Combining Texts

All the ideas for 'The Facts of Causation', 'Modal Logic' and 'Cardinality, Counting and Equinumerosity'

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21 ideas

3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
10365 We might use 'facta' to refer to the truth-makers for facts [Mellor, by Schaffer,J]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / b. System K
14970 Normal system K has five axioms and rules [Cresswell]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
14971 D is valid on every serial frame, but not where there are dead ends [Cresswell]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
14972 S4 has 14 modalities, and always reduces to a maximum of three modal operators [Cresswell]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
14973 In S5 all the long complex modalities reduce to just three, and their negations [Cresswell]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
14976 Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds [Cresswell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
17453 The meaning of a number isn't just the numerals leading up to it [Heck]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
17457 A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17448 In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
17455 Is counting basically mindless, and independent of the cardinality involved? [Heck]
17456 Counting is the assignment of successively larger cardinal numbers to collections [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
17450 Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
17451 We can know 'just as many' without the concepts of equinumerosity or numbers [Heck]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17459 Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
17454 Children can use numbers, without a concept of them as countable objects [Heck]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
17458 Equinumerosity is not the same concept as one-one correspondence [Heck]
17449 We can understand cardinality without the idea of one-one correspondence [Heck]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
14974 A relation is 'Euclidean' if aRb and aRc imply bRc [Cresswell]
10. Modality / A. Necessity / 4. De re / De dicto modality
14975 A de dicto necessity is true in all worlds, but not necessarily of the same thing in each world [Cresswell]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
4785 Causal statements relate facts (which are whatever true propositions express) [Mellor, by Psillos]
26. Natural Theory / C. Causation / 8. Particular Causation / e. Probabilistic causation
8408 Probabilistic causation says C is a cause of E if it increases the chances of E occurring [Mellor, by Tooley]