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From Domains Towards a Logic of Universals: A Small Calculus for the Continuous Determination of Worlds

Brillowski, Dr. Claus (2010) From Domains Towards a Logic of Universals: A Small Calculus for the Continuous Determination of Worlds. [Preprint]

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Abstract

At the end of the 19th century, 'logic' moved from the discipline of philosophy to that of mathematics. One hundred years later, we have a plethora of formal logics. Looking at the situation form informatics, the mathematical discipline proved only a temporary shelter for `logic'. For there is Domain Theory, a constructive mathematical theory which extends the notion of computability into the continuum and spans the field of all possible deductive systems. Domain Theory describes the space of data-types which computers can ideally compute -- and computation in terms of these types. Domain Theory is constructive but only potentially operational. Here one particular operational model is derived from Domain Theory which consists of `universals', that is, model independent operands and operators. With these universals, Domains (logical models) can be approximated and continuously determined. The universal data-types and rules derived from Domain Theory relate strongly to the first formal logic conceived on philosophical grounds, Aristotelian (categorical) logic. This is no accident. For Aristotle, deduction was type-dependent and he too thought in term of type independent universal `essences'. This paper initiates the next `logical' step `beyond' Domain Theory by reconnecting `formal logic' with its origin.

Item Type:Preprint
Keywords:Logic, Aristotelian logic, Domain Theory, Computability, Data-types, Modes of being, Universals, Topological Information Storage, Problem of Induction
Subjects:Computer Science > Language
Computer Science > Dynamical Systems
Linguistics > Semantics
Linguistics > Syntax
Philosophy > Logic
ID Code:6948
Deposited By: Brillowski, Dr Claus
Deposited On:13 Sep 2010 03:57
Last Modified:11 Mar 2011 08:57

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