
3. Truth / A. Truth Problems / 9. Rejecting Truth
The truth is what gives us the minimum of spiritual effort, and avoids the exhaustion of lying [Nietzsche]
3. Truth / B. Truthmakers / 5. What Makes Truths / c. States of affairs make truths
We need to grasp not number-objects, but the states of affairs which make number statements true [Frege, by Wright,C]
3. Truth / D. Coherence Truth / 1. Coherence Truth
Judgements can't be true and known in isolation; the only surety is in connections and relations [Nietzsche]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
Frege agreed with Euclid that the axioms of logic and mathematics are known through self-evidence [Frege, by Burge]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The null set is only defensible if it is the extension of an empty concept [Frege, by Burge]
It is because a concept can be empty that there is such a thing as the empty class [Frege, by Dummett]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
We can introduce new objects, as equivalence classes of objects already known [Frege, by Dummett]
Frege introduced the standard device, of defining logical objects with equivalence classes [Frege, by Dummett]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Frege, unlike Russell, has infinite individuals because numbers are individuals [Frege, by Bostock]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
A class is, for Frege, the extension of a concept [Frege, by Dummett]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Convert "Jupiter has four moons" into "the number of Jupiter's moons is four" [Frege]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
Despite Gödel, Frege's epistemic ordering of all the truths is still plausible [Frege, by Burge]
The primitive simples of arithmetic are the essence, determining the subject, and its boundaries [Frege, by Jeshion]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
The values of variables can't determine existence, because they are just expressions [Ryle, by Quine]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Each horse doesn't fall under the concept 'horse that draws the carriage', because all four are needed [Oliver/Smiley on Frege]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
We can show that a concept is consistent by producing something which falls under it [Frege]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
To understand axioms you must grasp their logical power and priority [Frege, by Burge]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
We cannot define numbers from the idea of a series, because numbers must precede that [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
Treating 0 as a number avoids antinomies involving treating 'nobody' as a person [Frege, by Dummett]
For Frege 'concept' and 'extension' are primitive, but 'zero' and 'successor' are defined [Frege, by Chihara]
If objects exist because they fall under a concept, 0 is the object under which no objects fall [Frege, by Dummett]
Nought is the number belonging to the concept 'not identical with itself' [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
We can say 'a and b are F' if F is 'wise', but not if it is 'one' [Frege]
One is the Number which belongs to the concept "identical with 0" [Frege]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
We need 'unities' for reckoning, but that does not mean they exist [Nietzsche]
You can abstract concepts from the moon, but the number one is not among them [Frege]
Units can be equal without being identical [Tait on Frege]
Frege says only concepts which isolate and avoid arbitrary division can give units [Frege, by Koslicki]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
Frege's 'isolation' could be absence of overlap, or drawing conceptual boundaries [Frege, by Koslicki]
Non-arbitrary division means that what falls under the concept cannot be divided into more of the same [Frege, by Koslicki]
Our concepts decide what is countable, as in seeing the leaves of the tree, or the foliage [Frege, by Koslicki]
A concept creating a unit must isolate and unify what falls under it [Frege]
Frege says counting is determining what number belongs to a given concept [Frege, by Koslicki]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Frege's one-to-one correspondence replaces well-ordering, because infinities can't be counted [Frege, by Lavine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
The number of natural numbers is not a natural number [Frege, by George/Velleman]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Arithmetical statements can't be axioms, because they are provable [Frege, by Burge]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
A statement of number contains a predication about a concept [Frege]
Frege's problem is explaining the particularity of numbers by general laws [Frege, by Burge]
Individual numbers are best derived from the number one, and increase by one [Frege]
'Exactly ten gallons' may not mean ten things instantiate 'gallon' [Rumfitt on Frege]
Numerical statements have first-order logical form, so must refer to objects [Frege, by Hodes]
The Number for F is the extension of 'equal to F' (or maybe just F itself) [Frege]
Numbers are objects because they partake in identity statements [Frege, by Bostock]
Frege had a motive to treat numbers as objects, but not a justification [Hale/Wright on Frege]
Frege claims that numbers are objects, as opposed to them being Fregean concepts [Frege, by Wright,C]
Numbers are second-level, ascribing properties to concepts rather than to objects [Frege, by Wright,C]
For Frege, successor was a relation, not a function [Frege, by Dummett]
Numbers are more than just 'second-level concepts', since existence is also one [Frege, by George/Velleman]
"Number of x's such that ..x.." is a functional expression, yielding a name when completed [Frege, by George/Velleman]
Frege gives an incoherent account of extensions resulting from abstraction [Fine,K on Frege]
For Frege the number of F's is a collection of first-level concepts [Frege, by George/Velleman]
A cardinal number may be defined as a class of similar classes [Frege, by Russell]
Numbers need to be objects, to define the extension of the concept of each successor to n [Frege, by George/Velleman]
The number of F's is the extension of the second level concept 'is equipollent with F' [Frege, by Tait]
Frege showed that numbers attach to concepts, not to objects [Frege, by Wiggins]
Frege replaced Cantor's sets as the objects of equinumerosity attributions with concepts [Frege, by Tait]
Zero is defined using 'is not self-identical', and one by using the concept of zero [Frege, by Weiner]
Frege said logical predication implies classes, which are arithmetical objects [Frege, by Morris,M]
Frege started with contextual definition, but then switched to explicit extensional definition [Frege, by Wright,C]
Each number, except 0, is the number of the concept of all of its predecessors [Frege, by Wright,C]
Frege's account of cardinals fails in modern set theory, so they are now defined differently [Dummett on Frege]
Frege's incorrect view is that a number is an equivalence class [Benacerraf on Frege]
The natural number n is the set of n-membered sets [Frege, by Yourgrau]
A set doesn't have a fixed number, because the elements can be seen in different ways [Yourgrau on Frege]
If you can subdivide objects many ways for counting, you can do that to set-elements too [Yourgrau on Frege]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
'The number of Fs' is the extension (a collection of first-level concepts) of the concept 'equinumerous with F' [Frege, by George/Velleman]
Frege's cardinals (equivalences of one-one correspondences) is not permissible in ZFC [Frege, by Wolf,RS]
Hume's Principle fails to implicitly define numbers, because of the Julius Caesar [Frege, by Potter]
Frege thinks number is fundamentally bound up with one-one correspondence [Frege, by Heck]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
The words 'There are exactly Julius Caesar moons of Mars' are gibberish [Rumfitt on Frege]
'Julius Caesar' isn't a number because numbers inherit properties of 0 and successor [Frege, by George/Velleman]
From within logic, how can we tell whether an arbitrary object like Julius Caesar is a number? [Frege, by Friend]
Frege said 2 is the extension of all pairs (so Julius Caesar isn't 2, because he's not an extension) [Frege, by Shapiro]
Fregean numbers are numbers, and not 'Caesar', because they correlate 1-1 [Frege, by Wright,C]
One-one correlations imply normal arithmetic, but don't explain our concept of a number [Frege, by Bostock]
Our definition will not tell us whether or not Julius Caesar is a number [Frege]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
If numbers can be derived from logic, then set theory is superfluous [Frege, by Burge]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
If numbers are supposed to be patterns, each number can have many patterns [Frege]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Numbers seem to be objects because they exactly fit the inference patterns for identities [Frege]
Frege's platonism proposes that objects are what singular terms refer to [Frege, by Wright,C]
How can numbers be external (one pair of boots is two boots), or subjective (and so relative)? [Frege, by Weiner]
Identities refer to objects, so numbers must be objects [Frege, by Weiner]
Numbers are not physical, and not ideas - they are objective and non-sensible [Frege]
Numbers are objects, because they can take the definite article, and can't be plurals [Frege]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Frege's logicism aimed at removing the reliance of arithmetic on intuition [Frege, by Yourgrau]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
There is no physical difference between two boots and one pair of boots [Frege]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
It appears that numbers are adjectives, but they don't apply to a single object [Frege, by George/Velleman]
Numerical adjectives are of the same second-level type as the existential quantifier [Frege, by George/Velleman]
'Jupiter has many moons' won't read as 'The number of Jupiter's moons equals the number many' [Rumfitt on Frege]
The number 'one' can't be a property, if any object can be viewed as one or not one [Frege]
For science, we can translate adjectival numbers into noun form [Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Arithmetic is analytic [Frege, by Weiner]
Logicism shows that no empirical truths are needed to justify arithmetic [Frege, by George/Velleman]
Frege offered a Platonist version of logicism, committed to cardinal and real numbers [Frege, by Hale/Wright]
Mathematics has no special axioms of its own, but follows from principles of logic (with definitions) [Frege, by Bostock]
Arithmetic must be based on logic, because of its total generality [Frege, by Jeshion]
Numbers are definable in terms of mapping items which fall under concepts [Frege, by Scruton]
Arithmetic is analytic and a priori, and thus it is part of logic [Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Frege only managed to prove that arithmetic was analytic with a logic that included set-theory [Quine on Frege]
Frege's platonism and logicism are in conflict, if logic must dictates an infinity of objects [Wright,C on Frege]
Why should the existence of pure logic entail the existence of objects? [George/Velleman on Frege]
Frege's belief in logicism and in numerical objects seem uncomfortable together [Hodes on Frege]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism fails to recognise types of symbols, and also meta-games [Frege, by Brown,JR]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Logic and maths refer to fictitious entities which we have created [Nietzsche]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Frege was completing Bolzano's work, of expelling intuition from number theory and analysis [Frege, by Dummett]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Abstraction from things produces concepts, and numbers are in the concepts [Frege]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism
Mental states are irrelevant to mathematics, because they are vague and fluctuating [Frege]
7. Existence / A. Nature of Existence / 1. Nature of Existence
Affirmation of existence is just denial of zero [Frege]
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
The nature of being, of things, is much easier to understand than is becoming [Nietzsche]
7. Existence / A. Nature of Existence / 4. Abstract Existence
If abstracta are non-mental, quarks are abstracta, and yet chess and God's thoughts are mental [Rosen on Frege]
The equator is imaginary, but not fictitious; thought is needed to recognise it [Frege]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
Many of us find Frege's claim that truths depend on one another an obscure idea [Heck on Frege]
Parallelism is intuitive, so it is more fundamental than sameness of direction [Frege, by Heck]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Frege refers to 'concrete' objects, but they are no different in principle from abstract ones [Frege, by Dummett]
7. Existence / D. Theories of Reality / 8. Facts / e. Facts rejected
There are no facts in themselves, only interpretations [Nietzsche]
There are no 'facts-in-themselves', since a sense must be projected into them to make them 'facts' [Nietzsche]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
Vagueness is incomplete definition [Frege, by Koslicki]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
For Frege, ontological questions are to be settled by reference to syntactic structures [Frege, by Wright,C]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / c. Commitment of predicates
Second-order quantifiers are committed to concepts, as first-order commits to objects [Frege, by Linnebo]
7. Existence / E. Categories / 5. Category Anti-Realism
Nihilism results from valuing the world by the 'categories of reason', because that is fiction [Nietzsche]
8. Modes of Existence / A. Relations / 4. Formal Relations / c. Ancestral relation
'Ancestral' relations are derived by iterating back from a given relation [Frege, by George/Velleman]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Frege treats properties as a kind of function, and maybe a property is its characteristic function [Frege, by Smith,P]
8. Modes of Existence / B. Properties / 12. Denial of Properties
We realise that properties are sensations of the feeling subject, not part of the thing [Nietzsche]
8. Modes of Existence / C. Powers and Dispositions / 5. Powers and Properties
A thing has no properties if it has no effect on other 'things' [Nietzsche]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
Not all objects are spatial; 4 can still be an object, despite lacking spatial co-ordinates [Frege]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Frege says singular terms denote objects, numerals are singular terms, so numbers exist [Frege, by Hale]
Frege establishes abstract objects independently from concrete ones, by falling under a concept [Frege, by Dummett]
9. Objects / A. Existence of Objects / 3. Objects in Thought
For Frege, objects just are what singular terms refer to [Frege, by Hale/Wright]
Without concepts we would not have any objects [Frege, by Shapiro]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
Frege's universe comes already divided into objects [Frege, by Koslicki]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
We saw unity in things because our ego seemed unified (but now we doubt the ego!) [Nietzsche]
9. Objects / F. Identity among Objects / 1. Concept of Identity
The idea of a criterion of identity was introduced by Frege [Frege, by Noonan]
Frege's algorithm of identity is the law of putting equals for equals [Frege, by Quine]
9. Objects / F. Identity among Objects / 3. Relative Identity
Geach denies Frege's view, that 'being the same F' splits into being the same and being F [Perry on Frege]
9. Objects / F. Identity among Objects / 6. Identity between Objects
Identity between objects is not a consequence of identity, but part of what 'identity' means [Frege, by Dummett]
10. Modality / A. Necessity / 11. Denial of Necessity
For me, a priori 'truths' are just provisional assumptions [Nietzsche]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
We can't know whether there is knowledge if we don't know what it is [Nietzsche]
11. Knowledge Aims / A. Knowledge / 2. Understanding
To understand a thought you must understand its logical structure [Frege, by Burge]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
Every belief is a considering-something-true [Nietzsche]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
A note for asses: What convinces is not necessarily true - it is merely convincing [Nietzsche]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
For Frege a priori knowledge derives from general principles, so numbers can't be primitive [Frege]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Mathematicians just accept self-evidence, whether it is logical or intuitive [Frege]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
An a priori truth is one derived from general laws which do not require proof [Frege]
A truth is a priori if it can be proved entirely from general unproven laws [Frege]
12. Knowledge Sources / A. A Priori Knowledge / 7. A Priori from Convention
The forms of 'knowledge' about logic which precede experience are actually regulations of belief [Nietzsche]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
Frege tried to explain synthetic a priori truths by expanding the concept of analyticity [Frege, by Katz]
12. Knowledge Sources / B. Perception / 1. Perception
All sense perceptions are permeated with value judgements (useful or harmful) [Nietzsche]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
We can have two opposite sensations, like hard and soft, at the same time [Nietzsche]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Intuitions cannot be communicated [Frege, by Burge]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / d. Rational foundations
Justifications show the ordering of truths, and the foundation is what is self-evident [Frege, by Jeshion]
13. Knowledge Criteria / E. Relativism / 1. Relativism
The extreme view is there are only perspectives, no true beliefs, because there is no true world [Nietzsche]
14. Science / C. Induction / 1. Induction
Induction is merely psychological, with a principle that it can actually establish laws [Frege]
In science one observation can create high probability, while a thousand might prove nothing [Frege]
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
Ideas are not spatial, and don't have distances between them [Frege]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
It is a major blunder to think of consciousness as a unity, and hence as an entity, a thing [Nietzsche]
16. Persons / C. Self-Awareness / 2. Knowing the Self
Great self-examination is to become conscious of oneself not as an individual, but as mankind [Nietzsche]
16. Persons / E. Rejecting the Self / 4. Denial of the Self
Perhaps we are not single subjects, but a multiplicity of 'cells', interacting to create thought [Nietzsche]
17. Mind and Body / A. Mind-Body Dualism / 6. Epiphenomenalism
Consciousness is a terminal phenomenon, and causes nothing [Nietzsche]
18. Thought / A. Modes of Thought / 1. Thought
Thought is the same everywhere, and the laws of thought do not vary [Frege]
18. Thought / A. Modes of Thought / 3. Emotions / b. Types of emotion
Passions are ranked, as if they are non-rational and animal pleasure seeking [Nietzsche]
18. Thought / A. Modes of Thought / 3. Emotions / f. Emotion and reason
We fail to see that reason is a network of passions, and every passion contains some reason [Nietzsche]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Early Frege takes the extensions of concepts for granted [Frege, by Dummett]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
Concepts are, precisely, the references of predicates [Frege, by Wright,C]
A concept is a non-psychological one-place function asserting something of an object [Frege, by Weiner]
Fregean concepts have precise boundaries and universal applicability [Frege, by Koslicki]
Psychological accounts of concepts are subjective, and ultimately destroy truth [Frege]
18. Thought / D. Concepts / 5. Concepts and Language / b. Concepts are linguistic
A concept is a possible predicate of a singular judgement [Frege]
18. Thought / E. Abstraction / 1. Abstract Thought
Defining 'direction' by parallelism doesn't tell you whether direction is a line [Dummett on Frege]
18. Thought / E. Abstraction / 2. Abstracta by Selection
Frege accepts abstraction to the concept of all sets equipollent to a given one [Tait on Frege]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
Frege himself abstracts away from tone and color [Yablo on Frege]
If we abstract 'from' two cats, the units are not black or white, or cats [Tait on Frege]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Frege's logical abstaction identifies a common feature as the maximal set of equivalent objects [Frege, by Dummett]
Frege's 'parallel' and 'direction' don't have the same content, as we grasp 'parallel' first [Yablo on Frege]
Frege put the idea of abstraction on a rigorous footing [Frege, by Fine,K]
Fregean abstraction creates concepts which are equivalences between initial items [Frege, by Fine,K]
We create new abstract concepts by carving up the content in a different way [Frege]
You can't simultaneously fix the truth-conditions of a sentence and the domain of its variables [Dummett on Frege]
From basing 'parallel' on identity of direction, Frege got all abstractions from identity statements [Frege, by Dummett]
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
Words in isolation seem to have ideas as meanings, but words have meaning in propositions [Frege]
Never ask for the meaning of a word in isolation, but only in the context of a proposition [Frege]
19. Language / E. Analyticity / 1. Analytic Propositions
A statement is analytic if substitution of synonyms can make it a logical truth [Frege, by Boghossian]
Frege considered analyticity to be an epistemic concept [Frege, by Shapiro]
19. Language / E. Analyticity / 2. Analytic Truths
All analytic truths can become logical truths, by substituting definitions or synonyms [Frege, by Rey]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
Frege fails to give a concept of analyticity, so he fails to explain synthetic a priori truth that way [Katz on Frege]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
The concept of the 'will' is just a false simplification by our understanding [Nietzsche]
20. Action / B. Preliminaries of Action / 2. Willed Action / b. Volitionism
There is no such things a pure 'willing' on its own; the aim must always be part of it [Nietzsche]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
None of the ancients had the courage to deny morality by denying free will [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
'Conscience' is invented to value actions by intention and conformity to 'law', rather than consequences [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
There is an extended logic to a great man's life, achieved by a sustained will [Nietzsche]
The highest man can endure and control the greatest combination of powerful drives [Nietzsche]
The highest man directs the values of the highest natures over millenia [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / g. Will to power
There is a conspiracy (a will to power) to make morality dominate other values, like knowledge and art [Nietzsche]
The basic tendency of the weak has always been to pull down the strong, using morality [Nietzsche]
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
All evaluation is from some perspective, and aims at survival [Nietzsche]
The ruling drives of our culture all want to be the highest court of our values [Nietzsche]
22. Metaethics / B. Value / 2. Values / f. Altruism
How can it be that I should prefer my neighbour to myself, but he should prefer me to himself? [Nietzsche]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
Utilitarians prefer consequences because intentions are unknowable - but so are consequences! [Nietzsche]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
It is a sign of degeneration when eudaimonistic values begin to prevail [Nietzsche]
We have no more right to 'happiness' than worms [Nietzsche]
22. Metaethics / C. The Good / 3. Pleasure / a. Nature of pleasure
Pleasure and pain are mere epiphenomena, and achievement requires that one desire both [Nietzsche]
23. Ethics / A. Egoism / 1. Ethical Egoism
The question about egoism is: what kind of ego? since not all egos are equal [Nietzsche]
The ego is only a fiction, and doesn't exist at all [Nietzsche]
Egoism is inescapable, and when it grows weak, the power of love also grows weak [Nietzsche]
23. Ethics / B. Contract Ethics / 2. Golden Rule
The Golden Rule prohibits harmful actions, with the premise that actions will be requited [Nietzsche]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
The great error is to think that happiness derives from virtue, which in turn derives from free will [Nietzsche]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / b. Living naturally
Not "return to nature", for there has never yet been a natural humanity [Nietzsche]
'Love your enemy' is unnatural, for the natural law says 'love your neighbour and hate your enemy' [Nietzsche]
Be natural! But how, if one happens to be "unnatural"? [Nietzsche]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
We would avoid a person who always needed reasons for remaining decent [Nietzsche]
Virtue is pursued from self-interest and prudence, and reduces people to non-entities [Nietzsche]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
The instinct of the herd, the majority, aims for the mean, in the middle [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
A path to power: to introduce a new virtue under the name of an old one [Nietzsche]
Modesty, industriousness, benevolence and temperance are the virtues of a good slave [Nietzsche]
Many virtues are merely restraints on the most creative qualities of a human being [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
When powerless one desires freedom; if power is too weak, one desires equal power ('justice') [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / e. Honour
The supposed great lovers of honour (Alexander etc) were actually great despisers of honour [Nietzsche]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
The categorical imperative needs either God behind it, or a metaphysic of the unity of reason [Nietzsche]
23. Ethics / E. Utilitarianism / 3. Motivation for Altruism
Utilitarianism criticises the origins of morality, but still believes in it as much as Christians [Nietzsche]
23. Ethics / F. Existentialism / 1. Existentialism
If faith is lost, people seek other authorities, in order to avoid the risk of willing personal goals [Nietzsche]
23. Ethics / F. Existentialism / 6. Authentic Self
Virtuous people are inferior because they are not 'persons', but conform to a fixed pattern [Nietzsche]
23. Ethics / F. Existentialism / 7. Existential Action
Morality used to be for preservation, but now we can only experiment, giving ourselves moral goals [Nietzsche]
24. Political Theory / B. Nature of a State / 5. Culture
The high points of culture and civilization do not coincide [Nietzsche]
25. Social Practice / B. Equalities / 2. Political equality
In modern society virtue is 'equal rights', but only because everyone is zero, so it is a sum of zeroes [Nietzsche]
25. Social Practice / E. Policies / 5. Education / b. Education principles
To learn something, you must know that you don't know [Frege]
26. Natural Theory / C. Causation / 7. Eliminating causation
Science has taken the meaning out of causation; cause and effect are two equal sides of an equation [Nietzsche]
26. Natural Theory / C. Causation / 8. Particular Causation / a. Observation of causation
We derive the popular belief in cause and effect from our belief that our free will causes things [Nietzsche]
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
The laws of number are not laws of nature, but are laws of the laws of nature [Frege]
27. Natural Reality / G. Biology / 3. Evolution
A 'species' is a stable phase of evolution, implying the false notion that evolution has a goal [Nietzsche]
28. God / A. Divine Nature / 1. God
The concept of 'God' represents a turning away from life, and a critique of life [Nietzsche]
28. God / A. Divine Nature / 6. Divine Morality / a. Divine morality
Those who have abandoned God cling that much more firmly to the faith in morality [Nietzsche]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
Morality cannot survive when the God who sanctions it is missing [Nietzsche]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
Existence is not a first-level concept (of God), but a second-level property of concepts [Frege, by Potter]
Because existence is a property of concepts the ontological argument for God fails [Frege]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Primitive Christianity is abolition of the state; it is opposed to defence, justice, patriotism and class [Nietzsche]