41 ideas
| 18261 | A simplification which is complete constitutes a definition [Kant] |
| 10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
| 10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
| 10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
| 10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
| 10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
| 22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
| 10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
| 10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
| 10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
| 10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
| 10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
| 10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
| 10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
| 12747 | Monads are not extended, but have a kind of situation in extension [Leibniz] |
| 12748 | Only monads are substances, and bodies are collections of them [Leibniz] |
| 13184 | The division of nature into matter makes distinct appearances, and that presupposes substances [Leibniz] |
| 13188 | The only indications of reality are agreement among phenomena, and their agreement with necessities [Leibniz] |
| 12752 | Only unities have any reality [Leibniz] |
| 13187 | In actual things nothing is indefinite [Leibniz] |
| 19383 | A man's distant wife dying is a real change in him [Leibniz] |
| 13179 | A complete monad is a substance with primitive active and passive power [Leibniz] |
| 12749 | Derivate forces are in phenomena, but primitive forces are in the internal strivings of substances [Leibniz] |
| 12722 | Thought terminates in force, rather than extension [Leibniz] |
| 19379 | The law of the series, which determines future states of a substance, is what individuates it [Leibniz] |
| 13182 | Changeable accidents are modifications of unchanging essences [Leibniz] |
| 13178 | Things in different locations are different because they 'express' those locations [Leibniz] |
| 19411 | In nature there aren't even two identical straight lines, so no two bodies are alike [Leibniz] |
| 19412 | If two bodies only seem to differ in their position, those different environments will matter [Leibniz] |
| 18260 | If we knew what we know, we would be astonished [Kant] |
| 19410 | Scientific truths are supported by mutual agreement, as well as agreement with the phenomena [Leibniz] |
| 13183 | Primitive forces are internal strivings of substances, acting according to their internal laws [Leibniz] |
| 19409 | Soul represents body, but soul remains unchanged, while body continuously changes [Leibniz] |
| 11873 | Our notions may be formed from concepts, but concepts are formed from things [Leibniz] |
| 13186 | Universals are just abstractions by concealing some of the circumstances [Leibniz] |
| 13185 | Even if extension is impenetrable, this still offers no explanation for motion and its laws [Leibniz] |
| 13177 | An entelechy is a law of the series of its event within some entity [Leibniz] |
| 13093 | The only permanence in things, constituting their substance, is a law of continuity [Leibniz] |
| 13096 | The force behind motion is like a soul, with its own laws of continual change [Leibniz] |
| 13180 | Space is the order of coexisting possibles [Leibniz] |
| 13181 | Time is the order of inconsistent possibilities [Leibniz] |