Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Academica' and 'Human Freedom and the Self'

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19 ideas

2. Reason / C. Styles of Reason / 1. Dialectic
Dialectic is speech cast in the form of logical argument [Cicero]
3. Truth / A. Truth Problems / 1. Truth
There cannot be more than one truth [Cicero]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem [Cicero]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
12. Knowledge Sources / B. Perception / 1. Perception
If we have complete healthy senses, what more could the gods give us? [Cicero]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
How can there be a memory of what is false? [Cicero]
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
Every true presentation can have a false one of the same quality [Cicero]
16. Persons / F. Free Will / 4. For Free Will
If actions are not caused by other events, and are not causeless, they must be caused by the person [Chisholm]
16. Persons / F. Free Will / 5. Against Free Will
For Hobbes (but not for Kant) a person's actions can be deduced from their desires and beliefs [Chisholm]
If free will miraculously interrupts causation, animals might do that; why would we want to do it? [Frankfurt on Chisholm]
20. Action / C. Motives for Action / 4. Responsibility for Actions
Responsibility seems to conflict with events being either caused or not caused [Chisholm]
Desires may rule us, but are we responsible for our desires? [Chisholm]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Virtues must be very detached, to avoid being motivated by pleasure [Cicero]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Causation among objects relates either events or states [Chisholm]