Different kinds of truth
Coherence and correspondence
Historically speaking, the search for certainty was always associated with the idea that the truth is to be found in a logico-deductive system. And, because the system was seen as being able to stand on its own, independently of reality, the test of truth was seen to be its coherence within itself, rather than its correspondence with reality.
The notion that truth is tested by correspondence between the system (what would today be called the model for your theory) and the facts of the real world, came on the scene much later.
The police and the courtroom
However, the lesson has apparently not yet been learned by people in public life.
One example of the way in which we still suffer in practical matters from the notion that truth is to be defined as coherence is in legal matters. Our lawyers and our police are still taught that the truth is what can be established within the closed walls of a courtroom, and is tested by whether it stands up as complete. Unfortunately, they are as a consequence also taught not to worry too much about whether what is establishable in court also corresponds with what really happened in the world outside. This doctrine appears to be one of the main causes of the frequent miscarriages from which the system suffers.
Politicians and scientific proof about beef
You will also probably have noticed another hangover from the old ideas. Our politicians, many of whom are legally trained, clearly believe that scientific research arrives at certain truth. For example, statements by them that take the form of "science proves that British beef is safe" are inevitably contradicted by the scientists, who have to point out that this is not what they meant, with the result that the scientists are labelled as incompetent and unable to make up their minds.
The positivist tradition
You may recognise this approach as falling generally within the positivist tradition. Positivists, such as Auguste Comte, asserted that we must abandon all claim to have any means of attaining knowledge other than that available to science; and that whatever questions cannot be answered by scientific methods we must be content to leave permanently unanswered.
Later, the philosophers of the Vienna Circle developed 'logical positivism'. The logical positivists are perhaps best known for their 'verifiability principle', according to which the meaning of a proposition depends on its method of verification. If it is unverifiable, then it is neither true nor false, but simply meaningless.
This principle was therefore used as a means of drawing a precise boundary around the territory of science, and asserting that anything outside that territory is meaningless. In subsequent years, this principle has quite properly been criticised and relaxed. (Although Popper later pointed out that it is falsifiability that distinguishes science from non-science.)
However, the original position was something of a strategic error, because if you say that science cannot understand anything outside its own territory, you open the way for its enemies to retaliate by setting up their own territories, and asserting that, within these, they have no obligation to be scientifically meaningful.
Whereas the positivist claim was that there was only one kind of truth, unfortunately its division of that truth into logical and empirical, together with its rejection of such areas as theology and metaphysics as meaningless, inadvertently gave rise to the opposed position that there are several different kinds of truth, only one of which is the concern of science, but all of which are equally valid.
Unfortunately, even some eminent and successful scientists have been so strongly influenced by the logical positivists that they have been too willing to surrender to this claim about different kinds of truth. The result has been a great weakening of the influence of science, because its enemies are only too ready to draw the conclusion that, if there are some places where science has nothing to say, then those must be the places where all the important things are.
The territorial conflict
Although we can approve of the intellectual temper of the positivist tradition, we should avoid following it to these dangerous conclusions, but instead take a different direction.
The heuristic method is more widely applicable than people think, or want to think, and to call it 'scientific method'—together with this trick of defining science by subject-matter, instead of by methodology—is a way of making it seem safely restricted. (This is convenient for those vehement opponents of the wider claims of the approach who are never-the-less happy to enjoy the material benefits of its success.)
So I advocate that we claim back these 'other territories'—by showing how the heuristic way can be applied to them after all.
Kinds of knowledge, truth, and proof
While there may be many and varied human activities, only one of them provides a way of achieving knowledge that has proved itself by its success. And that is what I have called the 'heuristic method'—in which the search for certain knowledge, or 'eternal truths', is abandoned, and replaced by the use of intellect in an incessant, logico-empirical circular process. I claim that it is a mistake to assert that there are other, equally valid and effective, ways to knowledge.
It is also my contention that there is only one kind of knowledge, namely that which can be achieved by the heuristic way. Of course, it is often useful to make distinctions between different types within this main kind—just so long as it is not implied that there are occasions when the heuristic way either cannot, or must not, be used.
There are two particular cases where a technical philosophical distinction between different kinds of propositions has caused misunderstandings when taken out of context. These are both important to us, so let us look at them.
Logico-mathematical and empirical propositions
You often hear it said that logical propositions and empirical propositions represent different kinds of truth. The idea that mathematics and logic are somehow more reliable or more certain than empirical methods has a long history. This idea goes back to Euclid, who successfully derived theorems of geometry from a few axioms, and also to Plato, who regarded the objects of the real world as pale, imperfect imitations of mathematical objects laid up in heaven.
But there are at least four comments that have to be made about this notion of a specially reliable kind of logical truth:
Firstly, at all levels of the structure, the propositions need to have two interpretations, one as a formula in a purely formal substitution game, and the other as an empirical proposition about the real world. This is often achieved in specific instances, but it can never be perfect and can never be certain.
Secondly, the axioms have to be both useful as foundations for the logical structure and also self-evidently true in their empirical interpretations. This can never be achieved with certainty.
Thirdly, the process of deduction has to be absolutely reliable, with no possibility of an error having been made, and you can never be certain of that. In practice, we are all well aware that our psychological feeling of certainty is much greater for empirical propositions, such as that we are now reading these words, than it is for mathematical theorems, such as that the angles of a cyclic quadrilateral add up to 180° ... or is it 360°?
Fourthly, the actual process of constructing mathematico-deductive structures is itself an heuristic process, with much trial and error. Whatever the layout that you find in the maths books, the process of discovery is very different from the eventual process of justification.
Moral obligation and evaluation
A territory to which even most scientists do not usually lay claim is that of obligation. The formal statement of the discontinuity (or boundary) is in Hume's Law (that you cannot derive ought from is). Hume's Law applies not only to moral obligation, but also to aesthetic and other kinds of preference. So we are talking about not only moral but also any other kind of evaluation and its relation to facts.
The question, of whether the territory beyond the discontinuity implied by Hume's Law can be brought within the realm of science, lies at the roots of Ternality Theory and Ternary Analysis.