The proximate predecessor of metaphysical positivism is logical positivism. Semantic positivism descends in direct line from Russell's embryonic conception of Logical Analysis, and the philosophy of Rudolf Carnap inspired by and intended to realise that conception.

Here I outline what I consider the most important sources of confusion, error and irrelevance, and mention some possible remedies.

Metaphysical positivism is concerned primarily with the articulation of a conception of rationality (the positivist connection is not our present concern). At the core of this conception is deductive inference, which may be used in the establishment of logical truths. Around this central core rationality consists first in the appropriate application of deductive reasoning using abstract models. The description of appropriate methods, languages and tools for this kind of deductive modelling provides a base from which we may approach an understaning of ways in which one may rationally go beyond the scope of deduction.

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 philososphy. 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.

Here the limits of positivism are tested as we seek to identify real philosophical problems concerning the nature of reality which are not not directly soluble either by the methods of empirical science or those of logic. Much of metaphysics as it is and has been practiced remains beyond the pale, but reasons are discussed for taking some metaphysical problems seriously, for telling which ones they are, and for making some progress on them.

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.

Though Hume predates the coining of the term, he is nevertheless often considered a positivist. This is perhaps largely due to his skepticism, his conviction that philosophy should emulate the methods of empirical science which he admired in the work of Isaac Newton, and his robust condemnation of metaphysics. Key elements of Hume's philosophy find their way down to metaphysical positivism. Most notably the central position in Hume's philosophy of what we now call the analytic/synthetic dichotomy, and the further logical distinction between matters of logic or of fact and evaluative or ethical discourse.

The term positivism derives from Comte's idea of positive science, science shorn of speculation and confined to what could be known. Scientific theories for Comte should be no more than summaries or systematisations of the data of experience. This phenomenalistic tendency is present in many positivist philosophies, right down to logical positivism, but is supplanted in metaphysical positivism with a more liberal pragmatism. Closely associated is the rejection of metaphysics. In metaphysical positivism there remains a skepticism about metaphysical problems but there is no outright rejection of metaphysics, and metaphysics is considered an important domain of investigation.

Despite Comte's insistance on scientific rigour, his interests were not narrow. He is better known as the founder of sociology than for his philosophy, and his vision was utopian.

Pragmatism is related to positivism, and there is an element of pragmatism in metaphysical positivism (falling short of a pragmatic definitions of meaning or truth).

Russell considered Frege's work and then his own work with A.N.Whitehead leading to Principia Mathematica, as the first examples of a new method of logical analysis whose scope extended beyond mathematics into the empirical sciences and which was also the correct method for philosophy. Though an empiricist Russell is not himself usual considered a positivist, but his enthusiasm for logical analysis was taken up by Carnap and became the most distinctive new feature in the positivism of the Vienna Circle. Methods for formal logical analysis, in any domain in which deductive reason is applicable, are at the core of metaphysical analysis.

Russell's vision of philosophy made scientific by the adoption of the method of logical analysis was the principle philosophical inspiration for the philosphical programme undertaken by Rudolf Carnap. Carnap worked extensively on the development formal logical methods and their application to philosophy and science in the context of a positivistic philosophical culture.

Carnap's philosophy may be thought of as a starting point for metaphysical positivism. In fact Ayer's Language Truth and Logic was probably more influential (on metaphysical positivism), though Ayer was less concerned with the detail of formal methods and so a comparison with Carnap is more informative (for which, see below).

Roger Bacon's views on what was wrong and on what needed to be done didn't fit together. In describing sources of error, bad influences predominated. But the path to truth is through the application of scientific method.

There is a gap here which we have to fill in for ourselves. We must first be influenced by his critique not to follow either fashion or authority, but to enquire into the truth using our own resources. Then we may adopt the experimental method he describes for that purpose.

If this caricature of Bacon wasn't unrealistic in his day it certainly is now. However great we may think the problems with accepted authority, or with the institutions which shape our perception of the world, we can't ignore them and come to out own views.

There are then at least two distinct kinds of ailment to be diagnosed here. One concerns the accepted methods of arriving at "the truth" in various domains. The other concerns the ways in which these methods, good or bad, are subverted by human nature and our social institutions.

A century ago the primary source of bad philosophy was thought by positivists to be metaphysics, and the solution was thought to be to confine philosophy to an appropriate kind of analysis. By mid century positivism was falling into decline, and the character of analysis changed radically. Most importantly, the change was from making meaning clear, possibly by adopting new language, to understanding language as it is.

The predominant interest of metaphysical

In this introduction is given a first sketch of the system which will be expanded in the subsequent sections.

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 chosing 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.

When science is approached by the construction of abstract models of aspects of reality, metaphysical considerations such as the structure of space and time and the nature of the ultimate constituents of the universe become a part of the construction of such a model. When viewed strictly as abstract definitions their characteristics can be established by demonstration, but the utility of these concepts is only established through applicable scientific theories built on them.

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, and 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 formaulated 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.