Combining Texts

All the ideas for 'fragments/reports', 'Evidence' and 'Mathematics without Foundations'

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18 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
We understand some statements about all sets [Putnam]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
I do not believe mathematics either has or needs 'foundations' [Putnam]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Maybe mathematics is empirical in that we could try to change it [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Science requires more than consistency of mathematics [Putnam]
7. Existence / D. Theories of Reality / 4. Anti-realism
You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]
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
Does spotting a new possibility count as evidence? [McGrew]
Absence of evidence proves nothing, and weird claims need special 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]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]