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The curious structure of an MTN: Difference between revisions
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{{bluetable|align=right|width=50}} | {{bluetable|align=right|width=50}} | ||
'''On what kind of ball may be used with what kind of game''' <br> | '''On what kind of ball may be used with what kind of game''' <br> | ||
A single, branching proposition: | A single, branching proposition where the subject is the ball: | ||
<small>{{subtable| | <small>{{subtable| | ||
1. A ball: <br> | 1. A ball: <br> | ||
(a) if it is red | (a) if it is red | ||
:(i) if it is round | :(i) if it is round | ||
::(A) | ::(A) must not be used for rugby union | ||
::(B) | ::(B) must not be used for rugby league | ||
::(C) may be used for test cricket | ::(C) may be used for test cricket | ||
::(D) | ::(D) must not be used for one-day cricket | ||
:(ii) if it is oval: | :(ii) if it is oval: | ||
::(A) may be used for rugby union | ::(A) may be used for rugby union | ||
::(B) may be used for rugby league | ::(B) may be used for rugby league | ||
::(C) | ::(C) must not be used for test cricket | ||
::(D) | ::(D) must not be used for one-day cricket | ||
(b) if it is white: | (b) if it is white: | ||
:(i) if it is round: | :(i) if it is round: | ||
::(A) | ::(A) must not be used for rugby union | ||
::(B) | ::(B) must not be used for rugby league | ||
::(C) | ::(C) must not be used for test cricket | ||
::(D) may be used for one-day cricket | ::(D) may be used for one-day cricket | ||
:(ii) if it is oval: | :(ii) if it is oval: | ||
::(A) may be used for rugby union | ::(A) may be used for rugby union | ||
::(B) may be used for rugby league | ::(B) may be used for rugby league | ||
::(C) | ::(C) must not be used for test cricket | ||
::(D) | ::(D) must not be used for one-day cricket | ||
}}</small> | }}</small> | ||
Two branching propositions: | Two branching propositions where the subject is the ball: | ||
<small>{{subtable| | <small>{{subtable| | ||
1. An ball that is oval: <br> | 1. An ball that is oval: <br> | ||
:(i) may be used for rugby | :(i) may be used for rugby | ||
:(ii) | :(ii) must not be used for cricket | ||
2. A ball that is round: | 2. A ball that is round: | ||
:(i) | :(i) must not be used for rugby | ||
:(ii) if it is red: | :(ii) if it is red: | ||
::(a) may be used for test cricket | ::(a) may be used for test cricket | ||
:::(b) | :::(b) must not be used for one-day cricket | ||
:(iii) if it is white: | :(iii) if it is white: | ||
::(a) | ::(a) must not be used for test cricket | ||
:::(b) may be used for one-day cricket | :::(b) may be used for one-day cricket | ||
}}</small> | }}</small> | ||
Three non-branching propositions. | Three non-branching propositions where the subject is the game. | ||
<small>{{subtable| | <small>{{subtable| | ||
1. Rugby must be played with a ball that is oval <br> | 1. Rugby must be played with a ball that is oval <br> | ||
2. | 2. Cricket must be played with a ball that is round and:<br> | ||
:(i) in test cricket, red <br> | |||
:(ii) in one-day cricket, white<br> | |||
}}</small> | }}</small> | ||
{{tablebottom}} | {{tablebottom}} | ||
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*test or one-day cricket | *test or one-day cricket | ||
*rugby union or rugby league | *rugby union or rugby league | ||
There are ten variables here, but how you structure them can great more or less complicatedness. | 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. | ||
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 | |||
{{sa}} | {{sa}} | ||