Combining Philosophers
Ideas for Empedocles, Robert S. Wolf and Carlo Rovelli
expand these ideas
|
start again
|
choose
another area for these philosophers
display all the ideas for this combination of philosophers
11 ideas
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13534
|
In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS]
|
13535
|
First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS]
|
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
13519
|
Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS]
|
13531
|
Model theory reveals the structures of mathematics [Wolf,RS]
|
13532
|
Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS]
|
13533
|
First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS]
|
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
13537
|
An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS]
|
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13539
|
The LST Theorem is a serious limitation of first-order logic [Wolf,RS]
|
5. Theory of Logic / K. Features of Logics / 4. Completeness
13538
|
If a theory is complete, only a more powerful language can strengthen it [Wolf,RS]
|
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
13525
|
Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS]
|
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
20457
|
Zeno assumes collecting an infinity of things makes an infinite thing [Rovelli]
|