The Method of Formal Logical Analysis
Overview
A broadly applicable method for modelling and analysis method exploiting symbolic logic.
Ideas
Key features of the method are its applicability to deductive reasoning in any domain through the use of abstract models defined using formal notations supported by appropriate computern software.
When deduction is possible, conditions for soundness.
The universality of abstract models. Their advantages.
The advantages of abstract modelling in conceptual clarification.
The use of formal notations is made feasible by the availability of software support.
Some Details
Philosophical Underpinnings
This method of analysis is a central feature of the philosophy of Metaphysical Positivism, which provides a conceptual framework and rationale for the method and its applications.
This work in progress is intended to provide a history of the developments over a period of 2500 years which lead to the establishment of this method, and applies the method to historical exegesis.
Introduction
Key features of the method are its applicability to deductive reasoning in any domain through the use of abstract models defined using formal notations supported by appropriate computern software.
The method is applicable whenever it is thought useful and possible to reason deductively about some subject matter. It offers ways in which this can be done more precisely and reliably than might otherwise be possible. This increase in precision and rigour often brings with it a clearer insight into the subject matter, and enables results to be obtained which might otherwise have proved illusive.
The key elements of the method are:
  • Some ideas about when deductive reasoning is likely to be feasible.
  • An account of the conditions necessary for sound deductive reasoning.
  • The use of abstract models to make concepts precise.
  • The use of intuitions about abstract models to achieve greater understanding of the subject matter, and to discover specific results about them.
  • The use of formal notations and supporting computer software in the definition of abstract models and in proving results about those models.
  • Information about what the formal abstract models cannot deliver.
  • Ideas about how the formal methods fit in with informal methods.
  • An abstract conceptual framework in terms of which the method can be understood.
  • Some philosphy and some formal analysis underpinning the method, based on the abstract models associated with the conceptual framework.
Deduction
When deduction is possible, conditions for soundness.
The method of formal logical analysis is intended for application wherever arguments are under consideration which are though to be, in part or in whole, deductive.

A deductive argument is an APriori argument in which some conclusion is shown to follow, as a matter of necessity, from some declared set of premises. That the conclusion follows from the premises will, in a sound deductive argument, be a consequence of the meanings of the premises and conclusions of the argument.

A deductive argument may also be Formal, in which case formal rules will have been established for constructing arguments in the relevant notations.

Once these rules have been shown to be sound with respect to the semantics of the notations, checking the correctness of arguments is reduced to a mechanical process.
The premises from which the conclusions have been deduced represent our knowledge of the subject matter under consideration, and should be examined carefully to secure a proper understanding of the scope of applicability of the conclusions.

Usually informal arguments fail to make clear what their premises are. This makes it difficult to check the soundness of the argument, and makes it difficult to determine in any particular circumstance whether the argument is applicable and its conclusion true.

Formal analysis involves exposure of the premises of the argument so that their consistency can be established, so that the soundness of the argument can be checked and so that the scope of the conclusions is made clear.
Abstract Models
The universality of abstract models. Their advantages.
The process of establishing the premises for a deductive argument can be beneficially thought of as defining or constructing an abstract model of the intended subject matter.

This process, which may be thought of either as creative abstract modelling, or as conceptual analysis, and which may extend to the development of new notations, is the most creative and beneficial aspect of logical analysis. It is the failure to give proper attention to this activity which is the most damaging defect of wholly informal methods.
Any deductive argument will proceed from some finite set of premises about its subject matter. These will normally be only a partial characterisation of the subject matter and will then be true of a wider range of systems. These system will be the models of an abstract theory which treats the essence of the concepts whose logic is exploited in the argument.

In all areas of knowledge, advances are dependent on the development of new terminology, concepts, or notations. These permit expression of those finer distinctions upon which the advance of knowledge so often depends.
Concepts
The advantages of abstract modelling in conceptual clarification.
The use of formality in logical analysis, which may be thought of primarily as permitting the detailed mechanical checking of deductive arguments, is in fact much more significant in enabling the meaning of new concepts and notations to be located more precisely than they can be by informal means.

In the development of modern mathematics, Frege first devised notations suitable for formal development of mathematics. The greater precision of these notation made it possible for Russell to locate a defect in the reasoning which they supported (now known as Russell's paradox). This in turn prompted further developments in our understanding of the formal theory. In particular, they resulted in the axiomatisation of well-founded set theories backed by the semantic intuitions constituting the iterative conception of set
Without the formal activities it is doubtful that we could have arrived at that clearer appreciation of the universe of well-founded sets which has been the basis for the development of mathematics in the 20th century. However, once the notion of set has been pinned down in this way (notwithstanding that there remains some looseness), the precision can be imported back into the less formal notations employed by working mathematicians.

The central plank of the method of formal logical analysis is the use of abstract models to pin down the meaning of the concepts under consideration. This brings semantics into the foreground and encourages recognition that when we wish to use language precisely we must chose the precise meanings of concepts rather suppose that precise meanings can be distilled from precedent or can be done without.
Software
The use of formal notations is made feasible by the availability of software support.
Metaphysical Positivism
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.
Materials on the history of philosophy which provide context for an understanding of Metaphysical Positivism.
In essence Metaphysical Positivism is a positivisitic philosophy with negative dogmas excised, with a positive attitude towards metaphysics, based around a method of logical analysis together with appropriate philosophical (including metaphysical) underpinnings.
The motivation.
Metaphysical Positivism is a positivistic philosophical system formulated for the twenty first century, building on a heritage going back at least as far as David Hume; cognisant of developments in logic and computer science which have taken place in the 20th Century, but turning away from some of the recent tendencies in analytic philosophy.
An Analytic History of Philosophical Logic
An analytic examination of varieties of analysis (mostly but not necessarily philosophical) and their philosophical, technical and technological underpinnings, historical and contemporary, formal and informal.
Background
A few words on the purposes and character of the work.
Part II of Analyses of Analysis is the part where I seek to present and subject to comparative analysis modern analytic methods and their philosophical underpinnings.
First part of an analytic history of Philosophical Analysis, consisting of examples of exegetical analysis pertinent to the origins of modern methods.
Part III
A condensation of the formal backbone to the formal analyses, presenting the naked analytic truths obtained by deduction in the context of the formal models.
Current Drafts in PDF

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