Already at the beginning of the 18th century, the German mathematician and philosopher Gottfried Wilhelm Leibniz aspired to achieving objectivity in human affairs by logic and computation. Today we are somewhat closer to achieving Leibniz's dream when he wrote:

... when controversies arise, it will not be a work of learned disputation between two philosophers, but between two computists. It will be enough for them to take pen in hand, sit at the abacus, and say to each other, as friends: ``Let us calculate!''
We begin with the problem of initiating change.

Who has the right of initiative?

Everyone has the experience of thinking some government policy, business policy, school policy or social custom is wrong and ought to be changed and feeling frustrated by his inability to communicate his objections or even to learn what the rationale of the policy is or who is in charge. Even if the people responsible for the policy are nominally reachable, if the office is high, they have hundreds of letters or emails proposing change. Often the person who can be reached hasn't the power, and the people with the power are responsible for too many policies to pay attention. In many matters no one person has the power of initiative. In matters of social custom, no group, not even Congress, can initiate changes.

We can describe this situation by saying that only certain positions in social organization give a person the power of initiative, i.e. the power to propose a change and get it seriously considered. Moreover, a persons power to propose a change will be specific to his position in relation to the kind of change he wants to propose.

I propose some possible partial remedies. These ideas are somewhat farther out than most of these essays, because the necessary science is still undeveloped. I include them, because they involve my own field of research. As we shall see, the idea goes back to the German mathematician and philosopher, Gottfried Wilhelm Leibniz.

A happy scenario

Consider the following extreme example of a desirable future state of affairs. A super-smart high school student gets the idea that the U.S. admit foreign tourists without visas to reduce red tape and promote good will.

He sits down at his trusty computer console and asks for a description of the present policy and its rationalization. Back comes a set of sentences from the Immigration Service computer in Washington expressed in a formal but readable language. The rationalization is a non-monotonic pseudo-proof that the policy is in the best interests of the country and is in accordance with the currently accepted principles of justice. (A pseudo-proof is like a proof except that it contains steps wherein something that has been asserted to be plausible is assumed or wherein the known phenomena of a certain kind are assumed to be all there are. Non-monotonicity will be explained later.)

Our student does not believe the pseudo-proof and after much labor discovers that one of the assumptions is not valid or that there is an important consideration not taken into account and succeeds in making a pseudo-proof that his proposed policy is better than the official one. The computer proof-checker accepts his pseudo-proof, and the public information system tells him that the relevant official is the head of the Immigration Service. Next morning the head of the Immigration Service is informed by his console that someone he has never heard of has proved that the policy ought to be changed. This does not happen often, and he is rather annoyed because all previous policy changes in this area have come as a result of the work of his staff. Nevertheless, he has to pay attention, because there is a rule that if a government official ignores a computer checked pseudo-proof that his policy should be changed for a month, the request for change goes up a level in the hierarchy. Therefore, he has his staff examine the assumptions of the argument carefully, and after a while everyone is convinced that the new assumptions are more plausible than the old, and the policy is changed.

The example of the student is non-typical, because such challenges to policy will more likely come as a result of professional work by employees of businesses and other institutions affected by the policy. I chose it to emphasize the fact that if the information is universally available and the criteria for evaluation are sufficiently objective and are implemented by computer, then anyone can play.

This happy scenario is based on the future achievement of several goals, some of which are rather distant:

  1. There is a formal language in which facts about policies and their effects can be expressed, and which allows conclusions to be drawn about the relative merit of different policies.
  2. The criteria that determine whether one state of affairs is socially better than another are agreed upon and formalized to a sufficient extent.
  3. There is sufficient public confidence in the above to cause government use of the formal methods.
  4. The existing policies are formally described and formal arguments justifying them are publicly available.
  5. The technique for manipulating the formalism is widely understood by people who want to affect policy.
  6. The arguments are checkable by a computer program.

If these goals are met, the effects will be good. Anyone who feels offended by a policy, even esthetically, can know precisely what it is and why it is thought to be correct.

Further, if he can show formally that some other policy would be better, officials will pay attention. This depends on the computer acting as a filter so that the policy making officials will not be overloaded with half-baked ideas. On the other hand, getting official attention will not depend on his status in society.


Let us compare this desired state of affairs with the present state of affairs in our society, in which people have great trouble agreeing about deciding what to do. The main reason this is so is that theories about how the world works are tools in struggles for political power. For example, arguing that the death penalty deters crime helps put conservatives in political office, and arguing that it doesn't helps put liberals in office. As long as the social sciences are weak and subject to wishful thinking, social science arguments will often be subordinated to politics --- even by social scientists. Contrast this lack of objectivity with the fact that both liberals and conservatives accept the engineering investigations that determined that Challenger exploded because the O-rings between the solid rocket booster segments failed.

Marxists used to say that Marxism provides a basis for objective political decisions, and some of them still say it. Jewish, Christian and Islamic fundamentalists say that their sacred books provide a sure guide for these decisions.

The most common belief among Westerners, whether they be intellectuals, academics, or politicians is that there is an intrinsic difference between political decisions involving human conflicts of interest and purposes and engineering decisions. There is a recent trend towards denying the possibility of making even engineering decisions objectively, on the grounds that they always involve conflicting interests.

My own position is that political decisions can be made just as objectively as engineering decisions, but not yet, because the necessary science has not been developed and is not immediately about to be. Marxism represented an attempt to wish such a science into existence. Once Marxism had a scientific style even though Marxists often reached wrong conclusions because its theories were inadequate. However, its objective character was not strong enough to withstand the demands put on it by seekers of political power, and its practice entirely lost its original proto-scientific character. A new attempt to base political practice on a science might suffer the same fate if the science was too weak to provide truly objective answers by widely understood methods and if power struggles strained objectivity too much.

Marxism failed, but we have to try again and again until we succeed. If 10,000 years goes without success, it may be time to give up. Nevertheless, we have to remain skeptical about the claims of any particular attempt and avoid wishful thinking.

Returning to our high school student wishing to influence policy, his chances today are small even if he can find out what the present policy is. He still won't be able to find its rationale written down in a form subject to challenge. His chances of influence are much greater in other areas of endeavor. The degree of objectivity of policies depends on the subject matter, and the number of people who can affect the policy is greater, the greater the objectivity of the matter.

The most objective area is the body of theorems of mathematics. Anyone can submit a paper to a mathematical journal. The referees of a paper are not supposed to pay attention to the status of the writer and often referee papers written by people they have never heard of. Once a paper is published, it will affect the mathematical ideas of the time.

When someone makes a mathematical assertion, he is expected to prove it. Mathematical proof is an extremely reliable process. Less than one in a thousand of published mathematical assertions are later found to be mistaken or even occasion any controversy. There is plenty of controversy over what is useful, important, or beautiful in mathematics. It certainly happens that important results are ignored for some time.

This objectivity of mathematics has important, useful consequences. Namely, anyone who has an idea for improving mankind's state of mathematical knowledge can write a paper and submit it to a journal. Important contributions have been made by very young people and quickly recognized.

It is important to note that the only equipment required for mathematical work is paper and pencil and access to a library. To make a living doing mathematics requires an academic job, but there are very few scandals where someone unable to get such a job was found many years later to have done first class work which was ignored. There are a number of success stories like that of the early 20th century Indian mathematician Ramanujan, where someone in an obscure position was found to have done first class work and brought into a first class environment.

This situation is not a consequence of some superior virtue of mathematicians. Rather it is a consequence of the objectivity of merit in mathematics. This objectivity also exists in athletics and in chess (Fischer became U.S. champion at the age of 14 and was thereby recognized as a grandmaster).

The situation is almost as good in physics and chemistry. However, the possibility of verifying an idea may depend on the facilities for making experiments, and this may depend on the reputation of the person proposing the idea. However, in the theoretical branches of these subjects, the outsider has a good chance. Recall that Einstein was an examiner in the Swiss patent office and entirely unknown when he sent his paper proposing the theory of relativity to Annalen der Physik, then the world's leading physics journal.

In engineering the matter is more difficult because the ability to try out ideas is even more expensive. Nevertheless, there are large areas of engineering that are quite uncontroversial, because it can be objectively calculated whether something will work or not, even if it is not so clear which of several methods that will work is the best.

Quantitative Considerations

In the previous sections I have concentrated on the non-quantitative components of objectivity, because this was where I have new ideas. However, where quantitative considerations are applicable, they often provide very objective results. For example, if someone were to propse that every American family live on a 160 acre farm, just dividing the are of the U.S. by then number of families shows that this is impossible. If someone proposes a one acre garden for each family, a simple division won't show it impossible, and maybe it is possible. However, a more complex calculation would show that few metropolitan areas could afford it, so people would have to spread out more.

Of course, it is necessary to combine quantitative calculations with the qualitative considerations handled by logic. The way to do this is to express the quantitative facts also in logical form.

Non-monotonic logic

The goal of making policy decisions objective goes back to Leibniz at the end of the 17th century. He advanced the idea that eventually people will say ``Let us calculate'' instead of arguing about policy. The development of mathematical logic, and this is the relevant science, has been slow. To explain mathematical logic would take us too far afield, but its essential idea is that the allowed formulas should be precisely described and checkable by computer and so should the allowed reasoning steps. Leibniz didn't get very far, and real mathematical logic dates from George Boole's Laws of Thought written in the 1840s. Mathematical logic reached a mature level in the 1920s, and subsequent developments relevant to making policy arguments mathematical have been mainly technical. Unfortunately, mathematical logic as it developed until the late 1970s is inadequate for arguments in the social sciences or about the common sense world, and it has been applied mainly to studying the foundations of mathematics rather than to realizing Leibniz's goal.

Research in artificial intelligence has led, since the middle 1970s, to what's called non-monotonic logic, and this provides new hope for dealing with the common sense world and the world of social science. Since the subject is less than ten years old, what can be done isn't entirely clear, and maybe my hopes for it will prove illusory.

The usual systems of mathematical logic are monotonic in the following sense. If a conclusion p follows from a set A of facts, then it will also follow from any collection B of facts that include all the facts in A. We shall see why methods of reasoning that aren't monotonic are wanted.

Monotonic logic and present mathematical theories work well when the phenomena to be taken into account can be delimited at the beginning. This delimitation of the theory is not carried out within the theory, but in the surrounding English prose. For example, in physics the law discovered by Galileo that the distance an object will fall is governed by the formula s = (1/2)gt2 is subject to the condition that nothing interrupt the fall of the object during the time considered, but the formula says nothing about that. Whoever proposes to use the formula must worry about that outside of the mathematical theory itself.

Artificial intelligence is concerned with making computer programs with common sense that reason about such matters. If this is to be done, the computer program must be able to reason about what might interrupt the body's fall. When we contemplate putting such facts about falling bodies in the computer for programs to use we encounter the difficulty that no one can list in advance all the phenomena that may interrupt a body's fall.

The solution seems to involve supplementing the reasoning methods of logic with a rigorous version of the principle philosophers call Ockham's razor after a 14th century philosopher William of Ockham who said, ``Do not multiply entities beyond necessity''. In the case of falling objects, it amounts to concluding the object will fall until stopped by one of the interruptions we are taking into account. If we have failed to consider a relevant fact we will still get a conclusion, but it may be wrong. Human reasoning takes this into account and it seems that intelligent computer programs will also have to reach conclusions on the basis of collections of facts that may not include all that is relevant. Thus artificial intelligence will also have to risk error, though not necessarily every kind of error that humans make.

Computer checked proofs and interactive theorem proving

Our scenario involved a computer-checks "pseudo-proof" that a changed policy would be better. We are far from being able to do that today. Interactive theorem proving involves interacting with a computer program that checks each reasoning step as it is offered and which can do some big steps on its own.

The state of the art is that simple mathematical proofs can be constructed interactively. Substantial theorems have been proved as PhD theses, but the amount of work done by the person is usually quite a bit more than is needed to convince a person. The best developed subfield is the verification of computer programs and computer hardware. The largest mathematical project is Mizar, based in Poland. It has (1999) definitions of more than 2,000 concepts and proofs of more than 20,000 theorems. However, its use is still a special enthusiasm rather than routine in mathematics.

Very little has been done for arguments involving non-monotonic reasoning. There is one small example in my Applications of Circumscription to Formalizing Common Sense Knowledge which was first published in Artificial Intelligence in 1986. There is a long way to go to make the goals of this essay feasible. There is more discussion in some of the papers listed on my web page.

Social science and its application to human affairs involve non-monotonic reasoning to a much greater degree than physical science, because if the theories are to be useful they must include the processes that allow limiting the facts taken into account in some situations, while going beyond these limitations in other situations. I believe that formalizing non-monotonic reasoning will make possible social science theories that are more powerful, more realistic, more explicit about what phenomena they are taking into account, and more capable of being supplemented by additional facts.

In conclusion, I think there is hope for achieving increased objectivity in human affairs. This will provide increased scope to people with good ideas talents rather than the skills of a politician or courtier.


  1. How many ideas from the public could an official reasonably be asked to look at per month? How many officials would be looking at the ideas in different fields?
  2. How much would the system have to cut down the number of ideas in order to make it workable to pay attention to them?
  3. Would the number submitted tend to increase or decrease?
  4. What long term effects would there be?
  5. What would be the effect on ideas generated within the establishment?
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