The Quantification of FormWe need to quantify the amount of information in a material object, and therefore the amount of information implicit in a reference to the object designated by a word or other symbol. References to objects in the external world are called ostensive definitions (made by pointing a finger at the object and uttering its name). They are relatively uncontroversial. This will be a small step toward the information content of pure ideas or concepts designated by other words. Since one cannot point at an idea or concept, their names are more controversial. Definitions are said to be "intensive," dependent on elaborate descriptions of what we mean by a word, what we "have in mind" when we use a term. This is often called the "sense" of a word, after Gottlob Frege's German term Sinn, which he distinguished from "reference" or Bedeutung, literally fingering. We need to agree on some preliminary facts about human language to avoid spilling more philosophical ink on theories of language and theories of meaning (semantics).
With the exceptions of some symbols that are iconic (rudimentary pictures of objects), and what Charles Sanders Peirce called indexicals (symbols with causal connections to their designated objects, e.g., onomatopoeic words or sounds, smoke as a symbol for fire), all symbols in natural languages have an arbitrary connection with their objects or concepts. Both words (graphemes) and their voiced sounds (phonemes) are equally arbitrary. The Greeks knew this (e.g, Plato's Cratylus). Peirce used it in his triadic theory of signs known as semiotics (icons, indexicals, symbols). Ferdinand de Saussure ' s semiology describes a sign as a dyadic relationship between a signifier and its signified (usually a concept, described by other signifiers, as words in a dictionary are all circular definitions). Every word in every language only has a definite meaning (or meanings) by a conventional agreement among its users in some community (generally smaller than the total number of speakers of the language). Names (or proper nouns) generally have been invented to designate uniquely an individual person, animal, or thing. No description of any or all attributes (a "bundle of properties") of that person can as precisely and efficiently identify the person as can the name. No property or group of properties is therefore "identical" to the name. Such "descriptions" cannot be substituted for the name in sentences or propositions. Furthermore, since all names are arbitrary and can be used for multiple persons or things, they share the same fundamental ambiguity as any words and can be used figuratively and metaphorically to refer to anything. Saul Kripke's view that once created (or "baptized" by association with its referent) a name is a necessary or "rigid designator" for its referent and true in all possible worlds does severe violence to the logical concept of necessity, which does not apply to anything in the material world, any aspect of which could have been otherwise. And of course any particular name is arbitrary and could have been otherwise, unless one's view of the material universe is deterministic . The information content of the codes used in biological communication, inside cells, between cells, and between multicellular organisms, are equally arbitrary, so their "meanings" depend on conventions "agreed upon" by the members of their species. Biosemioticians see human language as the natural evolutionary extension of all biological information creation and communication.
Quantifiers for PropositionsIn ordinary grammar, words or numbers that modify a noun to indicate the quantity of some thing (for example, “many,” “few,” “some,” “two,” “2,” "each," "no") are called quantifers. In analytic language philosophy and philosophical logic, Charles Sanders Peirce, Gottlob Frege, and others invented quantification operators, for example, ∀ x ("for all x") Willard van Orman Quine described these prefixed operators as "binding" the variables in a logical formula by specifying their quantity.
Quantity of InformationBy analogy, we can specify the amount of abstract information in a physical object, Q(x), as a number that would include the many qualitative bits of information that describe the various individual properties, relations, and other attributes of a subject or object. Although Q(x) may be impossible to calculate in many cases as a practical matter, it is a philosophical tool that "binds" an "ontological commitment," as Quine would put it, to the existence of such information. It asserts the reality of form as an ontological entity.
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