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- Object_theory abstract "Object theory is a theory in philosophy and mathematical logic concerning objects and the statements that can be made about objects.[citation needed]In some cases "objects" can be concretely thought of as symbols and strings of symbols, here illustrated by a string of four symbols " ←←↑↓←→←↓" as composed from the 4-symbol alphabet { ←, ↑, →, ↓ } . When they are "known only through the relationships of the system [in which they appear], the system is [said to be] abstract ... what the objects are, in any respect other than how they fit into the structure, is left unspecified." (Kleene 1952:25) A further specification of the objects results in a model or representation of the abstract system, "i.e. a system of objects which satisfy the relationships of the abstract system and have some further status as well" (ibid).A system, in its general sense, is a collection of objects O = {o1, o2, ... on, ... } and (a specification of) the relationship r or relationships r1, r2, ... rn between the objects: Example: Given a simple system = { { ←, ↑, →, ↓ }, ∫ } for a very simple relationship between the objects as signified by the symbol ∫ : ∫→ => ↑, ∫↑ => ←, ∫← => ↓, ∫↓ => →A model of this system would occur when we assign, for example the familiar natural numbers { 0, 1, 2, 3 }, to the symbols { ←, ↑, →, ↓ }, i.e. in this manner: → = 0, ↑ = 1, ← = 2, ↓ = 3 . Here, the symbol ∫ indicates the "successor function" (often written as an apostrophe ' to distinguish it from +) operating on a collection of only 4 objects, thus 0' = 1, 1' = 2, 2' = 3, 3' = 0. Or, we might specify that ∫ represents 90-degree counter-clockwise rotations of a simple object → .↑".
- Object_theory wikiPageExternalLink theory.html.
- Object_theory wikiPageID "1441528".
- Object_theory wikiPageRevisionID "600036534".
- Object_theory hasPhotoCollection Object_theory.
- Object_theory subject Category:Metalogic.
- Object_theory subject Category:Theories_of_deduction.
- Object_theory type Abstraction100002137.
- Object_theory type Cognition100023271.
- Object_theory type Explanation105793000.
- Object_theory type HigherCognitiveProcess105770664.
- Object_theory type Process105701363.
- Object_theory type PsychologicalFeature100023100.
- Object_theory type TheoriesOfDeduction.
- Object_theory type Theory105989479.
- Object_theory type Thinking105770926.
- Object_theory comment "Object theory is a theory in philosophy and mathematical logic concerning objects and the statements that can be made about objects.[citation needed]In some cases "objects" can be concretely thought of as symbols and strings of symbols, here illustrated by a string of four symbols " ←←↑↓←→←↓" as composed from the 4-symbol alphabet { ←, ↑, →, ↓ } . When they are "known only through the relationships of the system [in which they appear], the system is [said to be] abstract ...".
- Object_theory label "Object theory".
- Object_theory sameAs m.051w5x.
- Object_theory sameAs Q7075066.
- Object_theory sameAs Q7075066.
- Object_theory sameAs Object_theory.
- Object_theory wasDerivedFrom Object_theory?oldid=600036534.
- Object_theory isPrimaryTopicOf Object_theory.