Ideas of Gottlob Frege, by Theme
[German, 1848  1925, Led a quiet and studious life as Professor at the University of Jena.]
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1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
13876

The syntactic category is primary, and the ontological category is derivative [Wright,C]

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
8415

Never lose sight of the distinction between concept and object

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
9841

Frege was the first to give linguistic answers to nonlinguistic questions

9840

Frege initiated linguistic philosophy, studying number through the sense of sentences [Dummett]

1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
15948

Frege developed formal systems to avoid unnoticed assumptions [Lavine]

2. Reason / A. Nature of Reason / 3. Pure Reason
10804

Thoughts have a natural order, to which human thinking is drawn. [Yablo]

2. Reason / A. Nature of Reason / 5. Objectivity
9832

Frege sees no 'intersubjective' category, between objective and subjective [Dummett]

8414

Keep the psychological and subjective separate from the logical and objective

7740

There exists a realm, beyond objects and ideas, of nonspatiotemporal thoughts [Weiner]

2. Reason / B. Laws of Thought / 1. Laws of Thought
8939

We should not describe human laws of thought, but how to correctly track truth [Fisher]

2. Reason / D. Definition / 2. Aims of Definition
9821

A definition need not capture the sense of an expression  just get the reference right [Dummett]

13886

Later Frege held that definitions must fix a function's value for every possible argument [Wright,C]

2. Reason / D. Definition / 3. Types of Definition
16877

A 'constructive' (as opposed to 'analytic') definition creates a new sign

2. Reason / D. Definition / 7. Contextual Definition
9844

Originally Frege liked contextual definitions, but later preferred them fully explicit [Dummett]

9822

Nothing should be defined in terms of that to which it is conceptually prior [Dummett]

9845

We can't define a word by defining an expression containing it, as the remaining parts are a problem

2. Reason / D. Definition / 10. Stipulative Definition
11219

Frege suggested that mathematics should only accept stipulative definitions [Gupta]

2. Reason / D. Definition / 11. Ostensive Definition
10019

Only what is logically complex can be defined; what is simple must be pointed to

2. Reason / E. Argument / 6. Conclusive Proof
17495

Proof aims to remove doubts, but also to show the interdependence of truths

16878

We must be clear about every premise and every law used in a proof

2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes
8632

You can't transfer external properties unchanged to apply to ideas

3. Truth / A. Truth Problems / 2. Defining Truth
19466

The word 'true' seems to be unique and indefinable

3. Truth / A. Truth Problems / 5. Truth Bearers
8187

Frege was strongly in favour of taking truth to attach to propositions [Dummett]

3. Truth / B. Truthmakers / 5. What Makes Truths / c. States of affairs make truths
13881

We need to grasp not numberobjects, but the states of affairs which make number statements true [Wright,C]

3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
19465

There cannot be complete correspondence, because ideas and reality are quite different

3. Truth / H. Deflationary Truth / 1. Redundant Truth
19468

The property of truth in 'It is true that I smell violets' adds nothing to 'I smell violets'

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
18806

Frege thought traditional categories had psychological and linguistic impurities

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
9154

Frege agreed with Euclid that the axioms of logic and mathematics are known through selfevidence [Burge]

9585

Since every definition is an equation, one cannot define equality itself

4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC
4971

I don't use 'subject' and 'predicate' in my way of representing a judgement

4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀
17745

For Frege, 'All A's are B's' means that the concept A implies the concept B [Walicki]

4. Formal Logic / F. Set Theory ST / 1. Set Theory
13455

Frege did not think of himself as working with sets [Hart,WD]

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
9157

The null set is only defensible if it is the extension of an empty concept [Burge]

9835

It is because a concept can be empty that there is such a thing as the empty class [Dummett]

16895

The null set is indefensible, because it collects nothing [Burge]

14238

A class is an aggregate of objects; if you destroy them, you destroy the class; there is no empty class

4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
9854

We can introduce new objects, as equivalence classes of objects already known [Dummett]

9883

Frege introduced the standard device, of defining logical objects with equivalence classes [Dummett]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
18104

Frege, unlike Russell, has infinite individuals because numbers are individuals

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
9834

A class is, for Frege, the extension of a concept [Dummett]

3328

Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Benardete,JA]

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
7728

Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Weiner]

16881

The laws of logic are boundless, so we want the few whose power contains the others

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
7622

In 1879 Frege developed second order logic [Putnam]

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
9179

Frege frequently expressed a contempt for language [Dummett]

16867

Logic not only proves things, but also reveals logical relations between them

5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
16862

The closest subject to logic is mathematics, which does little apart from drawing inferences

16863

Does some mathematical reasoning (such as mathematical induction) not belong to logic?

5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
13473

Frege thinks there is an independent logical order of the truths, which we must try to discover [Hart,WD]

5. Theory of Logic / E. Structures of Logic / 1. Logical Form
7729

Frege replaced Aristotle's subject/predicate form with function/argument form [Weiner]

8645

Convert "Jupiter has four moons" into "the number of Jupiter's moons is four"

4975

A thought can be split in many ways, so that different parts appear as subject or predicate

5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
8490

Firstlevel functions have objects as arguments; secondlevel functions take functions as arguments

5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
8492

Relations are functions with two arguments

5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
3319

Frege gives a functional account of predication so that we can dispense with predicates [Benardete,JA]

6076

For Frege, predicates are names of functions that map objects onto the True and False [McGinn]

5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
16891

Despite Gödel, Frege's epistemic ordering of all the truths is still plausible [Burge]

16906

The primitive simples of arithmetic are the essence, determining the subject, and its boundaries [Jeshion]

16865

'Theorems' are both proved, and used in proofs

5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
18772

We can treat designation by a few words as a proper name

8447

In 'Etna is higher than Vesuvius' the whole of Etna, including all the lava, can't be the reference

5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
14075

Proper name in modal contexts refer obliquely, to their usual sense [Gibbard]

10424

A Fregean proper name has a sense determining an object, instead of a concept [Sainsbury]

18773

People may have different senses for 'Aristotle', like 'pupil of Plato' or 'teacher of Alexander'

8448

Any object can have many different names, each with a distinct sense

5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
4978

The meaning of a proper name is the designated object

5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
10510

Frege ascribes reference to incomplete expressions, as well as to singular terms [Hale]

5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
18940

It is a weakness of natural languages to contain nondenoting names

18939

In a logically perfect language every wellformed proper name designates an object

18937

If sentences have a 'sense', empty name sentences can be understood that way [Sawyer]

5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
13733

Frege considered definite descriptions to be genuine singular terms [Fitting/Mendelsohn]

5. Theory of Logic / G. Quantification / 1. Quantification
9950

A quantifier is a secondlevel predicate (which explains how it contributes to truthconditions) [George/Velleman]

5. Theory of Logic / G. Quantification / 2. Domain of Quantification
9991

For Frege the variable ranges over all objects [Tait]

10536

Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett]

9871

Frege always, and fatally, neglected the domain of quantification [Dummett]

5. Theory of Logic / G. Quantification / 3. Objectual Quantification
7730

Frege introduced quantifiers for generality [Weiner]

7742

Frege reduced most quantifiers to 'everything' combined with 'not' [McCullogh]

5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
9874

Contradiction arises from Frege's substitutional account of secondorder quantification [Dummett]

5. Theory of Logic / G. Quantification / 6. Plural Quantification
14236

Each horse doesn't fall under the concept 'horse that draws the carriage', because all four are needed [Oliver/Smiley]

5. Theory of Logic / H. Proof Systems / 1. Proof Systems
13824

Proof theory began with Frege's definition of derivability [Prawitz]

5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
13609

Frege produced axioms for logic, though that does not now seem the natural basis for logic [Kaplan]

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
16884

Basic truths of logic are not proved, but seen as true when they are understood [Burge]

5. Theory of Logic / I. Semantics of Logic / 6. Intensionalism
9462

Frege is intensionalist about reference, as it is determined by sense; identity of objects comes first [Jacquette]

18936

Frege moved from extensional to intensional semantics when he added the idea of 'sense' [Sawyer]

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17624

To understand axioms you must grasp their logical power and priority [Burge]

16886

The truth of an axiom must be independently recognisable

16866

Tracing inference backwards closes in on a small set of axioms and postulates

16868

The essence of mathematics is the kernel of primitive truths on which it rests

16871

A truth can be an axiom in one system and not in another

16870

Axioms are truths which cannot be doubted, and for which no proof is needed

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
16869

To create order in mathematics we need a full system, guided by patterns of inference

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
9886

Cardinals say how many, and reals give measurements compared to a unit quantity

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
18256

Quantity is inconceivable without the idea of addition

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
8640

We cannot define numbers from the idea of a series, because numbers must precede that

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
18252

Real numbers are ratios of quantities, such as lengths or masses

18253

I wish to go straight from cardinals to reals (as ratios), leaving out the rationals

9889

Real numbers are ratios of quantities [Dummett]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
9838

Treating 0 as a number avoids antinomies involving treating 'nobody' as a person [Dummett]

9564

For Frege 'concept' and 'extension' are primitive, but 'zero' and 'successor' are defined [Chihara]

10551

If objects exist because they fall under a concept, 0 is the object under which no objects fall [Dummett]

8653

Nought is the number belonging to the concept 'not identical with itself'

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
8636

We can say 'a and b are F' if F is 'wise', but not if it is 'one'

8654

One is the Number which belongs to the concept "identical with 0"

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
9989

Units can be equal without being identical [Tait]

17429

Frege says only concepts which isolate and avoid arbitrary division can give units [Koslicki]

8641

You can abstract concepts from the moon, but the number one is not among them

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
17426

A concept creating a unit must isolate and unify what falls under it

17428

Frege says counting is determining what number belongs to a given concept [Koslicki]

17427

Frege's 'isolation' could be absence of overlap, or drawing conceptual boundaries [Koslicki]

17437

Nonarbitrary division means that what falls under the concept cannot be divided into more of the same [Koslicki]

17438

Our concepts decide what is countable, as in seeing the leaves of the tree, or the foliage [Koslicki]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
15916

Frege's onetoone correspondence replaces wellordering, because infinities can't be counted [Lavine]

17446

Counting rests on oneone correspondence, of numerals to objects

9582

Husserl rests sameness of number on oneone correlation, forgetting the correlation with numbers themselves

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
10034

The number of natural numbers is not a natural number [George/Velleman]

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
18271

We can't prove everything, but we can spell out the unproved, so that foundations are clear

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
16883

Arithmetical statements can't be axioms, because they are provable [Burge]

16864

If principles are provable, they are theorems; if not, they are axioms

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17855

It may be possible to define induction in terms of the ancestral relation [Wright,C]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
10625

Frege had a motive to treat numbers as objects, but not a justification [Hale/Wright]

13871

Frege claims that numbers are objects, as opposed to them being Fregean concepts [Wright,C]

13872

Numbers are secondlevel, ascribing properties to concepts rather than to objects [Wright,C]

9816

For Frege, successor was a relation, not a function [Dummett]

9953

Numbers are more than just 'secondlevel concepts', since existence is also one [George/Velleman]

9954

"Number of x's such that ..x.." is a functional expression, yielding a name when completed [George/Velleman]

17636

A cardinal number may be defined as a class of similar classes [Russell]

17460

A statement of number contains a predication about a concept

10139

Frege gives an incoherent account of extensions resulting from abstraction [Fine,K]

10028

For Frege the number of F's is a collection of firstlevel concepts [George/Velleman]

10029

Numbers need to be objects, to define the extension of the concept of each successor to n [George/Velleman]

9856

Frege's account of cardinals fails in modern set theory, so they are now defined differently [Dummett]

9902

Frege's incorrect view is that a number is an equivalence class [Benacerraf]

17814

The natural number n is the set of nmembered sets [Yourgrau]

17819

A set doesn't have a fixed number, because the elements can be seen in different ways [Yourgrau]

17820

If you can subdivide objects many ways for counting, you can do that to setelements too [Yourgrau]

16890

Frege's problem is explaining the particularity of numbers by general laws [Burge]

8630

Individual numbers are best derived from the number one, and increase by one

11029

'Exactly ten gallons' may not mean ten things instantiate 'gallon' [Rumfitt]

10013

Numerical statements have firstorder logical form, so must refer to objects [Hodes]

18181

The Number for F is the extension of 'equal to F' (or maybe just F itself)

18103

Numbers are objects because they partake in identity statements [Bostock]

13897

Each number, except 0, is the number of the concept of all of its predecessors [Wright,C]

9973

The number of F's is the extension of the second level concept 'is equipollent with F' [Tait]

16500

Frege showed that numbers attach to concepts, not to objects [Wiggins]

9990

Frege replaced Cantor's sets as the objects of equinumerosity attributions with concepts [Tait]

7738

Zero is defined using 'is not selfidentical', and one by using the concept of zero [Weiner]

13887

Frege started with contextual definition, but then switched to explicit extensional definition [Wright,C]

3331

If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content [Benardete,JA]

9949

There is the concept, the object falling under it, and the extension (a set, which is also an object) [George/Velleman]

10623

Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Hale/Wright]

9975

Frege ignored Cantor's warning that a cardinal set is not just a conceptextension [Tait]

9586

In a numberstatement, something is predicated of a concept

10020

Frege's biggest error is in not accounting for the senses of number terms [Hodes]

10553

A number is a class of classes of the same cardinality [Dummett]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
9956

'The number of Fs' is the extension (a collection of firstlevel concepts) of the concept 'equinumerous with F' [George/Velleman]

13527

Frege's cardinals (equivalences of oneone correspondences) is not permissible in ZFC

17442

Frege thinks number is fundamentally bound up with oneone correspondence [Heck]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
11030

The words 'There are exactly Julius Caesar moons of Mars' are gibberish [Rumfitt]

10030

'Julius Caesar' isn't a number because numbers inherit properties of 0 and successor [George/Velleman]

8690

From within logic, how can we tell whether an arbitrary object like Julius Caesar is a number? [Friend]

10219

Frege said 2 is the extension of all pairs (so Julius Caesar isn't 2, because he's not an extension) [Shapiro]

13889

Fregean numbers are numbers, and not 'Caesar', because they correlate 11 [Wright,C]

18142

Oneone correlations imply normal arithmetic, but don't explain our concept of a number

9046

Our definition will not tell us whether or not Julius Caesar is a number

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
16896

If numbers can be derived from logic, then set theory is superfluous [Burge]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
8639

If numbers are supposed to be patterns, each number can have many patterns

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
13874

Numbers seem to be objects because they exactly fit the inference patterns for identities

13875

Frege's platonism proposes that objects are what singular terms refer to [Wright,C]

7731

How can numbers be external (one pair of boots is two boots), or subjective (and so relative)? [Weiner]

7737

Identities refer to objects, so numbers must be objects [Weiner]

8635

Numbers are not physical, and not ideas  they are objective and nonsensible

8652

Numbers are objects, because they can take the definite article, and can't be plurals

9580

Our concepts recognise existing relations, they don't change them

9589

Numbers are not real like the sea, but (crucially) they are still objective

6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
9831

Geometry appeals to intuition as the source of its axioms

17816

Frege's logicism aimed at removing the reliance of arithmetic on intuition [Yourgrau]

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
8633

There is no physical difference between two boots and one pair of boots

9577

The naďve view of number is that it is like a heap of things, or maybe a property of a heap

6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
9951

It appears that numbers are adjectives, but they don't apply to a single object [George/Velleman]

9952

Numerical adjectives are of the same secondlevel type as the existential quantifier [George/Velleman]

11031

'Jupiter has many moons' won't read as 'The number of Jupiter's moons equals the number many' [Rumfitt]

8637

The number 'one' can't be a property, if any object can be viewed as one or not one

9999

For science, we can translate adjectival numbers into noun form

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
9945

Logicism shows that no empirical truths are needed to justify arithmetic [George/Velleman]

7739

Arithmetic is analytic [Weiner]

8782

Frege offered a Platonist version of logicism, committed to cardinal and real numbers [Hale/Wright]

13608

Mathematics has no special axioms of its own, but follows from principles of logic (with definitions) [Bostock]

16905

Arithmetic must be based on logic, because of its total generality [Jeshion]

5658

Numbers are definable in terms of mapping items which fall under concepts [Scruton]

8655

Arithmetic is analytic and a priori, and thus it is part of logic

16880

Frege aimed to discover the logical foundations which justify arithmetical judgements [Burge]

8689

Eventually Frege tried to found arithmetic in geometry instead of in logic [Friend]

8487

Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism

18165

My Basic Law V is a law of pure logic

18166

The loss of my Rule V seems to make foundations for arithmetic impossible

6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10607

Frege's logic has a hierarchy of object, property, propertyofproperty etc. [Smith,P]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
10831

Frege only managed to prove that arithmetic was analytic with a logic that included settheory [Quine]

10010

Frege's belief in logicism and in numerical objects seem uncomfortable together [Hodes]

13864

Frege's platonism and logicism are in conflict, if logic must dictates an infinity of objects [Wright,C]

10033

Why should the existence of pure logic entail the existence of objects? [George/Velleman]

9545

Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Chihara]

6. Mathematics / C. Sources of Mathematics / 7. Formalism
9631

Formalism fails to recognise types of symbols, and also metagames [Brown,JR]

9887

Formalism misunderstands applications, metatheory, and infinity [Dummett]

8751

Only applicability raises arithmetic from a game to a science

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
9875

Frege was completing Bolzano's work, of expelling intuition from number theory and analysis

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
8642

Abstraction from things produces concepts, and numbers are in the concepts

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism
8621

Mental states are irrelevant to mathematics, because they are vague and fluctuating

7. Existence / A. Nature of Existence / 1. Nature of Existence
11008

Existence is not a firstorder property, but the instantiation of a property [Read]

8643

Affirmation of existence is just denial of zero

7. Existence / A. Nature of Existence / 2. Types of Existence
19470

Thoughts in the 'third realm' cannot be sensed, and do not need an owner to exist

7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
5657

Frege's logic showed that there is no concept of being [Scruton]

7. Existence / A. Nature of Existence / 5. Abstract Existence
8911

If abstracta are nonmental, quarks are abstracta, and yet chess and God's thoughts are mental [Rosen]

8634

The equator is imaginary, but not fictitious; thought is needed to recognise it

7. Existence / A. Nature of Existence / 7. Criterion for Existence
18899

Frege takes the existence of horses to be part of their concept

18995

Frege mistakenly takes existence to be a property of concepts, instead of being about things [Yablo]

7. Existence / C. Structure of Existence / 4. Ontological Dependence
17443

Many of us find Frege's claim that truths depend on one another an obscure idea [Heck]

17445

Parallelism is intuitive, so it is more fundamental than sameness of direction [Heck]

7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
10539

Frege refers to 'concrete' objects, but they are no different in principle from abstract ones [Dummett]

7. Existence / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
9578

If objects are just presentation, we get increasing abstraction by ignoring their properties

7. Existence / D. Theories of Reality / 7. Facts / c. Facts and truths
19471

A fact is a thought that is true

7. Existence / D. Theories of Reality / 9. Vagueness / d. Vagueness as semantic
17431

Vagueness is incomplete definition [Koslicki]

7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
13879

For Frege, ontological questions are to be settled by reference to syntactic structures [Wright,C]

7. Existence / D. Theories of Reality / 10. Ontological Commitment / c. Commitment of predicates
10642

Secondorder quantifiers are committed to concepts, as firstorder commits to objects [Linnebo]

8. Modes of Existence / A. Relations / 4. Formal Relations / c. Ancestral relation
10032

'Ancestral' relations are derived by iterating back from a given relation [George/Velleman]

8. Modes of Existence / B. Properties / 1. Nature of Properties
10606

Frege treats properties as a kind of function, and maybe a property is its characteristic function [Smith,P]

8. Modes of Existence / B. Properties / 10. Properties as Predicates
4028

Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver]

10317

It is unclear whether Frege included qualities among his abstract objects [Hale]

8. Modes of Existence / D. Universals / 1. Universals
10533

We can't get a semantics from nouns and predicates referring to the same thing [Dummett]

9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
8647

Not all objects are spatial; 4 can still be an object, despite lacking spatial coordinates

9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10309

Frege says singular terms denote objects, numerals are singular terms, so numbers exist [Hale]

10550

Frege establishes abstract objects independently from concrete ones, by falling under a concept [Dummett]

18269

Logical objects are extensions of concepts, or ranges of values of functions

9. Objects / A. Existence of Objects / 3. Objects in Thought
8785

For Frege, objects just are what singular terms refer to [Hale/Wright]

10278

Without concepts we would not have any objects [Shapiro]

8489

The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place

10535

Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Dummett]

9877

Late Frege saw his nonactual objective objects as exclusively thoughts and senses [Dummett]

9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
17432

Frege's universe comes already divided into objects [Koslicki]

9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9891

The first demand of logic is of a sharp boundary

9388

Every concept must have a sharp boundary; we cannot allow an indeterminate third case

9. Objects / F. Identity among Objects / 1. Concept of Identity
16022

The idea of a criterion of identity was introduced by Frege [Noonan]

11100

Frege's algorithm of identity is the law of putting equals for equals [Quine]

4893

Frege was asking how identities could be informative [Perry]

9. Objects / F. Identity among Objects / 3. Relative Identity
12153

Geach denies Frege's view, that 'being the same F' splits into being the same and being F [Perry]

9. Objects / F. Identity among Objects / 5. SelfIdentity
3318

Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x' [Benardete,JA]

9. Objects / F. Identity among Objects / 6. Identity between Objects
9853

Identity between objects is not a consequence of identity, but part of what 'identity' means [Dummett]

11. Knowledge Aims / A. Knowledge / 2. Understanding
17623

To understand a thought you must understand its logical structure [Burge]

16885

To understand a thought, understand its inferential connections to other thoughts [Burge]

12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
9158

For Frege a priori knowledge derives from general principles, so numbers can't be primitive

12. Knowledge Sources / A. A Priori Knowledge / 2. SelfEvidence
8657

Mathematicians just accept selfevidence, whether it is logical or intuitive

16887

Frege's concept of 'selfevident' makes no reference to minds [Burge]

12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
9352

An a priori truth is one derived from general laws which do not require proof

16889

A truth is a priori if it can be proved entirely from general unproven laws

16894

An apriori truth is grounded in generality, which is universal quantification [Burge]

12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
2514

Frege tried to explain synthetic a priori truths by expanding the concept of analyticity

12. Knowledge Sources / E. Direct Knowledge / 1. Intuition
16900

Intuitions cannot be communicated [Burge]

13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / d. Rational foundations
16903

Justifications show the ordering of truths, and the foundation is what is selfevident [Jeshion]

13. Knowledge Criteria / C. External Justification / 2. Causal Justification
11052

Psychological logic can't distinguish justification from causes of a belief

14. Science / B. Scientific Theories / 1. Scientific Theory
16882

The building blocks contain the whole contents of a discipline

14. Science / C. Induction / 1. Induction
8624

Induction is merely psychological, with a principle that it can actually establish laws

8626

In science one observation can create high probability, while a thousand might prove nothing

15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
8648

Ideas are not spatial, and don't have distances between them

18. Thought / A. Modes of Thought / 1. Thought
8620

Thought is the same everywhere, and the laws of thought do not vary

9581

Many people have the same thought, which is the component, not the private presentation

19469

We grasp thoughts (thinking), decide they are true (judgement), and manifest the judgement (assertion)

8162

Thoughts have their own realm of reality  'sense' (as opposed to the realm of 'reference') [Dummett]

9818

A thought is distinguished from other things by a capacity to be true or false [Dummett]

18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
18265

We don't judge by combining subject and concept; we get a concept by splitting up a judgement

18. Thought / A. Modes of Thought / 9. Indexical Thought
16379

Thoughts about myself are understood one way to me, and another when communicated

18. Thought / B. Mechanics of Thought / 5. Mental Files
16876

We need definitions to cram retrievable sense into a signed receptacle

16875

We use signs to mark receptacles for complex senses

18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
9870

Early Frege takes the extensions of concepts for granted [Dummett]

18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
13878

Concepts are, precisely, the references of predicates [Wright,C]

7736

A concept is a nonpsychological oneplace function asserting something of an object [Weiner]

17430

Fregean concepts have precise boundaries and universal applicability [Koslicki]

8622

Psychological accounts of concepts are subjective, and ultimately destroy truth

9947

Concepts are the ontological counterparts of predicative expressions [George/Velleman]

10319

An assertion about the concept 'horse' must indirectly speak of an object [Hale]

8488

A concept is a function whose value is always a truthvalue

18752

'The concept "horse"' denotes a concept, yet seems also to denote an object [McGee]

9839

Frege equated the concepts under which an object falls with its properties [Dummett]

9190

A concept is a function mapping objects onto truthvalues, if they fall under the concept [Dummett]

13665

Frege took the study of concepts to be part of logic [Shapiro]

18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
9948

Unlike objects, concepts are inherently incomplete [George/Velleman]

18. Thought / D. Concepts / 5. Concepts and Language / b. Concepts are linguistic
8651

A concept is a possible predicate of a singular judgement

4973

As I understand it, a concept is the meaning of a grammatical predicate

18. Thought / E. Abstraction / 1. Abstract Thought
9846

Defining 'direction' by parallelism doesn't tell you whether direction is a line [Dummett]

18. Thought / E. Abstraction / 2. Abstracta by Selection
9976

Frege accepts abstraction to the concept of all sets equipollent to a given one [Tait]

18. Thought / E. Abstraction / 3. Abstracta by Ignoring
9988

If we abstract 'from' two cats, the units are not black or white, or cats [Tait]

10803

Frege himself abstracts away from tone and color [Yablo]

9579

Disregarding properties of two cats still leaves different objects, but what is now the difference?

9587

How do you find the right level of inattention; you eliminate too many or too few characteristics

9890

The modern account of real numbers detaches a ratio from its geometrical origins

18. Thought / E. Abstraction / 7. Abstracta by Equivalence
9855

Frege's logical abstaction identifies a common feature as the maximal set of equivalent objects [Dummett]

10802

Frege's 'parallel' and 'direction' don't have the same content, as we grasp 'parallel' first [Yablo]

10526

Fregean abstraction creates concepts which are equivalences between initial items [Fine,K]

10525

Frege put the idea of abstraction on a rigorous footing [Fine,K]

10556

We create new abstract concepts by carving up the content in a different way

9881

From basing 'parallel' on identity of direction, Frege got all abstractions from identity statements [Dummett]

9882

You can't simultaneously fix the truthconditions of a sentence and the domain of its variables [Dummett]

18. Thought / E. Abstraction / 8. Abstractionism Critique
5816

Frege said concepts were abstract entities, not mental entities [Putnam]

9588

Numberabstraction somehow makes things identical without changing them!

11846

If we abstract the difference between two houses, they don't become the same house

19. Language / A. Nature of Meaning / 2. Meaning as Mental
9167

Frege felt that meanings must be public, so they are abstractions rather than mental entities [Putnam]

9583

Psychological logicians are concerned with sense of words, but mathematicians study the reference

9584

Identity baffles psychologists, since A and B must be presented differently to identify them

19. Language / A. Nature of Meaning / 4. Meaning as TruthConditions
7307

A thought is not psychological, but a condition of the world that makes a sentence true [Miller,A]

4980

The meaning (reference) of a sentence is its truth value  the circumstance of it being true or false

19. Language / A. Nature of Meaning / 6. Meaning as Use
16879

A sign won't gain sense just from being used in sentences with familiar components

19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
8646

Words in isolation seem to have ideas as meanings, but words have meaning in propositions

7732

Never ask for the meaning of a word in isolation, but only in the context of a proposition

8446

We understand new propositions by constructing their sense from the words

19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
9180

Holism says all language use is also a change in the rules of language

19. Language / B. Reference / 1. Reference theories
4981

The reference of a word should be understood as part of the reference of the sentence

19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
18778

Every descriptive name has a sense, but may not have a reference

15597

Frege's Puzzle: from different semantics we infer different reference for two names with the same reference [Fine,K]

17002

Frege's 'sense' is ambiguous, between the meaning of a designator, and how it fixes reference

7805

Frege started as antirealist, but the sense/reference distinction led him to realism [Benardete,JA]

4976

The meaning (reference) of 'evening star' is the same as that of 'morning star', but not the sense

4977

In maths, there are phrases with a clear sense, but no actual reference

4979

We are driven from sense to reference by our desire for truth

8449

Senses can't be subjective, because propositions would be private, and disagreement impossible

19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
15155

Expressions always give ways of thinking of referents, rather than the referents themselves [Soames]

19. Language / B. Reference / 5. Speaker's Reference
4972

I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false

19. Language / C. Assigning Meanings / 5. Fregean Semantics
7309

Frege's 'sense' is the strict and literal meaning, stripped of tone [Miller,A]

7312

'Sense' solves the problems of bearerless names, substitution in beliefs, and informativeness [Miller,A]

11126

'Sense' gives meaning to nonreferring names, and to two expressions for one referent [Margolis/Laurence]

8164

Frege was the first to construct a plausible theory of meaning [Dummett]

9817

Earlier Frege focuses on content itself; later he became interested in understanding content [Dummett]

8171

Frege divided the meaning of a sentence into sense, force and tone [Dummett]

4954

Frege uses 'sense' to mean both a designator's meaning, and the way its reference is determined [Kripke]

7304

Frege explained meaning as sense, semantic value, reference, force and tone [Miller,A]

19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
4974

For all the multiplicity of languages, mankind has a common stock of thoughts

16873

Thoughts are not subjective or psychological, because some thoughts are the same for us all

16872

A thought is the sense expressed by a sentence, and is what we prove

19467

A 'thought' is something for which the question of truth can arise; thoughts are senses of sentences

19. Language / D. Propositions / 5. Unity of Propositions
16874

The parts of a thought map onto the parts of a sentence

19472

A sentence is only a thought if it is complete, and has a timespecification

19. Language / E. Analyticity / 1. Analytic Propositions
9370

A statement is analytic if substitution of synonyms can make it a logical truth [Boghossian]

8743

Frege considered analyticity to be an epistemic concept [Shapiro]

7725

'P or notp' seems to be analytic, but does not fit Kant's account, lacking clear subject or predicate [Weiner]

19. Language / E. Analyticity / 2. Analytic Truths
20295

All analytic truths can become logical truths, by substituting definitions or synonyms [Rey]

7316

Analytic truths are those that can be demonstrated using only logic and definitions [Miller,A]

19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
2515

Frege fails to give a concept of analyticity, so he fails to explain synthetic a priori truth that way [Katz]

25. Society / E. State Functions / 4. Education / a. Education principles
8619

To learn something, you must know that you don't know

26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
8656

The laws of number are not laws of nature, but are laws of the laws of nature

28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
3307

Frege put forward an ontological argument for the existence of numbers [Benardete,JA]

28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
7741

The predicate 'exists' is actually a natural language expression for a quantifier [Weiner]

8644

Because existence is a property of concepts the ontological argument for God fails

8491

The Ontological Argument fallaciously treats existence as a firstlevel concept
