103 ideas
19359 | Leibniz aims to give coherent rational support for empiricism [Leibniz, by Perkins] |
13086 | Metaphysics is a science of the intelligible nature of being [Leibniz, by Cover/O'Leary-Hawthorne] |
16710 | Leibniz tried to combine mechanistic physics with scholastic metaphysics [Leibniz, by Pasnau] |
16897 | Reason is the faculty for grasping apriori necessary truths [Leibniz, by Burge] |
3346 | For Leibniz rationality is based on non-contradiction and the principle of sufficient reason [Leibniz, by Benardete,JA] |
3347 | Leibniz said the principle of sufficient reason is synthetic a priori, since its denial is not illogical [Leibniz, by Benardete,JA] |
8627 | Leibniz is inclined to regard all truths as provable [Leibniz, by Frege] |
9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
9147 | Number cannot be defined as addition of ones, since that needs the number; it is a single act of abstraction [Fine,K on Leibniz] |
19375 | The continuum is not divided like sand, but folded like paper [Leibniz, by Arthur,R] |
18080 | A tangent is a line connecting two points on a curve that are infinitely close together [Leibniz] |
18081 | Nature uses the infinite everywhere [Leibniz] |
7565 | Leibniz proposes monads, since there must be basic things, which are immaterial in order to have unity [Leibniz, by Jolley] |
10419 | If relations can be reduced to, or supervene on, monadic properties of relata, they are not real [Leibniz, by Swoyer] |
13078 | Relations aren't in any monad, so they are distributed, so they are not real [Leibniz] |
12713 | Forms have sensation and appetite, the latter being the ability to act on other bodies [Leibniz, by Garber] |
13087 | The essence of a thing is its real possibilities [Leibniz, by Cover/O'Leary-Hawthorne] |
12701 | Leibniz moved from individuation by whole entity to individuation by substantial form [Leibniz, by Garber] |
13105 | The laws-of-the-series plays a haecceitist role [Leibniz, by Cover/O'Leary-Hawthorne] |
16513 | Identity of a substance is the law of its persistence [Leibniz] |
12035 | Leibniz bases pure primitive entities on conjunctions of qualitative properties [Leibniz, by Adams,RM] |
13091 | Leibnizian substances add concept, law, force, form and soul [Leibniz, by Cover/O'Leary-Hawthorne] |
7561 | Substances are essentially active [Leibniz, by Jolley] |
12715 | Leibniz strengthened hylomorphism by connecting it to force in physics [Leibniz, by Garber] |
11878 | Leibniz's view (that all properties are essential) is extreme essentialism, not its denial [Leibniz, by Mackie,P] |
11862 | Leibniz was not an essentialist [Leibniz, by Wiggins] |
16504 | Two eggs can't be identical, because the same truths can't apply to both of them [Leibniz] |
13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
8650 | Things are the same if one can be substituted for the other without loss of truth [Leibniz] |
13828 | Necessary truths are those provable from identities by pure logic in finite steps [Leibniz, by Hacking] |
13084 | How can things be incompatible, if all positive terms seem to be compatible? [Leibniz] |
4307 | A reason must be given why contingent beings should exist rather than not exist [Leibniz] |
15883 | Leibniz narrows down God's options to one, by non-contradiction, sufficient reason, indiscernibles, compossibility [Leibniz, by Harré] |
18822 | Each monad expresses all its compatible monads; a possible world is the resulting equivalence class [Leibniz, by Rumfitt] |
7837 | Leibniz proposed possible worlds, because they might be evil, where God would not create evil things [Leibniz, by Stewart,M] |
13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
13080 | Leibniz has a counterpart view of de re counterfactuals [Leibniz, by Cover/O'Leary-Hawthorne] |
13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
19332 | For Leibniz, divine understanding grasps every conceivable possibility [Leibniz, by Perkins] |
5509 | Leibniz said dualism of mind and body is illusion, and there is only mind [Leibniz, by Martin/Barresi] |
7568 | Leibniz is an idealist insofar as the basic components of his universe are all mental [Leibniz, by Jolley] |
13092 | The essence of substance is the law of its changes, as in the series of numbers [Leibniz] |
19354 | Leibniz introduced the idea of degrees of consciousness, essential for his monads [Leibniz, by Perkins] |
7841 | We think we are free because the causes of the will are unknown; determinism is a false problem [Leibniz] |
5510 | Leibniz has a panpsychist view that physical points are spiritual [Leibniz, by Martin/Barresi] |
7564 | Occasionalism give a false view of natural laws, miracles, and substances [Leibniz, by Jolley] |
19372 | Concepts are ordered, and show eternal possibilities, deriving from God [Leibniz, by Arthur,R] |
13467 | Leibniz was the first modern to focus on sentence-sized units (where empiricists preferred word-size) [Leibniz, by Hart,WD] |
19365 | Limited awareness leads to bad choices, and unconscious awareness makes us choose the bad [Leibniz, by Perkins] |
8110 | Leibniz identified beauty with intellectual perfection [Leibniz, by Gardner] |
7569 | Humans are moral, and capable of reward and punishment, because of memory and self-consciousness [Leibniz, by Jolley] |
7517 | I could take a healthy infant and train it up to be any type of specialist I choose [Watson,JB] |
7574 | Natural law theory is found in Aquinas, in Leibniz, and at the Nuremberg trials [Leibniz, by Jolley] |
12728 | Leibniz rejected atoms, because they must be elastic, and hence have parts [Leibniz, by Garber] |
19374 | Microscopes and the continuum suggest that matter is endlessly divisible [Leibniz] |
7560 | Leibniz struggled to reconcile bodies with a reality of purely soul-like entities [Jolley on Leibniz] |
16683 | Leibniz eventually said resistance, rather than extension, was the essence of body [Leibniz, by Pasnau] |
12725 | Leibniz wanted to explain motion and its laws by the nature of body [Leibniz, by Garber] |
16507 | The law within something fixes its persistence, and accords with general laws of nature [Leibniz] |
7859 | Leibniz had an unusual commitment to the causal completeness of physics [Leibniz, by Papineau] |
15307 | Leibniz uses 'force' to mean both activity and potential [Leibniz] |
3889 | God's existence is either necessary or impossible [Leibniz, by Scruton] |
7842 | Leibniz was closer than Spinoza to atheism [Leibniz, by Stewart,M] |