Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'Philosophy of Mathematics' and 'Principle of Life and Plastic Natures'

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20 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10882 Predicative definitions only refer to entities outside the defined collection [Horsten]
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 / 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 / J. Model Theory in Logic / 2. Isomorphisms
10884 A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10885 Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10881 The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
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]
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]
12. Knowledge Sources / B. Perception / 1. Perception
19419 Not all of perception is accompanied by consciousness [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
19421 Souls act as if there were no bodies, and bodies act as if there were no souls [Leibniz]
22. Metaethics / B. Value / 2. Values / e. Death
19420 Death and generation are just transformations of an animal, augmented or diminished [Leibniz]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / a. Early Modern matter
19416 Not all of matter is animated, any more than a pond full of living fish is animated [Leibniz]
19422 Every particle of matter contains organic bodies [Leibniz]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
19418 Mechanics shows that all motion originates in other motion, so there is a Prime Mover [Leibniz]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
19417 All substances are in harmony, even though separate, so they must have one divine cause [Leibniz]