The Philosophy of Quantification

Quantification is a theory of sign manipulation that represents in symbolic form, the orderly syntactic arrangement, development, or classification of a collection of information.  The basis of any quantificational theory is constructing a finite set of rules by which a well-formed lexicon of elements populates its ontological domain.  These grammatical elements can be of any determinable complexity derived legitimately by consequence of the formation rules.  This includes the well-formed formulation of an economy of tautologically true quantifiers (i.e. operators), operations, and functions.  The fundamental purpose of quantifying is the achievement of determination.  To determine is by definition demarcating limit, namely by discovering the extent or scope of an object.  An act of quantifying is essentially the binding of some set of elements to some set of quantifiers to form a function.  Therefore, the act of binding a free element to a quantifier is in effect stipulating that which can be expressly denoted about the quality and configuration of the quantified element, which provenances both a function and the means of its interpretation in the process.  For respective to the quantifier’s theoretical purpose, interpreting a function ultimately depends upon the content and form represented, whether in terms of inferential derivations, attributive or enumerative properties, or relations based upon equipollency or varying degrees of equivalency.  Indetermination within the operations of a quantificational theory is a failure of a quantificational theory’s process of expressing these determinations, and philosophically defines a limit to the application of the theory itself.  Here attests the fundamental problem of the philosophy of quantification.  The application of the totality of functions of a quantificational theory is philosophically intended to systematically correspond with the principle nature and formal structure constitutive of a particular field of knowledge.  Such paradox obfuscates this ideal philosophical project and renders error in the formal representation of reality.  The outstanding philosophical question remains whether the project is obtainable and awaits discovery, or whether the project is intrinsically impossible, a false presupposition as to what can be expected from the abstraction and reduction of the concrete and practical to theory and method.  From Pythagoras to Quine, this is the most fundamental question of Western philosophy. 

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~ by Scott Pellegrino on November 18, 2008.

2 Responses to “The Philosophy of Quantification”

  1. Brilliant! Hope you are doing well in furthering your studies. Josephine Damiani

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