The Oxford and Macquarie dictionaries [5, 6] define contradiction as, ‘a lack of agreement between facts, opinions, actions etc.’ From Roget’s Thesaurus [7], we can also add the synonyms; ‘being contrary; a contrast, dissent, discordance, difference, diversity, discrepancy, incompatibility, opposite, antithesis.’

     That said, what absolutely constitutes contradiction is, of course, a matter of opinion.

     The lack of agreement between observers/observations is totally a function of their respective starting positions (both conceptual axioms and assumptions or physical position and orientation) with respect to the object of interest. The discrepancies in their data are likely scale-dependent. Dissent may exist only in the reference frame within which one or other observer primarily operates -for we can certainly find a relationship of elements within contradiction, which simultaneously separates and unites concepts. And we can sanely redefine our starting points, to find that the contradictions were only apparent, and not ‘real’ - i.e. a paradox.

TRIZ a method for contradictions resolution

     Savransky presented the origin and the types of the concept "contradiction" and proposed a typology of various contradictions [Savransky 1998, Savransky 1999b]. TRIZ identifies two types of contradictions: physical and technical. The physical contradiction is the direct opposition of two values for a parameter formulated by the same system, for example, a roller should turn in big speed to ensure the production and slow speed to ensure its cleaning in safety conditions.
     The technical contradiction is a situation in which the improvement of a parameter A leads to the deterioration of a parameter B, for example, adding a material safeguarding to increase the safety decreases the accessibility.
     There are also in the exploitation of production systems the organizational contradictions. They are situations in which the improvement of a procedure increasesworkload or system complexity. For example, the application of blanket cleaning procedure required by designer needs stopping the system and a new setting up, and so, it increases operator workload. We notice that to resolve these contradictions we falls again on physical or technical contradictions.
     TRIZ proposes a systematic and exhaustive method by: - using the contradiction matrix to resolve problems of technical contradictions [Matrix 1997; Royzen 1997], -the separation principles (in time, space and phase) and the change towards a super-system or a sub-system to resolve problems of physical contradictions. These physical contradictions are normally of technological nature related to system but physical contradictions of organizational nature were recently handled by [Hipple on 1999].

3.3. Contradiction Matrix
     Altshuller [Domb 1998; Matrix 1997], creator of TRIZ, identified 39 Features (table 1) synthesizing the factors allowing modeling the technical contradictions.

     Contradiction matrix represents the interaction between these features. The Inventive Principles (Altshuller gives 40 presented in [William 1998]) are supplied to raising these contradictions [Royzen 1997; William 1998; Cavallucci & al 1998; Gogu 1999]. lines
represent the features to be damaged and columns the features to be improved. The designer inventiveness appears in the interpretation of this generic principle for his particular problem. [Domb 1998; Matrix 1997]. Also, Marsot [Marsot 2001] presented the way of using this matrix for safety problems. This matrix is not stable and there are more versions that decline more features and Inventive Principles [Savransky 1996].