Analytic Metaphysics
Overview
A discussion of metaphysics from the point of view of metaphysical positivism.
An outline of a positive conception of metaphysics.
What can be said about the existence of abstract entities.
The analysis of arguments about Space-Time.
Positive Metaphysics
An outline of a positive conception of metaphysics.
First Philosophy
First let me refer back to the metaphysics of Aristotle, which he called "First Philosophy". Some say that the term "metaphysics" owes its origin to the fact that the volume of Aristotle's works dealing with "First Philosophy" appears after the volume on Physics, "meta" being derived from the Greek "μετα", one meaning of which is simply "after". Today the prefix "meta" is frequently used to mean "above" or "beyond" and this gets us slightly closer to a semantic characterisation of metaphysics. However, for its use in metaphysical positivism it is best to think of it as connoting "before" (prerequisites) or "beneath" (foundations) [of physics], which sense is in reasonably harmony with that of Aristotle's First Philosophy.
Positive Science (I)

The term positive science was introduced by Comte and constitutes a conception of science which is conservative in its claims. In its most extreme manifestations the positivist conception of science demands that science does no more than describe the observations it makes. This position is complemented by the rejection of metaphysics, metaphysics consisting of claims about reality which go beyond what can be observed.

Thus the notion of positive science contributes to the positivist conception of what metaphysics is.

analytic metaphysics is a kind of metaphysics which is intended to be compatible with a positivistic outlook, and is also partly characterised through a (modified) conception of positive science.

Positivistic Conceptions of Metaphysics

In addition to the idea that metaphysics is science going too far, there are two other notions of metaphysics which are associated with positivism. The first, which is by no means peculiar to positivism, is that metaphysics is a priori knowledge of the nature of reality, and is hence synthetic a priori knowledge. Positivism rejects the possibility of such knowledge.

A final view is that metaphysics is simply meaningless, and hence is not about reality at all. It is meaningless because it goes beyond the content of experience, in which meaning for some positivists consists.

Analytic Metaphysics (I)

Analytic metaphysics is a kind of study of the real world which is goes beyond physics in attempting to probe the reality beyond appearances, but which is based on the logical analysis of scientific theories and recognised as yielding analytic rather than synthetic knowledge. Analytic metaphysics is concerned with meaningful, claims, but not synthetic claims.

A fuller characterisation depends upon on a moderated conception of positive science which follows.

Positive Science (II)

This version of positive science recognises that the utility of science depends upon its presentation in terms sufficiently abstract as to be intelligible and applicable, which a dogmatic constraint to reporting observational data will not permit. The restraint to observational data is respected not by constraining theoretical content but by making clear the basis in observation supporting the theory.

The admission of more liberal theoretical content is underpinned by the adoption of a modelling methodology. Such a methodology takes it to be the purpose of science to provide models of aspects of the physical world, the purpose of which is to permit prediction of phenomena and/or to provide a basis for engineering (e.g. to forecast the performance of designed artefacts). It is a part of the methodology that the content of science is the predictive content of the models, i.e. what the models tell us about how the world behaves rather than what a model might appear to be saying about how the world is. This latter is an important element of the flexibility of the modelling method, which permits different aspects of reality to be modelled in ways which are prima facie incompatible. Though presenting incompatible conceptions of space-time, Newtonian and relativistic physics are nevertheless both accepted scientific models applicable in their respective appropriate contexts.

The reconciliation of the theory of gravitation provided by general relativity, which is applicable to large scale phenomena, with quantum-electro-dynamics, which models phenomena on much smaller scales, was a preoccupation of physicists throughout the twentieth century. The failure of physicists to provide a coherent synthesis of these two theories is no impediment to their acceptance and application.

The acceptance that the scientific content of these models lies exclusively in their predictive capabilities resolves any problems which might arise from their disagreements in other respects. Predictive disagreement between models is itself acceptable, provided only that a basis is given for determining according to circumstances which model is applicable (e.g. Newtonian mechanics where velocities are small, relativistic where some velocities approach that of light).

Under this methodology therefore, science may employ apparently metaphysical language in the formulation of models, but deny literal content, and metaphysics may then be considered separately without having been prejudiced by empirical science.

Analytic Metaphysics (II)

In the context of a notion of positive science in which scientific models are for various practical reasons formulated without concern to avoid content which might turn out to be metaphysical, and first role for an analytic metaphysics is to use logical analysis to determine which aspects of the formulation of scientific models are inessential, and hence metaphysical. An example of this is the formulation of general relativity using a non-Euclidean conception of space-time. It is not uncommon to hear people speak as though the theory of general relativity brings the structure of space-time into the scope of science. There has been, however, throughout the twentieth century, ongoing controversy among some specialists about whether general relativity should be formulated using a curved or a flat space time. That the structure of space-time is not settled by physics may be argued in analytic metaphysics from the existence of models which are equivalent to the curved space-time models but which are formulated with a flat space-time.

Fundamental physics is riddled with material which looks metaphysical, and which is often a source controversy among physicists. The most conspicuous example is surely the various interpretations of quantum theory.

We have here a rather crude characterisation of a kind of "metaphysics". How should we go about refining this notion?

The identification of metaphysical elements in a model depends on the formulation of equivalent models lacking these elements. There is a question about what kind of equivalence is involved here, and therefore a methodological problem in identifying relevant notions of equivalence and considering how they contribute to the analysis of metaphysics. There are at least two which should be considered. The first is a strong notion of equivalence in which two models are equivalent if they have the same supposed domain of applicability and make exactly the same predictions in that domain. A weaker notion in which their predictions are not identical but which have the same degree of accuracy (neither model is perfect, but they have similar levels of fidelity).

This is a rather negative conception of metaphysics, in which analysis is used to identify the metaphysical content of scientific theories but does not claim to establish, refute, or even to explicate the content of such metaphysics.

I believe that similar analytic methods can yield more constructive results.

Abstract Ontology
What can be said about the existence of abstract entities.
Space-Time
The analysis of arguments about Space-Time.
Concrete Ontology

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