63 ideas
14721 | Metaphysical enquiry can survive if its conclusions are tentative [Sider] |
4642 | No fact can be real and no proposition true unless there is a Sufficient Reason (even if we can't know it) [Leibniz] |
2115 | Everything in the universe is interconnected, so potentially a mind could know everything [Leibniz] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
2111 | Falsehood involves a contradiction, and truth is contradictory of falsehood [Leibniz] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
14760 | Four-dimensionalism sees things and processes as belonging in the same category [Sider] |
7644 | The monad idea incomprehensibly spiritualises matter, instead of materialising soul [La Mettrie on Leibniz] |
11857 | He replaced Aristotelian continuants with monads [Leibniz, by Wiggins] |
7843 | Is a drop of urine really an infinity of thinking monads? [Voltaire on Leibniz] |
12751 | It is unclear in 'Monadology' how extended bodies relate to mind-like monads. [Garber on Leibniz] |
19363 | Changes in a monad come from an internal principle, and the diversity within its substance [Leibniz] |
19352 | A 'monad' has basic perception and appetite; a 'soul' has distinct perception and memory [Leibniz] |
14194 | Proper ontology should only use categorical (actual) properties, not hypothetical ones [Sider] |
14745 | If sortal terms fix the kind and the persistence conditions, we need to know what kinds there are [Sider] |
7931 | If a substance is just a thing that has properties, it seems to be a characterless non-entity [Leibniz, by Macdonald,C] |
14740 | If Tib is all of Tibbles bar her tail, when Tibbles loses her tail, two different things become one [Sider] |
14752 | Artists 'create' statues because they are essentially statues, and so lack identity with the lump of clay [Sider] |
14743 | The stage view of objects is best for dealing with coincident entities [Sider] |
14747 | 'Composition as identity' says that an object just is the objects which compose it [Sider] |
14757 | Mereological essentialism says an object's parts are necessary for its existence [Sider] |
14727 | Three-dimensionalists assert 'enduring', being wholly present at each moment, and deny 'temporal parts' [Sider] |
14738 | Some might say that its inconsistency with time travel is a reason to favour three-dimensionalism [Sider] |
14726 | Four-dimensionalists assert 'temporal parts', 'perduring', and being spread out over time [Sider] |
14728 | 4D says intrinsic change is difference between successive parts [Sider] |
14729 | 4D says each spatiotemporal object must have a temporal part at every moment at which it exists [Sider] |
14730 | Temporal parts exist, but are not prior building blocks for objects [Sider] |
14731 | Temporal parts are instantaneous [Sider] |
14758 | How can an instantaneous stage believe anything, if beliefs take time? [Sider] |
14762 | Four-dimensionalism says temporal parts are caused (through laws of motion) by previous temporal parts [Sider] |
14741 | The ship undergoes 'asymmetric' fission, where one candidate is seen as stronger [Sider] |
17554 | There must be some internal difference between any two beings in nature [Leibniz] |
14754 | If you say Leibniz's Law doesn't apply to 'timebound' properties, you are no longer discussing identity [Sider] |
2112 | Truths of reason are known by analysis, and are necessary; facts are contingent, and their opposites possible [Leibniz] |
14763 | Counterparts rest on similarity, so there are many such relations in different contexts [Sider] |
9344 | Mathematical analysis ends in primitive principles, which cannot be and need not be demonstrated [Leibniz] |
2110 | We all expect the sun to rise tomorrow by experience, but astronomers expect it by reason [Leibniz] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
2109 | Increase a conscious machine to the size of a mill - you still won't see perceptions in it [Leibniz] |
19362 | We know the 'I' and its contents by abstraction from awareness of necessary truths [Leibniz] |
12707 | The true elements are atomic monads [Leibniz] |
14725 | Maybe motion is a dynamical quantity intrinsic to a thing at a particular time [Sider] |
14735 | Space is 3D and lacks a direction; time seems connected to causation [Sider] |
14722 | Between presentism and eternalism is the 'growing block' view - the past is real, the future is not [Sider] |
14756 | For Presentists there must always be a temporal vantage point for any description [Sider] |
14724 | Presentists must deny truths about multiple times [Sider] |
14723 | Talk using tenses can be eliminated, by reducing it to indexical connections for an utterance [Sider] |
14736 | The B-theory is adequate, except that it omits to say which time is present [Sider] |
14734 | The B-series involves eternalism, and the reduction of tense [Sider] |
2114 | This is the most perfect possible universe, in its combination of variety with order [Leibniz] |
2113 | God alone (the Necessary Being) has the privilege that He must exist if He is possible [Leibniz] |