236 ideas
| 9199 | Wisdom for one instant is as good as wisdom for eternity [Chrysippus] |
| 20853 | Wise men should try to participate in politics, since they are a good influence [Chrysippus, by Diog. Laertius] |
| 20772 | Three branches of philosophy: first logic, second ethics, third physics (which ends with theology) [Chrysippus] |
| 13876 | The syntactic category is primary, and the ontological category is derivative [Frege, by Wright,C] |
| 8415 | Never lose sight of the distinction between concept and object [Frege] |
| 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] |
| 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] |
| 5969 | Chrysippus said the uncaused is non-existent [Chrysippus, by Plutarch] |
| 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] |
| 17495 | Proof aims to remove doubts, but also to show the interdependence of truths [Frege] |
| 8632 | You can't transfer external properties unchanged to apply to ideas [Frege] |
| 13881 | We need to grasp not number-objects, but the states of affairs which make number statements true [Frege, by Wright,C] |
| 21388 | The causes of future true events must exist now, so they will happen because of destiny [Chrysippus, by Cicero] |
| 20780 | Graspable presentations are criteria of facts, and are molded according to their objects [Chrysippus, by Diog. Laertius] |
| 20793 | How could you ever know that the presentation is similar to the object? [Sext.Empiricus on Chrysippus] |
| 8077 | Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin] |
| 20791 | Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius] |
| 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] |
| 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] |
| 9390 | Logic guides thinking, but it isn't a substitute for it [Rumfitt] |
| 8078 | Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin] |
| 6023 | Every proposition is either true or false [Chrysippus, by Cicero] |
| 8645 | Convert "Jupiter has four moons" into "the number of Jupiter's moons is four" [Frege] |
| 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] |
| 14236 | Each horse doesn't fall under the concept 'horse that draws the carriage', because all four are needed [Oliver/Smiley on Frege] |
| 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] |
| 8640 | We cannot define numbers from the idea of a series, because numbers must precede that [Frege] |
| 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] |
| 8654 | One is the Number which belongs to the concept "identical with 0" [Frege] |
| 8636 | We can say 'a and b are F' if F is 'wise', but not if it is 'one' [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] |
| 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] |
| 15916 | Frege's one-to-one correspondence replaces well-ordering, because infinities can't be counted [Frege, by Lavine] |
| 10034 | The number of natural numbers is not a natural number [Frege, by George/Velleman] |
| 16883 | Arithmetical statements can't be axioms, because they are provable [Frege, by Burge] |
| 10625 | Frege had a motive to treat numbers as objects, but not a justification [Hale/Wright on Frege] |
| 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] |
| 17636 | A cardinal number may be defined as a class of similar classes [Frege, by Russell] |
| 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] |
| 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] |
| 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] |
| 17460 | A statement of number contains a predication about a concept [Frege] |
| 17820 | If you can subdivide objects many ways for counting, you can do that to set-elements too [Yourgrau on 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 9945 | Logicism shows that no empirical truths are needed to justify arithmetic [Frege, by George/Velleman] |
| 16905 | Arithmetic must be based on logic, because of its total generality [Frege, by Jeshion] |
| 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] |
| 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] |
| 7739 | Arithmetic is analytic [Frege, by Weiner] |
| 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] |
| 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] |
| 5992 | Chrysippus says action is the criterion for existence, which must be physical [Chrysippus, by Tieleman] |
| 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] |
| 21673 | There are simple and complex facts; the latter depend on further facts [Chrysippus, by Cicero] |
| 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] |
| 16652 | Stoics categories are Substrate, Quality, Disposition, and Relation [Chrysippus, by Pasnau] |
| 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] |
| 17432 | Frege's universe comes already divided into objects [Frege, by Koslicki] |
| 16058 | Dion and Theon coexist, but Theon lacks a foot. If Dion loses a foot, he ousts Theon? [Chrysippus, by Philo of Alexandria] |
| 9389 | Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt] |
| 16059 | Change of matter doesn't destroy identity - in Dion and Theon change is a condition of identity [Chrysippus, by Long/Sedley] |
| 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] |
| 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] |
| 1875 | Dogs show reason in decisions made by elimination [Chrysippus, by Sext.Empiricus] |
| 20834 | Chrysippus allows evil to say it is fated, or even that it is rational and natural [Plutarch on Chrysippus] |
| 20833 | A swerve in the atoms would be unnatural, like scales settling differently for no reason [Chrysippus, by Plutarch] |
| 20808 | Everything is fated, either by continuous causes or by a supreme rational principle [Chrysippus, by Diog. Laertius] |
| 20835 | Chrysippus is wrong to believe in non-occurring future possibilities if he is a fatalist [Plutarch on Chrysippus] |
| 20836 | The Lazy Argument responds to fate with 'why bother?', but the bothering is also fated [Chrysippus, by Cicero] |
| 20837 | Fate is an eternal and fixed chain of causal events [Chrysippus] |
| 21679 | When we say events are fated by antecedent causes, do we mean principal or auxiliary causes? [Chrysippus] |
| 5971 | Destiny is only a predisposing cause, not a sufficient cause [Chrysippus, by Plutarch] |
| 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] |
| 9988 | If we abstract 'from' two cats, the units are not black or white, or cats [Tait on Frege] |
| 10803 | Frege himself abstracts away from tone and color [Yablo 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] |
| 10526 | Fregean abstraction creates concepts which are equivalences between initial items [Frege, by Fine,K] |
| 10525 | Frege put the idea of abstraction on a rigorous footing [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] |
| 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] |
| 20787 | A proposition is what can be asserted or denied on its own [Chrysippus] |
| 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] |
| 20850 | Passions are judgements; greed thinks money is honorable, and likewise drinking and lust [Chrysippus, by Diog. Laertius] |
| 20869 | The highest degree of morality performs all that is appropriate, omitting nothing [Chrysippus] |
| 3044 | Stoics say that beauty and goodness are equivalent and linked [Chrysippus, by Diog. Laertius] |
| 20838 | Fate initiates general causes, but individual wills and characters dictate what we do [Chrysippus] |
| 20813 | Human purpose is to contemplate and imitate the cosmos [Chrysippus] |
| 3045 | Stoics say justice is a part of nature, not just an invented principle [Chrysippus, by Diog. Laertius] |
| 20774 | Only nature is available to guide action and virtue [Chrysippus] |
| 20864 | Live in agreement, according to experience of natural events [Chrysippus] |
| 5972 | Living happily is nothing but living virtuously [Chrysippus, by Plutarch] |
| 1777 | Pleasure is not the good, because there are disgraceful pleasures [Chrysippus, by Diog. Laertius] |
| 5973 | Justice can be preserved if pleasure is a good, but not if it is the goal [Chrysippus, by Plutarch] |
| 20845 | There are shameful pleasures, and nothing shameful is good, so pleasure is not a good [Chrysippus, by Diog. Laertius] |
| 5967 | People need nothing except corn and water [Chrysippus, by Plutarch] |
| 5966 | All virtue is good, but not always praised (as in not lusting after someone ugly) [Chrysippus] |
| 20855 | Chrysippus says virtue can be lost (though Cleanthes says it is too secure for that) [Chrysippus, by Diog. Laertius] |
| 5970 | Chrysippus says nothing is blameworthy, as everything conforms with the best nature [Chrysippus, by Plutarch] |
| 20842 | Rational animals begin uncorrupted, but externals and companions are bad influences [Chrysippus, by Diog. Laertius] |
| 20856 | Justice, the law, and right reason are natural and not conventional [Chrysippus, by Diog. Laertius] |
| 8619 | To learn something, you must know that you don't know [Frege] |
| 1779 | We don't have obligations to animals as they aren't like us [Chrysippus, by Diog. Laertius] |
| 20857 | Justice is irrelevant to animals, because they are too unlike us [Chrysippus, by Diog. Laertius] |
| 20812 | Covers are for shields, and sheaths for swords; likewise, all in the cosmos is for some other thing [Chrysippus] |
| 21403 | The later Stoics identified the logos with an air-fire compound, called 'pneuma' [Chrysippus, by Long] |
| 20828 | Fire is a separate element, not formed with others (as was previously believed) [Chrysippus, by Stobaeus] |
| 5975 | Stoics say earth, air, fire and water are the primary elements [Chrysippus, by Plutarch] |
| 8656 | The laws of number are not laws of nature, but are laws of the laws of nature [Frege] |
| 20819 | The past and the future subsist, but only the present exists [Chrysippus, by Plutarch] |
| 20818 | The present does not exist, so our immediate experience is actually part past and part future [Chrysippus, by Plutarch] |
| 20821 | Time is continous and infinitely divisible, so there cannot be a wholly present time [Chrysippus, by Stobaeus] |
| 3048 | Stoics say that God the creator is the perfection of all animals [Chrysippus, by Diog. Laertius] |
| 20773 | The origin of justice can only be in Zeus, and in nature [Chrysippus] |
| 3042 | Stoics teach that law is identical with right reason, which is the will of Zeus [Chrysippus, by Diog. Laertius] |
| 5965 | The source of all justice is Zeus and the universal nature [Chrysippus] |
| 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] |
| 1782 | Stoics teach that God is a unity, variously known as Mind, or Fate, or Jupiter [Chrysippus, by Diog. Laertius] |
| 20830 | Death can't separate soul from body, because incorporeal soul can't unite with body [Chrysippus] |
| 21404 | There is a rationale in terrible disasters; they are useful to the whole, and make good possible [Chrysippus] |