Topic: self reference

topics > Group: naming

Liar's paradox and Russell's paradox
limitations of formalism
pronoun reference
recursive data structures
self-regulating systems
semantic truth; s iff p
thought is computational
type reflection and introspection
what is truth


Self-reference is defining an object by referencing the object itself. It is used for recursive functions and the Liar's paradox. For instance 'f = not f' defines the function f by a function call to f. Self-referencing depends on a localized viewpoint and abstraction so that something undefined can still be named. It makes the meaning of the object invisible, imaginary, a value which can only be understood through temporal behavior. It appears to be related to emergent phenomena.

In mathematics, self-reference results in imaginary numbers such as the square root of -1, which is the solution to the self-referencing equation x = -1/x.

In natural language, self-referencing structures are hard to understand, for instance, "This statement is false." (cbb 5/80)

Subtopic: denotation up

Quote: a denotation is a self-defining name for a value; e.g., '2' [»maclBJ12_1983]

Subtopic: abstraction up

QuoteRef: cbb_1973 ;;12/12/76 self referencing requires abstraction

Subtopic: reflective, self referential system up

Quote: the emergent phenomena in our brains is a kind of Strange Loop where the top level both influences and is defined by the bottom level [»hofsDR_1979]
Quote: almost all reflective systems use a meta-circular interpreter that is defined by the language itself; e.g., LISP's eval [»maesP12_1987]
Quote: a reflective system is causally connected to itself by a self-representation; can modify itself [»maesP12_1987]
Quote: can describe biology as a topology in a closed system; entirely self-referential, without an outside [»matuHR_1980]
Quote: autopoietic machine is a network of processes continuously regenerated by their interactions and transformations; topological [»matuHR_1980]
Quote: autopoietic machines--no inputs/outputs, perturbed by environment, primary goal to maintain the machine's organization [»matuHR_1980]
Quote: a reflective system is causally connected to itself by a self-representation; can modify itself [»maesP12_1987]
Quote: a stored plan for a mechanical brain can result from the preceding operations and thus be built from itself

Subtopic: self-reproducing program up

Quote: can recompile the C compiler with the character codes that it translates, e.g., \n; learning, self-reference [»thomK8_1984]
Quote: write a source program that reproduces itself; the discovery of how to do it is a revelation [»thomK8_1984]

Subtopic: type as reflective up

Quote: the type 'type' is a type; it is an instance of itself
Quote: hot swap modules need to change types while preserving type safety; use reflective mechanism with programmer-defined version adapters [»duggD9_2001]

Subtopic: circular reference up

Quote: in a semantic net, a token node will have many links to it; some circular [»quilMR_1967]

Subtopic: imaginary value as self-referential up

Quote: the imaginary number i is the solution to the self-referential equation x=-1/x [»browGS_1972, OK]
Quote: complex boolean values are the solution to self-referential boolean equations
Quote: after an unlimited number of steps from a self-referential expression can reach a non-equivalent expression [»browGS_1972]
Note: an imaginary value is self-referential, infinite sequence is change over time [»browGS_1972, OK]

Subtopic: universal domain up

Quote: need to prove that reflexive domains exist; i.e., domains defined by self-referential equations [»straC3_1973]
Quote: self-application in Scott's universal domain by allowing the same x to be used in two different ways

Subtopic: self-referential paradox up

Quote: avoid Russell's paradox by restricting abstraction to stratified conditions that do not reference the abstract class [»quinWV2_1937]
Quote: avoid Russell's paradox by separate rules for class existence and elementhood
Quote: because of self-reference, could not construct a set-theoretic model of the .lambda.-calculus

Subtopic: problems with self reference up

Quote: a program can be modified by computation; as long as this wire is not connected, the computer is easy to access and control [»zuseK_1984]
QuoteRef: chomN_1965 ;;13 "self-embedding contributes still more radically to unacceptability
Quote: if variables are place holders then problems with self-reference and aliasing [»backJ_1972, OK]

Related Topics up

Topic: Liar's paradox and Russell's paradox (25 items)
Topic: limitations of formalism (93 items)
Topic: pronoun reference (23 items)
Topic: recursion (16 items)
Topic: recursive data structures (18 items)
Topic: self-regulating systems (23 items)
Topic: semantic truth; s iff p (34 items)
Topic: thought is computational (60 items)
Topic: type reflection and introspection (28 items)
Topic: what is truth
(67 items)

Updated barberCB 1/05
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