248 ideas
9414 | Metaphysics is the mapping of possibilities [Lowe, by Mumford] |
16414 | Science needs metaphysics to weed out its presuppositions [Lowe, by Hofweber] |
8282 | Only metaphysics can decide whether identity survives through change [Lowe] |
16127 | Metaphysics tells us what there could be, rather than what there is [Lowe] |
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] |
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] |
8262 | How can a theory of meaning show the ontological commitments of two paraphrases of one idea? [Lowe] |
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] |
8315 | Maybe facts are just true propositions [Lowe] |
8319 | One-to-one correspondence would need countable, individuable items [Lowe] |
9154 | Frege agreed with Euclid that the axioms of logic and mathematics are known through self-evidence [Frege, by Burge] |
8309 | A set is a 'number of things', not a 'collection', because nothing actually collects the members [Lowe] |
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] |
8322 | I don't believe in the empty set, because (lacking members) it lacks identity-conditions [Lowe] |
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] |
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] |
8312 | It is better if the existential quantifier refers to 'something', rather than a 'thing' which needs individuation [Lowe] |
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] |
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] |
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] |
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] |
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] |
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] |
8297 | Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe] |
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] |
8266 | Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe] |
8302 | Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe] |
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] |
11030 | The words 'There are exactly Julius Caesar moons of Mars' are gibberish [Rumfitt on 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] |
8298 | Sets are instances of numbers (rather than 'collections'); numbers explain sets, not vice versa [Lowe] |
8311 | If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2 [Lowe] |
8310 | Does the existence of numbers matter, in the way space, time and persons do? [Lowe] |
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] |
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] |
8321 | All possible worlds contain abstracta (e.g. numbers), which means they contain concrete objects [Lowe] |
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] |
8300 | Perhaps possession of causal power is the hallmark of existence (and a reason to deny the void) [Lowe] |
8281 | Heraclitus says change is new creation, and Spinoza that it is just phases of the one substance [Lowe] |
8270 | Events are changes or non-changes in properties and relations of persisting objects [Lowe] |
8308 | Events are ontologically indispensable for singular causal explanations [Lowe] |
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] |
8314 | Are facts wholly abstract, or can they contain some concrete constituents? [Lowe] |
8316 | Facts cannot be wholly abstract if they enter into causal relations [Lowe] |
8318 | The problem with the structured complex view of facts is what binds the constituents [Lowe] |
8323 | It is whimsical to try to count facts - how many facts did I learn before breakfast? [Lowe] |
8313 | Facts are needed for truth-making and causation, but they seem to lack identity criteria [Lowe] |
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] |
8258 | Two of the main rivals for the foundations of ontology are substances, and facts or states-of-affairs [Lowe] |
8301 | Some abstractions exist despite lacking causal powers, because explanation needs them [Lowe] |
10642 | Second-order quantifiers are committed to concepts, as first-order commits to objects [Frege, by Linnebo] |
8283 | Ontological categories are not natural kinds: the latter can only be distinguished using the former [Lowe] |
8284 | The top division of categories is either abstract/concrete, or universal/particular, or necessary/contingent [Lowe] |
13122 | Lowe divides things into universals and particulars, then kinds and properties, and abstract/concrete [Lowe, by Westerhoff] |
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] |
8273 | Is 'the Thames is broad in London' relational, or adverbial, or segmental? [Lowe] |
8285 | I prefer 'modes' to 'tropes', because it emphasises their dependence [Lowe] |
8295 | Why cannot a trope float off and join another bundle? [Lowe] |
8286 | Tropes cannot have clear identity-conditions, so they are not objects [Lowe] |
8294 | How can tropes depend on objects for their identity, if objects are just bundles of tropes? [Lowe] |
8296 | Does a ball snug in plaster have one trope, or two which coincide? [Lowe] |
8288 | Sortal terms for universals involve a substance, whereas adjectival terms do not [Lowe] |
8293 | Real universals are needed to explain laws of nature [Lowe] |
8307 | Particulars are instantiations, and universals are instantiables [Lowe] |
16130 | To be an object at all requires identity-conditions [Lowe] |
8265 | Our commitment to the existence of objects should depend on their explanatory value [Lowe] |
8275 | Objects are entities with full identity-conditions, but there are entities other than objects [Lowe] |
8267 | Perhaps concrete objects are entities which are in space-time and subject to causality [Lowe] |
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] |
8263 | An object is an entity which has identity-conditions [Lowe] |
17432 | Frege's universe comes already divided into objects [Frege, by Koslicki] |
8268 | Some things (such as electrons) can be countable, while lacking proper identity [Lowe] |
8303 | Criteria of identity cannot individuate objects, because they are shared among different types [Lowe] |
8292 | Diversity of two tigers is their difference in space-time; difference of matter is a consequence [Lowe] |
8291 | Individuation principles identify what kind it is; identity criteria distinguish items of the same kind [Lowe] |
16128 | A 'substance' is an object which doesn't depend for existence on other objects [Lowe] |
8279 | The identity of composite objects isn't fixed by original composition, because how do you identify the origin? [Lowe] |
11976 | Aristotelian essentialism says essences are not relative to specification [Lewis] |
8271 | An object 'endures' if it is always wholly present, and 'perdures' if different parts exist at different times [Lowe] |
8272 | How can you identify temporal parts of tomatoes without referring to tomatoes? [Lowe] |
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] |
8305 | A clear idea of the kind of an object must precede a criterion of identity for it [Lowe] |
8290 | One view is that two objects of the same type are only distinguished by differing in matter [Lowe] |
9853 | Identity between objects is not a consequence of identity, but part of what 'identity' means [Frege, by Dummett] |
15079 | 'Conceptual' necessity is narrow logical necessity, true because of concepts and logical laws [Lowe] |
16063 | Metaphysical necessity is logical necessity 'broadly construed' [Lowe, by Lynch/Glasgow] |
8260 | Logical necessity can be 'strict' (laws), or 'narrow' (laws and definitions), or 'broad' (all logical worlds) [Lowe] |
11978 | Causal necessities hold in all worlds compatible with the laws of nature [Lewis] |
16131 | The metaphysically possible is what acceptable principles and categories will permit [Lowe] |
8320 | Does every abstract possible world exist in every possible world? [Lowe] |
11979 | It doesn't take the whole of a possible Humphrey to win the election [Lewis] |
16994 | Counterpart theory is bizarre, as no one cares what happens to a mere counterpart [Kripke on Lewis] |
11974 | Counterparts are not the original thing, but resemble it more than other things do [Lewis] |
11975 | If the closest resembler to you is in fact quite unlike you, then you have no counterpart [Lewis] |
11977 | Essential attributes are those shared with all the counterparts [Lewis] |
17623 | To understand a thought you must understand its logical structure [Frege, by Burge] |
8280 | While space may just be appearance, time and change can't be, because the appearances change [Lowe] |
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] |
8276 | Properties or qualities are essentially adjectival, not objectual [Lowe] |
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] |
8289 | The idea that Cartesian souls are made of some ghostly 'immaterial' stuff is quite unwarranted [Lowe] |
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] |
8299 | Abstractions are non-spatial, or dependent, or derived from concepts [Lowe] |
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] |
8306 | You can think of a direction without a line, but a direction existing with no lines is inconceivable [Lowe] |
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] |
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] |
8317 | To cite facts as the elements in causation is to confuse states of affairs with states of objects [Lowe] |
8656 | The laws of number are not laws of nature, but are laws of the laws of nature [Frege] |
8269 | Points are limits of parts of space, so parts of space cannot be aggregates of them [Lowe] |
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] |