Combining Philosophers

All the ideas for Anon (Lev), Michal Walicki and Graeme Forbes

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52 ideas

1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
12027 There must be a plausible epistemological theory alongside any metaphysical theory [Forbes,G]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
17749 Post proved the consistency of propositional logic in 1921 [Walicki]
17765 Propositional language can only relate statements as the same or as different [Walicki]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL
12005 The symbol 'ι' forms definite descriptions; (ιx)F(x) says 'the x which is such that F(x)' [Forbes,G]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
17764 Boolean connectives are interpreted as functions on the set {1,0} [Walicki]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
17752 The empty set is useful for defining sets by properties, when the members are not yet known [Walicki]
17753 The empty set avoids having to take special precautions in case members vanish [Walicki]
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
17759 Ordinals play the central role in set theory, providing the model of well-ordering [Walicki]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
17741 To determine the patterns in logic, one must identify its 'building blocks' [Walicki]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
12010 Is the meaning of 'and' given by its truth table, or by its introduction and elimination rules? [Forbes,G]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
17747 A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17748 The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17761 A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
17763 Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17758 Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki]
17755 Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]
17756 The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki]
17760 Two infinite ordinals can represent a single infinite cardinal [Walicki]
17757 Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
17762 In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17754 Inductive proof depends on the choice of the ordering [Walicki]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
12023 Vagueness problems arise from applying sharp semantics to vague languages [Forbes,G]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
12017 In all instances of identity, there must be some facts to ensure the identity [Forbes,G]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
12024 If we combined two clocks, it seems that two clocks may have become one clock. [Forbes,G]
9. Objects / D. Essence of Objects / 3. Individual Essences
11885 Only individual essences will ground identities across worlds in other properties [Forbes,G, by Mackie,P]
12014 An individual essence is a set of essential properties which only that object can have [Forbes,G]
12015 Non-trivial individual essence is properties other than de dicto, or universal, or relational [Forbes,G]
9. Objects / D. Essence of Objects / 5. Essence as Kind
12013 Essential properties depend on a category, and perhaps also on particular facts [Forbes,G]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
13804 A property is essential iff the object would not exist if it lacked that property [Forbes,G]
13805 Properties are trivially essential if they are not grounded in a thing's specific nature [Forbes,G]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
12012 Essential properties are those without which an object could not exist [Forbes,G]
13808 A relation is essential to two items if it holds in every world where they exist [Forbes,G]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
13806 Trivially essential properties are existence, self-identity, and de dicto necessities [Forbes,G]
9. Objects / D. Essence of Objects / 9. Essence and Properties
13807 A property is 'extraneously essential' if it is had only because of the properties of other objects [Forbes,G]
9. Objects / D. Essence of Objects / 11. Essence of Artefacts
12022 Same parts does not ensure same artefact, if those parts could constitute a different artefact [Forbes,G]
12025 Artefacts have fuzzy essences [Forbes,G]
13809 One might be essentialist about the original bronze from which a statue was made [Forbes,G]
9. Objects / E. Objects over Time / 12. Origin as Essential
12020 An individual might change their sex in a world, but couldn't have differed in sex at origin [Forbes,G]
9. Objects / F. Identity among Objects / 1. Concept of Identity
11888 Identities must hold because of other facts, which must be instrinsic [Forbes,G, by Mackie,P]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
10. Modality / A. Necessity / 4. De re / De dicto modality
12003 De re modal formulae, unlike de dicto, are sensitive to transworld identities [Forbes,G]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
12028 De re necessity is a form of conceptual necessity, just as de dicto necessity is [Forbes,G]
13810 The source of de dicto necessity is not concepts, but the actual properties of the thing [Forbes,G]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
12008 Unlike places and times, we cannot separate possible worlds from what is true at them [Forbes,G]
12009 The problem with possible worlds realism is epistemological; we can't know properties of possible objects [Forbes,G]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
12007 Possible worlds are points of logical space, rather like other times than our own [Forbes,G]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
12011 Transworld identity concerns the limits of possibility for ordinary things [Forbes,G]
12016 The problem of transworld identity can be solved by individual essences [Forbes,G]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
12004 Counterpart theory is not good at handling the logic of identity [Forbes,G]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
12021 Haecceitism attributes to each individual a primitive identity or thisness [Forbes,G]
12029 We believe in thisnesses, because we reject bizarre possibilities as not being about that individual [Forbes,G]
22. Metaethics / B. Value / 2. Values / g. Love
19941 Thou shalt love thy neighbour as thyself [Anon (Leviticus)]