Logic of Invariant Relations

Gustavo Esparza

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Chapter 4 Logic of Invariant Relations

In: The Universal Form of the Singular: The Early Philosophy of Ernst Cassirer (1898â1917)

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Gustavo Esparza

Gustavo Esparza
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Translator:

AndrÃ©s TÃ©llez-Parra

AndrÃ©s TÃ©llez-Parra
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Type:: Chapter

Pages:: 68â107

DOI:: https://doi.org/10.1163/9789004741126_006

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This chapter addresses two fundamental topics concerning the knowledge of singularity, discussed in Substance and Function: the logical structure and objectivity of conceptual knowledge. According to Cassirer, the purpose of forming concepts is to define the form of knowledge itself, thereby revealing Being and enabling the intellect to identify with reality by transforming a multitude of particular phenomena into a coherent whole. This is not achieved by abstracting common properties, but rather by subsuming particulars under an ideal form via a logical structure derived from mathematical methodology. This structure encompasses four criteria: relational (function), arithmetic (number), geometric (space), and continuity (time). Knowledge constitutes a functional coordination between a singular element and a general series, thereby assigning an object with a value and position within a systematic structure. Consequently, objectivity is redefined not as a substantial âthing-in-itself,â but as a âsameness thesis:â the continuous, measurable relation an object holds within its serial form. This functional understanding, in which meaning resides in relationality rather than substance, establishes the core logical principle of Cassirerâs system: all acts of knowledge are functional relations between a series member and a general form of sense. This sets the stage for his subsequent theory of symbolic forms and shifts the focus of the next inquiry toward the psychology of how the subject constructs objectively valid content.

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The Universal Form of the Singular: The Early Philosophy of Ernst Cassirer (1898â1917)

Series:Â New Research in the History of Western Philosophy, Volume: 11

E-Book ISBN:: 9789004741126

Publisher:: Brill

Print Publication Date:: 01 Apr 2026

Subjects
- Philosophy
  - Early Modern Philosophy
  - 19th & 20th Century Philosophy

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Chapter 4 Logic of Invariant Relations

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The Universal Form of the Singular: The Early Philosophy of Ernst Cassirer (1898â1917)

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The Universal Form of the Singular: The Early Philosophy of Ernst Cassirer (1898â1917)