Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'Russell's Mathematical Logic' and 'Truthmakers, Realism and Ontology'

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32 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10041 Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
3. Truth / B. Truthmakers / 2. Truthmaker Relation
18877 Moral realism doesn't seem to entail the existence of any things [Cameron]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
18868 Surely if some propositions are grounded in existence, they all are? [Cameron]
3. Truth / B. Truthmakers / 4. Truthmaker Necessitarianism
18867 Orthodox Truthmaker applies to all propositions, and necessitates their truth [Cameron]
18873 God fixes all the truths of the world by fixing what exists [Cameron]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
18879 What the proposition says may not be its truthmaker [Cameron]
18880 Rather than what exists, some claim that the truthmakers are ways of existence, dispositions, modalities etc [Cameron]
18874 Truthmaking doesn't require realism, because we can be anti-realist about truthmakers [Cameron]
3. Truth / B. Truthmakers / 6. Making Negative Truths
18869 Without truthmakers, negative truths must be ungrounded [Cameron]
3. Truth / B. Truthmakers / 11. Truthmaking and Correspondence
18871 I support the correspondence theory because I believe in truthmakers [Cameron]
18870 Maybe truthmaking and correspondence stand together, and are interdefinable [Cameron]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21716 In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10035 Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
18739 Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18741 Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10042 Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
18744 Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10038 A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10046 The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10039 Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10043 Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
10045 Impredicative definitions are admitted into ordinary mathematics [Gödel]
7. Existence / A. Nature of Existence / 1. Nature of Existence
18740 If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
7. Existence / D. Theories of Reality / 2. Realism
18875 Realism says a discourse is true or false, and some of it is true [Cameron]
18878 Realism says truths rest on mind-independent reality; truthmaking theories are about which features [Cameron]
18881 For realists it is analytic that truths are grounded in the world [Cameron]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
18745 A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
18747 The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
18748 Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
18746 Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
18750 Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
18872 We should reject distinct but indiscernible worlds [Cameron]