## Reviews | ||||

## Sung: Part II - Their Exibits## Chapter IV - Logical ExhibitsThis chapter is subtitled "A Whole System of the Symbols of Yi King" and presents an anlysis of the syllogism and then of dichotomous categorization.An good explanation of the syllogism on the web is given by
Wikipedia.
A good book source is Copi's The syllogism analysis begins by considering the figure of a syllogism (pp59-60). There are generally taken to be four figures, determined by the placement of the middle term, but Sung choses to align them with the trigrams, thus requiring an eight way characterization. This is obtained by taking the four figures associated each with one trigram with a yang base line, and then taking them again with converted conclusions, each associated with a trigram with a yin base line. However, converting the conclusion does not create new figures.
For example, taking the first figure with a converted conclusion is
equivalent to the forth figure. This would imply that the trigram
connected with the first figure with the converted conclusion
( ). Sung does not mention
this logical equivalence and therefore does not discuss its
implications for the trigrams.
100A more natural association would be between the figures and the bigrams: - 1st:
**10** - 2nd:
**00** - 3rd:
**11** - 4th:
**01**
1 when
distributed, 0 when not) and the second line as symbolizing the
midde term in the second premise in a similar manner. No doubt there
are other mappings that are equally appropriate.
Sung next discusses the moods of the syllogisms (pp61-63). There are sixtyfour moods, derived as from the three-place permutation of four basic sentence types. The obvious connection then, is of the sentence types to bigrams, and the resulting moods to the hexagrams. This is indeed the route that the author takes. He makes the following associations: - A (universal affirmative):
, greater yang.**11** - E (universal negative):
, greater yin.**00** - I (particular affirmative):
, smaller yang.**10** - O (particular negative):
, smaller yin.**01**
is the complement
of 00, so we might expect 11 to
represent the negation of 00. But the negation of the
universal affirmative is the particular negative, not the universal
negative.
11What this shows, and what Russell's diagram emphasises, is that the analysis is not Given that logic, and indeed the Yi itself, both have a strongly compositional nature, I take this to be a serious draw back. More could be said on this topic: there are different types of
logical negation (see, for example, Copi's description of the square
of opposition [Cop72, p155-159]).
However, such a view does not give us a consistent picture of the role
of the complement operator. When negating A or E it must be seen as a
This lack of a consistent interpretation of the complement operator is not satisfying. Instead, I suggest the following mapping is more appropriate to the syllogistic domain: - A (universal affirmative):
**11** - E (universal negative):
**10** - I (particular affirmative):
**01** - O (particular negative):
**00**
and the complement of that
is 11. However, under the revised mapping,
00 represents the particual negative, which is correct
as the negation of the universal affirmative. Thus, we can
consistently view the complement operator as producing
00contradictories, which is the usual interpretation of negation.
Whatever mapping is chosen, there is then a clear relationship
between moods and hexagrams: AAA is and so on. Sung presents this on p61.
011000This is interesting, but what the author does not address is that not all of the combinations of moods and figures (totalling 256 distinct syllogism types) represents a valid argument. I'd venture to suggest that without some way of distinguishing valid from invalid syllogisms, on the basis of their resulting hexagram/bigram mappings, that the translation is a pointless exercise. Without such a mechanism, all the author has shown is that there is a systematic way of mapping a given 64-way characterization on to the hexagrams. It seems to me that the point of mapping any domain onto the symbols of the Yi is either to illuminate some aspect of that domain or to investigate the Yi from a new perspective. Or both. If it does neither of these things then it is an empty intellectual exercise. The discussion of dichotomy (pp64-65) is straightforward and
follows the development of gua by repeated addition of lines
( |