Fact, Theory and Dogma

Chris Lucas

Introduction

Intelligent people often pride themselves on their ability to make decisions based on facts, rather than on ungrounded opinions, but few of us delve very deeply into the basis of this assertion. Truth and Falsity seem such easy concepts to use, yet what exactly do they mean ? Is dogma a valid unchangeable fact or invalid ignorant opinion, or both ? On what basis can we believe our theories, and can we have contradictory ones ? Here we will try to look a little deeper into the basis of our convictions and their relation to the world around us, and attempt to establish a more balanced viewpoint in which to determine the validity of our thoughts.

Conceptual Maps

I have a theory: that my acts are based on facts and your acts are based on fantasies. Strangely you have exactly the same theory. So do we agree ? Not at all, in fact we totally disagree ! But how can we agree to a theory yet disagree about its consequences ? Quite simply, because the words mean different things to each of us. My 'my' is what you call 'your' and vice versa - simply replace these referents by proper names to see this. The syntax of the theories are identical, but their semantics (meaning) is different. When we converse, we do so based upon meanings but the forms we use can be variable and interchangeable. For example all these mean the same:

'The cat sat on the dog'
'The dog has a cat sat upon it'
'Sitting on the dog is a cat'
'On the dog a cat is sitting'

How we actually decode such sentences is still somewhat of a mystery, but we can represent them all by a conceptual map:

Cat sitting Dog

Here the cat and dog are objects and sitting is a directed relation or action between them. Imagine, if you will, all the concepts in your mind laid out in such maps. You should have an incredibly complicated layout up there ! Not only can the relations be in both directions - 'The dog sat on the cat' , but they can have loose ends 'The cat grinned...' (at what?) or complex strings of adjectives 'The smiling black tom cat blissfully curled up on the warm brown rug'. When we read a sentence we have to find a decoding method that fits some meaningful conceptual map in our language - this is the selection of an actual from a set of potential mappings. Yet why should the maps I have available agree at all with those available to you ? And if they do not, then how do we communicate effectively ?

When we are born we have no linguistic skills, these develop quickly as we grow (in whatever language is native), based upon our experiences and the words we hear about us. We make random connections (perhaps) between the sounds, images and sensations until how we behave and speak fits into the society of which we are a part. Our set of mental maps is thus constrained by the beliefs and scope of our society. We only understand a sub-set of the possible classifications of our world, those of relevance to our particular place in this environment. The vocabulary employed by an average native English speaker is around 10,000 words, yet the definitive Oxford English Dictionary lists over 500,000 and this excludes the vast number of technical terms used in specialist fields. It is thus more than likely that we will misunderstand, at least in some way, much of what we hear or read ! Even for those words we have in common our understanding is not based on exactly the same learning process, so there will be minor differences in assumed meaning.

Facts

If we can never be certain that our understanding exactly matches that of anyone else, then the whole concept of 'fact' is called into question. A 'fact', in the popular understanding of the term, is something that is 100% correct. Excluding such things as mathematics (e.g. 2+2=4), which are tautologies, true by definition, how can we agree about what constitutes a 'fact' (e.g. 'the moon is in the sky') ? Is this statement true for a blind person ? If it is, then certainly their understanding of that fact is different than a sighted person !

Words, as Wittgenstein saw, are contextual things. They have meaning only within a social setting (e.g. would the word 'computer' have meaning to a jungle tribe, or their word for 'a poisonous toad' to a city economist ?). So the first requirement for any agreed meanings is social usage. We can point at an object and say its name to our children, if everyone says the same name then the kid will get the idea of our language-game. Is this usage 100% certain then ? No, pointing at a tree we could say: 'tree' or 'wood' or 'oak' or 'evergreen' or many other valid descriptions. In our mental maps all these concepts are connected, if we hear the word for one of them we immediately associate all the others, with a strength depending upon the frequency of their conjunction in our experience (e.g. 'swan' will be associated strongly with 'white', and weakly with 'black' - except perhaps in Australia where there are lots of 'black' swans !).

Note however that in any particular case not all of the mental associations will be valid, there will be some that do not apply ('alive' for example, if the swan happens to be 'dead'). These can include those concepts thought universal, e.g. releasing a ball we expect it to drop, but it could rise (if filled with helium for example !). Our classifications are at best probabilistic, we guess what will happen based upon what has happened in the past, and are surprised when this doesn't occur. In such cases we must revise our mental maps (e.g. when a child learns to distinguish between different animals, having previously called them all 'pussy' say). All new knowledge requires this splitting of previously undifferentiated concepts, the creation of new categories for classification or action.

What we regard as facts are classifications that have stood the test of time, they are used consistently in our society and behave the same in all contexts. Yet we have seen that these are only good as far as our experience goes, balls can defy gravity if unknown to us they are filled with a gas lighter than air (but should we then still call it a ball ?). This method of generalising from the past to the future is called induction, and forms the basis for our scientific theories. So let us now turn to our next subject, the theory.

Theory

A theory is, in essence, an isolated part of our mental map. We do not expect any particular theory to cover everything in our world, so simplify its scope to concentrate on a particular area of interest (e.g. for planetary motions, here we ignore the structure of planets and treat suns, spacecraft and moons as just equivalent to points of different masses). Are theories deliberate, conscious and logical constructions then? We often assume so, but no, there are two types of theories that are present in us all of which we are usually unaware. Theories are beliefs, ways of interpreting the world we inhabit in ways that make sense. May we leave such interpretations until we are old enough to be able to think logically ? No, children (and animals) exist in a world without logic, yet are fully aware of many aspects of it, they behave in ways that correspond to adult theories, in some sense pre-empting those theories.

Two aspects of our biology are involved here. In the first, that of instinct, we have evolved over long periods of history in such a way as to behave appropriately in the environment we occupy. These in-built (genetic) theories have been tested in the hardest school of all, that of survival itself - natural selection. The higher organisms however have a more general facility available, that of learning. This is seen clearly in the growth of children, where trial and error methods gradually build up behaviours that are effective, whether in actions or in language. These mental (neural) theories form a large part of our adult world view, but like their genetic cousins we are generally unaware of their presence. So let us ask what distinguishes our more explicit conscious theories from these unconscious ones ?

It relates, I think, to one word - abstraction. Our in-built theories are in the world, closely linked with our ongoing actions and behaviour. They are only partly intellectual, and generally have a strong emotional bias - we act out our feelings intuitively, not considering what we are doing beforehand. In contrast, the explicit theories that form such a strong part of our educational systems are mental abstractions, we can talk about them, write about them, and calculate with them in a way completely divorced from any real world actions. Such actions, if they take place at all, are secondary and generally simply follow a plan resulting from intellectual manipulation of the relevant theories.

Because of their abstract status, we tend to regard theories as prior to action, 'we think therefore we act' (as Descartes nearly said...). Yet where did these theories come from in the first place ? Can we say 'the real world' ? Sorry, we can't - that consists only of facts (if it consists of anything at all !). Theories are linkages between facts, relations that we claim are met in our dealings with the reality of our experience. How many theories can we generate from, let's say, 3 facts then ? Well, consider three dots on a sheet of paper. How many formulae can mathematicians generate whose graphs will link those three dots ? There is no limit, an infinite number are possible ! If our theories likewise are unconstrained then how can we decide which to use, and how can we generate them all in the first place ?

To answer the latter problem first, we don't bother ! How any theory is initially conceived is an unsolved problem, generally thought to be linked to intuition (whatever that is !), but normally all we tend to do is think up any old theory and just use that until it doesn't work. In other words scientific (and other) theories have much in common with a child's attempt to make sense of the world... How sophisticated our theories become does depend on our education and experience. As we learn more we can put together our knowledge in many different ways, and as our experience grows we can include or exclude different areas from particular theories. Yet theory building isn't always a personal act, it becomes a social one as soon as we become members of a society. A solitary hermit can believe anything, yet a group of people with wildly different theories would cause great problems (e.g. worship of different Gods, different political theories, even differing fashion or food ideas can cause major conflicts within a society). How do we rationalise such diversity ?

Axioms

Two ways are available, the first scientific, the second axiomatic. In science where two or more theories are competing it is usual to test them and choose the one that best fits the facts. If more than one does so equally well, then it is usual to choose the simplest one, the one using the fewest concepts or variables. Yet these criteria themselves form a theory, the theory of scientific method. How do we test these in turn ? Answer is that we don't ! At some stage we have to stop trying to justify our concepts and just accept them - they become what we call axioms, unchallenged starting points that form the basis for all our other ideas. Normally these axioms are not explicitly specified, we take them as background assumptions and use them without thinking about it, but here we shall look a little more deeply into these crucial assumptions behind our actions.

The axioms best known perhaps (to those with some formal education) are those of Euclid, the dreaded axioms behind his geometry. Having encountered the vagaries of these, and the deductive methods associated with them, it is perhaps no surprise that most people would run a mile (or a couple of kilometres to taste !) before having anything more to do with them, yet this would consign to obscurity something of great importance. That is the idea that axioms constrain our entire way of thinking about our world. Would it surprise the reader to know that there are many different forms of geometry than that loved by Euclid ? Ignorance of this fact led us to spend some 2000 years pursuing only those ideas and theories that fitted into this framework. Only when we threw off one of Euclid's prized axioms and realised that there were alternative geometries could we then think in new ways about old problems. One of these 'non-Euclidean geometries' later formed the basis of Einstein's General Theory of Relativity, which revolutionised astrophysics.

Regarding axioms as self-evident and necessarily true, prevents us from considering new approaches to our world. This view, that certain ideas are unchallengable, is the basis for what we call dogma, our third subject. On what basis can we possibly assert that any idea cannot be questioned ? We saw earlier that facts are constrained by our experience, we cannot know what we have not yet experienced. We also saw that endless theories can be generated to cover the same facts, so it seems clear that inherent barriers cannot be validly erected to say what is or is not possible. If a 'fact' does not fit our theory, then two possible solutions are obvious, either the 'fact' is wrong or the theory is wrong (of course both may be wrong !). Assuming the fact is a valid one then we need to look for a new theory (or modify the existing one). Again two approaches are available. We can try other theories within the same axioms (constraints) or we can adopt other axioms.

The axioms we use are rarely made explicit, so it requires a leap of the imagination before we can even become aware of them. Yet that leap needs to take us outside our own experience into new dimensions of possibility. Imagine a flat two dimensional world, or to make it easier, try our own world where your feet cannot leave the ground. You walk along and come to a barrier, a wall - how do you cross it ? Within the belief that your feet cannot leave the ground you cannot go beyond, the wall constrains your world. But now relax that constraint, allow for another dimension of movement, an upwards one, and now you can jump over the wall into a new alternative world ! Easy isn't it ? Yet now try to do that in a fourth dimension, what new possibilities are available to you, and how do they change your beliefs ? This is much more difficult to imagine ! Yet in such an hyperspace system travel faster than light is possible, the paranormal becomes normal and past and future become one - surprisingly, in the world of quantum physics, such a dimension seems to have been found...

It is often assumed that we take facts and construct theories from them, yet this is misleading. We have seen that, before we start logical theory building, we already have many inherent genetic and neural theories in operation. Thus those facts we collect to form the basis of our theories are already pre-selected to conform to our beliefs - we see what we want to see, not what is there. All measurements suffer from this problem, whether using instruments (constructed for a specific purpose - thus with design limitations) or simply our senses (our eyes cannot detect infra-red for example). Everything we do and think is ultimately subjective, based upon prior beliefs.

Dogma

Dogma, as an unchallenged belief, puts many constraints upon our knowledge. Not only does it prevent us from realising the possibilities of other worlds but it even changes the way we perceive the world we are in and what we regard as truth. For example, take the previously universal dogmatic axiom that 'the Earth is flat'. Sailors feared to sail from Europe towards what we now know as America because they thought they would fall off the edge of the world ! Experiments to measure the curvature of the Earth were dismissed as meaningless ( the axiom meant it obviously had none). Yet the experiment had already been made, by the ancient Greeks, and the spherical nature of the Earth seen and measured ! The dogma suppressed this truth for 2000 years...

Surely however we are now more sophisticated and don't fall into that error today ? Sadly that is not the case. Today we have vast amounts of information, yet our dogmas constrain us to ignore most of it, most of the time ! Take our values for example. What is the worth of a human being ? What will you take into account ? Is an American worth more than an Iraqi ? Or a Moslem more than a Jew ? How about a scientist versus an artist ? A rich man over a poor one ? Educated or caring ? When we answer any such question we allow dogmatic considerations to filter out valid data that we prefer not to consider. The Holocaust made a single parameter (being a Jew) the only criteria of note, and that was justly condemned worldwide. Yet the same people condemning that fatal error exhibit their own versions of the same error every day, only the labels and scale of consequences differ...

Simplifying decisions is an essential part of our nature, we are unable to cope with vast amounts of information at any time. We have seen that facts are not isolated objective things, but exist relative to our values and within a vast web of associations. We recognise that theories are only one way out of many of structuring our world and the assumptions behind them restrict our viewpoint considerably. We now see that selected facts can bias our understanding and lead to prejudicial actions based on dogmatic values. How then can we ensure that our thoughts are valid ?

Parallel Intuition

Given our human limitations this is difficult. The short answer is that we should move away from a way of thinking that emphasises one-dimensional decisions (based on race, colour, wealth, religion, politics etc.) towards a system based on multi-dimensional values (where all aspects are taken into account). The difficulty comes in that for any complex system there are almost infinite possible ways of looking at it. Take a simple flower for example, we can describe it in many different ways: flower, plant, daffodil, yellow, living, Narcissi, hydrocarbon, chlorophyll, CO cycle, Ionic bonds etc. Considering human beings the possibilities increase dramatically and for societies even more aspects are needed. How can we even attempt to do this ?

For 2000 years Western thought has followed the example of Greek thinkers in concentrating on the intellect, on logical thought as the means by which to make decisions. This is a conscious mode of thought, but has the disadvantage of being a serial mode, we can think of only one thing at a time - yet that is precisely the problem we wish to overcome ! Another dogma, that 'only logical thought is of value' has self-created the very problems we now recognise. But have we any other mode of decision making ? Of course ! We saw earlier that our concepts and relationships form an immense web of interconnected maps, and this, our in-built parallel processing matrix, automatically relates all aspects together. When we perceive (or imagine) any situation those associations and their triggered strengths creates a decision map for that area, our task is just to recognise the result - a probabilistic output that biases us in a particular direction, our choice.

This intuitive, holistic value system, like all systems, needs to be developed, otherwise our weighting in the network will be inappropriate and lead to faulty (unfit) decisions. Initially our matrix is based almost entirely on instinct, later childhood experience extends it, but the main shaping process must be education. It is here that our logical abilities help, by allowing us to examine and discuss (one by one) our concepts, biases, axioms and theories. In this way we can refine and replace our maps over time, as expertise grows, but always remembering that any logical analysis is, by definition, a selective simplification of a more complex whole, and should not be employed as if it reflected an isolated factual 'truth'.

Conclusion

Going back to our original questions, we can see that Truth and Falsity are just the opposite ends of a continuum of probability, with most concepts somewhere between - neither always true nor always false. Dogma is seen as a constraint on knowledge, a partitioning of the world by axioms that are valid only in restricted circumstances. We believe our theories because they are useful simplifications and, as such, we can have many conflicting ones used in different contexts (e.g. war is 'bad' or 'good', depending on what another country does). We can view our belief system as a bubble selecting and enclosing those concepts of interest to us, but excluding at the same time many other possibilities. To develop a balanced viewpoint we need to recognise that all our decisions are based on simplifications that exclude, axiomatically, information that may sometimes be important. Thus we should be always willing to consider alternative interpretations of what are invariably multi-faceted and complex issues, and look for a synthesis of views rather than assuming dogmatically one must be right and the other wrong. My view and your view are based on differing contexts, selfish ones, neither is correct for making judgements that affect both parties. To do this, a new context, combining both views equally, is clearly necessary, and this 'fact' (the need to revise our assumptions in differing circumstances) is the main message that we offer here.

Page Version 4.83 October 2004 (paper V1.0 March 1999)