By Denis J. Hilton
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Extra info for Contemporary Science and Natural Explanation: Commonsense Conceptions of Causality
And as a body of knowledge, metaphysics has not only returned to the principles of Aristotle's unaccomplished science of being qua being, proposed in Metaphysics, it has also rejected the universal significance of the modern turn to linguistics put forth by analytic philosophy. From this vantage point, when a thinker such as John Searle uses the term ontology to speak of the "intentionality" that drives our understanding, he limits ON ALAIN BADIOU 'S TREATMENT OF CATEGORY THEORY 25 ontological inquiry merely to ontical questions: to the empirical facts of language acts.
However, this idea of bond as an original condition of ontology seems best conceptualized in the concept of Relation , only after which Being becomes its sub ject of inquiry. The question is whether outside of Being there is identity between the event, or non·being, and the relation, or whether there is also an order of an· tecedence. To settle the question in favor of the former, it would surely be helpful to find a notion of the event within categorical thought. This does not seem to be possible.
For starters, many category theorists no longer accept a single definition given to the term foundational. Bell, for instance, cites two senses of foundational: strong and weak. The strong sense would allow all mathematical operations, as well as the current logico-metatheorical framework for mathematics-proof the ory-to be reducible to category theory. Given that such a reduction involves both a combinatorial component, regarding the inscriptional properties of the formal language, and a semantic component, regarding the interpretation and truth of the expressions of that language, Bell considers category theory to be unable to achieve its foundational ends.