Combining Texts

All the ideas for 'Science and Method', 'A Powers Theory of Modality' and 'Cardinality, Counting and Equinumerosity'

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25 ideas

3. Truth / B. Truthmakers / 11. Truthmaking and Correspondence
Unlike correspondence, truthmaking can be one truth to many truthmakers, or vice versa [Jacobs]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
One geometry cannot be more true than another [Poincaré]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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
A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
Is counting basically mindless, and independent of the cardinality involved? [Heck]
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
Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
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
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
Children can use numbers, without a concept of them as countable objects [Heck]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Equinumerosity is not the same concept as one-one correspondence [Heck]
We can understand cardinality without the idea of one-one correspondence [Heck]
8. Modes of Existence / A. Relations / 3. Structural Relations
If structures result from intrinsic natures of properties, the 'relations' between them can drop out [Jacobs]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
Science aims at identifying the structure and nature of the powers that exist [Jacobs]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
Powers come from concrete particulars, not from the laws of nature [Jacobs]
10. Modality / A. Necessity / 10. Impossibility
Possibilities are manifestations of some power, and impossibilies rest on no powers [Jacobs]
10. Modality / B. Possibility / 1. Possibility
States of affairs are only possible if some substance could initiate a causal chain to get there [Jacobs]
10. Modality / B. Possibility / 9. Counterfactuals
Counterfactuals invite us to consider the powers picked out by the antecedent [Jacobs]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Possible worlds are just not suitable truthmakers for modality [Jacobs]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
All modality is in the properties and relations of the actual world [Jacobs]
10. Modality / C. Sources of Modality / 6. Necessity from Essence
We can base counterfactuals on powers, not possible worlds, and hence define necessity [Jacobs]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
Concrete worlds, unlike fictions, at least offer evidence of how the actual world could be [Jacobs]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
If some book described a possibe life for you, that isn't what makes such a life possible [Jacobs]
Possible worlds semantics gives little insight into modality [Jacobs]