In his "picture theory" Wittgenstein suggested that the relation between language and fact was similar to that between a picture and the thing portrayed. In metaphysical positivism language is construed as providing models of the world, the "true structure" of which is inaccessible to scientific method. Insofar as it is possible to go beyond the exhibition and evaluation of (mathematical) models with enquiries into the true structure of the universe this is the domain of metaphysics.

Positive science, a term coined by Auguste Comte which gave rise to the notion of positivism, is revived in metaphysical positivism as an idealised model of scientific method, broad enough to encompass what Russell talked of as "scientific philosophy".

Logical analysis is the analytic part of positive science and scientific philosophy. It consists of methods for maximising the rigour of reasoning using abstract models of the domain of discourse. The logical aspects are thereby rendered as rigorous and reliable as mathematics, and other aspects are exposed for other kinds of scrutiny.

An abstract semantics is a (not necessarily complete) account of the meaning of some language in terms of abstract entities. If the intended subject matter of a language is concrete, its semantics can be factored into abstract and concrete parts. The abstract part suffices to determine the relation of semantic entailment, which in turn settles the question of which inferences are deductively sound. Abstract semantics can be defined with much greater precision than concrete semantics, but cannot be made absolutely unambiguous. When we strive for limits in semantic precision, foundational problems come to the fore.

The reducibility of rationality to abstract analysis receives its greatest test when the domain of discourse moves from the hard to the social sciences, from descriptive to evaluative, when economic, political and ethical considerations are at stake. Can we then expect rigour?

Metaphysical Positivism is described by comparison with Logical Positivism, with particular reference to the philosophy of Rudolf Carnap. In this we follow Carnap's own account of his philosophy as given in the Carnap volume of the library of living philosophers, using his own headings.

Notes on Critical Rationalism from a Metaphysical Positivist standpoint.

The slogan of logical analysis is sets and sugar suffice. "For what, and how?" you may ask. But before that, "what on earth does he mean?".

What this slogan means it that the ontology of sets, the language of set theory, and the formal deductive system it comes with, made more readable by what computer scientists call syntactic sugar, i.e. just nicer ways of writing down things which could have been said in the primitive language of set theory, suffice for rigorous science and philosophy.

Well, for the kind of idealised model of how science might be which is typical of a positivistic philosophical system. Alternatively, for the foundations of abstract semantics, and hence for defining analyticity, the notion of sound deduction, for underpinning the a priori sciences, via the nomologico-deductive model for the deductive aspects of empirical sciences and for the deductively sound aspects of analytic philosophy, including abstract ontology and such metaphysics as a positivist may be prepared to comprehend.

How, is a longer story, but there is a short version.

The short version is: "by abstract modelling". The underlying insight is that, whatever your subject matter, its structure can be replicated in an abstract domain. You can do this either by choosing an appropriate language for talking about your subject and giving that language an abstract semantics in set theory, or alternatively just using set theory itself (sugared probably) to construct an abstract model. Set theory then provides a foundation for reasoning rigorously about your subject.

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.

Links below to "Carnap IAB" are links to my notes on Carnap's "Intellectual Autobiography" in his volume of the Library of Living Philosophers [Carnap63].

You may find it helpful to refer to my other account of Carnap's philosophy which this comparison parallels.

Though the verification principle is not adopted by metaphysical positivism, the avoidance of nonsense of various kinds remains a central concern. The methods of metaphysical positivism are intended to permit rigorous analysis and to avoid nonsense and sophistry (witting or not).

Metaphysical positivism has nothing very specific to the foundations of mathematics to add to the broad outlines of Carnap's philosophy in this matter.

Metaphysical positivism sits on a fence here, recognising that there is something interesting to be said in this area, but not going as far as Carnap appears to do.

This early central feature of Carnap's philosophy was later significantly changed by Carnap's shift to semantics.

This is the ameliorisation of foundationalism and the verification principle.

Semantics is of central to metaphysical positivism, but is an area in which methods have advanced considerably since Carnap's work.

Carnap was a linguistic pluralist, advocating not a single language for science but the use of languages appropriate to the domain under consideration. This gives rise to particular difficulties when one has an application involving several branches of science formulated in different languages. This was the problem which he addressed in "Language Planning".

There's a pretty large gulf here. Metaphysical positivism gives no credit to the idea of inductive inference, and is skeptical about the value of confirmation theory.

This approach of Carnap's to the formalisation of science is the one with which metaphysical positivism has greatest sympathy.

Descriptions of areas of agreement.

Descriptions of areas of disagreement.

Metaphysical Positivism is systematic constructive positivist philosophy. We present here sketches of Metaphysical Positivism together with some related historical material which might possibly help the reader come to an understanding of this system and its place in the history of ideas.