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All the ideas for 'Physics', 'Grundlagen der Arithmetik (Foundations)' and 'Propositions'

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278 ideas

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 / 4. Aims of Reason
Reason grasps generalities, while the senses grasp particulars [Aristotle]
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 / 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 / 5. Truth Bearers
Are the truth-bearers sentences, utterances, ideas, beliefs, judgements, propositions or statements? [Cartwright,R]
Logicians take sentences to be truth-bearers for rigour, rather than for philosophical reasons [Cartwright,R]
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]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Are a part and whole one or many? Either way, what is the cause? [Aristotle]
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 / 2. Geometry
Geometry studies naturally occurring lines, but not as they occur in nature [Aristotle]
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 / g. Real numbers
Two is the least number, but there is no least magnitude, because it is always divisible [Aristotle]
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
One is the Number which belongs to the concept "identical with 0" [Frege]
We can say 'a and b are F' if F is 'wise', but not if it is 'one' [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 / a. The Infinite
Without infinity time has limits, magnitudes are indivisible, and numbers come to an end [Aristotle]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
Aristotle's infinity is a property of the counting process, that it has no natural limit [Aristotle, by Le Poidevin]
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 / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
Lengths do not contain infinite parts; parts are created by acts of division [Aristotle, by Le Poidevin]
A continuous line cannot be composed of indivisible points [Aristotle]
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
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]
A cardinal number may be defined as a class of similar classes [Frege, by Russell]
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]
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]
A statement of number contains a predication about a concept [Frege]
If you can subdivide objects many ways for counting, you can do that to set-elements too [Yourgrau on 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]
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 / a. Mathematical empiricism
Ten sheep and ten dogs are the same numerically, but it is not the same ten [Aristotle]
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
Logicism shows that no empirical truths are needed to justify arithmetic [Frege, by George/Velleman]
Arithmetic must be based on logic, because of its total generality [Frege, by Jeshion]
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]
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]
Arithmetic is analytic [Frege, by Weiner]
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]
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
The incommensurability of the diagonal always exists, and so it is not in time [Aristotle]
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
Change is the implied actuality of that which exists potentially [Aristotle]
The sophists thought a man in the Lyceum is different from that man in the marketplace [Aristotle]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
Aristotle's formal and material 'becauses' [aitiai] arguably involve grounding [Aristotle, by Correia/Schnieder]
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 / 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 / 1. Nature of Relations
The separation from here to there is not the same as the separation from there to here [Aristotle]
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 / 8. Properties as Modes
The features of a thing (whether quality or quantity) are inseparable from their subjects [Aristotle]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
Heavy and light are defined by their tendency to move down or up [Aristotle]
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 / a. Intrinsic unification
Natural objects include animals and their parts, plants, and the simple elements [Aristotle]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
Substance is not predicated of anything - but it still has something underlying it, that originates it [Aristotle]
We only infer underlying natures by analogy, observing bronze of a statue, or wood of a bed [Aristotle]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
A nature is related to a substance as shapeless matter is to something which has a shape [Aristotle]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
Form, not matter, is a thing's nature, because it is actual, rather than potential [Aristotle]
9. Objects / C. Structure of Objects / 2. Hylomorphism / c. Form as causal
A thing's form and purpose are often the same, and form can be the initiator of change too [Aristotle]
9. Objects / C. Structure of Objects / 2. Hylomorphism / d. Form as unifier
Unity of the form is just unity of the definition [Aristotle]
9. Objects / C. Structure of Objects / 3. Matter of an Object
In feature-generation the matter (such as bronze) endures, but in generation it doesn't [Aristotle, by Politis]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
We first sense whole entities, and then move to particular parts of it [Aristotle]
There is no whole except for the parts [Aristotle]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
The four explanations are the main aspects of a thing's nature [Aristotle, by Moravcsik]
A thing's nature is what causes its changes and stability [Aristotle]
9. Objects / E. Objects over Time / 2. Objects that Change
Coming to be is by shape-change, addition, subtraction, composition or alteration [Aristotle]
Natural things are their own source of stability through change [Aristotle]
9. Objects / E. Objects over Time / 6. Successive Things
A day, or the games, has one thing after another, actually and potentially occurring [Aristotle]
9. Objects / E. Objects over Time / 10. Beginning of an Object
Coming-to-be may be from nothing in a qualified way, as arising from an absence [Aristotle]
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 / 4. Type Identity
A token isn't a unique occurrence, as the case of a word or a number shows [Cartwright,R]
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 / B. Possibility / 4. Potentiality
Matter is potentiality [Aristotle, by Politis]
10. Modality / B. Possibility / 7. Chance
Intrinsic cause is prior to coincidence, so nature and intelligence are primary causes, chance secondary [Aristotle]
Maybe there is no pure chance; a man's choices cause his chance meetings [Aristotle]
Chance is a coincidental cause among events involving purpose and choice [Aristotle]
11. Knowledge Aims / A. Knowledge / 2. Understanding
To understand a thought you must understand its logical structure [Frege, by Burge]
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 / E. Direct Knowledge / 2. Intuition
Intuitions cannot be communicated [Frege, by Burge]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
To know something we need understanding, which is grasp of the primary cause [Aristotle]
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 / 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 / D. Explanation / 1. Explanation / b. Aims of explanation
We know a thing if we grasp its first causes, principles and basic elements [Aristotle]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Science refers the question Why? to four causes/explanations: matter, form, source, purpose [Aristotle]
Four Explanations: the essence and form; the matter; the source; and the end [Aristotle, by Politis]
Aristotle's four 'causes' are four items which figure in basic explanations of nature [Aristotle, by Annas]
There are as many causes/explanations as there are different types of why-question [Aristotle]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Chance is inexplicable, because we can only explain what happens always or usually [Aristotle]
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]
18. Thought / A. Modes of Thought / 1. Thought
Thought is the same everywhere, and the laws of thought do not vary [Frege]
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
You can't abstract natural properties to make Forms - objects and attributes are defined together [Aristotle]
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
Mathematicians study what is conceptually separable, and doesn't lead to error [Aristotle]
If we abstract 'from' two cats, the units are not black or white, or cats [Tait on Frege]
Frege himself abstracts away from tone and color [Yablo 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]
Fregean abstraction creates concepts which are equivalences between initial items [Frege, by Fine,K]
Frege put the idea of abstraction on a rigorous footing [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 / 1. Meaning
For any statement, there is no one meaning which any sentence asserting it must have [Cartwright,R]
People don't assert the meaning of the words they utter [Cartwright,R]
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 / C. Assigning Meanings / 3. Predicates
Predicates are substance, quality, place, relation, quantity and action or affection [Aristotle]
19. Language / D. Propositions / 1. Propositions
We can pull apart assertion from utterance, and the action, the event and the subject-matter for each [Cartwright,R]
'It's raining' makes a different assertion on different occasions, but its meaning remains the same [Cartwright,R]
19. Language / D. Propositions / 4. Mental Propositions
We can attribute 'true' and 'false' to whatever it was that was said [Cartwright,R]
To assert that p, it is neither necessary nor sufficient to utter some particular words [Cartwright,R]
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 / 2. Assertion
Assertions, unlike sentence meanings, can be accurate, probable, exaggerated, false.... [Cartwright,R]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
We assign the cause of someone's walking when we say why they are doing it [Aristotle]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
Goodness is when a thing (such as a circle) is complete, and conforms with its nature [Aristotle]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
All moral virtue is concerned with bodily pleasure and pain [Aristotle]
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 / A. Speculations on Nature / 1. Nature
Nature is a principle of change, so we must understand change first [Aristotle]
Nothing natural is disorderly, because nature is responsible for all order [Aristotle]
'Nature' refers to two things - form and matter [Aristotle]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
Nature has purpose, and aims at what is better. Is it coincidence that crops grow when it rains? [Aristotle]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / b. Limited purposes
The nature of a thing is its end and purpose [Aristotle]
A thing's purpose is ambiguous, and from one point of view we ourselves are ends [Aristotle]
Teeth and crops are predictable, so they cannot be mere chance, but must have a purpose [Aristotle]
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
Is ceasing-to-be unnatural if it happens by force, and natural otherwise? [Aristotle]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Continuity depends on infinity, because the continuous is infinitely divisible [Aristotle]
The heavens seem to be infinite, because we cannot imagine their end [Aristotle]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
Matter desires form, as female desires male, and ugliness desires beauty [Aristotle]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
When Aristotle's elements compound they are stable, so why would they ever separate? [Weisberg/Needham/Hendry on Aristotle]
26. Natural Theory / C. Causation / 2. Types of cause
The 'form' of a thing explains why the matter constitutes that particular thing [Aristotle, by Politis]
A 'material' cause/explanation is the form of whatever is the source [Aristotle, by Politis]
Causes produce a few things in their own right, and innumerable things coincidentally [Aristotle]
26. Natural Theory / C. Causation / 3. Final causes
The four causes are the material, the form, the source, and the end [Aristotle]
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 / 8. Scientific Essentialism / d. Knowing essences
Scientists must know the essential attributes of the things they study [Aristotle]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Motion fulfils potentiality [Aristotle]
If movement can arise within an animal, why can't it also arise in the universe? [Aristotle]
When there is unnatural movement (e.g. fire going downwards) the cause is obvious [Aristotle]
27. Natural Reality / C. Space / 4. Substantival Space
The universe as a whole is not anywhere [Aristotle]
If everything has a place, this causes an infinite regress, because each place must have place [Aristotle]
27. Natural Reality / C. Space / 5. Relational Space
Place is not shape, or matter, or extension between limits; it is the limits of a body [Aristotle]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
If there were many cosmoses, each would have its own time, giving many times [Aristotle]
27. Natural Reality / D. Time / 1. Nature of Time / c. Idealist time
Would there be time if there were no mind? [Aristotle]
It is unclear whether time depends on the existence of soul [Aristotle]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time does not exist without change [Aristotle]
Time measures rest, as well as change [Aristotle]
For Aristotle time is not a process but a means for measuring processes [Aristotle, by Bardon]
Time is not change, but the number we associate with change [Aristotle]
Change only exists in time through its being temporally measure [Aristotle]
Time is an aspect of change [Aristotle]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
How can time exist, when it is composed of what has ceased to be and is yet to be? [Aristotle]
If all of time has either ceased to exist, or has not yet happened, maybe time does not exist [Aristotle]
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
Time is not change, but requires change in our minds to be noticed [Aristotle]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
The present moment is obviously a necessary feature of time [Aristotle]
27. Natural Reality / D. Time / 2. Passage of Time / h. Change in time
Unlike time, change goes at different rates, and is usually localised [Aristotle, by Le Poidevin]
27. Natural Reality / D. Time / 3. Parts of Time / b. Instants
Time has parts, but the now is not one of them, and time is not composed of nows [Aristotle]
Nows can't be linked together, any more than points on a line [Aristotle]
27. Natural Reality / D. Time / 3. Parts of Time / d. Measuring time
Circular motion is the most obvious measure of time, and especially the celestial sphere [Aristotle]
We measure change by time, and time by change, as they are interdefined [Aristotle]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
The present moment is a link (of past to future), and also a limit (of past and of future) [Aristotle]
We can't tell whether the changing present moment is one thing, or a succession of things [Aristotle]
27. Natural Reality / E. Cosmology / 2. Eternal Universe
Do things come to be from what is, or from what is not? Both seem problematical. [Aristotle]
28. God / A. Divine Nature / 2. Divine Nature
The source of all movement must be indivisible and have no magnitude [Aristotle]
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]