The curious structure of an MTN: Difference between revisions

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 Take the alternative statements about cricket and rugby balls in the panel at right. The variables at play are:
-*round or oval ball
+*round or oval ball (relevant to all games)
-*red or white ball
+*red or white ball (relevant to all cricket games)
-*rugby or cricket
+*rugby or cricket, (relevant to all games) which in turn breaks into
-*test or one-day cricket
+:*test or one-day (relevant to cricket)
-*rugby union or rugby league
+:*union or league (relevant to rugby
-There are ten variables here, but how you structure them can great more or less complicatedness. If we try to create a single proposition that covers all eventuality, we commit ourselves to a lot downstream branching.
+How you structure these variables can great more or less complicatedness. If we try to create a single proposition that covers all eventualities, we commit ourselves to a lot downstream branching, because that our single logical structure must accommodate all the permutations.
-The '''subject''' of the sentence and '''sequence''' of the branches makes a difference. In the first example the ball is the subject. Since all four codes use a ball, we must explain all of them, and we commit to a permissive “may” rather than a constrictive “must”. If we then put our first gate on the colour of the ball — irrelevant in rugby — we commit to articulating some propositions with no limited significance. As far as this proposition is concerned there is no difference between rugby union and rugby league, but we have committed ourselves to a particular structure that exhausts all permutations, whether or not they have any difference. By splitting proposition in two we can deal with both rugby codes without any logic
+The '''subject''' of the sentence and '''sequence''' of the branches makes a difference.  For example, focussing on the ball first then its colour then its shape, and articulating these by reference to the games, commits to sixteen branches. If we break the proposition into two and focus first on shape, we can reduce this to five. if we reframe the proposition to focus on the game, we can get it down to the three, which is the minimum.
+There is doubtless some information theory that optimises the logical structure, but intuitively it seems to us common options should be delayed as far as possible, and where games are largely common, separating out the points where they differ into a separate set of propositions may help.
+Back to our medium term notes:
 {{sa}}