Philosophy and Formal Analysis

Overview:

How might analytic philosophy contribute to or benefit from the formalisation and mechanisation of a priori knowledge through A Framework for Formal Analysis?
History
varieties of 20thC philosophical analysis are contrasted with the formal analysis advocated here
Epistemology familiar fundamental epistemological distinctions are identified on which formal analysis is predicated
Logic an analysis of the nature of logical truth leads to firm logical foundations for formal analysis
Mathematics the logicist thesis is re-affirmed and related to other positions in mathematical philosophy
Engineering a formal analytic position is elaborated on the application of logic through mathematics in science and engineering
Philosophy applications of formal analysis in philosophy are considered

History:

Varieties of Philosophical Analysis in recent history are examined and contrasted with the formal analysis under consideration.

logicism: the seminal work by Frege and Russell identifying mathematics with logic
logical atomism: first attempts by Wittegenstein and Russell to export lessons from the new logic into a general philosophical context
logical positivism: the "Vienna Circle" attempt to assasinate metaphysics. Formality and syntax become more conspicuous in analytic method.
linguistic analysis: formality into the wilderness as the influence of the later Wittgenstein pushes common discourse front stage
formal analysis: our proposed new analytic method, appropriately formal, shorn of empiricist excess, presented in comparison with its ill-fated predecessors.

Epistemology:

see also: Logicist Epistemology
  • Key distinctions between necessary/analytic/a priori and contingent/synthetic/a posteriori re-established.
  • The scope and relevance of the a priori is considered.

The Fundamental Triple-Dichotomy is pushed back center stage, to re-emphasise key distinctions essential to effective exploitation of the a priori.
Logic: the nature of logical truth is examined to provide a basis for methods for establishing and exploiting logical truths.
establishing analytic truths: the epistemological basis for proposed methods for reliably establishing analytic truths is presented
applying analytic truths: the epistemological basis for proposed methods for effectively exploiting analytic truths is presented

Logic:

Higher Order Set Theory
  • Logical truths are analytic.
  • They are best established using a strong "foundation system"...
  • ... which must be well-defined and well supported.
Necessity and Analyticity: logical and analytic truths are identified.
Universal Notations
Yes, they exist, and we call foundation systems.
Which Foundation? why you should chose or invent one, and what features to look for
Defining Foundations? A chicken and egg problem. How to get your foundations solid.
Supporting Foundations: as a paper and pencil exercise, logic isn't much use; you need computer support to help with the drudgery and reap the benefits.

Mathematics:

  • Logicism repaired
  • Formalism asset-stripped
  • Constructivism sidestepped
  • Lakatos and Social Constructivism rejected
logicism re-affirmed
logicism through analyticity, ontological liberalism
formalism in collusion with semantics, Gödel fully assimilated.
constructivism: the role of intuition and the importance of computation recognised, weak logics spurned
Lakatos, Social Constructivism: historical tales appreciated, pedagogical lessons absorbed, relativistic tendency rejected
A New Mathematics We advocate expanding mathematics to encompass all complex analytic truths.
New Tools Mathematicians should be teaching computers to do maths proper.

Engineering:

How can analytic truths help us in the real world?
By providing us with hard facts about abstract models of aspects of the real world.
Scientists
use mathematics to build abstract models of the real world
Engineers
use abstract mathematical models to engineer changes to the real world, enabling them to establish in advance of fabrication the effects of design decisions
Facts about Models are analytic truths. They are susceptible of logical proof
Models Themselves are not facts. They are judged by utility or fidelity, neither of which is quite the same as truth.
Applicability of Models... involves pragmatics, which models are good for which kind of purpose. Special considerations, such as safety, may make the use of models a regulatory matter. These kinds of facts fall outside the scope of our formal framework.

Philosophy:

The relevance of the a priori to philosophy is considered, with particular reference to the applicability of the formal analysis framework to philosophical problems.
Scope:
the framework for formal analysis is mainly targetted at science and engineering, but is applicable in all contexts where complex deductive arguments play a role.
Analytic Philosophy, insofar as it is engaged in logical analysis, should yield results which are demonstrable and hence uncontentious. Such results may best be reached through the framework.
Other Philosophy may yet present arguments in which there is a significant deductive element. The isolation of this deductive part using the framework, serves to make clear what the deductive part of the argument is taking for granted.


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