The conceptual foundations of decision-making in a democracy

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Part Three B
Knowledge and Truth, Scientific Theories.

3b.l) Introduction.

Having explained why - in democratic decision-making - the judgement about a proposed bit of knowledge should be as objective as possible, we will now investigate to what extent - if at all - it is possible to decide objectively about a scientific theory or about statements deduced from it and what we can do to achieve the highest degree of objectivity which can be achieved.

There is wide agreement that it is impossible to establish objectively the truth of a scientific theory, a view which also follows from the previous parts about information and knowledge. The current disputes about objectivity centre around three positions:

-	It is logically impossible to prove the truth of an empirical scientific theory; but the notion of a totally objective truth of a scientific theory is a legitimate one. It then is logically possible to prove a theory to be false, and a theory thus falsified is factually and objectively proven to be false. (Popper)
-	there is no method by which we can objectively decide about either the truth or the falseness of a scientific theory, nor is there any method for justifying with any degree of objectivity the choice for or against a scientific theory. We should not even attempt to establish any such method. (Feyerabend)
-	A not quite clear position in between. (Lakatos)

The purpose of this section is to develop a synthesis which can provide a way out.

The opportunity for such a synthesis is provided by showing that both extreme positions cannot be justified. Feyerabend's is easy to refute. He first argued that full objectivity is a chimera, a position which is congruent with what has been said in this book. But then he deduces that therefore striving for objectivity makes no sense. That deduction is not allowed by logic and he presents no further cogent argument in his book. (See volume two: ‘Against Feyerabend's anarchy’, p.279)

The well-known paradox of Hume about induction and Russell's paradox about an objective rationality are at the root of much of the disagreement about scientific knowledge. The theory of life and information provides a solution for these paradoxes. Therefore, this section will start with a chapter on the rationality of induction.

3b.2) Induction: the Rationality of Learning from Experience.

As used by me, Popper and Hume, induction refers to the ubiquitous practice of deducing from events (of which we do have experience) something about events of which we have no experience. That generates a paradox which has bedevilled the community of philosophers ever since Hume sounded the alarm. For the simple knowledge that a certain event has occurred does not say anything about the probability that it will recur: by itself, knowledge that up to now the sun

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has risen every morning provides no justification for expecting that it will do so tomorrow. Penicillin has never failed to kill staphylococci for many years and was considered totally reliable .... until a resistant strain emerged.

However often we have experienced dawn, it takes something more than just that experience to deduce that the sun will rise tomorrow. Any time we deduce, from facts about which we have experience, something about the probability of future events we add something (namely whatever leads us to extrapolate that past experience into the future) which exists only in our own mind. The core of the discussion is the status, the rationality of that addition. Hume's contention is that this extrapolation can never be totally objective and that our tendency to practice induction is subjective and has to be explained in terms of our mind.

Popper claims to have solved Hume's problem. He agrees that from experience alone we can never in a totally objective way derive any confidence that a certain theory is true. But we can, he asserts, from the experience of a falsifying event deduce in a totally objective and conclusive way that the theory is false. We will further on show that Popper, in this one respect, makes an error. His ‘negative solution’ is shown to be insufficient for most decision-making. It is not a solution of Hume's problem but mainly shifts it to other issues (see Volume tow: ‘Popper's non-solution of Hume's Problem of Induction and Rationality’, p.287).

Yet most of us think it is rational to learn from experience to decide that a statement is false. We also use induction as corroboration, we tend to take repetitive occurrence of a certain event as an indication of an above 50% probability of its recurrence. And we are not alone. Life also does so: evolution as the process of learning from experience shows us a way out of Hume's dilemma, namely functionality. The whole system of reproducing genetic information-which-has-survived and discarding that which has not will lead to a bias away from chaos, will generate the process of life only if there is some reason, regularity, law, ‘something’, which justifies the expectation that events are not causally independent from each other. The process of learning, of forming representations of reality on the basis of past experience, can improve our decision making only if there is in nature some mechanism which relates a past event to a future one. Without a minimum of causality, the process of taking decisions based on knowledge would be totally irrelevant to the achievement of our aims. Kant has already shown that causality can never be part of our experience, that causality is something which we already have in our mind when we use experience to make a representation of our world, that it therefore must be a priori. An attempt to ground the assumption of causality in our experience therefore is equivalent to pulling us up by our own bootstraps.

Hume's ‘paradox’ finds its origin in the notion that if it is to be rational, such an assumption must be objective. According to Russell as well as the functional view of knowledge, an objective rationality is a chimera: we cannot define it without recourse to some inane tautology like ‘based on our reason’. The reader can himself control the correctness of that conclusion by trying to define objective rationality.

The only ‘rational’ way to define rationality is to abandon the chimera of total objectivity and to define it in connection with some purpose. We will then consider induction to be rational as

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soon as we can justify the expectation - in the light of the available knowledge - that we will be better off in our decision-making when applying induction than we would have been by rejecting it. The primary interest of an individual is not to find any totally objective representation of the process which ties a future event to a past one. What he wants is to take that decision which is most likely to help him achieve his (very subjective) purpose. If he succeeds, why should he care whether that decision meets some theoretical standard of absolute objectivity? Some people might regret that such rationality is the closest we can come to being ‘objective’, but that must be for sentimental or metaphysical reasons. For such rationality is all we will ever need in practice: it defines the highest level of perfection in decision-making which is both conceivable and necessary. Induction can be very rational, as will be proved by showing it at work.

Suppose that we have to take a yes-no decision. Without any knowledge to help us, we must expect the probability of taking the right decision, of achieving our objective, to be 50/50. Any knowledge which can improve the odds is welcome.

Take a predator. He must decide where to hunt. He can divide his territory into sectors to be covered by a stalk or ambush. His problem is to decide which sector to choose, and his objective is to find prey. Is he justified in choosing a sector exhibiting features of landscapes in which he has previously killed game? If the decision as to the area to hunt hinges on past success, he would be practising induction. And that is exactly what predators do: they show a preference for locations of the type in which they have previously found game. In terms of rationality, the justification is that their sort has survived on that strategy.

But they do not act as if they considered that knowledge to be universally true. They are always willing to test and revise it. If they find no game in such a location, they try another one. Thus, they increase their knowledge quantitatively as well as qualitatively. Induction always plays the main role, either in the decision to return to a successful location, or to temporarily avoid it if they have learned from experience that a territory in which a hunt was successful will be avoided by game for some time. Such learning can be the result of individual experience, but the sort also can learn if the experience has coalesced in an instinct.

The key to all induction is the expectation of the minimum of stability which is associated with causality. The justification of induction thus lies in the rationality of expecting a certain stability in nature. Are we justified in assuming such a stability in the absence of any proof? Is the decision to assume stability a rational decision? The answer again depends on our concept of rationality. Philosophers like Hume and Popper apparently assumed that to be rational, a decision has to be justified by showing that it followed from a logically impeccable proof of the assumptions about reality on which it is founded. If this criterion were to be applied to practical decision-making, it would grind to a halt. The bulk of my life has been devoted to decision-making at a fairly high level of sophistication, yet never has such a criterion been applied.

In real life, we hark to the concept of functional rationality presented above: we consider a decision to be rational if we have a good reason for it, if we can justify it as being more likely to achieve our purpose than available alternatives, given the information at our disposal. In all theories about decision-making, for instance in the theory of games, the criterion

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leading to the qualification of ‘rational’ is not some a priori standard, but a decision matrix showing the payoff of the various choices we can make. If we subscribe to a certain payoff matrix and then are confronted with an individual who does not choose for the alternative which on our matrix has the highest payoff, our first assumption would (or should) be that he uses a payoff matrix which differs from ours. Only if we are satisfied that both are similar will we presume that he acts irrationally. But as we cannot look into his mind, we cannot know all the elements of his decision matrix. If an individual of a social species like man takes a decision favouring the society over his own interests as an individual, that provides insufficient justification for calling - a some theories do - that decision irrational; for the good feeling of having done something for society is a value, a utility as any other. Only the fact that he did not engage his faculty of reason could provide such a justification.

Let us have a look at the payoff matrix of accepting or rejecting the assumption of a stability underlying causality. We need not assign exact values to the payoffs. If there are only two alternatives to choose from, we can do with three values, ‘even’, ‘better’ or ‘worse’, expressed below as equal to, higher or lower than a 50% probability of taking the right decision. The conclusion is that in the absence of any evidence as to some stability in nature, it is rational to assume that stability exists. We can never score lower than if we do not assume stability, but we can score higher. For without stability the result is random (50/50), and without its assumption our decision also will be random.

	THE REAL SITUATION
ASSUMPTION about STABILITY	there is stability	there is no stability
Assume stability	payoff: above 50%	payoff: 50%
Do not assume stability	payoff: 50%	payoff: 50%

Note that this stability implies some correlation between events. That correlation may be positive but also negative, as it would be if success in a hunt causes prey animals to temporarily avoid the area. But in both cases knowledge about it can bias our decision-making towards success.

To be of any help, we must therefore decide whether to choose for a positive or negative correlation. At the very least that requires two experiences, which is the absolute minimum of data for any induction to have even the smallest possibility for improving our odds of taking the right decision. The higher the number of similar experiences, the more confidence we will have in the application of induction, at least in the absence of other evidence.

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Incidentally, as Popper has noted, induction is not a means for gathering knowledge: that is done by observation and deduction. Induction is rational mainly for the evaluation of knowledge as to its potential use for predicting the outcome of the various alternatives we consider when making decisions.

Pure induction is based on very specific events, namely those of which we had experience. Without the help of other information, it is applicable only to that specific kind of event. If we have gained knowledge from specific past events and if we want to extend that knowledge to events which are different in kind, we must generalise, which requires deduction and combination with other knowledge.

The full power of induction is achieved only if it is used in conjunction with all other relevant information that is available. We pool odds from various fields of experience. That pooling process is what science is about, is what makes it a social venture and gives it its power. The better the theoretical and experimental basis for induction, the more likely that we will make correct decisions by inferring - from these theories and experiments - events of which we still are ignorant.

Concluding: induction is a legitimate and rational procedure provided we use it in the correct way, namely to improve our decision-making, and not as a means to endow judgements about the truth of statements with an objectivity which they cannot have.

3b.3) Scientific Theories.

Practically all of our knowledge is based on experience, either our own or that of our progenitors. Whenever we use such knowledge in decision-making to predict the consequences of our choices, we ‘induce’ these predictions from the knowledge that in the past certain events have usually occurred in a certain combination with other events. We can enormously improve both the scope and the accuracy of such prediction if we also know why they have occurred in that particular combination instead of another one, what ‘caused’ them to do so.

That presumes that events have a cause, that there is no spontaneous generation nor disappearance. That assumption is ‘natural’ to us and underlies the rules defining connectives in standard logic. The justification for that assumption is its success in its application to decision-making and the consequent survival and propagation of the creatures holding it.

Explanations of the ‘how’ and ‘why’ are not plain statements referring to facts, to objects or events of our experience. They add to that experience certain relations between such facts - such as the laws of physics - which we assume (at least tentatively) to correspond to a fact, to be true. The most prominent statements for explaining such relations are scientific theories.

What a theory adds to our experience must contain more than just a statement of how and why things are thought to be the way they are, more than a mathematical formula like Plank's constant or Sayer's law that bad money drives out good money. It must also contain an explanation of how it enables us to deduce, from facts which we know, facts about which we have

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as yet no knowledge; and it must contain the justification for accepting, at least provisionally, the theory or the statements deduced from it as ‘true’. These additions form an integral part of a scientific theory and are necessary to distinguish it from other types of knowledge such as religion or intuition. Most of these explanations are not themselves available for inspection; only the sequence of events which they attempt to explain can be directly observed. We do not see the force of gravity, we see the falling of the apple. Statements which assert the truth of scientific theories can never be factually objective. If we apply the theory, the facts involved are available for observation and can often serve in the evaluation of the theory. The evaluation of a theory through confrontation with its application can be factually objective, namely whenever it is based on the acceptance of the truth or falsity of a statement which can be factually objective. Given the importance of scientific theories in today's decision making about facts, the selection of which theory to apply in a given case is of vital importance and is the main subject of this part.

3b.3.1) Empirical scientific knowledge. Empirical means ‘dealing with the real world’, or in Popper's terms, ‘our world of experience’. The object of empirical science is to enable us to ‘understand’, to construct representations of, those aspects of reality which cannot be apprehended through direct observation.

‘Scientific’ to many is a synonym for complex, difficult, requiring specialised tools like mathematics. That is understandable, for a simple statement of the existence of a fact which we can all observe does not to our mind merit the qualification of scientific. But complexity is neither unique to scientific theories, nor is it one of their primary characteristics. Bach's music is extremely complex, while the theory that the earth orbits around the sun is very simple. Others equate ‘scientific’ with ‘true’ or ‘objective’, an unwarranted association as every scientist worthy of that name will know.

More prominent is the idea that scientific knowledge does not rest for its acceptance on subjective belief but on its realism, on its pretension that it is substantiated by our experience of what things are, so that all those who are capable of observation and are willing to be as objective as possible must admit its plausibility. Its performance in predicting the outcome of actions is often used as a criterion for this plausibility.

The aura of objectivity which hangs about ‘real’ scientists is the self-proclaimed hallmark of their work. Students of the history of science know that such an aura is undeserved. Objectivity may be a standard, a virtue for scientists. But like any such standard, it is a target, not a reality. The extent to which the products of scientists meet that standard depends on:

-	the motivation of scientists to make the necessary efforts and sacrifices
-	the extent to which the organisation of the cooperative venture of science is directed by the goal of promoting that objectivity.

Objectivity as a property of scientific knowledge therefore is questionable and has been questioned. It definitely cannot serve as the sole criterion for distinguishing scientific from other knowledge. As a target it can however be part of the evaluation of the activity which leads to that knowledge.

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An uncontroversial definition of scientific knowledge would be something like: scientific knowledge is the knowledge produced by individuals claiming to be engaged in the activity of science. That begs the question: ‘What is science?’. Answering that it is the activity of producing scientific knowledge is not very enlightening. Fortunately, we can dispense in this book with such a definition. What concerns us here is the suitability of knowledge for the establishment of facts for social decision-making in a democracy.

As explained, such knowledge should be as objective as we can make it, and the maximum attainable objectivity is knowledge which can be factually objective (see 3a.2.1). A theory contributes to our knowledge and to science precisely because, as stated above, (in addition to whatever observable facts it mentions) it contains an explanation of the existence or occurrence of facts.

3b.3.2) The need for a demarcation criterion for scientific theories. In social decision-making we are often faced with different theories which compete for recognition as a ‘scientific’ representation of reality. Inevitably, we must choose, and to be democratie that choice must be directed by a generally accepted criterion which is as objective as possible and also is practical. Testing and comparing social theories on basis of observable facts often is not possible. Even when it is, the results will not be conclusive. And in most cases the effort and time for obtaining the necessary date will render it prohibitive. It then makes sense to investigate whether - by just analysing a theory - we can eliminate it as irrelevant or as not pertaining to empirical science. To that end we need a criterion which draws a demarcation line between such theories and those that merit further investigation. In the chapter 3a.2, ‘Can Knowledge be Objective’, p.86, we have established a hierarchy of objectivity: total objectivity (unattainable), factual objectivity (first choice) and, if not possible, rule objectivity derived from the democratie principle as explained in Part Five.

The demarcation criterion we will propose for accepting a theory as worthwhile, scientific and empirical requires that:

-	it can teil us more about reality than we would know without it
-	its truth or falsity can be decided by accepting as true a factually objective statement, that is a statement asserting the existence of a fact whose existence can be established by observation (Popper calls them ‘basic’ statements).

Popper has convincingly argued that the first property is connected to the second one; therefore the second requirement will not eliminate any worthwhile theories.

We will not however follow Popper all the way, and in Volume Two, ‘Popper on Scientific Theories’, p 291, we will explain why in detail. In a nutshell, Popper requires of scientific theories not only that they be logically ‘falsifiable’ through confrontation with facts. He also rerquires that they can be objectively and conclusively decidable by an actual confrontation with facts. As explained in the next chapter (about the testability of scientific theories), the failure to meet that strict criterion need not be due to a deficiency of the theory. It may follow from the nature of the phenomenon they are attempting to explain, for instance that its structure is a complex, interdependent, dynamic and stochastic system of learning elements, in short ‘holistic’, such as human social decision-making. We should not eliminate them from the field of empirical scientific knowledge for the sake of a quest for total objectivity which anyway is a chimera.

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The justification of Popper's requirement of conclusive decidability derives from his assertion (or wish) that the falsification of theories meeting his criterion can be totally objective. He also asserts that a theory meeting his stringent criterion could be a ‘true’ representation of reality, even if that can never be proved, while theories which fail can never even hope to be a true representation. Both assertions are based on the assumption that the abstract concepts contained in a scientific theory (energy, the laws of thermodynamics) can and do refer to entities, facts, which have an own, autonomous, existence and which therefore are independent from the mind of any individual. That assumption is unwarranted (see Volume Two, ‘Against the autonomous existence of Popper's world three objects’, p.296).

3b.3.3) Problems generated by the interdependency of scientific theories. Imre Lakatos is less well known than Popper. Yet his contribution to epistemology is substantial, and my proposals for evaluating scientific theories differ from the theory of Lakatos mainly because they derive from a different perspective. His perspective is that of the historian explaining the growth of scientific theories while I am concerned with scientific knowledge as a basis for decision-making. But we both search for a safe passage between the Scilla of Popper's absolutist demarcation criterion and the Charybdis of Feyerabend's radical anarchism.

As previously noted, the very fact that knowledge is the product of an information process introduces a subjective element. Lakatos points to another cause of the impossibility of an objective and conclusive evaluation of a single theory: they are part of a whole research program and can be adequately evaluated only in the context of that program. What he refers to is in fact the above-mentioned holistic property of any living system (science also is such a system). Unfortunately his modesty and his reluctance to engage in an open conflict with Popper have prevented Lakatos from following his theory through to its logical conclusion, namely that any evaluation of a scientific theory is conventional and that the ultimate basis for any such convention is its purpose. (See Volume Two: ‘Lakatos: research as a program’. P.304). The interdependency of scientific theories has four major causes.

1)

Many theories consist of a system of sub-theories. We can separately test all sub-theories, but only the test of the system as a whole is conclusive. If the test of the whole system is negative, that failure could be due to the failure of just one sub-theory. If all sub-theories meet their tests, the failure of the whole could have various causes, for instance an error in the aggregation of sub-theories into a whole or the omission of a relevant sub-theory. That a complex system of theories has flunked the test against facts just tells us that the system as a whole is false. But where do we go from there? It is highly unlikely that a really complex system of theories will ever be totally correct in all its details. What we need is not a decision about its absolute truth or falsity. If faced with some flaw, we must choose between an attempt to improve the system or to start from scratch and develop a new system. Whatever choice he makes, the decision-maker must also answer the question: until there is a better system, what to do with all decisions hinging on facts pertaining to a theory that has been exposed as false? Can we define a more limited scope than the one which the original theory claimed and within which we can apply the theory with confidence? If not, are we better off in decision-making by applying that theory rather than using an alternative one, for example the always available ‘zero-hypothesis’ that we know nothing about the subject?

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2)	Many axioms on which a theory is based are derived from theories belonging to other scientific disciplines or from logic and mathematics. These theories are invested with the same objectivity that we assign to facts which can be directly observed and which are endowed with the status of ‘observational’, as Lakatos appropriately calls it. I cannot judge to what extent theories of physics use other theories in that way, but in social science the practice is prevalent and evident: the behaviour of groups must be based on a theory about the behaviour of individuals, production functions presume relations between input and output resulting from the application of technology, which in turn is based on the theories of physics, chemistry, biology etc. Evidently, the truth of a theory of social science is dependent on the truth of the theories to which is has assigned observational status. Yet we cannot ‘observe’ these theories themselves, only their popularity and the results of their applications. Giving them observational status therefore is totally conventional. The system itself may be sound but fail a test because of the falseness of a theory to which we have given observational status and treated as fact in the set of axioms.
3)	Testing a theory against facts requires the definition of initial conditions which for a large part are based on other scientific theories properly called auxiliary theories. Testing the second law of thermodynamics by enclosing clouds of gas in isolating and rigid receptacles requires a theory about metallurgy to define the degree of thermal conductivity and the resistance to deformation of these receptacles. The degree of objectivity of the decision to accept these auxiliary theories will vary; the highest degree we can achieve is that this decision will be ‘factually objective’ in the sense we have given those words. If we decide to accept that a certain auxiliary theory is factually objective, we may have good reasons for doing so. But that can be established only after we have identified this auxiliary theory and justified its acceptance by the same kind of procedure which we use for the theory to be tested. Until then a failure of the main theory to meet the test cannot be attributed to that theory. Justifying the auxiliary theories runs into the same problems, a regress which we can only end by the conventional decision to grant one of them ‘observational’ status. (See also Volume Two, ‘The role of initial conditions in evaluating tests’, p.293)
4)	Even if the structure of theory to be tested is fairly simple, the structure of the test (or application) usually is complex. That can generate other problems besides the reliability of its assumptions. The most prevalent is circularity. Circularity occurs for instance if one of the theories we use as an axiom, auxiliary theory or initial condition of the tests does itself use an element of the main theory as its axiom or vice versa. In that case we cannot evaluate them separately and cannot know what the test results mean. If unsuspected, such circularity may enable the proponent of a theory to ‘immunise’ it against any critical evaluation. The evaluation problem is not due to the nature of the phenomenon investigated but follows from the structure of the theory and is a ground for its disqualification. If the theory is amenable to mathematical or logical analysis, such circularity will become evident; but it can easily be dissimulated in a long and obscure text. In such texts the error often takes the form of a petitio principii: the conclusion is already ‘implied’ in the definitions or axioms. The frequency with which such circularity is encountered in academie texts

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is somewhat disconcerting. Whatever the other problems of evaluating scientific theories, this one alone justifies the requirement of axiomatisation proposed in the chapter of that name.

3b.4) The Testability of Scientific Theories.

We can evaluate an empirical scientific theory on many counts: its logical consistency, its elegance, its simplicity, the way it fits into the rest of our knowledge. But the preferred method of evaluation is to test it against facts. And rightly so. The prevalent use of scientific theories is to provide an answer to the question: ‘what will happen if...’. The best way to get an impression of how a theory performs that task is to see it at work.

Testing a theory through its use in actual decision-making is very costly in terms of wrong decisions. It is much more efficiënt to devise experiments enabling us to judge its probable predictive performance before applying it. An artificial test situation has another advantage: it can give us better control over the ‘initial conditions’, more certainty about what we ‘really’ test.

All statements of tests of scientific theories have the following logical form:

-	If... (some facts, the initial conditions)
-	then... (expected facts: the results allowed by the theory-plus-initial-conditions)

What to put in the ‘if’ and ‘then’ depends on the theory.

From the theory of thermodynamics we can deduce the following statements:

-	If in a closed system two clouds of gas of different temperature are in sufficiently close contact to exchange molecules, and if the experimental set-up satisfies these conditions,
-	Then the difference in temperature between these two clouds of gas will decrease.

The ‘if’ part states the initial conditions of the test. Unless we have total control of the ‘if’ we will not know whether a failure of the ‘then’ to materialise is due to the theory being incorrect or the initial situation being different from what we assumed. In real-life situations the ‘if’ happens whenever and wherever it chooses to happen, which may not be the most convenient time and place to observe it. The answer is the experiment. Except for the extremely large or small, theories about the inert world usually allow experiments giving us a reasonably adequate control. When testing the second law of thermodynamics it seems fairly easy to conceive an experiment where we can control the initial conditions to a sufficiënt degree so that we can with confidence let our evaluation of the theory be decided by its outcome.

Two kinds of theories will usually defy even the conception of a factually objective and conclusive test:

-	theories dealing with living systems (3b.4.1)
-	stochastic theories; that is, theories from which we cannot deduce any actual occurrence or non-occurrence of an event, but only the probability of that (non-)occurrence. (3b.4.2)

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3b.4.1) Theories about living systems. We can and do develop theories about living systems from which we can logically deduce facts whose occurrence would be in contradiction with the theory. The monetarist theory of economics would be falsified if the central bank froze the quantity of money and yet inflation would rise. Observing the occurrence of such a fact would lead to the factually objective statement that the theory is false... provided we are confident that the initial conditions were exactly those specified by the theory and by the deduction of the ‘falsifying’ facts. In the case of the monetarist theory, one such initial condition would be the absence of a sudden and autonomous reduction of the supply of goods, such as an oil shortage or erop failure.

When testing theories dealing with complex living systems it is usually impossible to design and execute experiments which give us sufficient control of the initial conditions to justify any confidence in the conclusiveness of test results, for the following reason. In the above case of the monetarist theory we must be confident not only that there have been no changes in ‘external’ conditions, but also that there have been no changes in any of the ‘internal factors’ such as the propensity to save, international trade etc. That is an unwarranted assumption.

To live, a being has to interact with its environment. This interaction is directed by the information process. Breathing is regulated by information about the oxygen content of the blood, about the rate of extraction of oxygen (which depends amongst others on its density in the surrounding air) and about other factors such as the expected requirements of the body which not only depend on the present physical situation but also on anticipation, for instance on fear caused by the suspicion that a predator is nearby.

A being continuously has to process information, seeking out, selecting and evaluating it according to its own built in criteria. It will keep changing as a consequence of this information processing which also takes account of the results from past decisions. The basic difference, between a living being and the heap of chemicals of which it is composed, is the effect of the order in which the chemicals are assembled, both in space and in time.

The interaction of a living being with its environment as well as the information process which guides it cannot be stopped for any meaningful length of time and isolated from its ‘natural’ surroundings. Doing so will destroy the one property which distinguishes a living being from an inert object: being alive. But there is more.

It may be possible to freeze a bacterium without killing it for a period of time sufficient to make a total analysis of its constituent elements and form. (The status of a frozen but potentially viable bacterium is a philosophical problem which illustrates the conventionality and the instrumental character of any abstract classification such as ‘living versus inert’).

Suppose that this bacterium did live in an experimental environment controlled by us. We freeze the bacterium, change the environment and then thaw the bacterium. We might then obtain factual knowledge about the reaction of this bacterium to the change in environment. In this experiment we can have some confidence that only those factors which we have taken into account in designing the experiment influenced its outcome, that the test meets the ceteris

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paribus clause. If we draw a conclusion as to the status of our theory about the reaction of that individual bacterium to the specific change in its surroundings which we brought about, we might justifiably argue that this conclusion is as factually objective as we can make it.

But we do not go to the trouble of developing and testing a theory to explain the behaviour of just a single bacterium. We want a theory for explaining and predicting the behaviour of all bacteria of a certain sort. Extension of the results of an experiment on a limited number of bacteria to its whole sort might be justified if the other bacteria contain exactly the same genetic information, for instance because they are all descendants from a specific bacterium which were not yet subject to a mutation. We also must assume that freezing it does not in any way affect the bacterium so that it will react differently from one which did not enjoy that experience; a justifiable assumption in case of water, but a very dubious one in case of a bacterium.

A theory about one line of identical bacteria is of little use for dealing with bacteria in practice. For a fundamental property of living beings is that reproduction is not perfect, that the genes of bacteria are subject to mutations. These mutations are not spurious phenomena which we can ignore when dealing with bacteria. They are a basic means of bacteria to adapt to their environment and delighting man with surprises like a penicillin-resistant strain.

Most mutations have little influence on the functioning of bacteria. Mutations that do have a significant impact arise only at a frequency of about one in a million to one in a billion genes. Any sort of bacterium therefore seems quite stable... until we realise that in a glass of water there may be billions of bacteria and that we can expect - in every such glass of water - at least one relevant mutation to occur in one of the genes composing the chromosomes of the original strain of bacteria. Even if we start with genetically identical bacteria, we will in a few hours be confronted with a population of bacteria with a wide variety in genetic composition. Limiting the theory to genetically identical bacteria might make it conclusively testable but also irrelevant except as an element of a more general theory which includes mutations and which ipso facto cannot be conclusively tested.

As we move from individual bacteria to more complex living systems, especially those which can learn from experience at the level of the individual, the control of initial conditions required for any test to be conclusive will in practice grow totally beyond our reach. For in addition to an identical genetic make-up we would have to ensure identity of experience right from the conception.

At the scale of humans, that problem is compounded by their ability to learn from each other, so that the knowledge of the very theory we want to test or of their participation in a test becomes part of the experience which influences their behaviour, a problem well known to my fellow market researchers. It is the ability to learn which confers upon living systems the property ‘holistic’ which undermines the applicability of the method of analysis essential for designing and executing conclusive tests. Worse, the experience of man is not limited to his actual experience: through his imagination he can generate experience which his reason can evaluate in terms of probable consequences if translated into practice. Until now, computers did not essentially improve our ability to deal with the holistic nature of living systems. Developing new conceptual

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and mathematical tools specifically aimed at dealing with holistic systems is at least as important as computing power.

In conclusion: for the foreseeable future we can assume that any theory which we use in decision making about the expected behaviour of living systems like a human individual and certainly a human society will not be conclusively testable. To avoid any misunderstanding, let me emphasise that any theory should as far as possible be tested against facts. Such tests will provide valuable information as to the strengths and weaknesses of a theory, and help us to arrive at the most objective judgement we can make as to their applicability in decision-making. But that judgement cannot be expected to be conclusive. The highest (but adequate) qualification it can attain is: ‘to the best of our current knowledge’.

3b.4.2 Stochastic theories. Stochastic theories are theories from which we can deduce only that a certain fact is more (or less) likely to occur in a certain situation than we would have expected in the absence of that theory. Such a theory, if correct, can help us in decision-making. But from stochastic theories we cannot deduce any statement of a singular fact which could be in contradiction with that theory; we only can deduce frequency distributions of singular facts, and thus their probability. However often an experiment shows the same result, we cannot from the theory exclude the possibility that the next time the outcome will be different, we cannot even imagine tests which might lead us conclusively to qualify such a theory as true or false.

Such theories exist even in physics. Examples are all the theories based on the place and mass of elementary particles. Another is the Brownsian movement of molecules which are random; any theory of a process involving molecules ipso facto can define only probabilities. At the level of quanta the problem is even more intractable. Strict interpretation of factual objectivity and conclusiveness of a test would lead us to reject any theory dealing with objects made from atoms and processes involving molecules because it is not conclusively testable. For however unlikely that occurrence may be, we can never exclude the possibility that a cumulation of deviations from the ‘average’ thwarted the laws of physics or chemistry based on probability which we used to define an initial condition in our test. It is theoretically possible that the difference in temperature of gas in two receptacles permitting exchange of gas will for a short time increase instead of diminishing as predicted by physics.

We can to some extent deal with that problem - as Popper did - by requiring that a falsifying test result be reproducible at will. For if the cause of failure of the experiment is not due to such an extremely unlikely cumulation of deviations of chance events, but is caused by some error in the theory, then repeating the experiment should produce more such failures. In case of physics or chemistry, the probability that failure of an experiment at the level at which we usually have to take decisions is due to the chance element of quantum mechanics or Brownsian movement is so unimaginably small that we can safely ignore it. We will certainly not be able to reproduce that error at will. It is then justifiable to present theories like the second law of thermodynamics as one which can for all practical purposes be conclusively tested, instead of a stochastic theory.

Accepting causality presumes that the probability element in a stochastic theory about a system must arise from our ignorance about the exact state of certain factors which are involved in it.

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The exception is the above-mentioned quantum theory. Social decision-making hardly if ever deals with atoms and their particles, so we can forego that discussion. (The reader who is interested in a discussion about causality and quantum theory is referred to Volume Two, ‘Determinism versus Free Will’, p.377 and ‘The Confusion about Reality’, paragraph ‘Quantum Theory and Reality’, p.423)

A theory becomes stochastic if it contains one or more factors whose occurrence is (to us) a chance event, like the exact place at which a photon from the sun will strike our planet, the path and speed of individual molecules etc. Nearly all theories which deal with living systems contain such chance factors and are stochastic. More relevant to our subject, man's imagination is a prime source of uncontrollable variation. Consequently, hardly any reaction of an individual to events in his surroundings is totally predictable. If a theory contains substantial stochastic factors, then we cannot deduce from it a definite ‘if’ which always has to lead to a definite ‘then’; even in theory we have no control over at least some relevant initial conditions.

3b.4.3) The ceteris paribus clause. The core of a theory consists of the factors which determine the process leading from the ‘if’ to the ‘then’. For a test to be conclusive, we must ensure that no factors other than those specified by the theory and by the initial conditions defined in the design of the experiment can influence the outcome of the test.

Any experimental set-up then must (implicitly or explicitly) - as an initial condition - contain the statement that no other factor than those specified in the test had any influence on the outcome of the test. The simple existence of other factors need not be excluded by it. For very often the simple existence of other factors will not influence the outcome of a test provided the state of such factors does not change during the test. The condition that no such change has occurred is called the ‘ceteris paribus clause’. Problem: how do we establish that no such other factor did in fact influence the outcome of the test, that the ceteris paribus clause has been met?

The answer is: in social science that usually is not possible. With experiments in small groups we can try to increase the likelihood of the absence of unknown disturbing factors by isolating the experiment from the rest of the world. But - as stated - this very isolation is an ‘unnatural’ factor which will have an unmeasurable but not necessarily negligible influence. Usually, we cannot even set up an experiment but have to rely on the history of the field concerned. To pass judgement on the significance of the experiment or historical data we must define the level of influence which we will accept as unlikely to lead to an error. What is that level? There can be no general answer, because it depends on the sensitivity of the experiment to variations in various factors which are not under our control. Complex and dynamic systems can be very sensitive to unsuspected disturbances because their effect can increase exponentially or because one factor may depend on the difference between two other factors of similar size which explodes the significance of even a very small error in estimation. A property of information systems is that their sensitivity can be and very often is enormous. A minimal change in one factor erroneously excluded by the experimental design, for instance an unsuspected mutation in just a few molecules of a chromosome of an egg-cell, can result in a change in the system which surpasses the combined effect of all the factors which we did specify. Only a (preferably mathematical) model of the system can teil us how sensitive it is.

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Note that any conclusion we draw from the analysis of sensitivity of the theory assumes the theory to be true. But that is exactly what the experiment is supposed to test. A nice puzzle which I can leave to those who relish the kind of argumentation required to solve it, for its solution does not affect any of the conclusions of this book.

To conclude, the usual situation in most tests in any field of science dealing with living systems is that we cannot in any factually objective way conclusively decide whether a failure to achieve the results predicted by the theory is due to the falseness of the theory or to a failure of the experimental set-up to meet the initial conditions or the ceteris paribus clause. At best such failure will incite us to be suspicious of that theory and attempt to improve it or try another one. Similarly, if the outcome of the test is what we have predicted on the basis of the theory, that is a good reason for increasing our confidence in the theory but can never lead to a conclusive judgement that it is really better than one which flunked the test. Testing a theory always increases our knowledge, and does so in a way which is as objective as we can hope to make it.

3b.5) A Demarcation Criterion for Empirical Scientific Theories.

I want to emphasise that I do not have the presumption to dictate general standards for scientists. I am concerned only with scientific theories in their ubiquitous use in establishing facts. If a scientist does not intend his theory to be used for that purpose, it is his responsibility to state so explicitly. Any theory intended to help us in decision-making must include a prescription about how to use it to deduce facts. That in any case requires a definition of the sectors of reality to which (the symbols used in) the theory refers. To help us in decision-making, a theory must meet Popper's requirement that it should teach us something about our world of experience, be empirical.

Both history and what we know about information and knowledge tells us that nobody is infallible. Neither is society. Really fundamental discoveries were often rejected as rubbish or simply ignored for as long as possible by the scientific establishment. (See Volume Two, Volume Two, chapter ‘Knowledge and Human Understanding as a Social Venture’, paragraph ‘the Social Responsibility of Science, Ravetz’, p. 410). Note that only those cases where the discovery was finally accepted are documented in history. We are totally ignorant of those that were not. Failing to acknowledge a worthwhile discovery is not only a waste of time and effort; it is also a loss to society of the discovery itself and the benefits it might have generated. Both to improve on that situation and to meet our democratie criterion, we should ensure that anybody proposing a new theory can have that theory evaluated by the most objective and effective procedures we can design and afford. For the same reason we should also insure that theories which cannot help us will be eliminated from consideration for decision-making.

The most objective selection method consists of confronting the theory with facts, designing experiments if possible, and collecting and analysing historical data if not. Both are usually very costly and time consuming. If - by just examining the theory - we could make a first selection, that would greatly enhance the effectiveness of the whole selection process. Such a

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first selection method is available and it is very cheap: logical evaluation. It can teil us whether a theory is not empirical and scientific (because it cannot teil us anything new about our real world of experience) and thus is of no use for decision-making. Logical analysis may also reveal a reluctance of its author to have his theory submitted to an evaluation which is as objective as we can make it, which would be a cause for at least temporary disqualification. Following Popper, we will call a logical Standard for the selection of empirical scientific theories a demarcation criterion’.

Theories always assert the existence of certain types of relations between certain classes of facts, of events. These relations enable us to deduce something about future events from known events: ‘if “A” happens, then “B” will happen’. That is useful only if ‘B’ does not refer to all kinds of events, but only to a restricted class and if many of the events which do not pertain to class ‘B’ can be predicted not to happen. Any theory useful for decision-making therefore must exclude events, must enable us to deduce from it that some events are less likely to happen than others. (The exception are tautologies which, as mentioned in the chapter ‘Can Knowledge be Objective?’, paragraph. ‘Truth and Falsity’, p.93, may be helpful in organising our own information processing even if they cannot teil us anything new about the world of which we want to obtain information, are not empirical). Popper has extensively and so far as I know conclusively argued that case. For a more comprehensive argumentation the reader is referred to his ‘The Logic of Scientific Discovery’, hereafter abbreviated as LSD (even though I do not agree with all his claims of objectivity).

A very first requirement of our demarcation criterion therefore is that it eliminates all theories from which we can deduce no singular statements of facts which would be in contradiction with the theory. Any theory meeting that criterion can in theory be tested by confronting it with its performance in prediction by devising experiments (or using relevant historical data) where that prediction consists of the non-concurrence of certain events. If these events do occur, that would be a refutation of the theory.

The question is: should our demarcation criterion do more? Specifically, should we require that these tests be both practically feasible and conclusive? Popper answers ‘yes’, but that seems unwarranted. As has been argued in the two previous chapters, whether a theory is conclusively and practically testable depends on the subject. If a theory claims universal validity, we can require that its form be such that we can deduce from it negative singular statements whose falsity would lead us to reject the theory (including its claim to universality) as false and to design at least fictive experiments to that effect. Failure of a universal theory to meet that requirement is a justification for rejecting it as either irrelevant or as attempting to evade objective evaluation. Our demarcation criterion should eliminate such theories. But the requirement that we can translate that into ‘conclusive decidability by (actual) confrontation with facts’ is another matter.

As explained in the chapter ‘The Testability of Scientific Theories’, p.108) there are theories which do help us in decision making but which lay no claim to universal validity, namely stochastic theories. These theories may however claim a qualified universal validity, namely that they are valid as long as we take account of the probability which they assert. We can apply the same reasoning which we applied to universal theories, except that instead of facts which

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can never occur we must be able to deduce facts whose probability is substantially below 50%. Our demarcation criterion should admit such theories as relevant and pertaining to empirical science.

If we test such a theory and if the fact whose probability was estimated to be below 50% does occur, we cannot of course deduce that the theory is false, only that it is likely to be so. Such a judgment can thus never be conclusive and can lay no claim to factual objectivity, for it depends on the answer to the question: ‘which level of risk (of being wrong) are we willing to accept when deciding to reject a theory on the basis that a fact has occurred whose occurrence the theory has given a low probability’. That level is totally conventional. But once we have decided in a democratie procedure on a Standard level of risk which we find acceptable, judging a theory on the basis of such tests is the most objective procedure possible given the nature of that part of reality about which the theory attempts to provide some knowledge. It also allows the comparison with competing theories.

As stated, deciding on that acceptable risk of error introduces a subjective element. But Popper's decision to allow only conclusively decidable theories does not avoid that subjective element: he just sets his subjective Standard of acceptable risk at near zero and of objectivity at near 100%, a Standard which - as explained in the previous chapters - is beyond our reach in social science. And of course the theories of social science usually and through no fault of their own preclude conclusive testing. There is then no valid reason for excluding theories which defy conclusive testing as long as they provide the ‘closest fit’ and are the most objective and means to decide about facts.

We will then require from the demarcation criterion only that it eliminates theories which cannot increase our empirical knowledge and those theories which are presented in a form which does not permit the most severe evaluation allowed by the nature of the field of investigation. The following demarcation criterion satisfies that condition:

WE SHALL REQUIRE OF AN EMPIRICAL SCIENTIFIC SYSTEM THAT ITS STRUCTURE, ITS LOGICAL FORM, BE SUCH THAT IT CAN BE AT LEAST THEORETICALLY REFUTED BY EMPIRICAL TESTS, THAT IS BY CONFRONTATION WITH FACTS, GIVEN AN A PRIORI DETERMINED RISK - SMALLER THAN 50% - OF TAKING THE WRONG DECISION. As will be explained further on, such a system must be axiomatisable.

3b.6) Comparing Empirical Scientific Theories.

One ‘theory’ is always available: admitting total ignorance, the ‘we-cant-know theory’, the ‘zero-hypothesis’. Deciding that a theory has met our demarcation criterion just means that it is worth considering. The next step is to decide whether it is the best available representation of reality for deciding about the facts concerned. It must in any case score higher than the zero-hypothesis. For if it does not, we are better off by admitting our ignorance, because navigating on the basis of a theory which may be false stands a good chance of leading us away from our objectives instead of towards them, and at best will give us a false sense of security or objectivity. If a

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theory is an improvement over the zero-hypothesis and if there is no competing theory for explaining the same facts, we will accept the proposed theory. If there is a competing theory we must chose. Can we define rules and criteria for the comparison of theories having met the demarcation criterion?

The comparison of scientific theories is a very complex field which cannot be adequately dealt with in a book like the present. The very rough sketch presented in this book will have achieved its purpose if it has given the reader a feel for the demarcation criterion and for the prohibition of ‘ad hoc’ modifications (see below), both leading to a requirement which we should impose on any theory which claims validity in social decision making: that it be axiomatised, or at least be axiomatisable, to the extent that this is permitted by the nature of the field about which the theory pretends to give us an explanation. What axiomatisation means will be explained further on.

Some epistemologists have argued that comparing scientific theories is often impossible because of incommensurability. However, if the theories meet the above conditions, that problem can be dealt with or should not even arise. It has therefore been relegated to Volume Two, ‘The Incommensurability of Scientific theories’, p.285, and ‘Knowledge and Human Understanding as a Social Venture’, paragraph ‘Incommensurability of conceptual systems’, p.407.

3b.6.1) The rule against ‘ad hoc’ modifications. Suppose we deal with a sector of reality permitting tests which provide a sufficiënt control over the test conditions for stating with confidence that failure of the theory to meet the test is to be imputed to the theory. We can then compare theories on the basis of the variety and the severity of tests which they have successfully met. We can declare, always provisionally, valid that theory which has - in Popper's terms - the highest verisimilitude, the highest empirical content because it is more precise, excludes more events, allows a higher variety of tests, and has:

-	met all tests which also have been met by its rivals
-	also met tests in which its rivals have failed.

Note that if we have performed the test just once, and have been successful, we have learned only that we have as yet no reason to consider the theory to be false. As we repeat that test with positive results, our confidence that it might provide a correct answer if applied in decision-making will progressively increase. So besides the variety of tests which a theory allows us to conceive, the number of tests it has successfully passed is a major factor in the confidence we can have in it. That is pure common sense.

Simple as that recipe appears, its application is not. Suppose one test was not met by a theory. It is often possible with hindsight to construct a new theory which meets all the tests which the falsified theory met plus those tests in which it failed. The trick is to add to the falsified theory some hypotheses or axioms exclusively designed to provide a plausible explanation for these failures, thus reducing the number of events excluded by the theory. Such a modification is termed ‘ad hoc’. Theories which are an ‘ad hoc’ modification of a previously falsified theory are to be rejected.

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But how do we determine that a modification is ‘ad hoc’ without the ability to look into the brain of its author? Popper translates the rule into the requirement that the new theory must have a higher ‘empirical content’; Lakatos uses the term 'a higher heuristic. The matter is too complicated to deal with in the context of this book, but I will attempt to give the reader a feeling for it.

Suppose your friend pretends to be able to predict the future. Telling you that you will take a trip abroad in the coming year will not give you much confidence in his foresight, as most readers of this book will travel abroad for business or private reason. A real test would be a prediction of an event which at the time would seem to be highly unlikely, for instance that you will not travel abroad in the next three years.

The more a theory leads to the expectation of events which - on your own - you would not have considered likely to happen, the more it tells you what you did not already know. The more it restricts the range of possible events, the more precise the conclusions which you can draw from the theory, the more it can teil you about reality, the higher its ‘empirical content’, and the more your confidence in it will increase if it repeatedly and successfully passed the tests.

A test which is met because the theory was especially designed to meet that test is no test at all: the success was a foregone conclusion. Meeting such a test does not increase our confidence in the theory. It lowers the variety of possible falsifying tests and by reducing the number of events excluded by the theory it reduces its precision and relevancy. The net result of the modification of the theory for its users is negative.

We can formulate the rule against ‘ad-hocness’ as follows: any modification of a theory is admissible only to the extent that it will increase the variety of tests, and thus of singular statements deducible from the theory whose truth would falsify the theory. There may be a good but previously unsuspected reason why a theory is not applicable in certain circumstances. If a modification follows from such a consideration, it is not ad hoc. Such an improvement will provide a whole new series of tests, namely of the theory explaining why in those circumstances it does not apply.

3b.6.2) The need for axiomatisation. There are other considerations besides testing which can help us in choosing amongst theories meeting the demarcation criterion. One of them is our confidence in the axioms on which they are based. If theories differ as to the axioms they use, then we will - other things being equal - prefer the theory whose axioms are less suspect, for instance because they are deduced from theories which are accepted as valid in other fields of science on basis of our criteria and mies, or because they refer to statements of facts which we all have observed and admitted as valid. Again, that is pure common sense.

It presumes however that we know all the axioms implied in the theories. We also require that these axioms must be consistent with each other, which presumes that we know all the relationships which the theory assumes to exist between these axioms.

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To apply the demarcation criterion and the rule against ad hoc modifications, to design tests which we will accept as conclusive, we must be able to determine which singular statements - whose truth is excluded by the theory - can be deduced from that theory, we must know the relationship between the axioms and the conclusions drawn from them by the theory. We must make sure that the conclusions are not built into the axioms, that there is no petitio principii. In short, to apply the above-mentioned means for comparing theories and to engage in a democratie argumentation about the merits of competing theories, we must know all axioms assumed by the theory and be able to exactly define the logical components and structure of the theory: the theory should be ‘axiomatised’.

If the logical structure of the theory is sufficiently clear, and if more than one theory survives the scrutiny of its logical structure and its axioms, we will then proceed with tests. If we can design tests leading to factually objective decisions, we will then be able to reach a decision to which no one can have a legitimate objection, and call the test conclusive but remember that this judgement is only provisional and can never claim total objectivity. That includes stochastic theories. For if the verdict is that one theory is more likely to be of use in decision making than another, given a preset level of risk of taking the wrong decision, then accepting it is better than ‘no decision’.

As explained in the chapter about the testability of scientific theories, there is one field of science which often precludes the design and execution of conclusive tests: living systems. Deciding what will be considered as a test rests heavily on the interpretation of whatever data we have been able to collect from other tests and from history. We cannot then take a decision on the basis of factually objective statements like the reading of a thermometer. We will have to draw much of our argumentation from a comparison of the theories in terms of the other qualifications of theories, such as empirical content, consistency and the confidence we accord their assumptions, especially those derived from theories of other fields of science. Such theories will also be far more complex in their structure, and contain more assumptions from other fields of science than the theories of physics and chemistry. That complexity increases the causes of internal inconsistencies and other flaws which render a theory of dubious value, if not completely worthless. These shortcomings can be exposed only by logical analysis which requires axiomatisation. Both the limited possibilities to test them and the greater risks of structural shortcomings render axiomatisation all the more effective and decisive in theories about living systems.

The fact that about all theories of social science will fail to meet Popper's strict demarcation criterion has provided many with a welcome but unwarranted excuse for also abandoning the search for other relatively objective ways of evaluation such as axiomatisation. An ubiquitous but pernicious substitute for testing and logical analysis often is the fame and authority of the protagonist of a theory.

The prominent function of science in social decision-making mandates that we use any effective means to improve it. It puts on the shoulders of philosophers of science, especially methodologists, the task of that analysis. The core of a theory, for instance an equation like E = hv (where ‘h’ is Planck's constant) or Sayer's law about bad money may be extremely

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simple; its justification and the deduction of (falsifying) statements about facts are not. They engage arguments, deductions and deductive systems and therefore are subject to the rules of democratie argumentation, which for scientific theories translate into axiomatisation. Knowing the logical structure of that argumentation will also increase its usefulness to decision-makers which may include other scientists needing the theory as an axiom for their own.

3b.7) The Axiomatisation of Scientific Theories.

3b.7.1) The four steps of the evaluation of scientific thoeries. One can disagree with Popper, for instance about totally objective knowledge, but his exposition of the logic of scientific discovery is still the best I have found. There is no point in trying to redo his work whenever it can serve. Popper proposes four steps in the evaluation of scientific theories (LSD, pp 32/33):

1)	check the inner consistency of the theory
2)	Make sure it is an empirical scientific theory (the demarcation criterion)
3)	See if it really adds something to existing theories (empirical content)
4)	Test it against facts, try to falsify it.

That seems a reasonable approach which provides some basic principles for the selection of theories as a basis for establishing facts in social decision-making in a democracy. What is to be axiomatised then is not necessarily the theory itself, which - especially at its initial stage - may be simply a new way to look at things. What must be axiomatisable is the justification of using the theory to establish specific facts.

The first two steps weed out theories which do not merit further evaluation. They can be applied to any single theory. The next two steps concern the comparison of theories. There always is a comparison, for - as previously explained - the falsification of a theory by a test is not a sufficient cause for us to reject it if the theory scores better than the ‘know nothing theory’.

The first three steps will be explained below. They consist of logical analysis and are largely preliminary steps for the fourth step. It is they who require axiomatisation. The fourth needs no further comment.

1)

Consistency covers a wide range of requirements which a system has to meet to allow deduction of unequivocal and decisive conclusions. In the chapter about scientific theories I have already mentioned that in the system of statements which form a theory, a hypothesis should never also be implied in an assumption such as an axiom or a definition (see also the last paragraph about the interdependency of scientific theories, p.107). That would generate a petitio principii. For instance, the theory under investigation could be part of the axioms in one of the theories from other fields of science which are used as axioms by the theory to be evaluated. Inner contradictions are another form of inconsistency. Using the truth of a certain fact as an axiom and then using that same fact as a singular statement whose truth would falsify the theory entails that either the axiom or the theory would always and per definition prove to be false. The rules of logic require that if a statement of fact is used as implicans in an

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	implication, the theory cannot allow for that fact to be false. In an ‘if..., then...’ statement the ‘if’ must always be assumed to be true. The common denominator of these sins against consistency is that from inconsistent theories we can either derive all facts we can imagine, or none at all. ‘Ex falsibus onmii’. Such theories then cannot provide any help in decision-making except for the decision to reject them. Common-sense consistency requires that the same symbol or word should keep the same meaning throughout the argument. As obvious as that requirement seems to be, it is often sinned against, for example by Feyerabend, as shown in Volume Two. Such inconsistencies occur more often than one would expect because they usually are not explicit and can be exposed only through careful analysis.
2)	This step is the application of the demarcation criterion we have defined in the chapter of that name, p.115. It is materiaily different from Popper's and should meet the criticisms which have been levelled at his.
3)	The ratio for the third step has been explained in the previous chapter about the comparison of theories: we need to determine what a theory can teil us, its ‘empirical content’, both because it is one of the criteria for choosing between theories and because we need it to enforce the rule against modifications of a theory which are ad-hoc.

3b.7.2) The starting point of axiomatisation is to collect all assumptions which are used to form the apex of the system, and from which all others are deduced. These are called axioms by Popper and I will follow him, although the term is often applied only to the first of the two classes mentioned below. In this use, the term does not imply that they have been proved (or generally acknowledged) to be true, but only that they are assumed to be true in the system under investigation. Their common feature is that they contain statements about (assumed) facts or events and of the relations between them. There are two classes of axioms, and it must be clear for every axiom to which of these it belongs:

a)

Conventions, consisting of statements which we agree to accept as true, such as: - logical or mathematical relations between events (see PART FIVE) - relations postulated by other scientific theories, - the existence or non-existence of certain objects or events. We do not require that this type of axiom actually be true, but only that they are accepted as such consistently and by all concerned throughout the development and application of the theory.

b)

hypotheses which form the core of the theory. They are what the theory pretends to teach us in addition to what we already have accepted as knowledge.

We also require that these axioms are sufficient and necessary to deduce all other statements we hold to be part of the theory or of its consequences. They will do so only if the system of axioms meets the four conditions below, a prerequisite for qualifying the system as ‘axiomatised’. (These conditions are to some extent equal to or implied by the above three steps of logical analysis).

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1)	The system of axioms should be free from contradictions amongst each other, whether self-contradiction or mutual contradiction. The system must be such that not every arbitrarily chosen statement can be deduced from it. It cannot contain any statement which another statement holds to be false, no false implicans etc.
2)	The axioms must be independent from each other in the sense that no axiom can be deduced from any other single axiom or group of axioms. (Such an axiom would be redundant and thus fail to meet condition 4). To avoid any misunderstanding: this condition applies only to the axioms, not to the variables; variables may well be interdependent, and in systems of living beings usually are. Income and the rate of saving may well be correlated with each other, but neither of them figures as an axiom in economic theory but as something which has to be explained.
3)	The axioms must be sufficient to deduce from them all statements which belong to the theory which is to be axiomatised. If not, the theory is ‘underdetermined’ and cannot lead to unequivocal deductions of facts.
4)	All axioms must be necessary for that theory. No superfluous assumptions are allowed. A superfluous axiom which both in its occurrence and in its consequences is identical to one of the others is just unnecessary baggage. If it is different in one of those aspects, it will lead to ‘overdetermination’ and thus inner contradiction.

Perfect axiomatisation is usually neither possible nor really necessary. All we require is that the theory be sufficiently axiomatised to allow a decisive assessment of the logical structure of that theory. To the extent that this can be shown to be impossible, we will require the maximal level of axiomatisation that - given good will - can be achieved. Popper attempted to define totally objective and universally valid criteria for the evaluation of scientific theories. Our objective is more limited: we only want to decide whether they are to be admitted in social decision making in a democracy as a means to establish the de factii. A criterion will do as long as it is established in a democratic way and no better criteria are available and practicable.

I add a general rule which may have seemed too evident for Popper to mention, or which he may have omitted because he was mainly concerned with the logical evaluation of a single theory, but which is necessary in evaluating theories for social decision-making:

To establish actual or hypothetical facts for axioms of type 1 or 2 below we must use facts or theories which have been previously established according to the rules proposed below in preference to any other.

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3B.7.3) The complete set of rules for a scientific theory to be axiomatised (or axiomatisable) would then read as follows:

A)	To qualify for consideration, a theory should consist of - or be reducible to - a set of only the following kind of statements:

Axioms:

1)	Actual ‘facts’ agreed upon to be true, including relations between facts as well as scientific theories which have previously been accepted on the basis of these rules.
2)	Hypothetical facts (or relations between them) accepted as true for the sake of the argument (for instance the initial conditions, the ‘if’)
3)	Hypotheses that form the actual theory. In tests the initial conditions will be treated as axioms.

Deduction:

4)	All deductions admitted by the rules of logic and mathematics. They should use as input the above, and only the above, axioms and follow in their totality from them.

The theory must be constructed and formulated in such a way that it is always clear to which of the above categories any statement belongs. The theory is then a candidate for evaluation.

B)

To qualify it as scientific and axiomatised, we further require that: 5 The system formed by these statements must be consistent, that it is free of self or mutual contradiction 6) No statements of type 1, 2 or 3 can be deduced from one or more other statements of the theory, whatever their type 7) The axioms, the statements of type 1, 2, 3, must be sufficient for deducing all statements of type 4 8) All axioms must be necessary for the deduction of at least one statement of type 4 9) No statement of type 1 or 2 may be in contradiction with an existing theory that has been accepted according to the rules for the evaluation of scientific theories. If a statement is in contradiction with an accepted theory it must be presented as an hypothesis and be included in the statements of type 3.

If a theory meets these qualifications, we can proceed with Popper's four steps of justification of a choice of a scientific theory presented at the beginning of this chapter. Much of the work involved in the first three steps will already have been done.

The reader may ask why we should weaken our demarcation criterion by accepting for consideration systems that are not axiomatised, but only amenable to axiomatisation. The answer is that the best system one can imagine is irrelevant unless it is read and understood by other people. Understanding requires that its concepts relate to concepts which people have ‘interiorised’, which are alive for the readers, generate some representation of reality, mental or physical. Full axiomatisation imposes its own structure and rhythm on the presentation of the system

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which might disrupt the flow of argumentation to such an extent that it becomes difficult to follow. Considerations of ‘understandability’ also legitimise the use of metaphors, analogies and illustrations which are redundant for the axiomatised system. While inevitable, they generate a constant danger of introducing implicit and illegitimate connotations and assumptions. To fulfil their legitimate function and minimise this danger, metaphors etc. must be clearly identifiable as such and never imply any notion of justification of the theory.

Actual axiomatisation is mainly necessary to enable a critical and decisive evaluation of the system, for instance as to its acceptability for social decision-making. That evaluation requires specialised knowledge and substantial effort. Efficiency and objectivity suggest that we should entrust that job to a special discipline. Once a theory is accepted, its application for decision-making will not require its presentation in its fully axiomatised form provided the above evaluation is available to the public.

3b.8): Summary of Truth in Social Decision Making.

Decisions always involve a de factii. In a democracy the most important and contested property of statements about these facts is truth. Truth itself is not a fact and never is conclusively provable. The next best substitute for truth is objectivity. The decision of selecting one of the competing statements about these facts as being true, as being the most realistic, objective representation currently available to us, can never be more than tentative,

The maximal possible objectivity can be achieved with statements about facts which (whatever their origin) exist independently from any individual and are available for observation and which are factually objective in that sense. Whenever that is possible, we must reduce decisions about facts to decisions about such statements. If all concerned are willing to strive for truth and if all are able to correctly observe these facts, then a maximally objective evaluation of the truth of statements about them is theoretically possible provided the necessary effort is made.

In the second chapter of Part Three A, paragraph ‘Establishing facts for social decision-making’, p. 93, these two ‘ifs’ have been investigated, leading to the conclusion that there is no totally objective way to prove either unwillingness or incapability to establish the truth about factually objective statements even if the facts concerned are available for observation. Therefore we must have - conventional - rules and procedures whose sole objective is to achieve the most objective decision that is possible if a statement about facts is contested. The objectivity of any decision about them depends on the presence of a large majority who:

-	de facto subscribes to the democratic principle
-	is willing to give priority to truth and to accept and apply these rules and procedures
-	is able to correctly apply them and observe the fact.

Establishing simple facts like the reading of a thermometer usually is unproblematic as the cheater stands a good chance of being exposed as such. Contestations mostly concern the facts which are not available for direct observation. Decision-making always implies a decision about the consequences of the various decision alternatives which lie in the future and therefore

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are never available for direct observation. In deciding about these expected consequences we will engage knowledge gained from past experience and use statements about other facts which are accepted as true. To deduce from them to the facts we want to establish requires some form of inference, some procedure of deduction. Two kinds of (systems of) statements are of particular importance in that process:

-	relations which are accepted to hold between all facts, mainly those defined by logic and mathematics. We assume consensus in this field, and for a justification of that assumption refer the reader to Part Five.
-	scientific theories.

The selection of scientific theories used in decision-making is crucial to the viability of the society and should be as objective as possible. Total objectivity is impossible, but there are degrees of objectivity, some methods of selection are more objective than others. The democratic principle requires that we devise and apply methods, procedures and rules for selecting scientific theories in the most objective way we can achieve.

A first proposal consists of the four steps mentioned at the beginning of the previous chapter (three steps of logical analysis plus testing against facts) and the rule that any theory claiming the status of empirical and scientific must be axiomatisable (and preferably axiomatised) to the extent allowed by the nature of the sector of reality with which the theory pretends to deal. That seems fairly in tune with what many, possibly most, scientists would accept as reasonable (especially if applied to somebody else's theory or statement).

The proposal for evaluation of a scientific theory is not itself an empirical scientific theory. It deals with such theories and thus is above, or at least beyond them: it pertains to the field of metaphysics, to philosophy. It differs from the usual writings in that the standards for the evaluation of scientific theories are deduced from their application in social decision-making in a viable and democratic society. From this last goal, and by the same type of argumentation, we deduce the requirement that any philosophic system which is intended to tell us how we should organise social decision-making in a democracy should be amenable to axiomatisation.

If a philosophical system is in no way amenable to axiomatisation, it is impossible to critically evaluate it in terms of its relation to whatever concept of reality one may have. It will be accepted only because it appeals to subjective feelings like aesthetics or because the reader - being unable to really understand it - is overwhelmed by its semblance of intellectual brilliance or the authority of its protagonists. Such means of persuasion are fundamentally undemocratic, as will further be explained in Part Five.

While the above four steps in the evaluation of scientific theories are easy to write down, translating them into more concrete procedures and methods is another matter. Especially the comparison of scientific theories in terms of empirical content is a highly sophisticated venture. We can assert with confidence that it is impossible to design procedures and methods which will always yield unequivocal results. Actual judgements about a certain scientific theory will then reflect both the professional proficiency and the objectives of its judge. For social decision making in a democracy, all we can ask is that science acknowledges this objective to be the

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construction of a representation of reality which is as free as possible of subjective elements and comes as close to reality as we can make it. As stated in Part Two, perfection is not a category of life. This selection process is most emphatically not aimed at regulating the development of science, only at the application of its findings in social decision-making (which includes the development of science in other fields which use the findings as axioms in their own theories).

In the next part we will find that the elimination of subjective bias is also the main problem in deciding about what is just in a democracy and we will discuss methods and procedures to that effect. These methods and procedures can then serve to deal with subjective bias in decision-making about facts, including the selection of scientific theories, whenever these theories are not decidable by confrontation with facts or if logical analysis has not provided a clear answer. So we will first turn to justice, and then in Part Five will pull the threads together.