To: |
"[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx> |
---|---|

Cc: |
Avril Styrman <Avril.Styrman@xxxxxxxxxxx> |

From: |
"Stavros Macrakis" <macrakis@xxxxxxxxxxxx> |

Date: |
Mon, 19 Nov 2007 14:25:10 -0500 |

Message-id: |
<8b356f880711191125q4c196af5l449a890b8ab4ed7c@xxxxxxxxxxxxxx> |

Re "motivation" and "intention" in mathematics, see Imre Lakatos's classic Proofs and Refutations. This is a fabulous work which should be read by everyone with an interest in mathematics. It doesn't really discuss the microstructure of proofs (why was this step taken here), but it does discuss the motivation and intention of proofs, examples, counterexamples, theorems, definitions, etc. To compress the argument to the absolute minimum, he essentially shows that you don't "have" the axioms, rules of inference, theorem, and proof; they are generated by the process of doing math.
The amazing thing about this book is that it manages to be philosophy of mathematics at the same time as history of mathematics (the Euler characteristic in particular). And it is a good read. I can't recommend it too highly. And you know what, this is not a tangent: it is actually directly relevant to the Ontology forum: for example, how do you deal with exceptional cases (penguins are birds without wings)? Which comes first, definitions (sc. ontologies) or theorems (sc. systems)? Etc. -s Imagine you have _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (01) |

Previous by Date: | Re: [ontolog-forum] formal systems, common logic and lbase, Avril Styrman |
---|---|

Next by Date: | Re: [ontolog-forum] formal systems, common logic and lbase, Pat Hayes |

Previous by Thread: | Re: [ontolog-forum] formal systems, common logic and lbase, Avril Styrman |

Next by Thread: | Re: [ontolog-forum] formal systems, common logic and lbase, Pat Hayes |

Indexes: | [Date]
[Thread]
[Top]
[All Lists] |