Combining Philosophers
Ideas for Rescher,N/Oppenheim,P, Bertrand Russell and David Lewis
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50 ideas
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
5401
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The mortality of Socrates is more certain from induction than it is from deduction [Russell]
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14453
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The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell]
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4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / e. Existential quantifier ∃
16484
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There are four experiences that lead us to talk of 'some' things [Russell]
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4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
16456
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For modality Lewis rejected boxes and diamonds, preferring worlds, and an index for the actual one [Lewis, by Stalnaker]
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4. Formal Logic / F. Set Theory ST / 1. Set Theory
18395
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Sets are mereological sums of the singletons of their members [Lewis, by Armstrong]
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15496
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We can build set theory on singletons: classes are then fusions of subclasses, membership is the singleton [Lewis]
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10807
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Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis]
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4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
15500
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Classes divide into subclasses in many ways, but into members in only one way [Lewis]
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15499
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A subclass of a subclass is itself a subclass; a member of a member is not in general a member [Lewis]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14113
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The null class is a fiction [Russell]
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15503
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We needn't accept this speck of nothingness, this black hole in the fabric of Reality! [Lewis]
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15498
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We can accept the null set, but there is no null class of anything [Lewis]
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15502
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There are four main reasons for asserting that there is an empty set [Lewis]
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10809
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We can accept the null set, but not a null class, a class lacking members [Lewis]
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10811
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The null set plays the role of last resort, for class abstracts and for existence [Lewis]
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10812
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The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
15506
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If we don't understand the singleton, then we don't understand classes [Lewis]
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6103
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Normally a class with only one member is a problem, because the class and the member are identical [Russell]
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15497
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We can replace the membership relation with the member-singleton relation (plus mereology) [Lewis]
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15511
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If singleton membership is external, why is an object a member of one rather than another? [Lewis]
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15513
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Maybe singletons have a structure, of a thing and a lasso? [Lewis]
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10813
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What on earth is the relationship between a singleton and an element? [Lewis]
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10814
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Are all singletons exact intrinsic duplicates? [Lewis]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
14427
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We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
15507
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Set theory has some unofficial axioms, generalisations about how to understand it [Lewis]
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10191
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Set theory reduces to a mereological theory with singletons as the only atoms [Lewis, by MacBride]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
14428
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Members define a unique class, whereas defining characteristics are numerous [Russell]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
14440
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We may assume that there are infinite collections, as there is no logical reason against them [Russell]
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14447
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Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
14443
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The British parliament has one representative selected from each constituency [Russell]
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14445
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Choice shows that if any two cardinals are not equal, one must be the greater [Russell]
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14444
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Choice is equivalent to the proposition that every class is well-ordered [Russell]
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14446
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We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
18130
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Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock]
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14459
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Reducibility: a family of functions is equivalent to a single type of function [Russell]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
15508
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If singletons are where their members are, then so are all sets [Lewis]
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15514
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A huge part of Reality is only accepted as existing if you have accepted set theory [Lewis]
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15523
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Set theory isn't innocent; it generates infinities from a single thing; but mathematics needs it [Lewis]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
21563
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The 'no classes' theory says the propositions just refer to the members [Russell]
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14461
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Propositions about classes can be reduced to propositions about their defining functions [Russell]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
15894
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Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine]
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4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
14126
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Order rests on 'between' and 'separation' [Russell]
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14127
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Order depends on transitive asymmetrical relations [Russell]
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4. Formal Logic / F. Set Theory ST / 7. Natural Sets
8469
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Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein]
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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
11064
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Classes can be reduced to propositional functions [Russell, by Hanna]
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7548
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Classes, grouped by a convenient property, are logical constructions [Russell]
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8745
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Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell]
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6436
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I gradually replaced classes with properties, and they ended as a symbolic convenience [Russell]
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4. Formal Logic / G. Formal Mereology / 1. Mereology
14121
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The part-whole relation is ultimate and indefinable [Russell]
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10806
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Megethology is the result of adding plural quantification to mereology [Lewis]
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