276 ideas
| 13876 | The syntactic category is primary, and the ontological category is derivative [Frege, by Wright,C] |
| 14122 | Analysis gives us nothing but the truth - but never the whole truth [Russell] |
| 8415 | Never lose sight of the distinction between concept and object [Frege] |
| 14109 | The study of grammar is underestimated in philosophy [Russell] |
| 9841 | Frege was the first to give linguistic answers to non-linguistic questions [Frege, by Dummett] |
| 9840 | Frege initiated linguistic philosophy, studying number through the sense of sentences [Frege, by Dummett] |
| 15948 | Frege developed formal systems to avoid unnoticed assumptions [Frege, by Lavine] |
| 14165 | Analysis falsifies, if when the parts are broken down they are not equivalent to their sum [Russell] |
| 10804 | Thoughts have a natural order, to which human thinking is drawn [Frege, by Yablo] |
| 9832 | Frege sees no 'intersubjective' category, between objective and subjective [Dummett on Frege] |
| 8414 | Keep the psychological and subjective separate from the logical and objective [Frege] |
| 9844 | Originally Frege liked contextual definitions, but later preferred them fully explicit [Frege, by Dummett] |
| 9822 | Nothing should be defined in terms of that to which it is conceptually prior [Frege, by Dummett] |
| 14115 | Definition by analysis into constituents is useless, because it neglects the whole [Russell] |
| 14159 | In mathematics definitions are superfluous, as they name classes, and it all reduces to primitives [Russell] |
| 17495 | Proof aims to remove doubts, but also to show the interdependence of truths [Frege] |
| 14148 | Infinite regresses have propositions made of propositions etc, with the key term reappearing [Russell] |
| 8632 | You can't transfer external properties unchanged to apply to ideas [Frege] |
| 18002 | As well as a truth value, propositions have a range of significance for their variables [Russell] |
| 14102 | What is true or false is not mental, and is best called 'propositions' [Russell] |
| 13881 | We need to grasp not number-objects, but the states of affairs which make number statements true [Frege, by Wright,C] |
| 10017 | Truth in a model is more tractable than the general notion of truth [Hodes] |
| 10018 | Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes] |
| 14176 | "The death of Caesar is true" is not the same proposition as "Caesar died" [Russell] |
| 9154 | Frege agreed with Euclid that the axioms of logic and mathematics are known through self-evidence [Frege, by Burge] |
| 9157 | The null set is only defensible if it is the extension of an empty concept [Frege, by Burge] |
| 9835 | It is because a concept can be empty that there is such a thing as the empty class [Frege, by Dummett] |
| 14113 | The null class is a fiction [Russell] |
| 9854 | We can introduce new objects, as equivalence classes of objects already known [Frege, by Dummett] |
| 9883 | Frege introduced the standard device, of defining logical objects with equivalence classes [Frege, by Dummett] |
| 18104 | Frege, unlike Russell, has infinite individuals because numbers are individuals [Frege, by Bostock] |
| 9834 | A class is, for Frege, the extension of a concept [Frege, by Dummett] |
| 15894 | Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine] |
| 14126 | Order rests on 'between' and 'separation' [Russell] |
| 14127 | Order depends on transitive asymmetrical relations [Russell] |
| 14121 | The part-whole relation is ultimate and indefinable [Russell] |
| 10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
| 14106 | Implication cannot be defined [Russell] |
| 14108 | It would be circular to use 'if' and 'then' to define material implication [Russell] |
| 14167 | The only classes are things, predicates and relations [Russell] |
| 10011 | Identity is a level one relation with a second-order definition [Hodes] |
| 8645 | Convert "Jupiter has four moons" into "the number of Jupiter's moons is four" [Frege] |
| 14105 | There seem to be eight or nine logical constants [Russell] |
| 18722 | Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell] |
| 14104 | Constants are absolutely definite and unambiguous [Russell] |
| 14114 | Variables don't stand alone, but exist as parts of propositional functions [Russell] |
| 16891 | Despite Gödel, Frege's epistemic ordering of all the truths is still plausible [Frege, by Burge] |
| 16906 | The primitive simples of arithmetic are the essence, determining the subject, and its boundaries [Frege, by Jeshion] |
| 14137 | 'Any' is better than 'all' where infinite classes are concerned [Russell] |
| 14236 | Each horse doesn't fall under the concept 'horse that draws the carriage', because all four are needed [Oliver/Smiley on Frege] |
| 10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
| 22294 | We can show that a concept is consistent by producing something which falls under it [Frege] |
| 17624 | To understand axioms you must grasp their logical power and priority [Frege, by Burge] |
| 14149 | The Achilles Paradox concerns the one-one correlation of infinite classes [Russell] |
| 15895 | Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine] |
| 14152 | In geometry, Kant and idealists aimed at the certainty of the premisses [Russell] |
| 14154 | Geometry throws no light on the nature of actual space [Russell] |
| 14151 | Pure geometry is deductive, and neutral over what exists [Russell] |
| 14153 | In geometry, empiricists aimed at premisses consistent with experience [Russell] |
| 14155 | Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective) [Russell, by PG] |
| 10027 | Mathematics is higher-order modal logic [Hodes] |
| 18254 | Russell's approach had to treat real 5/8 as different from rational 5/8 [Russell, by Dummett] |
| 14144 | Ordinals result from likeness among relations, as cardinals from similarity among classes [Russell] |
| 14128 | Some claim priority for the ordinals over cardinals, but there is no logical priority between them [Russell] |
| 14129 | Ordinals presuppose two relations, where cardinals only presuppose one [Russell] |
| 14132 | Properties of numbers don't rely on progressions, so cardinals may be more basic [Russell] |
| 8640 | We cannot define numbers from the idea of a series, because numbers must precede that [Frege] |
| 14141 | Ordinals are defined through mathematical induction [Russell] |
| 14142 | Ordinals are types of series of terms in a row, rather than the 'nth' instance [Russell] |
| 14139 | Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic [Russell] |
| 14145 | For Cantor ordinals are types of order, not numbers [Russell] |
| 14146 | We aren't sure if one cardinal number is always bigger than another [Russell] |
| 14135 | Real numbers are a class of rational numbers (and so not really numbers at all) [Russell] |
| 9838 | Treating 0 as a number avoids antinomies involving treating 'nobody' as a person [Frege, by Dummett] |
| 9564 | For Frege 'concept' and 'extension' are primitive, but 'zero' and 'successor' are defined [Frege, by Chihara] |
| 10551 | If objects exist because they fall under a concept, 0 is the object under which no objects fall [Frege, by Dummett] |
| 8653 | Nought is the number belonging to the concept 'not identical with itself' [Frege] |
| 8636 | We can say 'a and b are F' if F is 'wise', but not if it is 'one' [Frege] |
| 8654 | One is the Number which belongs to the concept "identical with 0" [Frege] |
| 8641 | You can abstract concepts from the moon, but the number one is not among them [Frege] |
| 9989 | Units can be equal without being identical [Tait on Frege] |
| 17429 | Frege says only concepts which isolate and avoid arbitrary division can give units [Frege, by Koslicki] |
| 14123 | Some quantities can't be measured, and some non-quantities are measurable [Russell] |
| 14158 | Quantity is not part of mathematics, where it is replaced by order [Russell] |
| 14120 | Counting explains none of the real problems about the foundations of arithmetic [Russell] |
| 17427 | Frege's 'isolation' could be absence of overlap, or drawing conceptual boundaries [Frege, by Koslicki] |
| 17437 | Non-arbitrary division means that what falls under the concept cannot be divided into more of the same [Frege, by Koslicki] |
| 17438 | Our concepts decide what is countable, as in seeing the leaves of the tree, or the foliage [Frege, by Koslicki] |
| 17426 | A concept creating a unit must isolate and unify what falls under it [Frege] |
| 17428 | Frege says counting is determining what number belongs to a given concept [Frege, by Koslicki] |
| 14118 | We can define one-to-one without mentioning unity [Russell] |
| 15916 | Frege's one-to-one correspondence replaces well-ordering, because infinities can't be counted [Frege, by Lavine] |
| 10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
| 14119 | We do not currently know whether, of two infinite numbers, one must be greater than the other [Russell] |
| 14133 | There are cardinal and ordinal theories of infinity (while continuity is entirely ordinal) [Russell] |
| 14134 | Infinite numbers are distinguished by disobeying induction, and the part equalling the whole [Russell] |
| 10034 | The number of natural numbers is not a natural number [Frege, by George/Velleman] |
| 14143 | ω names the whole series, or the generating relation of the series of ordinal numbers [Russell] |
| 14138 | You can't get a new transfinite cardinal from an old one just by adding finite numbers to it [Russell] |
| 14140 | For every transfinite cardinal there is an infinite collection of transfinite ordinals [Russell] |
| 14124 | Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater [Russell] |
| 16883 | Arithmetical statements can't be axioms, because they are provable [Frege, by Burge] |
| 7530 | Russell tried to replace Peano's Postulates with the simple idea of 'class' [Russell, by Monk] |
| 18246 | Dedekind failed to distinguish the numbers from other progressions [Shapiro on Russell] |
| 14147 | Denying mathematical induction gave us the transfinite [Russell] |
| 14125 | Finite numbers, unlike infinite numbers, obey mathematical induction [Russell] |
| 14116 | Numbers were once defined on the basis of 1, but neglected infinities and + [Russell] |
| 13871 | Frege claims that numbers are objects, as opposed to them being Fregean concepts [Frege, by Wright,C] |
| 13872 | Numbers are second-level, ascribing properties to concepts rather than to objects [Frege, by Wright,C] |
| 9816 | For Frege, successor was a relation, not a function [Frege, by Dummett] |
| 9953 | Numbers are more than just 'second-level concepts', since existence is also one [Frege, by George/Velleman] |
| 9954 | "Number of x's such that ..x.." is a functional expression, yielding a name when completed [Frege, by George/Velleman] |
| 10139 | Frege gives an incoherent account of extensions resulting from abstraction [Fine,K on Frege] |
| 10028 | For Frege the number of F's is a collection of first-level concepts [Frege, by George/Velleman] |
| 17636 | A cardinal number may be defined as a class of similar classes [Frege, by Russell] |
| 10029 | Numbers need to be objects, to define the extension of the concept of each successor to n [Frege, by George/Velleman] |
| 9973 | The number of F's is the extension of the second level concept 'is equipollent with F' [Frege, by Tait] |
| 16500 | Frege showed that numbers attach to concepts, not to objects [Frege, by Wiggins] |
| 9990 | Frege replaced Cantor's sets as the objects of equinumerosity attributions with concepts [Frege, by Tait] |
| 7738 | Zero is defined using 'is not self-identical', and one by using the concept of zero [Frege, by Weiner] |
| 23456 | Frege said logical predication implies classes, which are arithmetical objects [Frege, by Morris,M] |
| 13887 | Frege started with contextual definition, but then switched to explicit extensional definition [Frege, by Wright,C] |
| 13897 | Each number, except 0, is the number of the concept of all of its predecessors [Frege, by Wright,C] |
| 9856 | Frege's account of cardinals fails in modern set theory, so they are now defined differently [Dummett on Frege] |
| 9902 | Frege's incorrect view is that a number is an equivalence class [Benacerraf on Frege] |
| 14117 | Numbers are properties of classes [Russell] |
| 17814 | The natural number n is the set of n-membered sets [Frege, by Yourgrau] |
| 17819 | A set doesn't have a fixed number, because the elements can be seen in different ways [Yourgrau on Frege] |
| 17820 | If you can subdivide objects many ways for counting, you can do that to set-elements too [Yourgrau on Frege] |
| 17460 | A statement of number contains a predication about a concept [Frege] |
| 16890 | Frege's problem is explaining the particularity of numbers by general laws [Frege, by Burge] |
| 8630 | Individual numbers are best derived from the number one, and increase by one [Frege] |
| 11029 | 'Exactly ten gallons' may not mean ten things instantiate 'gallon' [Rumfitt on Frege] |
| 10013 | Numerical statements have first-order logical form, so must refer to objects [Frege, by Hodes] |
| 18181 | The Number for F is the extension of 'equal to F' (or maybe just F itself) [Frege] |
| 18103 | Numbers are objects because they partake in identity statements [Frege, by Bostock] |
| 10625 | Frege had a motive to treat numbers as objects, but not a justification [Hale/Wright on Frege] |
| 9956 | 'The number of Fs' is the extension (a collection of first-level concepts) of the concept 'equinumerous with F' [Frege, by George/Velleman] |
| 13527 | Frege's cardinals (equivalences of one-one correspondences) is not permissible in ZFC [Frege, by Wolf,RS] |
| 22292 | Hume's Principle fails to implicitly define numbers, because of the Julius Caesar [Frege, by Potter] |
| 17442 | Frege thinks number is fundamentally bound up with one-one correspondence [Frege, by Heck] |
| 11030 | The words 'There are exactly Julius Caesar moons of Mars' are gibberish [Rumfitt on Frege] |
| 10030 | 'Julius Caesar' isn't a number because numbers inherit properties of 0 and successor [Frege, by George/Velleman] |
| 8690 | From within logic, how can we tell whether an arbitrary object like Julius Caesar is a number? [Frege, by Friend] |
| 10219 | Frege said 2 is the extension of all pairs (so Julius Caesar isn't 2, because he's not an extension) [Frege, by Shapiro] |
| 13889 | Fregean numbers are numbers, and not 'Caesar', because they correlate 1-1 [Frege, by Wright,C] |
| 18142 | One-one correlations imply normal arithmetic, but don't explain our concept of a number [Frege, by Bostock] |
| 9046 | Our definition will not tell us whether or not Julius Caesar is a number [Frege] |
| 16896 | If numbers can be derived from logic, then set theory is superfluous [Frege, by Burge] |
| 8639 | If numbers are supposed to be patterns, each number can have many patterns [Frege] |
| 9977 | Ordinals can't be defined just by progression; they have intrinsic qualities [Russell] |
| 13874 | Numbers seem to be objects because they exactly fit the inference patterns for identities [Frege] |
| 13875 | Frege's platonism proposes that objects are what singular terms refer to [Frege, by Wright,C] |
| 7731 | How can numbers be external (one pair of boots is two boots), or subjective (and so relative)? [Frege, by Weiner] |
| 7737 | Identities refer to objects, so numbers must be objects [Frege, by Weiner] |
| 8635 | Numbers are not physical, and not ideas - they are objective and non-sensible [Frege] |
| 8652 | Numbers are objects, because they can take the definite article, and can't be plurals [Frege] |
| 10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes] |
| 10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes] |
| 14162 | Mathematics doesn't care whether its entities exist [Russell] |
| 17816 | Frege's logicism aimed at removing the reliance of arithmetic on intuition [Frege, by Yourgrau] |
| 8633 | There is no physical difference between two boots and one pair of boots [Frege] |
| 9951 | It appears that numbers are adjectives, but they don't apply to a single object [Frege, by George/Velleman] |
| 9952 | Numerical adjectives are of the same second-level type as the existential quantifier [Frege, by George/Velleman] |
| 11031 | 'Jupiter has many moons' won't read as 'The number of Jupiter's moons equals the number many' [Rumfitt on Frege] |
| 8637 | The number 'one' can't be a property, if any object can be viewed as one or not one [Frege] |
| 9999 | For science, we can translate adjectival numbers into noun form [Frege] |
| 7739 | Arithmetic is analytic [Frege, by Weiner] |
| 9945 | Logicism shows that no empirical truths are needed to justify arithmetic [Frege, by George/Velleman] |
| 8782 | Frege offered a Platonist version of logicism, committed to cardinal and real numbers [Frege, by Hale/Wright] |
| 13608 | Mathematics has no special axioms of its own, but follows from principles of logic (with definitions) [Frege, by Bostock] |
| 16905 | Arithmetic must be based on logic, because of its total generality [Frege, by Jeshion] |
| 5658 | Numbers are definable in terms of mapping items which fall under concepts [Frege, by Scruton] |
| 8655 | Arithmetic is analytic and a priori, and thus it is part of logic [Frege] |
| 14103 | Pure mathematics is the class of propositions of the form 'p implies q' [Russell] |
| 21555 | For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x [Russell] |
| 18003 | In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless [Russell, by Magidor] |
| 10831 | Frege only managed to prove that arithmetic was analytic with a logic that included set-theory [Quine on Frege] |
| 13864 | Frege's platonism and logicism are in conflict, if logic must dictates an infinity of objects [Wright,C on Frege] |
| 10033 | Why should the existence of pure logic entail the existence of objects? [George/Velleman on Frege] |
| 10010 | Frege's belief in logicism and in numerical objects seem uncomfortable together [Hodes on Frege] |
| 9631 | Formalism fails to recognise types of symbols, and also meta-games [Frege, by Brown,JR] |
| 9875 | Frege was completing Bolzano's work, of expelling intuition from number theory and analysis [Frege, by Dummett] |
| 8642 | Abstraction from things produces concepts, and numbers are in the concepts [Frege] |
| 8621 | Mental states are irrelevant to mathematics, because they are vague and fluctuating [Frege] |
| 8643 | Affirmation of existence is just denial of zero [Frege] |
| 11010 | Being is what belongs to every possible object of thought [Russell] |
| 14161 | Many things have being (as topics of propositions), but may not have actual existence [Russell] |
| 8911 | If abstracta are non-mental, quarks are abstracta, and yet chess and God's thoughts are mental [Rosen on Frege] |
| 8634 | The equator is imaginary, but not fictitious; thought is needed to recognise it [Frege] |
| 14173 | What exists has causal relations, but non-existent things may also have them [Russell] |
| 17443 | Many of us find Frege's claim that truths depend on one another an obscure idea [Heck on Frege] |
| 17445 | Parallelism is intuitive, so it is more fundamental than sameness of direction [Frege, by Heck] |
| 10539 | Frege refers to 'concrete' objects, but they are no different in principle from abstract ones [Frege, by Dummett] |
| 10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
| 17431 | Vagueness is incomplete definition [Frege, by Koslicki] |
| 13879 | For Frege, ontological questions are to be settled by reference to syntactic structures [Frege, by Wright,C] |
| 10642 | Second-order quantifiers are committed to concepts, as first-order commits to objects [Frege, by Linnebo] |
| 14163 | Four classes of terms: instants, points, terms at instants only, and terms at instants and points [Russell] |
| 21341 | Philosophers of logic and maths insisted that a vocabulary of relations was essential [Russell, by Heil] |
| 10586 | 'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness [Russell] |
| 10585 | Symmetrical and transitive relations are formally like equality [Russell] |
| 10032 | 'Ancestral' relations are derived by iterating back from a given relation [Frege, by George/Velleman] |
| 10606 | Frege treats properties as a kind of function, and maybe a property is its characteristic function [Frege, by Smith,P] |
| 8647 | Not all objects are spatial; 4 can still be an object, despite lacking spatial co-ordinates [Frege] |
| 10309 | Frege says singular terms denote objects, numerals are singular terms, so numbers exist [Frege, by Hale] |
| 10550 | Frege establishes abstract objects independently from concrete ones, by falling under a concept [Frege, by Dummett] |
| 8785 | For Frege, objects just are what singular terms refer to [Frege, by Hale/Wright] |
| 10278 | Without concepts we would not have any objects [Frege, by Shapiro] |
| 7781 | I call an object of thought a 'term'. This is a wide concept implying unity and existence. [Russell] |
| 14166 | Unities are only in propositions or concepts, and nothing that exists has unity [Russell] |
| 17432 | Frege's universe comes already divided into objects [Frege, by Koslicki] |
| 14164 | The only unities are simples, or wholes composed of parts [Russell] |
| 14112 | A set has some sort of unity, but not enough to be a 'whole' [Russell] |
| 14170 | Change is obscured by substance, a thing's nature, subject-predicate form, and by essences [Russell] |
| 16022 | The idea of a criterion of identity was introduced by Frege [Frege, by Noonan] |
| 11100 | Frege's algorithm of identity is the law of putting equals for equals [Frege, by Quine] |
| 12153 | Geach denies Frege's view, that 'being the same F' splits into being the same and being F [Perry on Frege] |
| 9853 | Identity between objects is not a consequence of identity, but part of what 'identity' means [Frege, by Dummett] |
| 14107 | Terms are identical if they belong to all the same classes [Russell] |
| 11849 | It at least makes sense to say two objects have all their properties in common [Wittgenstein on Russell] |
| 22303 | It makes no sense to say that a true proposition could have been false [Russell] |
| 17623 | To understand a thought you must understand its logical structure [Frege, by Burge] |
| 9158 | For Frege a priori knowledge derives from general principles, so numbers can't be primitive [Frege] |
| 8657 | Mathematicians just accept self-evidence, whether it is logical or intuitive [Frege] |
| 9352 | An a priori truth is one derived from general laws which do not require proof [Frege] |
| 16889 | A truth is a priori if it can be proved entirely from general unproven laws [Frege] |
| 2514 | Frege tried to explain synthetic a priori truths by expanding the concept of analyticity [Frege, by Katz] |
| 16900 | Intuitions cannot be communicated [Frege, by Burge] |
| 16903 | Justifications show the ordering of truths, and the foundation is what is self-evident [Frege, by Jeshion] |
| 8624 | Induction is merely psychological, with a principle that it can actually establish laws [Frege] |
| 8626 | In science one observation can create high probability, while a thousand might prove nothing [Frege] |
| 8648 | Ideas are not spatial, and don't have distances between them [Frege] |
| 8620 | Thought is the same everywhere, and the laws of thought do not vary [Frege] |
| 9870 | Early Frege takes the extensions of concepts for granted [Frege, by Dummett] |
| 13878 | Concepts are, precisely, the references of predicates [Frege, by Wright,C] |
| 7736 | A concept is a non-psychological one-place function asserting something of an object [Frege, by Weiner] |
| 17430 | Fregean concepts have precise boundaries and universal applicability [Frege, by Koslicki] |
| 8622 | Psychological accounts of concepts are subjective, and ultimately destroy truth [Frege] |
| 8651 | A concept is a possible predicate of a singular judgement [Frege] |
| 9846 | Defining 'direction' by parallelism doesn't tell you whether direction is a line [Dummett on Frege] |
| 9976 | Frege accepts abstraction to the concept of all sets equipollent to a given one [Tait on Frege] |
| 10803 | Frege himself abstracts away from tone and color [Yablo on Frege] |
| 9988 | If we abstract 'from' two cats, the units are not black or white, or cats [Tait on Frege] |
| 9855 | Frege's logical abstaction identifies a common feature as the maximal set of equivalent objects [Frege, by Dummett] |
| 10802 | Frege's 'parallel' and 'direction' don't have the same content, as we grasp 'parallel' first [Yablo on Frege] |
| 10525 | Frege put the idea of abstraction on a rigorous footing [Frege, by Fine,K] |
| 10526 | Fregean abstraction creates concepts which are equivalences between initial items [Frege, by Fine,K] |
| 10556 | We create new abstract concepts by carving up the content in a different way [Frege] |
| 9882 | You can't simultaneously fix the truth-conditions of a sentence and the domain of its variables [Dummett on Frege] |
| 9881 | From basing 'parallel' on identity of direction, Frege got all abstractions from identity statements [Frege, by Dummett] |
| 10583 | Abstraction principles identify a common property, which is some third term with the right relation [Russell] |
| 10582 | The principle of Abstraction says a symmetrical, transitive relation analyses into an identity [Russell] |
| 10584 | A certain type of property occurs if and only if there is an equivalence relation [Russell] |
| 8646 | Words in isolation seem to have ideas as meanings, but words have meaning in propositions [Frege] |
| 7732 | Never ask for the meaning of a word in isolation, but only in the context of a proposition [Frege] |
| 14110 | Proposition contain entities indicated by words, rather than the words themselves [Russell] |
| 19164 | If propositions are facts, then false and true propositions are indistinguishable [Davidson on Russell] |
| 14111 | A proposition is a unity, and analysis destroys it [Russell] |
| 19157 | Russell said the proposition must explain its own unity - or else objective truth is impossible [Russell, by Davidson] |
| 9370 | A statement is analytic if substitution of synonyms can make it a logical truth [Frege, by Boghossian] |
| 8743 | Frege considered analyticity to be an epistemic concept [Frege, by Shapiro] |
| 20295 | All analytic truths can become logical truths, by substituting definitions or synonyms [Frege, by Rey] |
| 2515 | Frege fails to give a concept of analyticity, so he fails to explain synthetic a priori truth that way [Katz on Frege] |
| 8619 | To learn something, you must know that you don't know [Frege] |
| 14175 | We can drop 'cause', and just make inferences between facts [Russell] |
| 14172 | Moments and points seem to imply other moments and points, but don't cause them [Russell] |
| 8656 | The laws of number are not laws of nature, but are laws of the laws of nature [Frege] |
| 14174 | The laws of motion and gravitation are just parts of the definition of a kind of matter [Russell] |
| 14168 | Occupying a place and change are prior to motion, so motion is just occupying places at continuous times [Russell] |
| 14171 | Force is supposed to cause acceleration, but acceleration is a mathematical fiction [Russell] |
| 14160 | Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell] |
| 14156 | Mathematicians don't distinguish between instants of time and points on a line [Russell] |
| 14169 | The 'universe' can mean what exists now, what always has or will exist [Russell] |
| 22286 | Existence is not a first-level concept (of God), but a second-level property of concepts [Frege, by Potter] |
| 8644 | Because existence is a property of concepts the ontological argument for God fails [Frege] |