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Lesson 4 Contradictions

Lesson 4 Contradictions

| On 04, Nov 1999

Semyon D. Savransky,
The TRIZ Experts, Silicon Valley, USA
(E-mail: )


  1. Introduction
  2. Contradictions: Ontology
  3. Structure of a Problem
  4. Conclusion


Preface: The paper below is a part of the lesson from the “Hands-On TRIZ Training” that Dr. Semyon D. Savransky and The TRIZ Experts are running via the Internet. You can find the information about the course at

1 Introduction

Throughout the history of human knowledge, there have been two conceptions concerning the law of development of the universe, the idealistic conception and the materialistic conception, which form two opposite world outlooks. TRIZ ideology is based on 2 major cornerstones: Contradiction and Ideality – these global concepts and their application in engineering will be described here. As it is well known, the Contradiction is the basic law of materialist dialectics, and the second cornerstone is the essence of the idealism. These two opposite philosophic approaches are united in TRIZ that use their mutual co-operation. Perhaps, this amalgamate predetermines the unique power of TRIZ. The concepts of Ideality and/or Contradiction should be consciously included in any process of solving the inventive problems. Hence we consider these main TRIZ concepts in this and the next Lessons.

2 Contradictions: Ontology

The contradiction means literally “saying ‘No'”, but more generally refers to the propositions that assert apparently incompatible or opposite things. George Berkeley introduced the contradiction concept in the famous book “A treatise concerning the principles of human knowledge” in 1710. As the main point of critique of the formal logic developed by G.W.F. Hegel between 1812 and 1816, contradiction is the most popular concept for introducing dialectical ideas. For example, F. Engels wrote at the end of the XIXth century that the unity (interpenetration) of opposites is a basic law of dialectics, and V. I. Lenin said about it: “The splitting of a single whole and the cognition of its contradictory parts is the essence … of dialectics”. Lenin draws attention to the fact that the contradiction is central not just to “logic” (as normally understood) but to cognition (analysis), and that the dialectical concept of contradiction is not the contradiction between two things external to one another, but the contradiction which is at the essence of a thing. According to the dialectics contradictoriness within a thing is the fundamental cause of its development, and they have a universal presence in many fields. In the work “On the Question of Dialectics”V.I Lenin illustrated the universality of mutually contradictory phenomena as follows:

in mathematics: plus and minus, differential and integral;

in physics: positive and negative electrical charges, mechanical action and reaction;

in chemistry: the combination and dissociation of atoms;

in war: offense and defense, victory and fault;

and stressed that one contradiction cannot exist without the other.

As mentioned before, TRIZ states that often the most effective inventive solution of a problem is such solution that overcomes some contradictions. The contradiction occurs when we are trying to improve one parameter or characteristic of a technique (a technical system – TS or/and a technological process -TP) and then the same or other characteristics or parameters of the technique are affected negatively.

When a solver has extracted a contradiction in the problem that fits into the classes defined above it became easy to find a variety of creative and effective solutions of this problem. But usually a problem is NOT solved if its contradiction is NOT overcome as it shown in the following example:

A new and more powerful engine is installed at an airplane in order to increase the speed of the airplane. This engine increases the total weight of the airplane. However, the wings now cannot support the heavier airplane during take off. So, the size of the wings is increased. Now, there is more drag force that slows down the airplane.

The goal is not achieved here. This happens because the central contradiction was not resolved. A solver should keep or strengthen the characteristic (speed) in such a way that to keep or improve other properties (weight, wings size). This way is almost always non-obvious for solution and assumes some creativity of a problem solver, or …… just the knowledge of TRIZ and experience in this methodology. In contrast to a routine design that leads to a smoothing of the contradiction (the current TRADE-OFF dogma) and/or choosing one of the preferable combinations in conflict (the OROR principle), a design based on TRIZ aspires to permit and solve the contradiction, creating system, in which the improvement of one characteristics is not accompanied by deterioration of others (the ANDAND dogma, a new paradigm that perhaps will be the leading in the future engineering).

G. S. Altshuller [1] distinguished the following three types of contradictions:

    A). Administrative contradictions:

Something is required to make, to receive some result, to avoid the undesirable phenomenon, but it is not known how to achieve the result. For example, we want to increase quality of production and decrease cost of raw materials. Such form of a problem reminds one of an inventive situation. The administrative contradiction itself is provisional, has no heuristic value, and does not show a direction to the answer.

    B). Technical contradictions:

An action is simultaneously useful and harmful or it causes Useful Function(s) and Harmful Function(s) /UF and HF/; the introduction (or amplification) of the useful action or the recession (or easing) of the harmful effect leads to deterioration of some subsystems or the whole system, e.g., an inadmissible complexity of the system.

The technical contradiction represents the conflict between TWO SUBSYSTEMS of a system. For example, we want to increase the penetration depth of ions into a semiconductor and decrease the electrical power (energy source) that is necessary for the ion implanter operation.

Such contradictions occur if:

– the creation (intensification) of the useful function in one subsystem causes the creation of new harmful function or the intensification of the existing harmful function in another subsystem;

– the elimination (reduction) of the harmful function in one subsystem causes the deterioration of the useful function in another subsystem;

– the intensification of the useful function or reduction of the harmful function in one subsystem causes the unacceptable complication of other subsystem or even the whole technique.

    C). Physical contradictions:

A given subsystem (element) should have the property A to execute necessary function and the property non-A /anti-A/ to satisfy the conditions of a problem.

The physical contradiction implies inconsistent requirements to a physical condition OF THE SAME element of a Technical System (TS) or operation of a Technological Process (TP), i.e., the same key subsystem of a technique. For example, we want that an insulator in semiconductor chips has low dielectric constant k in order to reduce parasitic capacities and we want that insulator in semiconductor chips has high dielectric constant k in order to store information better.

Such contradictions occurs also if:

– the intensification of the useful function in a subsystem causes the simultaneously intensification of the existing harmful function in the same key subsystem;

– the reduction of the harmful function in a subsystem causes the simultaneously reduction of the useful function in the same key subsystem.

For example, if the gate bias voltage increases a metal-oxide semiconductor transistor can have bigger threshold voltage (good for power MOSFETs) but the transistor will operate at lower frequencies (bad); if the gate bias voltage decreases a metal-oxide semiconductor transistor can operate at higher frequencies (good) but the high-speed changes of the gate voltage will lead to unanticipated triggering of the transistor (bad).

The physical contradictions as well as the technical contradictions are usually crystallized during the special problem analysis that will be described particularly in the Lesson 18. Sometime the technical contradictions can be obtained by analysis of technique in the framework of Root Cause Analysis or Goldratt’s Theory of Constraints [2, 3] .

According to G.S. Altshuller [1] an inventive situation is usually inherent in some groups of the technical and/or physical contradictions in the technique. The choice of the certain contradiction from the group means transition from an inventive situation to the beginning of the problem solution. Successful formulation of the physical contradiction shows usually the problem’s nucleus. The contradiction is extremely intensified in this case, that often makes the problem’s solution straightforward. Let illustrate the simplification of a problem along with the names of logical operators for two most common contradictions in TRIZ

The administrative contradiction:

It is necessary to detect the number of small < 0.3 micrometers particles in a liquid with very high optical purity. Particles reflect light very badly even if we use a laser.

What to do?

The technical contradiction

If the particles are very small the liquid stays optical pure, but the particles are invisible. XOR if the particles are big they are detectable, but the liquid is not pure.

The physical contradiction:

The particles has to increase their sizes to be viewed ANDNOT to increase the sizes to keep the optical purity of the liquid.

After such transition we reduce the difficulty of the problem.

It is possible to label the so-called physical contradictions as ANDNOT operator and present the so-called technical contradictions through XOR operators, but these terms are not common in TRIZ researches yet.

The set of contradictions proposed by G.S. Altshuller [1] is not full for various problems outside engineering [5] .

In general various contradictions can be separated into three major groups:

  • Natural,
  • Social,
  • Engineering.

A more detail scheme of contradictions is shown in figure 1. The consecutive reformulation of the contradictions arouse by the problem occurs during the solution of a problem in the framework of TRIZ. Each following contradiction makes our understanding of the problem better.

Figure 1. Types of contradictions. Note, that usually difficulties of contradiction resolution increase from the bottom to the top, and from the left to the right side of the each line of this figure [5]

Let us discuss the first two groups of contradictions here, the last group – the engineering contradictions – will be described in great details in this course(hyperlink no longer available) later on.

We divided the natural contradictions into two groups.

Fundamental contradictions show that natural laws limit possible solution of the problem. The impossibility to have temperature below 0 degree K or speed above the light velocity are the examples of fundamental contradictions. Perhaps, such contradictions represent only our current knowledge and some of them can be eliminated in the future.

Cosmological contradictions represent restrictions caused by Earth conditions. For example, it is impossible to keep any weight at thin beam because of the gravity at our planet, or a car cannot exhaust pure hydrogen because of explosive interaction with oxygen in our atmosphere.

If a natural contradiction is not possible to overcome (at least currently for the cosmological contradictions), we can rather speak about constraints and trade-off solutions of the problem.

It seems useful to divide the social contradictions into three groups (see the figure 1 above) according to the major restraints to innovation at different society levels (see the table 1 below).

Table 1 Major Restraints to Innovation




Stereotyped thinking or/and lack of creativity (especially for elder specialists) or/and the psychological inertia Beliefs in some official functional method (often called a scientific) The “holiness” of the current political/economic system
Risk of failure Money-disposal programs Prejudice to change
Lack of knowledge or/and memory Decision-making or/and leadership styles The occidental-oriental differing views of goals
Self-imposed constraints (e.g., taboos, afraid of questioning) Time-handling schedules Bias against diagnosis of frontiers of the current paradigm

There is a simple hierarchy between different levels of the social contradictions, and it is easy to break Individual or Managerial restraints than Cultural ones.

The knowledge of the society level to which such contradiction belongs and types of restraints helps choose the strategy for the problem’s solution.

It is necessary to note that studies of social contradictions in TRIZ intersect with psychology, management and other social disciplines but, unfortunately, often the researchers don’t know results of studies in other fields.

At the first glance the administrative contradictions (as they were defined by G. S. Altshuller) should be included in the social contradictions, but more detailed analysis shows that the administrative contradictions can be often located between the social and engineering contradictions at the figure 1.

It seems possible to resolve the Managerial – Organizational contradictions in the framework of TRIZ methodology and such research is the outgoing activity of some TRIZ experts. Often cultural and individual contradictions can be presented as the problem’s constrains. On the other hand, the human problems often do not have a contradiction. There are two opposite ways for solving routine problems without contradictions:

Compromise Try not to strengthen too much a gain in one quality without loosing considerable in another quality.
Radical Keep or strengthen one quality at the expense of another quality if one of the requirements to the system in the problem is inconsiderable and does not lead to losses in the system.

Contrary to the solutions of the natural and engineering contradictions, “trade-offs” compromise solutions in the human problems can frequently provide good resolutions. Perhaps, this difference is based on various types of systems: the technical systems usually have determined nature while nature of the human systems is probable or stochastic.
We will discuss how to find the solutions for various contradictions in the following lessons.

3 Structure of a Problem

Because of diversity of various technical systems (TS) and technological processes (TP), variety of problems can occur in technique. Some relations between useful, neutral and harmful functions (see the Lesson 3 aboutUF, NF and HF) exist inherently in any TS or TP. On the other hand, any TS or TP can be presented as a set of subsystems. Initially the structures of technical systems or technological processes say almost nothing about the problem solving and requirements for the solution. They simply describe the status quo of a technique. When conflicts between the functions appear in a technique they can be presented in the structures of problems that reflect type of relations between UF, NF and HF and structure of technique. In order to present such conflicts through the technical or physical contradictions we will consider only UF and HF in this section.Representation of contradictions together with the hierarchical structure of technique allows one to figure out a topology (structure) of a problem.

It is possible to figure out a few generic problems’ structures [5] :

Point problems have the physical or natural contradictions inside a single subsystem or NO contradictions at all. Point problems with the physical contradiction are usually hidden, but they are often the root cause of all other problems. A point problem usually appears after reduction of semantic links of more complicated problems structures or due to careful analysis of problems set in a technique.

In non-contradiction case the point problems are required to produce practically unconstrained different ideas, so creative methods of idea generation such as brainstorming, synectics, lateral thinking, etc. are quite useful for this as well as for social contradictions.

Pair problems have the single technical contradiction between functions in two subsystems. They usually appear after reduction of inventive situation or more complicated structures to a set of independent technical contradictions.

Linear problems have chains of engineering contradictions. They usually can be presented as a sequence of dependent technical and physical contradictions in two or more different subsystems.

Network problems have a loop of several dependent contradictions (often so-called mathematical). They appear when l, m, and n subsystems depend on each other and/or can be dependent on k subsystem, hence we have several technical and/or physical contradictions that are linked.

Triangle problems have three dependent engineering contradictions. A triangleproblem is the simplest case of a network problem.

Star problems have sets of independent technical or mathematical contradictions with the common root (that is usually a physical contradiction). They usually appear when one characteristic (or subsystem) k of a system gets better, but other l, m, n, … get worse. If contradictions A with B, C and D are independent, the star problems can be reduced to the pair problems. Note that a star problem often has a hidden physical contradiction in the root, hence can be reduced to a point problem.

Beyond such generic (primitive) structures, some more complex and even puzzle structures exist, such as the hierarchical (that reflect usually the structure of TS and TP), etc. Such problems cannot be solved “as is” and should be reduced to one or a few generic structures. In the framework of TRIZ, in order to convert a complex structure of problem (e.g., non-single triangle or hierarchical) into a simple generic problem’s structure (e.g., point or pair or triangle), it is essential to reformulate the problem in terms of distinguish subsystems, functions (primary, secondary, etc. /see the previous lesson/) and resources /will be discussed in the following lesson/; it is imperative to crystallize a contradiction in the problem; and it is important to systematically collect, organize and document all important information related to the situation.

For simplicity problems in technical systems are discussed here, although the proposed ideas are also correct for the technological processes as well. The different structures of problems can be presented using the following questionnaire [4] as the guide to semantics of the problems:

  • Useful function

  • Harmful function

  • 1. Is this useful function UFn required for another useful function(s) UFn+l?
  • 2. Does this useful function UFn cause any harmful effect(s) HFn?
    1. Does this useful function UFn have been introduced to eliminate a harmful effect(s) HFn?
    2. Does this useful function UFn require another useful function(s) in order to perform UFn-1?
    1. Does this harmful function HFn cause another harmful function(s) HFn+1?
    2. Is this harmful function HFn-1caused by another harmful function(s) HFn?
  • 7. Is this harmful function HFn caused by a useful function(s) UFn?
  • 8. Does a useful function UFn have been introduced to eliminate this harmful function(s) HFn?
  • SIGNS: cause, require, eliminate

  • It seems beneficial to present some aims of a solver in terms of simple structures of problems [5] :

    POINT with the physical contradiction: Find a way to enhance, provide UFn that eliminates, reduces, prevents or does not cause HFn in the SAME subsystem if UFn causes HFn and visa versa:

    A high-k insulator improves the information storage in a semiconductor chip (UF) but increases the parasitic capacities in it, therefore decreases the speed of information exchange (HF) inside the same chip.

    PAIR: Find a way to resolve a SINGLE technical contradiction by which UF1 should rise or eliminate HF1 and should not cause some HF2 or increase of HF2 in ANOTHER subsystem or/and UF1 should provide another UF2 and should not cause grown or creation of HF2 in ANOTHER subsystem, i.e.

    UFn causes or/and require HFk (k n)

    The pair problem is defined by two subsystems and at least one link.

    Let consider PAIR problem “UFn requires HFk” in TS ground transport (cars, buses, petroleum sources, gas stations, etc.). Primary UF of subsystem N (transport carriers)

    “to transport objects” requires expenses refinery of petroleum into gas that is HF of subsystem K (energy suppliers and sources).

    TRIANGLE/NETWORK: Find a way to solve a loop of DEPENDENT contradictions, i.e.

    UFn causes HFk AND HFk causes UFl WHILE UFl causes HFn (k l n).

    Note that the illustration of a network problem reflects a hierarchy between {N} subsystems and the subsystem M.

    LINEAR: Find a way to benefit, eliminate, reduce or prevent HF under the SEQUENCE condition of UF or/and to perform the SEQUENCE steps of a system improvement, i.e.

    UFn-1 is required for UFn and UFn is required for UFn+1


    UFn is introduced to eliminate HFk , while UFn causes HFl(k n l)


    UFk is required for UFn , while UFn causes/increases HFk (k n).

    During the operations of an electrically heated furnace for melting of metals we can consider only walls of furnace as a working tool (subsystem N) and electrical heater as a energy source (subsystem K) as well as solid metal (raw object) and liquid metal (product). A transition solidliquid metal (the primary functions of the furnace) requests hot walls (UFn) and hence an additional electrical power (UFk), but high temperature of the walls destroys electrical heater or its parts (HFk)

    STAR: Find a way to resolve a FEW technical contradictions by which UF should eliminate a few INDEPENDENT HF, i.e.

    UFn causes HFk and HFp, requires UFl, and eliminates HFm (k l m p).

    It is important to recognize the problem’s structure because different TRIZ problem solving heuristics work better or worse for different problems. Clarification of a structure of a problem should also provide the easiest way to operate with the knowledge databases of TRIZ. The understanding of the problem’s structure gives a strategy and helps choose appropriate information needed for solving the inventive problems. It seems rational to label the so-called physical contradictions by ANDNOT logical operator and present the so-called technical contradiction through XOR logical operator[5] . Usually the simple logical operators AND together with OR are used only for representations of TS or TP. “New” (ANDNOT and XOR) and traditional operators can be used for graphs of problems in terms of contradictions and subsystems and functions of a technique that help resolve the technical problems. It gives a strategy for solving the problem and helps choose appropriate information needed to solve the problem.

    4 Conclusion

    In contrast with other methods of solving the technical problems, TRIZ emphasizes the contradictions and recommends resolve them instead of usual engineering trade-offs. Such approach allows to receive strong inventive solutions. The full set of contradictions known in TRIZ was reviewed in this Lesson. The schematic presentation of the technique and problems in it under consideration allows to reduce numerous different objects to few generic cases. It allows one to find solutions of the problems by analogy with already solved problems with similar structures more easily than in the framework of the other approaches to problem solving [1-4] .

    TRIZ actively uses models of the problem that describe the native contradictions in some primary functions of a technique. In this course we will consider mostly point and pair technical problems, which have the so-called physical and technical contradictions correspondingly. Several heuristics have been implemented by G. S. Altshuller and The TRIZExperts for resolution of the point and pair contradictions. These heuristics will be considered in great details in the lessons of this course. The triangle problems became recently one of targets in TRIZ researches. A heuristic method for triangle and network problems rupture has been developed by the author but it is out of the scope of our present studies (see The Advanced TRIZ Course [hyperlink unavailable at this time] ). It is unknown usually in advance how to eliminate this contradiction in reality, but there is always the possibility of formulating an imaginary solution named in TRIZ as the Ideal Final Result that will be discussed next .


    1. Altshuller, G. S., To Find an Idea, Nauka, Novosibirsk 1986 (In Russian).
    2. Wilson, P. F., Dell, L. D., and Anderson, G. F., Root cause analysis: a tool for total quality management; ASQC Quality Press, Milwaukee, 1993.
    3. Dettmer, H. W., Goldratt’s Theory of Constraints, Quality Press, Milwaukee, 1998.
    4. Terninko, J., Zusman, A., and Zlotin, B., Systematic Innovation : An Introduction to TRIZ (Theory of Inventive Problem Solving), Saint Lucie Press, Boca Raton, 1998.
    5. Savransky, S. D. (papers 1994-1999 + to be published).