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All the ideas for 'fragments/reports', 'Grundlagen der Arithmetik (Foundations)' and 'Causal Powers'

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277 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Like disastrous small errors in navigation, small misunderstandings can wreck intellectual life [Harré/Madden]
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]
Philosophy devises and assesses conceptual schemes in the service of worldviews [Harré/Madden]
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
Never lose sight of the distinction between concept and object [Frege]
Analysis of concepts based neither on formalism nor psychology can arise from examining what we know [Harré/Madden]
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]
Humeans see analysis in terms of formal logic, because necessities are fundamentally logical relations [Harré/Madden]
1. Philosophy / G. Scientific Philosophy / 2. Positivism
Positivism says science only refers to immediate experiences [Harré/Madden]
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]
2. Reason / D. Definition / 1. Definitions
Logically, definitions have a subject, and a set of necessary predicates [Harré/Madden]
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 / 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]
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 / 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 / b. Types of number
Points can be 'dense' by unending division, but must meet a tougher criterion to be 'continuous' [Harré/Madden]
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 / i. Reals from cuts
Points are 'continuous' if any 'cut' point participates in both halves of the cut [Harré/Madden]
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
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 / 3. Axioms for Geometry
Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
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 / 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]
There is not an exclusive dichotomy between the formal and the logical [Harré/Madden]
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 / 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 / B. Change in Existence / 1. Nature of Change
Humeans can only explain change with continuity as successive replacement [Harré/Madden]
7. Existence / B. Change in Existence / 4. Events / b. Events as primitive
Humeans construct their objects from events, but we construct events from objects [Harré/Madden]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
The induction problem fades if you work with things, rather than with events [Harré/Madden]
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 / 6. Fundamentals / a. Fundamental reality
Fundamental particulars can't change [Harré/Madden]
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 / C. Structure of Existence / 8. Stuff / a. Pure stuff
Hard individual blocks don't fix what 'things' are; fluids are no less material things [Harré/Madden]
7. Existence / C. Structure of Existence / 8. Stuff / b. Mixtures
Magnetic and gravity fields can occupy the same place without merging [Harré/Madden]
7. Existence / D. Theories of Reality / 6. Physicalism
Gravitational and electrical fields are, for a materialist, distressingly empty of material [Harré/Madden]
7. Existence / D. Theories of Reality / 9. States of Affairs
Events are changes in states of affairs (which consist of structured particulars, with powers and relations) [Harré/Madden]
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]
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 / 5. Natural Properties
Humeans see predicates as independent, but science says they are connected [Harré/Madden]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
Energy was introduced to physics to refer to the 'store of potency' of a moving ball [Harré/Madden]
Some powers need a stimulus, but others are just released [Harré/Madden]
Some powers are variable, others cannot change (without destroying an identity) [Harré/Madden]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
Scientists define copper almost entirely (bar atomic number) in terms of its dispositions [Harré/Madden]
We explain powers by the natures of things, but explanations end in inexplicable powers [Harré/Madden]
Maybe a physical field qualifies as ultimate, if its nature is identical with its powers [Harré/Madden]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
Powers are not qualities; they just point to directions of empirical investigation [Harré/Madden]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / d. Dispositions as occurrent
What is a field of potentials, if it only consists of possible events? [Harré/Madden]
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 / A. Existence of Objects / 6. Nihilism about Objects
The good criticism of substance by Humeans also loses them the vital concept of a thing [Harré/Madden]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
We can escape substance and its properties, if we take fields of pure powers as ultimate [Harré/Madden]
9. Objects / C. Structure of Objects / 3. Matter of an Object
The assumption that shape and solidity are fundamental implies dubious 'substance' in bodies [Harré/Madden]
9. Objects / C. Structure of Objects / 7. Substratum
The notorious substratum results from substance-with-qualities; individuals-with-powers solves this [Harré/Madden]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
In logic the nature of a kind, substance or individual is the essence which is inseparable from what it is [Harré/Madden]
9. Objects / D. Essence of Objects / 9. Essence and Properties
We can infer a new property of a thing from its other properties, via its essential nature [Harré/Madden]
9. Objects / D. Essence of Objects / 15. Against Essentialism
We say the essence of particles is energy, but only so we can tell a story about the nature of things [Harré/Madden]
9. Objects / E. Objects over Time / 2. Objects that Change
To say something remains the same but lacks its capacities and powers seems a contradiction [Harré/Madden]
Some individuals can gain or lose capacities or powers, without losing their identity [Harré/Madden]
A particular might change all of its characteristics, retaining mere numerical identity [Harré/Madden]
9. Objects / E. Objects over Time / 3. Three-Dimensionalism
'Dense' time raises doubts about continuous objects, so they need 'continuous' time [Harré/Madden]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
If things are successive instantaneous events, nothing requires those events to resemble one another [Harré/Madden]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
Humeans cannot step in the same river twice, because they cannot strictly form the concept of 'river' [Harré/Madden]
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 / 2. Nature of Necessity
What reduces the field of the possible is a step towards necessity [Harré/Madden]
10. Modality / A. Necessity / 3. Types of Necessity
There is 'absolute' necessity (implied by all propositions) and 'relative' necessity (from what is given) [Harré/Madden]
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessity is grounded in the logical form of a statement [Harré/Madden]
10. Modality / A. Necessity / 7. Natural Necessity
Natural necessity is not logical necessity or empirical contingency in disguise [Harré/Madden]
The relation between what a thing is and what it can do or undergo relate by natural necessity [Harré/Madden]
A necessity corresponds to the nature of the actual [Harré/Madden]
Natural necessity is when powerful particulars must produce certain results in a situation [Harré/Madden]
People doubt science because if it isn't logically necessary it seems to be absolutely contingent [Harré/Madden]
Property or event relations are naturally necessary if generated by essential mechanisms [Harré/Madden]
10. Modality / A. Necessity / 8. Transcendental Necessity
Transcendental necessity is conditions of a world required for a rational being to know its nature [Harré/Madden]
There is a transcendental necessity for each logical necessity, but the transcendental extends further [Harré/Madden]
10. Modality / B. Possibility / 9. Counterfactuals
Counterfactuals are just right for analysing statements about the powers which things have [Harré/Madden]
10. Modality / C. Sources of Modality / 3. Necessity by Convention
If natural necessity is used to include or exclude some predicate, the predicate is conceptually necessary [Harré/Madden]
Having a child is contingent for a 'man', necessary for a 'father'; the latter reflects a necessity of nature [Harré/Madden]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
Is conceptual necessity just conventional, or does it mirror something about nature? [Harré/Madden]
There is a conceptual necessity when properties become a standard part of a nominal essence [Harré/Madden]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
Necessity and contingency are separate from the a priori and the a posteriori [Harré/Madden]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / b. Conceivable but impossible
If Goldbach's Conjecture is true (and logically necessary), we may be able to conceive its opposite [Harré/Madden]
11. Knowledge Aims / A. Knowledge / 2. Understanding
To understand a thought you must understand its logical structure [Frege, by Burge]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
It is silly to say that direct experience must be justified, either by reason, or by more experience [Harré/Madden]
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 / 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 / 4. Sense Data / d. Sense-data problems
We experience qualities as of objects, not on their own [Harré/Madden]
12. Knowledge Sources / B. Perception / 6. Inference in Perception
Inference in perception is unconvincingly defended as non-conscious and almost instantaneous [Harré/Madden]
12. Knowledge Sources / D. Empiricism / 2. Associationism
Humean impressions are too instantaneous and simple to have structure or relations [Harré/Madden]
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]
14. Science / B. Scientific Theories / 1. Scientific Theory
Clavius's Paradox: purely syntactic entailment theories won't explain, because they are too profuse [Harré/Madden]
Simplicity can sort theories out, but still leaves an infinity of possibilities [Harré/Madden]
The powers/natures approach has been so successful (for electricity, magnetism, gravity) it may be universal [Harré/Madden]
14. Science / B. Scientific Theories / 2. Aim of Science
We prefer the theory which explains and predicts the powers and capacities of particulars [Harré/Madden]
Science investigates the nature and constitution of things or substances [Harré/Madden]
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]
14. Science / C. Induction / 3. Limits of Induction
Conjunctions explain nothing, and so do not give a reason for confidence in inductions [Harré/Madden]
Hume's atomic events makes properties independent, and leads to problems with induction [Harré/Madden]
14. Science / C. Induction / 5. Paradoxes of Induction / b. Raven paradox
Contraposition may be equivalent in truth, but not true in nature, because of irrelevant predicates [Harré/Madden]
The items put forward by the contraposition belong within different natural clusters [Harré/Madden]
The possibility that all ravens are black is a law depends on a mechanism producing the blackness [Harré/Madden]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
Only changes require explanation [Harré/Madden]
14. Science / D. Explanation / 1. Explanation / c. Direction of explanation
If explanation is by entailment, that lacks a causal direction, unlike natural necessity [Harré/Madden]
Powers can explain the direction of causality, and make it a natural necessity [Harré/Madden]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
If the nature of particulars explains their powers, it also explains their relations and behaviour [Harré/Madden]
Powers and natures lead us to hypothesise underlying mechanisms, which may be real [Harré/Madden]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Solidity comes from the power of repulsion, and shape from the power of attraction [Harré/Madden]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Essence explains passive capacities as well as active powers [Harré/Madden]
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 / C. Capacities of Minds / 5. Generalisation by mind
The very concepts of a particular power or nature imply the possibility of being generalised [Harré/Madden]
18. Thought / A. Modes of Thought / 1. Thought
Thought is the same everywhere, and the laws of thought do not vary [Frege]
18. Thought / C. Content / 5. Twin Earth
What properties a thing must have to be a type of substance can be laid down a priori [Harré/Madden]
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]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
We say there is 'no alternative' in all sorts of contexts, and there are many different grounds for it [Harré/Madden]
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 / B. Natural Kinds / 6. Necessity of Kinds
We can base the idea of a natural kind on the mechanisms that produce natural necessity [Harré/Madden]
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
Species do not have enough constancy to be natural kinds [Harré/Madden]
26. Natural Theory / C. Causation / 2. Types of cause
If the concept of a cause includes its usual effects, we call it a 'power' [Harré/Madden]
26. Natural Theory / C. Causation / 5. Direction of causation
Humean accounts of causal direction by time fail, because cause and effect can occur together [Harré/Madden]
26. Natural Theory / C. Causation / 6. Causation as primitive
Active causal power is just objects at work, not something existing in itself [Harré/Madden]
26. Natural Theory / C. Causation / 8. Particular Causation / a. Observation of causation
Causation always involves particular productive things [Harré/Madden]
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
Efficient causes combine stimulus to individuals, absence of contraints on activity [Harré/Madden]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
The cause (or part of it) is what stimulates or releases the powerful particular thing involved [Harré/Madden]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
Originally Humeans based lawlike statements on pure qualities, without particulars [Harré/Madden]
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]
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
Being lawlike seems to resist formal analysis, because there are always counter-examples [Harré/Madden]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
Necessary effects will follow from some general theory specifying powers and structure of a world [Harré/Madden]
Humeans say there is no necessity in causation, because denying an effect is never self-contradictory [Harré/Madden]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
In lawful universal statements (unlike accidental ones) we see why the regularity holds [Harré/Madden]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
We could call any generalisation a law, if it had reasonable support and no counter-evidence [Harré/Madden]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
We perceive motion, and not just successive occupations of different positions [Harré/Madden]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
'Energy' is a quasi-substance invented as the bearer of change during interactions [Harré/Madden]
'Kinetic energy' is used to explain the effects of moving things when they are stopped [Harré/Madden]
27. Natural Reality / C. Space / 2. Space
Space can't be an individual (in space), but it is present in all places [Harré/Madden]
27. Natural Reality / F. Chemistry / 1. Chemistry
Chemical atoms have two powers: to enter certain combinations, and to emit a particular spectrum [Harré/Madden]
Chemistry is not purely structural; CO2 is not the same as SO2 [Harré/Madden]
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]
28. God / C. Attitudes to God / 5. Atheism
Theism is supposed to make the world more intelligible - and should offer results [Harré/Madden]