Piero Scaruffi(Copyright © 2013 Piero Scaruffi | Legal restrictions )
These are excerpts and elaborations from my book "The Nature of Consciousness"
Histories of the World
During the 1980s several techniques were proposed for re-founding Physics on a more practical basis.
John McCarthy's “Situation Calculus” (“Situations, actions, and causal laws”, 1963) represents temporally limited events as "situations" (snapshots of the world at a given time), by associating a situation of the world (a set of facts that are true) to each moment in time. Actions and events are represented mathematically as mathematical functions from states to states. An interval of time is a sequence of situations, a "chronicle" of the world. The history of the world is a partially ordered sequence of states and actions. A state is expressed by means of logical expressions that relate objects in that state. An action is expressed by a function that relates each state to another state. The property of states is permanence, the property of actions is change. Each situation is expressed by a formula of first-order Predicate Logic. The advantage of this logical apparatus is that causal relations between two situations can be computed.
The elementary unit of measure for common sense is not the point, but the interval. Which interval makes sense depends on the domain: history is satisfied with years (and sometimes centuries), but birth dates require the day.
Points require Physics' differential equations, but intervals can be handled with a logic of time that deals with their ordering relationship.
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