I begin with a historical sketch, describing first the dogmatic opposition to metaphysics of the most extreme positivists, and then the evolution of Carnap's thought from his phenomenalistic beginings to his liberal conclusion.

The I take one step forward beyond the liberal Carnap, and give an analysis of positivistically acceptable varieties of metaphysics, and touch more generally on aspects of Aristotle's "first philosophy" which might not now be called metaphysics.

Hume's fork supports a rejection of metaphysics, and reappears with similar effect in the philosophy of Rudolf Carnap. A critique of the resulting conventionalist position makes a space for a kind of metaphysics.

Carnap's logical positivism matured into a position a hairs breath from embracing metaphysics.

Why choices about language should not be completely arbitrary.

Some notes on the idea that Hume's fork as represented in the philosophy of Rudolf Carnap is a pragmatic choice of language, underlying which is a fundamental and objective distinction between two kinds of judgement or proposition. As such this central doctrine qualifies as a kind of positivistically sanitised metaphysics.

The approach adopted here is to start from the positivist rejection of metaphysics through Hume's fork and its later presentation in the philosophy of Carnap. This leads to a conventionalist position, in which apparently metaphysical claims are presented as logical consequences of choices about language. A critique of radical conventionalism then make space in the positivist framework for a new kind of metaphysics.

Hume's fork divides matters of objective truth into truths of reason and matters of fact. Hume says that only truths of reason are intuitively or demonstratively certain, and that our conclusions about matters of fact are obtained by non-rational and less reliable means. Hume condemns metaphysics, by which he means any claim to objective truths which do not comply with this classification both in the character of the allegation and the method by which it is to be established.

Hume was inspired by Newton, and placed philosophy as concerned with matters of fact, as an empirical (though not experimental) science of Human nature.

The characterisation of metaphysics in terms of the analytic/synthetic distinction is initiated by Kant in response to Hume, and becomes the dominant simplistic conception of the issue between the Positivists and the Metaphysicians.

Hume not only condemned those matters which might normally have been regarded as metaphysical, but took a Platonic line on what we can know of the world of the senses. His conception of necessity was clearly one of logical necessity, and he first argues that causal connections are not necessary. On the further presumption that all our supposed knowledge of the external world is based on the evidence of our senses, which is at best causally related to the available (sensory) evidence, and the implicit demand that true knowledge can only be had of things which follow necessarily from the evidence he concludes that our knowledge of the external world is illusory, and our tendency to belief is rooted in habitual disposition.

By systematic application of the demand, in effect for demonstrative proof, Hume casts doubt on all knowledge except that of relations between ideas and of sensory impressions. Though he explains our beliefs as rooted in habit, he also effectively re-interprets these beliefs by attempting to construe them in terms which do not go beyond the available evidence.

This sets the pattern for a radical positivist conception of metaphysics as any conclusion about the external world which goes beyond conclusions logically entailed by the available evidence.

Hume's phenomenalism presents his philosophy as a mitigated scepticism. Hume grants a disposition to demonstrative knowledge, allowing by contrast with previous empiricists that this category of a priori knowledge is non-trivial and crucially includes mathematics.

However, the mitigation is confined to the a priori, in respect of empirical knowledge a full-blooded pyrrhonism is applied, denying that we have even probable knowledge of the external world.

This is characteristic of extreme positivism, in which scientists are expected go further than the evidence strictly warrants, and in terms of which any such speculation is regarded as metaphysical.

As positivists become more concerned with meaning, this provides an alternative motivator for the identification and exclusion of metaphysics. At first positivist conceptions of meaning are so closely coupled with the relationship between a proposition and the evidence which would suffice to verify it, that exclusion as meaningless is not clearly distinct from exclusion as going beyond any possible evidence.

Later the coupling is weakened, and the requirement for claims or questions to be meaningful becomes a more moderate demand than that of empirical verifiability.

On the division of propositions Carnap's view is similar to Hume's though the terminology has changed. There is considerably greater detail. The characterisation of the a priori as concerned with relations between ideas (in Hume) becomes in the early Carnap, via ``semantic ascent'', their characterisation as {\it about syntax} and in the later Carnap as tautological.

In the later Carnap the notion of analyticity is made precise by a model of language semantics as truth conditions, and matches precisely the concept of logical necessity understood as truth in all possible worlds.

Carnap was inspired by Russell, (and influenced by Frege and Wittgenstein), and held that philosophical propositions are analytic. His attitude towards metaphysics was affected by his internal/external distinction. In these terms, the "fork" is a statement about "internal" questions, i.e. questions put in some language with a well defined semantics. Analyticity in such a language is determined by the semantics. Questions about the legitimacy of the semantics are external questions, which Carnap considered meaningless and believed should be settled pragmatically.

For some reason he does not seem to consider the external questions as having meaning determined by the semantics of some meta-language. This may be connected with his conception of the significance of Gödel's theorems. Gödel's techniques for the arithmetisation of syntax Carnap saw as showing that one did not need a metalanguage distinct from the object language (this at a time when he thought semantic notions could be give syntactic definitions). Though he later embraced semantics more enthusiastically, he does not ever seem to have embraced formal meta-languages.

Carnap's position is {\it conventionalist} then in this respect. Insofar as true supposedly metaphysical propositions are necessary they must in his conceptual scheme also be analytic. Their truth therefore derives from the conventions which were adopted in defining the semantics of the language, and these are not themselves propositions but definitions.

Carnap may helpfully be thought of as progressing Russell's programme for scientific philosophy, of which the most important elements are:

• The logical techniques exemplified in Principia Mathematica
• The metaphysics of Logical Atomism
• The idea that Philosophy itself should consist in some kind of logical analysis

Russell had two techniques which had been employed in Principia, which he applied in his Logical Atomism and which he thought fundamental to the analytic methods which he advocated.

• The notion of "incomplete symbols"
• The construction of "logical fictions"

In the former, certain apparently referential phrases are explained away by syntactic devices which avoid the dependence on some object to be referred to. (as in Russell's theory of descriptions, see [Russell05]).

In the latter, Russell takes particulars alone as really existing. Everthing else is treated as a "logical construction" from particulars (e.g. classes of particulars). These logical constructions are considered to be theoretically convenient fictions.

Russell is ambivalent about what particulars are. As an empiricist he leans toward sense data as particulars. The other possibility is that they are events, which I think Carnap would describe as a physicalistic rather than a phenomenalistic ontology.

Carnap begin's positivistically with a phenomenalistic formalisation of physics in his Aufbau [Carnap28].

His subsequent migration through physicalistic to theoretical languages can be seen as a progressive liberalisation of his positivistic anti-metaphysic, admitting the existence of entities progressively further removed from the raw data of experience.

He has not abandoned a desire to see these languages all connected tangibly with their phenomenal evidential underpinning, but his pragmatism allows him to admit the languages first and worry about the philosophical connections later.

This corresponds broadly with Russell's logical atomism, in which Russell conceives of the world as populated

This aspect of anti-metaphysical positivism is stronger in the early than in the later Carnap, where it is virtually extinguished by the ``principle of tolerance''. Carnap's was concerned with formalisation of the language of science, and he began by attempting a phenomenalistic reduction consistent with a radical nominalism.

When Carnap comes to articulate the rationale (for he has one) underpinning his progressive liberalisation his initially rigorous positivism, the story he comes up with amounts to a complete elimination of dogmatic nominalism from positivism.

Carnap went on to consider {\it physicalistic} language and {\it theoretical} language. His principle of tolerance effectively admits any metaphysic to be incorporated into the semantics of a language. Once incorporated into a language in this way, the ``internal'' metaphysical questions become analytic, and the ``external'' questions (which relate to the legitimacy of such a semantics) can be dealt with on a purely pragmatic basis.

The most radical aspect of the later Carnap's conventionalism, insofar as it is anti-metaphysical, probably lies in his attitude towards "external questions". These he regards as meaningless, and considers that the acceptance or rejection of a language should be done on a pragmatic basis without regard to the external questions. For present purposes the external questions may be considered to be ontological questions about whether or not the things required to render the semantics of the language actually exist.

To persuade Carnap to take these questions seriously, a two pronged assault would probably be necessary.

Firstly, taking Carnap's pragmatism as a point on which to exert leverage, we can ask how these pragmatic questions might be progressed. Exhibiting ways in which one can provide convincing (not necessarily conclusive) reasons for or against some choice, is one way to give credence to the idea that the propositions at stake are not entirely meaningless.

Secondly, we may try to identify metaphysical choices which connect with important considerations which seem on their face to be objective features of reality rather rather than conventional distinctions rooted in language. One such is the distinction between logical and empirically factual propositions.

To reject external questions as meaningless is a dogmatic posture, out of character with the liberal attitudes of the mature Carnap.

Just as pure mathematics can be progressed without knowing whether it will ever have applications, so one may engage in metaphysics without any certainty of its applicability. Observers may accept it on that basis at least, and reserve judgement in default of convincing arguments as to whether it has any objective validity.

The investigation of questions of objective validity, or of other grounds for adopting a metaphysic, can itself be seen as an aspect of metaphysical research.

The approach adopted here is to start from the positivist rejection of metaphysics through Hume's fork and its later presentation in the philosophy of Carnap. This leads to a conventionalist position, in which apparently metaphysical claims are presented as logical consequences of choices about language. A critique of radical conventionalism then make space in the positivist framework for a new kind of metaphysics.

It is my purpose here simply to identify some problems which seem to me to be of philosophical interest That I can now exalt in such a purpose is symptomatic of the advance of my own personal scepticism. Previously I have sought to articulate some elementary philosophical principles as a prelude to the articulation of ideas which belong properly to engineering rather than philosophy. The perceived need for such an articulation lead swifly to an acute and debilitating awareness that these principles which seemed to me elementary, were regarded by many or most contemporary philosophers as false.

A significant element of the position here considered is Popper stance in the poker debate. By this I mean the philosophical issue at stake between Popper and Wittgenstein on the occasion of Popper's speaking at the Moral Sciences Club in Cambridge. The invitation to Popper invited him to speak upon some "Philosophical Riddle" and Popper chose to attach the presumption apparent in this form of invitation that philosophy is not concerned with substantive problems.

The philosophical position which I occupy, seems to me, rather than a collection of substantive disagreements on matters of (philosophical) fact, is accounted for primarily by a divergent philosophical interests and related idiomatic preferences. My disagreement with other philosophers on the truth of various statements is often the child of conflicting usage.

Because of this a bald statement of position has sometimes seemed to me more appropriate than a confrontation on points of controversy.

As I have become more aware of my own limitations in progressing the kinds of philosophical problem which I find most interesting, the mere formulation of problems has come to seem by itself worthwhile and interesting. The focus simply on the statement of problems reinforces my perception that my position consists in large parts of interests, languages and methods rather than of doctrine. The structure of this work is therefore oriented toward making explicit the extent to which my philosophical world view consists in choice of language and methods appropriate for certain problems of interest.

The first part of the work is simply a position statement, but its role is auxiliary. The next part attempts to recast as much as possible of that position as mere choice of language, appropriate for the formulation of the oroblems which appears in the final part.

Positive metaphysics consists in a neutral method for metaphysical research, allowing the analysis of alternative metaphysical systems on their merits, with a minimalistic metaphysic underlying the analytic method.

The proposed neutral method is the method of logical analysis, involving formal abstract modelling. This is done in a context in which a rich ontology of abstracts are available to model proposed metaphysical systems, without prejuduce, insofar as the model of a particular metaphysical system may make use of only a small part of the available ontology.

A single logical foundation, supported by appropriate computer software is advocated. This is intended to prejudice the modelling of metaphysical systems as little as possible. Some analysis will be undertaken of what the residual prejudice in the system is.

This should be thought of as providing the kind of relatively neutral context in which to conduct research as set theory provides for Mathematics.

It is true that many objections to set theory have been raised by philosophers and philosophically minded mathematicians, but it seems to be the case that most practicing mathematicians conduct their research without needing to pay much attention to the foundations of their subject. When investigating a new area of mathematics, mathematicians do not need to ask the question "what logical system should we use for this kind of mathematics?", they can and do take logic and set theory for granted, and rarely find themselves in areas where foundational issues are signficant.

Our neutral foundation is in effect set theory, messed about with for purely pragmatic reasons. This alignment with mathematics makes for a purely logical version of the positivistic theses of the "Unity of Science", in which, for deductive and nomologico-deductive sciences a single logical foundation is advocated. However, it is not supposed that all science can yield models suitable for deductive reasoning.