5. The Canons of Symbolism


The postulates of communication. -- Logic as the science of systematic symbolization, 87. The Canon of Singularity. The symbols of mathematics peculiar. -- The nature of mathematics, 88. Wittgenstein, Rignano, James Mill, 89. The sameness of references, 90. Symbol substitution, 91. The Canon of Definition. Identity of reference and identity of referent. -- Difficulties in discussion, 92. The Canon of Expansion. The source of 'philosophy.' -- Levels of reference. -- Expansion must show the sign-situations involved, 93. Symbolic overgrowths and contractions. -- 'Universal' symbolic conveniences. -- The illusion of a world of 'being,' 94. Russell, 96. Language as an instrument, 98. Incorrect distinguished from false symbols. -- The Universe of discourse, 102. The Canon of Actuality. The discovery of the referent. Bogus referents, 103. Examples of procedure, 104. The Canon of Compatibility. The avoidance of nonsense and 'antinomies.' The 'Laws of Thought,' 105. The Canon of Individuality. The 'place' of a referent. 'Place' as a symbolic accessory, 106. Translation and expansion of false propositions. -- Importance of expansion in education and controversy, 107.


Underlying all communication, and equally fundamental for any account of scientific method, are the rules or conventions of symbolism.

Some of these are obvious enough when stated, but, perhaps for this reason, have been generally neglected. Others have been cursorily stated by logicians, concerned hitherto with a narrow range of traditional problems. When, however, all are fully set forth in the forms implied by systematic discourse, the solutions of many long-standing problems are found to be de facto provided.

Examples of such problems are those of Truth, Reality, Universals, Abstractions, Negative Facts,Virtuous Triangles, Round-squares and so forth.

The rules or postulates in question which most needformulation are Six in number, and appear as the Canons of Symbolism. They derive from the nature of mental processes, but, being required for the control of symbolization, are stated in terms of symbols and referents.

The observance of these Canons ensures a clear prose style, though not necessarily one intelligible to men of letters.