Combining Texts

All the ideas for 'Evidence', 'Laudatio: Prof Ruth Barcan Marcus' and 'Cardinality, Counting and Equinumerosity'

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22 ideas

4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
If a property is possible, there is something which can have it [Williamson]
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]
Counting is the assignment of successively larger cardinal numbers to collections [Heck]
Is counting basically mindless, and independent of the cardinality involved? [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]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
Internalists are much more interested in evidence than externalists are [McGrew]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
Absence of evidence proves nothing, and weird claims need special evidence [McGrew]
Does spotting a new possibility count as evidence? [McGrew]
Every event is highly unlikely (in detail), but may be perfectly plausible [McGrew]
Criminal law needs two separate witnesses, but historians will accept one witness [McGrew]
Maybe all evidence consists of beliefs, rather than of facts [McGrew]
If all evidence is propositional, what is the evidence for the proposition? Do we face a regress? [McGrew]
Several unreliable witnesses can give good support, if they all say the same thing [McGrew]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / b. Evidentialism
Narrow evidentialism relies wholly on propositions; the wider form includes other items [McGrew]
14. Science / A. Basis of Science / 6. Falsification
Falsificationism would be naive if even a slight discrepancy in evidence killed a theory [McGrew]