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Topic: self reference
topics >
Liar's paradox and Russell's paradox
Topic:
limitations of formalism
Topic:
pronoun reference
Topic:
recursion
Topic:
recursive data structures
Topic:
self-regulating systems
Topic:
semantic truth; s iff p
Topic:
thought is computational
Topic:
type reflection and introspection
Topic:
what is truth
Summary
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: abstraction
Quote: a denotation is a self-defining name for a value; e.g., '2' [»maclBJ12_1983]
Subtopic: reflective, self referential system
QuoteRef: cbb_1973 ;;12/12/76 self referencing requires abstraction
Subtopic: self-reproducing program
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: type as reflective
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: circular reference
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: imaginary value as self-referential
Quote: in a semantic net, a token node will have many links to it; some circular [»quilMR_1967]
Subtopic: universal domain
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: self-referential paradox
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: problems with self reference
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
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]
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)