Sins and logical fallacies

Towards a Logico-mathematical Formalization of "Sin": Fundamental memetic organization of faith-based governance strategies (Part #3)

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In this respect, and in relation to the checklist of logical fallacies (cf Seven Deadly Sins of Fundamentalism, 2004), the author Stephen Downes (Stephen's Guide to the Logical Fallacies, 1995-2001) has separately distinguished what he terms a Categorical Converter (1996). This is a visual representation of all possible logical relationships between individual categorical propositions. It may be used to test the validity of an inference from one proposition to another. In other words, it represents all possible inferences using the rules of:

• Contradiction
• Contrary
• Subcontrary
• Subalternation
• Superalternation
• Obversion
• Conversion
• Transposition

Downes describes the use of the converter through a sequence of eight structured images (Using the Category Converter, 1996), as well as describing how this is constructed (Constructing the Categorical Converter, 1996). Such work focuses the question as to whether there is some kind of mapping from the "sins", variously understood, onto the geometric framework of Downes "converter". It is interesting to note that the rules he lists above all have some significance in geometric transformations, notably in relation to images -- and at least through the terminology used [more | more | more]. In this context, any reflection on the "music of the spheres" might benefit from recognition of the suggestive relationship of these operations to the rules of harmony.

A special interpretation of classical propositional calculus has been developed by Vladimir A Lefebvre (A Formal Approach to the Problem of Good and Evil, General Systems, 22, 1977, pp. 183-185). He notes:

The initial and indefinable concepts are good evil conflict union. The concepts "conflict" and "union" are spiritual categories and not part of the strategy of interaction. In the formal calculus of game theory, ethical problems are completely ignored; in the given approach stratgegical problems are ignored. In constructing a formalization of ethical problems, one must consider human reflection and reflective structures (outlined in Vladimir A Lefebvre, The Structure of Human Awareness: toward a symbolic language of human reflexion, 1977)

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