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==A Functional Conception of Propositional Calculus==
==A Functional Conception of Propositional Calculus==
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Out of the dimness opposite equals advance . . . .<br>
Always substance and increase,<br>
Always substance and increase,<br>
Always a knit of identity . . . . always distinction . . . .<br>
Always a knit of identity . . . . always distinction . . . .<br>
always a breed of life.</p>
always a breed of life.
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| align="right" | — Walt Whitman, ''Leaves of Grass'', [Whi, 28]
| align="right" | — Walt Whitman, ''Leaves of Grass'', [Whi, 28]
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In the general case, we start with a set of logical features {''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>} that represent properties of objects or propositions about the world. In concrete examples the features {''a''<sub>''i''</sub>} commonly appear as capital letters from an ''alphabet'' like {''A'', ''B'', ''C'', …} or as meaningful words from a linguistic ''vocabulary'' of codes. This language can be drawn from any sources, whether natural, technical, or artificial in character and interpretation. In the application to dynamic systems we tend to use the letters {''x''<sub>1</sub>, …, ''x''<sub>''n''</sub>} as our coordinate propositions, and to interpret them as denoting properties of a system's ''state'', that is, as propositions about its location in configuration space. Because I have to consider non-deterministic systems from the outset, I often use the word ''state'' in a loose sense, to denote the position or configuration component of a contemplated state vector, whether or not it ever gets a deterministic completion.
In the general case, we start with a set of logical features {''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>} that represent properties of objects or propositions about the world. In concrete examples the features {''a''<sub>''i''</sub>} commonly appear as capital letters from an ''alphabet'' like {''A'', ''B'', ''C'', …} or as meaningful words from a linguistic ''vocabulary'' of codes. This language can be drawn from any sources, whether natural, technical, or artificial in character and interpretation. In the application to dynamic systems we tend to use the letters {''x''<sub>1</sub>, …, ''x''<sub>''n''</sub>} as our coordinate propositions, and to interpret them as denoting properties of a system's ''state'', that is, as propositions about its location in configuration space. Because I have to consider non-deterministic systems from the outset, I often use the word ''state'' in a loose sense, to denote the position or configuration component of a contemplated state vector, whether or not it ever gets a deterministic completion.