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Let'stake a very simple example
¡Ýincolloquial American English, there is a common expression, often heard inexchanges between people in the context of working to resolve difference:

  No, that is unfair - you are comparing apples and oranges!¡¡


In particular, note the implication of the use of the idiom apples and orange. The commonly understood meaning of this is that there is something incomparable about the two sets of objects named by the terms, apples and oranges that renders the comparison invalid.

So, consider the two sets of objects in the world named by apples and oranges. Are these two sets to be classified as the same or different logical types? Now a gap in the original definition reveals itself with clarity. Consider the following descriptions of intention: 


From the point of view of bureaucrat with the intention of preparing a report on agricultural productivity of various parts of the country, when tallying the total production of fruit from some region of a country's agricultural resources, apples and oranges are of the same logical type. They are both fruits and will therefore be lumped together for purposes of determining that region's contribution to the total production of fruit.


From the point of view of a chef, with the intention of preparing a delicious dish that uses fruit as one of its ingredients, there are critical differences between apples and oranges. Canard aux Pomme (if indeed it exists) would be decidedly distinct from Canard a L'Orange.


So what is going on here? We propose that the critical variable is the intention of the person doing the classification. This intention defines a mental space in which an isomorphic mapping occurs or fails to occur.


There are features of the two sets involved in this example that are shared characteristics: both grow on trees, both contain significant amounts of certain natural vitamins, both are offered as snacks and dessert dishes, both are important commercial crops grown, for example, in the USA¡Ä


There are also features of these two sets of objects that are quite distinct: they are attacked by different agricultural pests, members of one set (apples) are typically eaten with the skin on while members of the other set (oranges) are not, they have quite distinctive flavors, their chemical analysis is distinct¡Ä


Therefore to determine whether two sets (or more) of objects are of the same or a different logical type requires the person proposing the classification to first specify their intention. Their intention thereby defines a mental space. Implicit in their intention (and explicit in the mental space so generated) will be a focus on certain characteristics of the members of the two (or more) sets involved
¡Ýthe difference between the bureaucrat and the chef. This is the operational meaning of the adjective essential in the originally flawed phrase, in all essential characteristics.


We may then conclude that apples and oranges are of the same logical type if the characteristics that are considered essential from the point of view of the intention carried by the classifying agent map isomorphically, or equivalently in the mental space generated by the intention of the classifying agent, and otherwise not.
('Whispering in the Wind' p.297-298)


Whispering In The Wind
John Grinder 
Carmen Bostic St. Clair
J & C Enterprises
2001-12-31



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There are two ways to specify a set:

1. A list or enumeration of the contents, the members of the set involved
¡¡¡¡¡Äextension

2. the set membership rules 
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Whispering In The Wind
John Grinder
Carmen Bostic St. Clair
John & Carmen Enterprise
2001-12-31






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µ­»ö¹¹¿·Æü¡§2022/06/03

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Logical Tyoes and Logical Levels


As mentioned in the text immediately above, there has been little or no attention until present given to making ordering relationships explicit within NLP practice. Without such an explicit discussion, work in NLP is significantly flawed ¡Ý thus, the care with which the issue, for example, of hierarchies was presented. In that discussion as well as in Part­µ, Epistemology, we developed the notion of several possible ordering relationships operating in hierarchies: more specifically, part/whole hierarchical orderings and what we referred to as logical level hierarchical orderings.

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Logical Levels


For any two (or more) arbitrary elements in a tree structure (hierarchy) generated by logical inclusion, a and b, say, element a will be said to be at a a higher logical level than b just in case a contains b in one of its partitions below a in the hierarchy.


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Logical inclusion itself is a well-defined ordering relationship specified by the two properties of constriction and inheritability (see Part­µ, Epistemology and Part­· and Chunking/Logical Levels for a fuller persentation):

1. constriction - reduced coverage under each successive partition induced by relative clause formation

2. inheritability - the preservation of the set membership criteria under partition by relative clause formation

This usage seems to accord well with the conventional use of the word level with its accompanying suggestion of a visual display¡Ýnamely, a vertically oriented ordering¡Ýa hierarchy.

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partition¡Ë¤Î£±¤Ä¤Ë b ¤¬´Þ¤Þ¤ì¤Æ¤¤¤ë¾ì¹ç¤Ë¤Î¤ß¡¢Í×ÁÇ a ¤Ï b ¤è¤ê¤â¹â¤¤ÏÀÍý¥ì¥Ù¥ë¤Ë¤¢¤ë¤È¸À¤¤¤Þ¤¹¡£

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¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡Äb¡Ä¡¡¡¡¡¡¡Äc¡Ä


ÏÀÍýŪÊñ´Þ¡ÊLogical inclusion¡Ë¼«ÂΤϡ¢¼ý½Ì¡Êconstriction¡Ë¤È·Ñ¾µÀ­¡Êinheritability¡Ë¤ÎÆó¤Ä¤ÎÆÃÀ­¤Ë¤è¤Ã¤ÆÌÀ³Î¤Ëµ¬Äꤵ¤ì¤¿½ç½ø´Ø·¸¤Ç¤¹¡£¡Ê¤è¤ê½¼¼Â¤·¤¿¥×¥ì¥¼¥ó¥Æ¡¼¥·¥ç¥ó¤Ï¡¢Part­µÇ§¼±ÏÀ¡¢Part­·¤ª¤è¤Ó¥Á¥ã¥ó¥­¥ó¥°¡¿ÏÀÍý¥ì¥Ù¥ë¤ò»²¾È¡Ë

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Hierarcies formed on the part/whole relationship are very different creatures than hierarchies generated by logical inclusion. The reduced scope principle ¡Ý constriction ¡Ý seems to be inverted ¡Ý that is, in general, the further down a hierarchy specified by the part/whole relationship you go, the larger the scope, the greater the coverage of events by the sets enumerated. Sets lower in the hierarchy have more members than those above them. There is no clear generalizatoin with respect to the inheritability requirement that we have been able to formulate. It seems that presently transparent to us.

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Amazon:

Whispering In The Wind
John Grinder
Carmen Bostic St. Clair
John & Carmen Enterprise
2001-12-31






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