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 non-linguistic questions [Dummett]
9840 Frege initiated linguistic philosophy, studying number through the sense of sentences [Dummett]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
22270 Frege changed philosophy by extending logic's ability to check the grounds of thinking [Potter]
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 non-spatio-temporal 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 / A. Truth Problems / 6. Verisimilitude
22317 Truth does not admit of more and less
3. Truth / B. Truthmakers / 5. What Makes Truths / c. States of affairs make truths
13881 We need to grasp not number-objects, 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 [Rumfitt]
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 self-evidence [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 [Bostock]
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
16863 Does some mathematical reasoning (such as mathematical induction) not belong to logic?
16862 The closest subject to logic is mathematics, which does little apart from drawing inferences
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 First-level functions have objects as arguments; second-level 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
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'
14075 Proper name in modal contexts refer obliquely, to their usual sense [Gibbard]
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
18937 If sentences have a 'sense', empty name sentences can be understood that way [Sawyer]
18940 It is a weakness of natural languages to contain non-denoting names
18939 In a logically perfect language every well-formed proper name designates an object
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 second-level predicate (which explains how it contributes to truth-conditions) [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 second-order 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 / J. Model Theory in Logic / 1. Logical Models
22294 We can show that a concept is consistent by producing something which falls under it
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
16870 Axioms are truths which cannot be doubted, and for which no proof is needed
16871 A truth can be an axiom in one system and not in another
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
8654 One is the Number which belongs to the concept "identical with 0"
8636 We can say 'a and b are F' if F is 'wise', but not if it is 'one'
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
8641 You can abstract concepts from the moon, but the number one is not among them
9989 Units can be equal without being identical [Tait]
17429 Frege says only concepts which isolate and avoid arbitrary division can give units [Koslicki]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
17427 Frege's 'isolation' could be absence of overlap, or drawing conceptual boundaries [Koslicki]
17437 Non-arbitrary 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]
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]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
15916 Frege's one-to-one correspondence replaces well-ordering, because infinities can't be counted [Lavine]
17446 Counting rests on one-one correspondence, of numerals to objects
9582 Husserl rests sameness of number on one-one 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 second-level, 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 'second-level 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]
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 first-level concepts [George/Velleman]
10029 Numbers need to be objects, to define the extension of the concept of each successor to n [George/Velleman]
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 self-identical', and one by using the concept of zero [Weiner]
23456 Frege said logical predication implies classes, which are arithmetical objects [Morris,M]
13887 Frege started with contextual definition, but then switched to explicit extensional definition [Wright,C]
13897 Each number, except 0, is the number of the concept of all of its predecessors [Wright,C]
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 n-membered sets [Yourgrau]
17819 A set doesn't have a fixed number, because the elements can be seen in different ways [Yourgrau]
17460 A statement of number contains a predication about a concept
17820 If you can subdivide objects many ways for counting, you can do that to set-elements 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 first-order 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]
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 concept-extension [Tait]
9586 In a number-statement, 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 first-level concepts) of the concept 'equinumerous with F' [George/Velleman]
13527 Frege's cardinals (equivalences of one-one correspondences) is not permissible in ZFC [Wolf,RS]
22292 Hume's Principle fails to implicitly define numbers, because of the Julius Caesar [Potter]
17442 Frege thinks number is fundamentally bound up with one-one 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 1-1 [Wright,C]
18142 One-one correlations imply normal arithmetic, but don't explain our concept of a number [Bostock]
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 non-sensible
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
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
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 second-level type as the existential quantifier [George/Velleman]
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]
16905 Arithmetic must be based on logic, because of its total generality [Jeshion]
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]
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
7739 Arithmetic is analytic [Weiner]
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, property-of-property 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 set-theory [Quine]
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]
10010 Frege's belief in logicism and in numerical objects seem uncomfortable together [Hodes]
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 meta-games [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 [Dummett]
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 first-order 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 / 4. Abstract Existence
8911 If abstracta are non-mental, 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 / 6. Criterion for Existence
18899 Frege takes the existence of horses to be part of their concept [Sommers]
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 / 8. Facts / c. Facts and truths
19471 A fact is a thought that is true
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
17431 Vagueness is incomplete definition [Koslicki]
7. Existence / D. Theories of Reality / 11. 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 / 11. Ontological Commitment / c. Commitment of predicates
10642 Second-order quantifiers are committed to concepts, as first-order 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 co-ordinates
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 non-actual 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. Self-Identity
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. Self-Evidence
8657 Mathematicians just accept self-evidence, whether it is logical or intuitive
16887 Frege's concept of 'self-evident' 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 [Katz]
12. Knowledge Sources / E. Direct Knowledge / 2. 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 self-evident [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 non-psychological one-place 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 truth-value
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 truth-values, 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
9882 You can't simultaneously fix the truth-conditions of a sentence and the domain of its variables [Dummett]
9881 From basing 'parallel' on identity of direction, Frege got all abstractions from identity statements [Dummett]
18. Thought / E. Abstraction / 8. Abstractionism Critique
5816 Frege said concepts were abstract entities, not mental entities [Putnam]
9588 Number-abstraction 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 Truth-Conditions
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
22318 Frege failed to show when two sets of truth-conditions are equivalent [Potter]
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 [Dummett]
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
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 [Kripke]
18778 Every descriptive name has a sense, but may not have a reference
7805 Frege started as anti-realist, 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 / 4. Compositionality
22280 Frege's account was top-down and decompositional, not bottom-up and compositional [Potter]
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 non-referring 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 time-specification
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 not-p' 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. Social Practice / E. Policies / 5. Education / b. 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]
22286 Existence is not a first-level concept (of God), but a second-level property of concepts [Potter]
8644 Because existence is a property of concepts the ontological argument for God fails
8491 The Ontological Argument fallaciously treats existence as a first-level concept