Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'The Ways of Paradox' and 'Preface to 'Principles of Philosophy''

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20 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
21962 Metaphysics is the roots of the tree of science [Descartes]
2. Reason / F. Fallacies / 4. Circularity
3659 I know the truth that God exists and is the author of truth [Descartes]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
21695 The set scheme discredited by paradoxes is actually the most natural one [Quine]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
21693 Russell's antinomy challenged the idea that any condition can produce a set [Quine]
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 / L. Paradox / 3. Antinomies
21691 Antinomies contradict accepted ways of reasoning, and demand revisions [Quine]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
21690 Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on [Quine]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
21689 A barber shaves only those who do not shave themselves. So does he shave himself? [Quine]
21694 Membership conditions which involve membership and non-membership are paradoxical [Quine]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
21692 If we write it as '"this sentence is false" is false', there is no paradox [Quine]
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]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
3657 Understanding, not the senses, gives certainty [Descartes]
28. God / C. Attitudes to God / 5. Atheism
3660 Atheism arises from empiricism, because God is intangible [Descartes]