To: |
<rick@xxxxxxxxxxxxxx>, "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx> |
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From: |
"Azamat" <abdoul@xxxxxxxxxxxxxx> |

Date: |
Sun, 2 Mar 2008 20:35:37 +0200 |

Message-id: |
<002201c87c94$37d6fee0$010aa8c0@homepc> |

Saturday, March 01, 2008 1:12 AM, Rick wrote: (01) > Could you please define *ontologism*, how it replaces logicism and how it *covers* category theory ? The references I'm finding don't seem relevant to the discussion. (02) Ontologism is the theory that all of scientific and mathematical principles can be derived from a universal ontology, its fundamental classes, rules, axioms or constraints. The core of it is an intersection of fundamental mathematics and universal ontology, resulting in mathematical ontology or ontological mathematics; don't mix with formal logical ontology. (03) In such extensive knowledge system, the axioms of the set theory and order theory, the category theory and mereology will appear as derived truths (theorems) of ontological axioms of entities and relations. (04) For instance, the undefined notions of the above mathematical theories (the set membership relation, the set inclusion relation, the mapping relation, the part-whole relation) come as special kinds of general relationship. (05) Considering the lack of a single foundation of mathematics and science, such a scenario is very and very possible, if unavoidable. (06) Since the proposal is rather new and highly controversial, I better refer you to a more detailed account: (07) Part III. THE WORLD CODE: Mathematical Ontology as the Real Road to Reality. (08) > I don't see the A word here: Abduction. I don't go anywhere without it. (09) I am aware of the Peirce's idea of scientific activity as involving induction, abduction, and deduction. As far as the range of connotations for abductive reasoning is fuzzy http://en.wikipedia.org/wiki/Abductive_reasoning, i try to avoid its use. It looks as a kind of inferential reasoning, where also included implication, corollary, analogy, extrapolation, derivation. But abduction is hardly an intuitive generalization. (010) >As an aside, have folks been tracking what Mark Greaves is up to at Vulcan > |

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