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Full Idea
Enlightened by the Cantorian grounding of mathematics, we can assert ontology to be nothing other than mathematics itself. This has been the case ever since its Greek origin.
Clarification
Cantorian mathematics concerns large infinite numbers
Gist of Idea
Ontology is (and always has been) Cantorian mathematics
Source
Alain Badiou (Briefings on Existence [1998], 1)
Book Ref
Badiou,Alain: 'Briefings on Existence', ed/tr. Madarsz,Norman [SUNY 2006], p.40
A Reaction
There seems to be quite a strong feeling among mathematicians that new 'realms of being' are emerging from their researches. Only a Platonist, of course, is likely to find this idea sympathetic.
| 22979 | Three main questions seem to be whether a thing is, what it is, and what sort it is [Augustine] |
| 13933 | Existence questions are 'internal' (within a framework) or 'external' (concerning the whole framework) [Carnap] |
| 6523 | Positivists regard ontology as either meaningless or stipulated [Ayer, by Robinson,H] |
| 12210 | Quine's ontology is wrong; his question is scientific, and his answer is partly philosophical [Fine,K on Quine] |
| 12320 | Ontology is (and always has been) Cantorian mathematics [Badiou] |
| 7679 | Ontology is the same as the conceptual foundations of logic [Jacquette] |
| 12217 | For ontology we need, not internal or external views, but a view from outside reality [Fine,K] |
| 14594 | Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer] |
| 3517 | 'Ontology' means 'study of things which exist' [Maslin] |
| 4474 | Existence theories must match experience, possibility, logic and knowledge, and not be self-defeating [Moreland] |
| 13925 | Ontology disputes rest on more basic explanation disputes [Haslanger] |
| 23768 | A metaphysic is a set of wider explanations derived from a basic ontology [Williams,NE] |
| 23773 | Humeans say properties are passive, possibility is vast, laws are descriptions, causation is weak [Williams,NE] |
| 23779 | We shouldn't posit the existence of anything we have a word for [Williams,NE] |
| 23786 | The status quo is part of what exists, and so needs metaphysical explanation [Williams,NE] |