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SIX KINDS OF PROPOSITION AND THE EDGES OF NORMALITY

Dave Robinson


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Some of the many great
thinkers who have
positively or negatively
influenced this essay
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CONTACT
Strawson Quine
Strawson Quine
Popper Ayer
Popper Ayer
Babbage Kant
Babbage Kant
Moore Wittgenstein
Moore Wittgenstein
Ramsey Hume
Ramsey Hume

Contents

1. Introduction
2. Propositions
3. Constitutive propositions
3.1 Unobservables
4. Diagnostic propositions
4.1 Analyticity
5. Generative propositions - translative synonymy
5.1 Synonymy
5.2 Intension and extension
6. Material and mental propositions
6.1 Investigability (verification)
6.2 Private and public
6.3 Immediacy and incorrigibility
6.4 Mental and physical
6.5 Space
6.6 Personal interactivity
7. Soluble propositions - pure logic rejected
7.1 Interpretations of formal logic
7.2 Logic, meaning and relevance
7.3 Systematic logic
7.4 Formalist logic
8. Arithmetic and structure
8.1 Space as structure
8.2 Formalist arithmetic
8.3 Number and tokens
8.4 Counting
8.5 Mathematics and meaning
8.6 Logic as inductive thinking
9. Of hexagons and hierarchies, truth and paradox,
    myths and mongrels
9.1 The propositional scheme
9.2 Truth hierarchies
9.3 Theories of truth
9.4 Preservation of type - universals and

     quantification
9.5 Assessment of type
9.6 Fiction
10. Concluding remarks
11. Postscript - mathematical empiricism and mathtech
12. References
13. Endnotes
Diagram - Classification of conventional propositions

Keywords:  analytic, attitudinal, a priori synthetic, arithmetic, calculation, certainty, conditionals, connotation, constitutive proposition, constructivism, contentfulness, contradiction, cosmology, counterfactual, counting, diagnostic proposition, empiricism, epistemology, essentialism, extension, falsification, fiction, formalism, formal logic, generative proposition, hierarchy of types, identity, immediacy, incorrigible, indirect speech, induction, inductive, infinity, intension, investigability, language, linguistics, logic, material proposition, mathematics, mathtech, meaning, mental proposition, metalanguage, metalogic, metamathematics, metaphysics, mongrel proposition, morphic, natural kinds, necessary, necessity, normality, number, organic process, paradox, paranormal, particulars, phenomenalism, philosophy, predicate, presupposition, private, progress, propositions, psychic, public, purportment, rationalism, recurrence, reductionism, reference, relevancy, repeatability, semantics, sentence, soluble proposition, space, statement, structure, subjunctive, synonymy, syntax, synthetic, systematic, theory of everything, tokens, truth, universals, unobservables, utterance, validity, verification, Austin, Ayer, Cantor, Collingwood, Davies, Hahn, Hume, Landauer, Mill, Moore, Peano, Pirsig, Popper, Quine, Ramsey, Ryle, Sheldrake, Tarski, Wittgenstein

©1996-2005 David Robinson                 2011 - additions made to Sections 5.3, 9.3, 9.6 and Endnotes


1. INTRODUCTION

"Every man, wherever he goes, is encompassed by a cloud of comforting convictions, which move with him like flies on a summer day" - Bertrand Russell, Sceptical Essays

Certainty is one of the most unyielding and malicious of prejudices. Throughout the development of civilisation, the belief in indubitabilities has contrived unceasingly to stifle progress in the sciences, mathematics, ethics and many other fields of intellectual and social endeavour. Yet the most dramatic achievements of mankind have been realised only by transcending the boundaries of conventional necessity. In any given society or epoch the nature and austerity of these boundaries are mirrored by, and sometimes determined by, the composition and scope of the current language. This is no less true of the new global society than of any other culture, and most recent philosophy has been unashamedly conducted within the confines of the language-based system of fundamental beliefs that characterises the present era.

Following the decline of logical positivism, the nuclear-age philosophers' confusions about the alleged existence of propositions that express necessary facts have been exacerbated by the lack of a clear picture of the kinds of proposition there are and the relationships between them. In a largely "back-to-basics" attempt to reorder the clutter, I shall argue that conventional language (including current scientific idiom) utilises propositions of at least six primary kinds, each distinguished by a particular method of validation - which I take to be equivalent to the possession of a unique kind of meaning or utility - and all of which radiate a characteristic aura of necessity but the truth or falsity of none of which is in any way guaranteed or irrefutable. Among the numerous implications of the metaphysics of this partitioning (but not of the propositional classification itself) are that there are no analytic propositions, no (properly called) systems of "formal logic", no physical propositions which are to be held true just because publicly verifiable, no universal physical propositions, no feasible interpretation of classical first order predicate calculus and no basis for the "logicism" of mathematics.

Regardless of these unorthodox implications, the scheme outlined here defines, as it were, the edges of normality, the walls within which, in the present era, the rational but conservative person ventures and thrives, perceives and reflects, calculates and communicates. These are the categories in terms of which philosophers of the twentieth century might have elected to present their ideas, but apparently never did. Although I believe they will remain good for most domestic purposes well into the future, from the point of view of radical scientific progress and the prospect of confrontation with new and unexpected aspects of our universe, they represent the death rattle of an outmoded ideology. We are fast approaching the close of a relatively comfortable era, one that has placed few demands on the adaptive talent of the human race. If the reaches of our knowledge and accomplishment are to be pushed far and fast enough to arrest the advancing tide of potential global disasters, the limits of normality must be transcended. By tracing the boundaries of our present habitat, we shall sooner discover windows to new vistas, where domains once considered sacrosanct dissolve one into another.

One of the most important and time-honoured of these boundaries is that which separates mathematical systems from observational data. This division cannot be upheld: mathematics is constrained by empirical factors, while at the same time the infrastructure and ultimate constituents of the material world answer only to mathematical models. A plausible consequence of this position is that physical reality can be both explored and manipulated by the construction in suitable circumstances of sufficiently elaborate models.

It seems necessary to mention up front that the overall approach of this article is uncompromisingly empirical. In my view there are no strictly logical connectives or operators. “Logic” takes its life from empirical propositions such as “If it’s sunny the Socceroos will win”. Every argument, if it has any meaning at all, has some kind of connectivity comparable to this, and if it is meaningless it is not an argument, nor even a template for an argument. There are no analytic propositions (see §7).

This article is indeed all about propositions, but what a pity so many philosophers are beguiled by the magic of words! In contrast to certain anthropocentrists, I do not for one moment believe that language is a pre-requisite for rational thought. Had this seemingly obvious fact been appreciated in earlier times, the development of logical theory would undoubtedly have taken a different course.

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