This page is taking me a while to get into a satisfactory state, and its not there yet.

This is exacerbated by my having only in the last day or two decided that what I should say about positive science in the context of metaphysical positivism lack normative of prescriptive content.

I'm looking to restructure this page so that there is some historical background which reflects the normative origins of the concept, but that the substance of the account should be a description of the opportunities for logical analysis in science leaving open the question of when these opportunities may be worth taking up.

Our positive science is neither inductivist, falsificationist, verificationist nor scientistic. It is based on the idea that positive science consists in the construction of models of aspects of reality, in theoretical and experimental evaluation of the models and in the presentation of the results of these evaluations.

This conception of science is neither descriptive nor prescriptive. It is constructive, analytic, and discretionary, i.e. we put forward the ideas, consider their merits and weaknesses, and speculate about their scope of application. Scientists may or may not find any of this interesting or useful.

Our positive science involves is not phenomenalistic, reductionist, verificationist, falsificationist. It is pragmatic, but does not have a pragmatic attitude towards truth, and it is not enthusiastic about, induction, confirmation theory, verisimilitude or other ways of quantifying closeness to truth, or even about the idea that scientific theories are ever "true".

It may be argued that fundamental theories in physics go beyond the facts in various ways. We discuss here some ideas about how they do that and how one might attempt to separate out the hard content of a theory from these more difficult areas.

Scientific theories present models of aspects of reality which are not true or false but are evaluated in term of their scope of applicability, accuracy and reliability.

Positive science is the application of formal analysis to empirical science. We do not wish to overstate the scope of such applications, and recognise the possibility that valuable scientific results might be obtained whose character defies formal analysis.

The position of our Positive Science may be thought of as arising from two kinds of adjustment to more traditional positivistic (and related, such as pragmatist or deductivist) ideas.

There are:

• Elimination of Negative Dogma
• Exploitation of Analytic Method

The most significant negative dogmas of positivism arise from the denial of inference from sense data to the external world, and it is this which leads to phenomenalism.

Though our conclusions about the external world may not be demonstrable, this does not necessarily or even probably, mean that they are false.

The inference from present or past phenomena even to future phenomena is no more sound than the inference to the existence of material objects, or to general scientific laws involving such objects. But if the phenomenal inference were eliminated then science could serve no purpose.

The idea that a scientist should do no more than describe what he has observed of the world can be squared with the formulation of general laws of physics by allowing that the experiments be oriented towards evaluation of such laws and experimental results should be presented comprehensively in the light of their significance to that end.

Phenomenalism, verificationism, falsificationism are all negative dogmas in all their variants and ideas like confirmation theory and verisimilitude and its successors are primarily motivated by the attempt to ameliorate the defects of the negative dogmas. Reductionism, when inspired by these dogmas is likely to be defective, but in general, when pragmatically inspired, may be useful.

The Positivistic idea that civilisation progresses, and that this is connected with the evolution of epistemological standards (how truth is established) is retained, and one further stage in this process is the enabling of logical analysis.

The idea here is that the formalisation of science enables rigorous formal analysis, possibly computer assisted.

I'd like to mention first, to put this discussion into philosophical context, the notion of "positive science" which originates with Comte and has variants in many kinds of positivism. In David Hume we see first the praise of science and the castigation of metaphysics. In Comte we see an awareness that not all that passes for science is good (some entire disciplines are regarded by him as worthless), and that even in domains which are productive, the manner of doing science and the conclusions which scientists draw may be inappropriate.

In positive science the scientist is engaged in undertaking experiments and in reporting the results of his experiments. His theories should not go beyond the experimental data, they should merely summarise it.

What I want to do here is keep this idea in mind, but moderate it somewhat so that we end up with some sense of how a theory of physics may go beyond its experimental mandate, discover some way to separate out the definite from the speculative, and then consider ways in which the issues which then remain uncertain can be progressed.

I don't know exactly what Comte had in mind when he talked about theories not going beyond the experimental data on which they are based, but there is one very basic way in which we do normally expect them to do so. We expect a scientific theory to be a generalisation, of which the experimental observations provide particular instances. The merit of such a theory lies precisely in its going beyond the experimental observations to tell us what the results would be if many other similar experiments which fall within its scope.

A second way in which positivists seek to limit science is phenomenalistically. Thus, one approach to formalisation of physics attempted by Carnap and others in the most recent major phase of positivism was to do so using a language which spoke only of the phenomena or sense data. This is not what I have in mind here. We need to think and talk about the things which cause these phenomena.

The Logical Positivists had another approach to separating science from metaphysics. This was to be liberal about the language of science but insist that a theory be empirically "verifiable". They ultimately failed to define this notion in a satisfactory way, but even if they had succeeded it would not suffice for my present purposes. For this tests the theory as a whole and I am interested in taking a single theory, say for example General Relativity, and distinguishing physical content from verbal or metaphysical content.

What remains may not qualify as positivist, it is so only in the limited sense of recognising that there may be differences in the character of different aspects of a physical theory which allow further discussion of certain aspects of a physical theory which has solid observational support. The distinctions include something which might reasonably be described as the distinction between physics and metaphysics, though in this case the attitude towards the metaphysics is not so negative as is typical for positivists. I cannot offer any kind of definition of the distinctions which are at stake here, it is part of the enterprise to make the distinctions clearer, but I have no expectation that they will become sharp.

The distinctions of interest here are between physical and verbal content (in which no great weight should be attached to the word "verbal") and that between metaphysical and other content.

Historically it is natural to think of the structure of space and time as metaphysics. In the twentieth century they have come to be viewed as physics, because first special and then general relativity put forward theories which depended upon changes to our ideas about space and time, and turned out to be better models of physical reality. However, though the theories are better models than their predecessors, there may be alternatives which are equally good in accounting for the observational data but which do not involve changes in our conception of space and time. In the case of special relativity, there are equivalent theories which retain Newtonian space-time and are equally consistent with experimental data. I'm not intimate enough with the detail but lets suppose that Newtonian mechanics with absolute motion and a lorentz contraction on bodies according to their absolute velocities is one such theory and call it NFL. Not sure whether there is a stronger relationship between SR and NFL that their joint consistency with the empirical data. Suppose that they are equivalent in a strong way.

I have come to the opinion that my own conception of positive science is closer to Plato than it is to Comte!

In Plato we have knowledge only of forms, we have opinions about the material world (world of appearances) but the things we find there are approximations to the Platonic forms, the correspondence is never exact.

Hume also held that we have knowledge only of relations between ideas, not of the material world, so there is a positivist connection. However, he accepted that people would, from habit, form beliefs about the material world by inference from the evidence provided by our senses, and sought in his sceptical arguments either to constrain those inferences or to interpret the conclusions in ways less distant from their evidential basis. This leads to the negative dogmas of phenomemalistic metaphysics.

The conception of positive science proposed here is similar to Plato and Hume in admitting certain knowledge only of logical or mathematical truths. We advocate that scientific theories be presented as abstract models of reality which are probably never exact, and in any case could never be known with certainty to be perfect even if they were.

Instead of claiming that a scientific theory is "true" we should instead offer it as an imperfect model, and provide information about the areas in which it is thought to be applicable and its accuracy and reliability in those areas (though there is a problem of regress here, are these claims to be considered true or false?).

The conformity with Plato is incomplete. For Plato, the world of forms, which corresponds in our analogy to the domain of abstract models, is "real" and the physical world is illusory. In our conception, the physical world is real, the abstract models are more like logical fictions.

Plato considered things in the real world to be imperfect copies of the forms. By contrast we see the abstract models as idealisations of or approximations to aspects of the real world. On the face of it these differences might be purely verbal, however, there are fundamental methodological differences which connect with these different viewpoints and prevent them from being purely verbal.

This corresponds roughly to the idea that Plato is a rationalistic metaphysician, whereas our position is closer to the modern conception of empirical science. In Plato's case the forms are discovered by the philosopher by contemplation or dialectic, in our case the abstract models are constructed to provide a good model of the physical world. Observation and experiment are relevant to obtaining a good match, and a crucial part of positive science. For Plato, the imperfect resemblance of the real world to the forms is not a point of central concern.

If we look objectively at scientific laws and ask whether they are literally and precisely true, then we find good reason for doubt. However, even in the many cases where the laws are known to be only approximations, they may nevertheless be of the greatest practical utility. Newtonian physics is a good example of this.

If scientific theories are normally idealisations or approximations rather than literal truths, then decisive verification is impossible and falsification too easy to warrant rejection. Confirmation theory no longer makes sense (for what is the point in assessing the probability that a theory is true if we accept that it is in fact false?).

If, instead of talking about the truth or falsity of scientific theories, we talk about the characteristics and utility of scientific models, then our language becomes less dogmatic, more flexible, and potentially more informative.

Typically, scientific law are mathematical in character. Talk of abstract models is helpful in rigourising this.

The idea is that the nomological part consists in the construction of an abstract model of some aspect of reality, and the deductive part consists in the logical analysis of the model and its application to specific circumstances.

We neither claim to infer to the model from observations, nor to attempt its falsification. Instead we use observations to gather data on the scope of applicability of the model, and present this data both in summary and detailed forms.

Positivist philosophies, and similar kinds of philosophical system such as critical rationalism, tend to result in prescription or proscriptive demarcation lines, which generally prove controversial and rarely reflect the practice of science or any probable amendment to it.

What I offer here is a method for consideration on its merits. I believe that possible benefits may flow from the conduct of science along the lines hinted at here, and advocate further investigation of that possibility. However, we have no inclination to prescribe the method, or to proscribe science conducted by other means.

There is a question which might be considered, whether a scientific theory which, for some reason, could not possibly be captured in an abstract model should be considered part of science. This is not a question which I intend to consider.

There is a related question which is of much greater interest to me, viz. how might it be possible for some supposed knowledge to be both useful and in principle unformalisable. In relation to this question a matter consideration is that vast realm of knowledge which consititutes sound judgement in various domains of expertise.