Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'Mathematics and the Metaphysicians' and 'Events as property exemplifications'

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19 ideas

5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
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
Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
In mathematic we are ignorant of both subject-matter and truth [Russell]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
A collection is infinite if you can remove some terms without diminishing its number [Russell]
7. Existence / A. Nature of Existence / 1. Nature of Existence
If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
How fine-grained Kim's events are depends on how finely properties are individuated [Kim, by Schaffer,J]
If events are ordered triples of items, such things seem to be sets, and hence abstract [Simons on Kim]
Events cannot be merely ordered triples, but must specify the link between the elements [Kim, by Simons]
Events are composed of an object with an attribute at a time [Kim, by Simons]
Since properties like self-identity and being 2+2=4 are timeless, Kim must restrict his properties [Simons on Kim]
Kim's theory results in too many events [Simons on Kim]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
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
Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Self-evidence is often a mere will-o'-the-wisp [Russell]