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Philosophical Logicism

Overview:

Philosophical Logicism revisits Bertrand Russell's dream of a philosophy made logically rigorous, taking advantage of a century of development in logic, mathematics and computing.
Introduction
Philosophical logicism investigates what analytic philosophy might be like if it were exclusively concerned with logical analysis.
Epistemology
Logicist Epistemology is an important subtheme of philosophical logicism.
Logic
A broad conception of logic is needed, encompassing as much as possible of the a priori. Logic also contributes formal notations, suitable for support by intelligent software, and modern analytic methods for effective man-machine collaboration.
Mathematics
Logic, as the formal treatment of the a priori, encompasses mathematics. An adequate foundation for logic must also suffice for mathematics. The philosophy of mathematics is therefore of importance to philosophical logicism.
Metaphysics
Metaphysics (in a rather constrained sense) has a contribution to make to our understanding both of the nature of logical truth, and of the application of analysis in science and engineering.
Science
Science is concerned with formulating and testing general empirical theories from which specific factual conclusions can be deduced. We consider the benefits of greater formality in this process.
Engineering
Engineering design applies scientific models to the design of desirable artefacts. We carry through from the formalisation of science to the automation of engineering design.

Introduction:

"Philosophy, if what has been said is correct, becomes indistinguishable from logic as that word has come to be used." Bertrand Russell, 1914
Philosophical logicism investigates what analytic philosophy might be like if it were exclusively concerned with logical analysis.
Foundations
The philosophical foundations required for logical analysis involve, inextricably intertwined, epistemology, philosophy of logic, philosophy of mathematics and metaphysics. A solid position in the relvant aspects of these fields is pre-requisite to the establishment of practical languages, methods and tools for logical analysis.
Logical Systems
When the philosophical foundations are in place there remain subtantial practical problems in devising languages, logics, methods and tools (software) to make logical analysis deliver its promise. Many of the substantial advances in logic and in information technology which have taken place since Russell's time are needed to make this work.
Applications
Formal analysis should encompass mathematics and should be as ubiquitous in its application. Not only is work in epistemology and the philosophy of science and engineering relevant here, but also applied philosophers could work with scientist, using logical methods in much the same close relationship as there is between theoretical science and applied mathematics.

Epistemology:

Logicist Epistemology is an important subtheme of philosophical logicism.
Foundations
To the foundations of logical analysis epistemology contributes the crucial epistemological distinction between a priori and a posteriori knowledge and its relationship to the necessary/contingent and analytic/synthetic dichotomies forming the fundamental triple-dichotomy.
Applications
Once the fundamental dichotomies are established their significance for all other kinds of knowledge can be investigated, leading to a clearer understanding of the scope of applicability of analytic methods. We require our epistemology to encompass knowledge by intelligent artifacts as well as human beings, and expect epistemology to contribute to the design of the global superbrain.
Tools
The role of logical analysis in achieving a practical understanding of our world is sensitive to the tools available to support this analysis. Without effective software systems, formal techniques involve too much detail to be practical. Epistemology can contribute to the foundations for building the necessary tools, and must then revise its assessment of the role of analysis in knowledge.

Logic:

A broad conception of logic is needed, encompassing as much as possible of the a priori. Logic also contributes formal notations, suitable for support by intelligent software, and modern analytic methods for effective man-machine collaboration.
What is Logic?
The first task for the philosophy of logic is to provide an answer to this question, which will provide a satisfactory starting point for the establishment of the formal languages, analytic methods and software tools necessary to apply formal analysis in all the areas where it is in principle applicable.
Formal Notations
Armed with a good understanding of what logic is, it is next necessary to develop formal notations and logical systems suitable for applications of analysis. Philosophy has a contribution to make here. Note that defining a logic is, on a larger scale, much the same kind of task as getting one's terminology clear.
Computation and Proof
A particular area of practical concern is the relationship between computation and proof. A contribution from the Philosophy of Logic may help here to ensure that a more widespread application of mechanised proof as a part of the application of formal analysis is not inhibited by too great a penalty in performance relative to more ad. hoc. algorithmic methods.

Mathematics:

Logic, as the formal treatment of the a priori, encompasses mathematics. An adequate foundation for logic must also suffice for mathematics. The philosophy of mathematics is therefore of importance to philosophical logicism.
Logicism
Logicism, as a doctrine about the relationship between logic and mathematics is an important part of our position, so a good story on why the now conventional wisdom that logicism is false should be disregarded is an important part of getting our foundations straight.
The Foundations of Mathematics
Supposing logicism accepted, the establishment of satisfactory formalisations of logic is the same problem as establishing a satisfactory formal foundation for mathematics. There is some important philosophical groundwork to be done here, in the context of which the detailed choices about notations and formal systems can be made on a pragmatic basis.
The Mechanisation of Mathematics
Formal analysis will only be practically feasible when the fine detail is fully automated, and will only be widely applicable if the automation encompasses engineering mathematics. Before philosophers can reap the benefits there must be some philosophical contribution to the problem of rigorously automating mathematics.

Metaphysics:

Metaphysics (in a rather constrained sense) has a contribution to make to our understanding both of the nature of logical truth, and of the application of analysis in science and engineering.
Ontology and Necessity
An understanding of abstract and concrete ontology and of their relationship is part of that comprehension of possible worlds through which logical necessity can be clarified. Metaphysics, in our scheme of things, contributes both to the foundations of logic and to those of science.
Abstract Ontology
Abstract ontology is discretionary within the bounds of logical consistency, and is settled for us by our choice of logico-mathematical foundation system. This is preliminary to the metaphysical consideration of concrete ontology.
Concrete Ontology
Within the context of an established abstract ontology, which provides the raw material for building mathematical models of our environment, we can adopt (many) concrete ontologies to serve the needs of particular modelling problems. To adopt a concrete ontology is to identify a class of mathematical structures for use in modelling the physical universe or some parts of it. Adoption of a concrete ontology is neither the promulgation of a logical truth nor the enunciation of a scientific theory. It is a necessary but untestable preliminary to the formulation of scientific theories.

Science:

Science is concerned with formulating and testing general empirical theories from which specific factual conclusions can be deduced. We consider the benefits of greater formality in this process.
Deduction in Science
Galileo was the most prominent renaissance contributor to a revolution in scientific method. General mathematically formulated physical theories were used as premises for the deduction of specific factual conclusions. These conclusions provided both applications of and tests for the general theory. The key features were the introduction of descriptive, mathematical models and their application by means of deduction.
Formalisation
The next revolution in scientific method could be the transition from informal mathematical theories to formal analytic models. This is predicated on the effective mechanisation of formalised mathematics, the primary benefit of formalisation being that it makes the models more accessible to machine intelligence.
Philosophy of Formal Science
Philosophical logicism concerns itself with the implications of the mechanisation of intelligent analytic problem solving for scientific method. It is concerned with the different benefits which derive from different kinds of model on which a scientific theory may be based. In the spectrum we believe that formal models offer the highest benefits in principle. The benefit in principle is offset at present by the intractibility of the formal detail required. We expose the benefits in anticipation of advances in computing which render the detail tractible.

Engineering:

Engineering design applies scientific models to the design of desirable artefacts. We carry through from the formalisation of science to the automation of engineering design.
Philosophy of Engineering
Consideration of the application of science in engineering may be beneficial in understanding the relative merits of alternative scientific methods. In particular the question "what is a good scientific theory?" may be answered by the engineer in an illuminating way. The answer to this and other questions will shift as the supporting technology advances (particularly information technology).
Models for Simulation
A key part of the engineering process is the ability to predict the behaviour of some proposed design. Where complex designs are concerned computerised simulation is likely to be used. Increased formality in the formulation of scientific models broadens the potential for intelligent machine support in simulating or reasoning about the behaviour of some proposed design.
Automation of Design
Once we have scientifically based formal design languages, providing a formal semantics for designs, the potential is there for automation of the design process. Once requirements are agreed intelligent machines with reliable formal models can search for satisfactory engineering solutions.


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