109 ideas
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 22309 | An idea can only be like another idea [Berkeley] |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
| 10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
| 10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
| 10635 | Second-order quantification and plural quantification are different [Linnebo] |
| 10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
| 10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
| 10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
| 10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
| 10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| 18091 | Infinitesimals are ghosts of departed quantities [Berkeley] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
| 6303 | Sets are positions in patterns [Resnik] |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| 6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
| 6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
| 6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| 6717 | Abstract ideas are impossible [Berkeley] |
| 3942 | I do not believe in the existence of anything, if I see no reason to believe it [Berkeley] |
| 3952 | I know that nothing inconsistent can exist [Berkeley] |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
| 18876 | Berkeley does believe in trees, but is confused about what trees are [Berkeley, by Cameron] |
| 10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
| 10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| 6715 | Universals do not have single meaning, but attach to many different particulars [Berkeley] |
| 6719 | No one will think of abstractions if they only have particular ideas [Berkeley] |
| 6714 | Universals do not have any intrinsic properties, but only relations to particulars [Berkeley] |
| 10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
| 6729 | Material substance is just general existence which can have properties [Berkeley] |
| 3959 | There is no other substance, in a strict sense, than spirit [Berkeley] |
| 16636 | A die has no distinct subject, but is merely a name for its modes or accidents [Berkeley] |
| 3946 | A thing is shown to be impossible if a contradiction is demonstrated within its definition [Berkeley] |
| 3958 | Since our ideas vary when the real things are said to be unchanged, they cannot be true copies [Berkeley] |
| 3943 | If existence is perceived directly, by which sense; if indirectly, how is it inferred from direct perception? [Berkeley] |
| 3931 | Sensible objects are just sets of sensible qualities [Berkeley] |
| 6722 | Perception is existence for my table, but also possible perception, by me or a spirit [Berkeley] |
| 5192 | Berkeley did not deny material things; he merely said they must be defined through sensations [Berkeley, by Ayer] |
| 5174 | Berkeley needed a phenomenalist account of the self, as well as of material things [Ayer on Berkeley] |
| 6724 | The only substance is spirit, or that which perceives [Berkeley] |
| 6723 | The 'esse' of objects is 'percipi', and they can only exist in minds [Berkeley] |
| 6732 | When I shut my eyes, the things I saw may still exist, but in another mind [Berkeley] |
| 1103 | 'To be is to be perceived' is a simple confusion of experience with its objects [Russell on Berkeley] |
| 6403 | For Berkelely, reality is ideas and a community of minds, including God's [Berkeley, by Grayling] |
| 3936 | Time is measured by the succession of ideas in our minds [Berkeley] |
| 3930 | There is no such thing as 'material substance' [Berkeley] |
| 3939 | I conceive a tree in my mind, but I cannot prove that its existence can be conceived outside a mind [Berkeley] |
| 3945 | There is nothing in nature which needs the concept of matter to explain it [Berkeley] |
| 3947 | Perceptions are ideas, and ideas exist in the mind, so objects only exist in the mind [Berkeley] |
| 3933 | Primary qualities (such as shape, solidity, mass) are held to really exist, unlike secondary qualities [Berkeley] |
| 6726 | No one can, by abstraction, conceive extension and motion of bodies without sensible qualities [Berkeley] |
| 6728 | Motion is in the mind, since swifter ideas produce an appearance of slower motion [Berkeley] |
| 6727 | Figure and extension seem just as dependent on the observer as heat and cold [Berkeley] |
| 3934 | A mite would see its own foot as large, though we would see it as tiny [Berkeley] |
| 3935 | The apparent size of an object varies with its distance away, so that can't be a property of the object [Berkeley] |
| 3937 | 'Solidity' is either not a sensible quality at all, or it is clearly relative to our senses [Berkeley] |
| 3940 | Distance is not directly perceived by sight [Berkeley] |
| 6495 | Berkeley's idealism resulted from fear of scepticism in representative realism [Robinson,H on Berkeley] |
| 3957 | Immediate objects of perception, which some treat as appearances, I treat as the real things themselves [Berkeley] |
| 6720 | Knowledge is of ideas from senses, or ideas of the mind, or operations on sensations [Berkeley] |
| 3953 | Real things and imaginary or dreamed things differ because the latter are much fainter [Berkeley] |
| 3938 | Geometry is originally perceived by senses, and so is not purely intellectual [Berkeley] |
| 3944 | It is possible that we could perceive everything as we do now, but nothing actually existed. [Berkeley] |
| 3932 | A hot hand and a cold hand will have different experiences in the same tepid water [Berkeley] |
| 23636 | Berkeley's idealism gives no grounds for believing in other minds [Reid on Berkeley] |
| 6736 | I know other minds by ideas which are referred by me to other agents, as their effects [Berkeley] |
| 3948 | Experience tells me that other minds exist independently from my own [Berkeley] |
| 6713 | If animals have ideas, and are not machines, they must have some reason [Berkeley] |
| 6491 | Berkeley replaced intentionality with an anti-abstractionist imagist theory of thought [Berkeley, by Robinson,H] |
| 6711 | The mind creates abstract ideas by considering qualities separated from their objects [Berkeley] |
| 10581 | I can only combine particulars in imagination; I can't create 'abstract' ideas [Berkeley] |
| 6721 | Ideas are perceived by the mind, soul or self [Berkeley] |
| 3941 | How can that which is unthinking be a cause of thought? [Berkeley] |
| 5374 | Berkeley probably used 'idea' to mean both the act of apprehension and the thing apprehended [Russell on Berkeley] |
| 6716 | Language is presumably for communication, and names stand for ideas [Berkeley] |
| 10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
| 6718 | I can't really go wrong if I stick to wordless thought [Berkeley] |
| 3954 | Immorality is not in the action, but in the deviation of the will from moral law [Berkeley] |
| 6731 | No one can explain how matter affects mind, so matter is redundant in philosophy [Berkeley] |
| 6730 | We discover natural behaviour by observing settled laws of nature, not necessary connections [Berkeley] |
| 15861 | The laws of nature are mental regularities which we learn by experience [Berkeley] |
| 6734 | If properties and qualities arise from an inward essence, we will remain ignorant of nature [Berkeley] |
| 6735 | All motion is relative, so a single body cannot move [Berkeley] |
| 6733 | I cannot imagine time apart from the flow of ideas in my mind [Berkeley] |
| 3950 | There must be a God, because all sensible things must be perceived by him [Berkeley] |
| 3951 | There must be a God, because I and my ideas are not independent [Berkeley] |
| 3949 | It has been proved that creation is the workmanship of God, from its beauty and usefulness [Berkeley] |
| 6737 | Particular evils are really good when linked to the whole system of beings [Berkeley] |
| 3956 | People are responsible because they have limited power, though this ultimately derives from God [Berkeley] |
| 3955 | If sin is not just physical, we don't consider God the origin of sin because he causes physical events [Berkeley] |