Combining Philosophers

All the ideas for Eubulides, Steven Pinker and Peter Koellner

expand these ideas     |    start again     |     specify just one area for these philosophers


19 ideas

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 / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
5. Theory of Logic / L. Paradox / 1. Paradox
If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]
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]
7. Existence / C. Structure of Existence / 2. Reduction
Good reductionism connects fields of knowledge, but doesn't replace one with another [Pinker]
12. Knowledge Sources / D. Empiricism / 2. Associationism
Connectionists say the mind is a general purpose learning device [Pinker]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
Is memory stored in protein sequences, neurons, synapses, or synapse-strengths? [Pinker]
16. Persons / F. Free Will / 5. Against Free Will
Roundworms live successfully with 302 neurons, so human freedom comes from our trillions [Pinker]
17. Mind and Body / E. Mind as Physical / 4. Connectionism
Neural networks can generalise their training, e.g. truths about tigers apply mostly to lions [Pinker]
There are five types of reasoning that seem beyond connectionist systems [Pinker, by PG]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Many think that accepting human nature is to accept innumerable evils [Pinker]
27. Natural Reality / G. Biology / 2. Life
In 1828, the stuff of life was shown to be ordinary chemistry, not a magic gel [Pinker]
27. Natural Reality / G. Biology / 3. Evolution
All the evidence says evolution is cruel and wasteful, not intelligent [Pinker]
Intelligent Design says that every unexplained phenomenon must be design, by default [Pinker]