CONTENTS

1    THE PROBLEM

2    A CONJECTURAL SOLUTION

3    TESTING THE CONJECTURE

4     CONCLUSIONS - A THEORY OF THEORY

2   A CONJECTURAL SOLUTION - continued

2.3            Articulation

Both analysis and decomposition, in Dummett’s senses, take place on a fully articulated sentences. All that we need to see has been placed before us, and if we have had the foresight to use Frege’s Begriffsschrift, this will be done in a way which shows how analysis should be done and what decompositions are possible. As Frege wrote, “… if the expression of the content of a possible judgement is to be analysable in this way it must already be articulated.” What we are concerned with here, in linking Frege’s philosophy of thought to the mysteries of understanding, is how we get to this situation, where the thought is articulated in language, in the first place. If we cede the words “analysis” and “decomposition” to Dummett’s senses, then we may use the word “articulation” for this process. The Central Conjecture then becomes the “Primacy of Articulation”. It shares with the original notion of primacy of analysis, before Dummett gave us a deeper understanding of the matter, the idea that the thought come first, and names and incomplete sentence and name fragments are extracted from them.

The distinction can be expressed as follows. Analysis explains how we grasp the sense of a sentence never expressed before. What we want from a theory of articulation is to explain how we can express a thought never grasped before.

2.3.1         Two Routes to Thought

The picture that is emerging is of two ways in which new thoughts can be presented to us. The first is as was indicated in the B2 thesis. The new thought is built up using the existing vocabulary of thought fragments. We can then wonder whether the thought is true or not; our grasp of the thought tells us at least in principle, how to set about determining the truth-value. The second is when the thought is presented to us empirically. The truth of something is not in question; what needs to be done is to articulate what that something is.

For many of the things we experience we have a perfectly adequate vocabulary. If I go outside after a storm and see that the tree has fallen over, I am happy to identify what I have been given empirically with the sense of “the tree has fallen over”. With our mental experiences however, we have a working vocabulary, but a little philosophical probing shows us that we only have the weakest of grasps of the thoughts involved, whatever they might be. Similarly when scientific experiments show us radically new phenomena, quantum mechanics being the obvious example, our attempts at expressing what we have been given, do not fully cohere.

If we accept this two-fold way of being presented with thoughts, we must come to grips with what it is that is immediately given to us by experience. When we talk about the brute facts, we must not, if we are realists, imply that the facts just come as a lump until we choose the structure with which they can be expressed. A realist Fregean ontology states that all the conceptual structure is there in the reality. What is brute and unformed is the way in which we first become aware of this reality. The process of conceptual analysis, of articulation, is a process of reconstruction, of putting back that which was not immediately apparent do us as the information was transferred into our brains. A partial analogy is with the function of the lens in our eye, taking the incoming light and focusing it into an image on the retina. At the plane of the lens, the different rays coming from the same part of the object are in different places. All the pieces are there, but they are not in an immediately intelligible form. The function of the lens is to reassemble these pieces to create the image of what was out there to begin with. Articulation is a little like this, although the recreation takes place in logical rather than in physical space.

2.3.2            Thoughts and Pre-Thoughts

Likewise, it is wrong to speak of the “unarticulated thought”, as if this is something without structure, or with only a partial structure. The thought is objective, and it is intrinsically complex. Contrary to what Sluga says, or at least attributes to Frege, it can not be grasped prior to the perception of its structure. Dummett says, “For Frege, he [Sluga] says, ‘thoughts are first grasped as wholes’: if there is any complexity in them, awareness of this complexity is inessential for a grasp of them.” On the contrary, my grasping the thought consists in my seeing at last what complexity was always in them from the very beginning.

We need a new term to describe what it is we have when something has been given to us empirically but we are not yet able to understand and to say what the particular something is. A useful term here might be pre-thought. The process of articulation consists in taking the basic givenness of a particular pre-thought and hauling the rest of it into understanding, converting it into a thought, expressed by means of a sentence made up of bits and pieces of vocabulary. This may involve identifying the pre-thought with a thought made out of existing vocabulary, testing this hypothesis by comparing the entailments of the thought, with what we feel the entailments of the pre-thought ought to be. (These inarticulate feelings about the entailments of pre-thoughts are what I often refer to as intuition.) Alternatively, when the pre-thought is radically new, the process of articulation may involve the development of new vocabulary.

The principal difficulty with a theory of pre-thoughts is that, by definition, we can not say what this pre-articulated knowledge, allegedly given directly to us by experience, is. Anything we say has already been articulated in some way, however inadequate this may be. All we can produce in evidence is our frustration as we grapple with something like the phenomenology of mind, which is perfectly well known to us, and fail repeatedly to grasp it in any satisfactory way. It is therefore difficult to devise a test, a success criterion, whereby one can explicitly compare the pre-thought and some thought which purports to express it. The pre-thought remains private, accessible only to our intuition. In the end all we can say when we think that an attempt at articulation has failed, is that such-and-such a feature of the articulated thought does not match our intuition. Of course, if these intuitions are given to us by experience, we may have some confidence that although they are private, we each have roughly the same one (given, that is, the same experience).

2.3.3           Expressing the Inarticulate

When we are presented by a phenomenon that challenges our understanding, there are various way in which we can begin to express the pre-thought.

Filler words can be characterised as possessing reference but not sense (a nice inversion of the case Frege made such good use of: sense without reference). The words have just enough sense to point out the referents from among the items of our experience, but then not nearly enough to "make sense" of what we are saying about those items. We are left completely floundering when it comes to the logical implications of the things we say, for example, about mind. As such, filler words are not strictly part of language. They are analogues of the pre-sentences discussed above.

The filler words tend to hunt in packs. If all the “surrounding” concepts had well defined senses, then we could use them to fill the gap and elucidate the missing sense. The intractible difficulties with understanding occur usually where there is a whole area of inarticulateness. Just as one piece of understanding might support the others, so conversely one piece of failure to understand infects its neighbours with related problems. Around “mind” there is a cluster of such concepts. For example, “knowing” and “believing” try to point at a relation between minds and facts. It is essential to minds that they can believe, and it is essential to believing that it is something done by minds and only by minds. We know the two senses are strongly intertwined. The problem is that we find it difficult in the extreme to get a grip on either.

2.3.4           The Rarity of Articulation

Full-blown articulation is something most of us rarely or never do. The normal mode of adult linguistic behaviour is to construct sentences using a pre-existing vocabulary. As children we rely largely on others passing on to us the vocabulary which is the common cultural heritage of the society into which we have been born. This mature vocabulary, derived over an unknown number of millennia, is good enough for most encounters with the everyday world. Most of our difficulties with articulation are not the fault of the vocabulary; someone with a better facility with the same language can express adequately what we have failed to express. Only when we have some acquaintance with philosophy, or with modern physics, do we begin to gain an inkling of where the vocabulary becomes seriously inadequate. Indeed, Western philosophy can be said truly to have begun when Socrates, or at least Plato’s character of that name, began systematically to expose how weak a grasp we have on the senses of some of the expressions we commonly use.

2.3.5         Towards Psychology

The unarticulated thought (the pre-thought) is not a logical entity at all; it does not belong in Frege’s philosophy of thought. It is instead a mental entity, relativised to the mental processes of someone who is struggling to reach a grasp of the objective Fregean thought. This difficult boundary between the logical and the psychological, and Frege’s struggle with it is described by Dummett.

“Suppose that someone were to ask why the question how we grasp the sense of an atomic sentence is the business of a philosopher at all; or why, if it is, it should be thought to have been any concern of Frege’s. Understanding is a mental act: and Frege professed himself unconcerned with psychology. Certainly, this was a difficulty that troubled Frege and that he failed to resolve. He struggled to remove sense from the domain of the psychological by declaring it independent of our grasping it; but he could not deny that the act of grasping it is an act of the mind.

‘But the act of grasping (a thought) is still a mental (seelischer) process! Yes: but a process which lies at the limit of the mental, and which therefore cannot be completely understood from the purely psychological standpoint, because it is essential to pay regard to what is no longer mental in the proper sense, namely the thought; perhaps this process is the most mysterious of all. But just because it is on a mental character, we do not need to concern ourselves with it in logic. It is enough for us that we can grasp thoughts and recognise them as true; how this takes place is a question on its own’

Here, in this unpublished work, we see Frege grappling with a difficulty he could not solve: his best answer was that he was not concerned to describe or explain the act of grasping a sense, but only to characterize the sense itself, which is not a mental content. This is unsatisfactory, because we need some access to the notion of sense, which is most readily provided by that of understanding.”

We have to go beyond Frege here, because we are talking about contingency. We are talking, not about the categories of concepts, but rather about which items fill the categories in the actual world. When we move on to talk about how we get to know these things, how we learn to grasp the senses and express them in language, we become involved in a second contingency, that of the epistemic interaction between the items and ourselves. An epistemic interaction is one between some item and a mind, and therefore we can not avoid straying into the field of psychology.

2.3.6       Further Articulation of Thought Components

The arrival at a satisfactory expression of a thought by means of a sentence is not the end of the process of articulation. One can take atomic components within the sentence and demand a further articulation of its sense. The atomic component expresses the sense only by means of a convention associating the symbol to the sense. Replacing it by a complex expression replaces some of this conventional association by a logical depiction of the sense.

Let us start by looking at the articulation of name senses. The fact that a name is atomic has lexical significance only. The sense is not atomic; structure can always be found inside it, and the atomic name can be replaced by a compound name expressing that structure. There are a number of ways, using the Fregean hierarchy of expressions in which this can be done:

•   with a one-place functional expression and another name:      a = _df   f(b) ,
  
  
•   with a two-place functional expression and two other names:   a = _df   g(b,c) ,  
    and so on;
  
  
• with the definite description operator and a predicate:          a =_df  üxp(x), 
  where p(x) is a predicate.

Functional expressions abound in mathematical discourse. They seem to be less common in a pure form in natural English; those that are present are explicitly a combination of the definite description operator and a relational expression, for example:

            the father of (x)  =_df  the x such that x is the father of x  .

Although this further articulation captures more of the sense as logical depiction, at the same time it introduces more atomic expressions. The demand to articulate the sense of anything atomic can be re-iterated, so in principle the process of articulation need never stop (unlike analysis, in Dummett’s sense, which stops when the atomic expressions have been reached). Moreover once we ask the question of predicates and relational expressions, the full apparatus of logic comes into play. As well as attempting to explain a first order predicate in terms of second order predicates, using a higher order definite description, we can provide explanations in terms of first order apparatus, as follows:

•    with a two-place relational expression and a name:      p(x) =_df  r(x, a) ,
  
  
•    with a three-place relational expression and two names      p(x) =_df  s(x, a, b) , 
     and so on;
  
  
•   with other predicates combined by sentential operators e.g.   p(x) = _df  m(x) ÙØ n(x )
  
  
•   with other predicates combined with quantifiers e.g.       p(x) =_df  "x$y[s(x,x,y)]

These forms are more usual than an appeal to second order predicates (which exist only in a very sketchy form in natural languages any way.)

At any stage in the process, there is the possibility of expressing the sense of an atomic expression explicitly. But as pointed out above, this will only introduce more atomic expressions, so we can not claim that the process has been completed (unless perhaps only logical constants remain, but since this did not happen for mathematics, it is even less likely to happen in the contingent sciences). Just because we have stopped the process at some point, this does not preclude us from claiming that we understand the sentences involved. As Quine says, “a maxim of shallow analysis prevails: expose no more logical structure than seems useful for the deduction or other inquiry at hand”.

2.3.7     Articulation versus New Senses

If we have several sets of properties, each of which uniquely defines an object, and which are logically independent of each other, how can we say that one set is a “better” choice for the sense of the name of the object? In the case of “Jupiter” above, why is “fifth planet from the sun” a more natural way of specifying the sense than talking about the path of a point of light across the night sky? The intuition is that the former properties are closer to the actual nature of the body than the latter. The purely observational properties contain a reference to ourselves as observers, and as such they are on the very “periphery” of the properties of Jupiter. Very little of Jupiter would change if a small fraction of the solar photons reflected off its clouds no longer fell into the eyes of these earthbound primates. The description in terms of position in the solar system still contains the extraneous reference to the sun, but then the sun has played and continutes to play a much bigger role in the formation and behaviour of Jupiter. The idea we are moving towards here is not a rigid distinction between essence and accidence, but of an objective continuum of more or less peripheral properties of an object. The example used was of a physical object, and the central-peripheral distinction was framed in terms of physics.

As with the original articulation of thoughts, the articulation of thought components works on something pre-linguistic and therefore pre-logical; something psychological. It is therefore a psychological matter to say whether the new, more articulated sense is identical to the original intuitive one. There are of course fairly clear cases when it is not. In the case of “Jupiter”, we are safe in saying that the original namers of the planets did not have in mind the Copernican concept of planet. (Aristarchus made the concept available to the later ancients, but they did not adopt it, that is to say, they did not believe the assertions needed to be true to give the concept-sense a reference.) Moreover when people are forced to explain their understanding, their mental effort is as likely to consist of creation as it is to be discovery. Much of our unarticulated grasp of sense turns out on closer inspection to be weak, and once placed under the obligation to define terms explicitly we have to make radical new choices of which we were previously unaware.

2.3.8       The Failure of Conceptual Structures

The argument from the ubiquity of theory within science to logical relativism can be summarised as follows. Within a conceptual framework different theories can formulated which give different answers to the same questions. The answers to these questions can be found empirically, and those theories which give the wrong answers are thereby falsified. Theories which give the right answers can be said to have survived this particular test. There is however no such testing between radically different conceptual frameworks, because there is no common ground between them in terms of which the decisive questions could be framed. Empirical, scientific truth is then relativised to the conceptual framework being used. Seen from one framework, assertions made within another are not simply false, they are inexpressible.

The picture of the history of science associated with this relativism (due to Kuhn), is of periods of normal science, being carried out entirely within an agreed conceptual framework, separated by scientific revolutions in which one framework is suddenly discarded and replaced by another. From a strictly relativist viewpoint, there can be no scientific justification for the revolution. Its causes must be found in matter external to science, such as changes in the dominant social ideology, of which the frameworks of science are a reflection. The most extreme interpretation would be to say that a scientific revolution is like a dramatic shift in fashions in clothes. Scientists simply get bored with the old framework and decide to adopt one which is completely different.

Such an extreme relativist view would be a complete travesty of the history of science. It is an attempt to impose an entirely alien dynamic on science. Scientific theories, and the conceptual frameworks in terms of which they are expressed ought to be changed only under two circumstances. The first is the pressure of new experimental results. The second is when a demonstrably better, deeper articulation of the existing facts has been made available. “Better” here means either expressing more of the intuitive understanding of the phenomena or exposing logical connections which were previously not noticed. This “ought” statement about scientific behaviour can be supplemented with a factual, historical assertion, that by and large, scientists have been good at following this precept.

The central, realist assertion here is that conceptual frameworks are as fallible as theories framed within the structures. Even without considering whether a framework can be compared with another, radically different one (that is, whether they have some core vocabulary of senses in common), we can tell when a framework collapses purely in its own terms, either because of new facts, or because of new articulation exposing previously unsuspected contradictions. Perhaps the most spectacular collapse of a framework in the history of science was the total inability of classical dynamics to deal with a whole range of new facts about the atomic realm. Even though to begin with no obvious alternative way of talking about things suggested itself, it was amply clear that the old way was no longer adequate.

To see how this internal collapse of a conceptual framework occurs, let us first go back to the example discussed above, and explore the way in which the Ptolemaic sense of the word “Jupiter” was not just not so good as the Copernican sense, but just plain wrong. To begin with we should note that although the word “planet” appears in both descriptions offered as definitions of “Jupiter”, it has a different sense in each. In the Ptolemaic system, “planet” means “body orbiting the earth, which is itself unmoving”, whereas in the Copernican system it means “body orbiting the sun”. (Originally for Copernicus there was the additional specification that the sun is the unmoving centre of the universe; in the radical conceptual revision which followed the advent of Newtonian physics, the need for any unmoving centre was quietly dropped, while the broadly Copernican view of the motion of the planets relative to each other and to the sun was retained.) Factually we discovered that Jupiter is not a body orbiting the earth, and that any way, the earth is not the unmoving centre of the universe. This latter fact means that the Ptolemaic concept of planet must lack a reference. We can not therefore use the process of definition to attach a sense containing the Ptolemaic concept of planet to any referent.

This example shows more generally how conceptual frameworks can fail. The concept-senses which make them up are produced by (higher order) definite description operators. The descriptions contain implicitly (or explicitly in a Russellian analysis) an existence claim. If this claim is falsified, then the reference of the corresponding concept-sense fails. This failure is the analogue for conceptual frameworks of the falsification of theories. This possibility of failure shows that articulation is not a matter of arbitrary choice of conceptual framework. Although the way we talk about facts may be theory-laden, our concepts are also fact-laden.

The next major transition, from Copernican to Newtonian, was largely sense driven. The major factor was not the advent of new facts but of a massively new way of defining the problem. The question of what is the geometry of the heavens was replaced by that of what are the laws of dynamics of all physical objects. The geometry and kinematics of planetary motion (Kepler’s laws) were then deduced from the dynamical laws. What was falsified was the assertion that there are separate laws for the heavens, so the definite description “the laws of the heavens” loses its reference.

In the quantal revolution, the Newtonian concept system collapsed in so many places almost simultaneously, it was difficult for a long time to say what was happening. One hundred years later, how to understand quantum mechanics is still largely an open question. The first breakdown, discovered by Planck, was in the assumption, implicit in classical mechanics, that all possible energies are possible for bound states. This feature gave quantum mechanics its name, although later understandings showed that the quantisation of energy was a rather peripheral consequence of deeper principles.

Rather go through here all the tangled conceptions and misconceptions (such as the misbegotten “wave-particle duality”) that marked the history of the development of quantum mechanics, let me here instead give a simplified account of the quantum revolution from the point of view of my Causation by Counterfactuals (CBC) interpretation. In this picture there were two profound shifts (and the fact that they occurred simultaneously added to the confusion of the situation):

                        from deterministic dynamics to probabilistic dynamics;

                        from classical probability theory to the calculus of amplitudes.

The second shift became clear only when Feynman replaced the Copenhagen emphasis on state and observable with a picture of quantum mechanics based on paths and amplitudes. The possibility that a probabilistic dynamics could be based, not on the addition of probabilities but on the addition of complex-valued amplitudes, simply had not occurred to anyone until it was forced on us as a reality. Even then it took the genius of Feynman to sift through the layers of confusion and understand for the first time clearly what was going on.

Seen in this light, there is a sense in which the transition from classical to quantal was less radical than that from Copernican to Newtonian. There is a conceptual core of Newtonian dynamics which is preserved in quantum theory: the belief in universal dynamical laws which combine with initial conditions to determine a history. What is different in quantum mechanics is that the dynamics acts on a superstructure of amplitudes: wavefunctions (the initial conditions) and propagators (the equations of motion), which then govern in a stochastic sense, the primary motion of the particles.

It is worth noting in passing here how changes in understanding can be reflected back on our accounts of history, especially the history of science. The brief descriptions above of scientific revolutions are examples of reconstructed history. The stories are told using current frameworks of understanding, rather than those in place while the changes were going on, and the result is deliberately anachronistic. This method is as valid as historical history, as long as the two are not mixed up. To understand properly the development of science, we have to look at its history though the conceptual spectacles of the present, however much this infuriates historians.

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