Gourt > Science > Math > Logic and Foundations > Nonstandard Logics and Extensions (13)
- In metaphysics, extension is the property of taking up space; see Extension (metaphysics).
- In semantics (with applications to both philosophy and mathematics), extension is the set of things to which a property applies; see extension (semantics).
- In dentistry, enamel extension.
- In general semantics, extension is a process that, as in this mathematical example, starts with unique individuals, and gives them unique names, e.g., I, II, III, etc., or 1, 2, 3, etc. The next step if needed generalizes or passes beyond extension to infinite-valued higher-order abstractions like 'numbers', and so on. The passing from lower-order abstractions (presented extensionally) to higher orders, e.g., from '1, 2, 3, etc.,' to 'numbers,' is said to follow the 'natural order of evaluation,' so that when one talks about order, extension is implied, and when one talks about extension, order is implied. An example of reversed order is when a particular higher-order abstraction such as race, e.g., 'white', 'black' etc., is projected onto the individuals comprising it. The individuals (each uniquely different by extension, no matter what is being discussed) comprise the 'race' (which exists only on higher-orders), not the other way around. This usage derives from extension (semantics). See extensional devices.
- In mathematics, an extension of some structure is another structure which contains the original structure.
- For the extension of a group or algebra, see group extension.
- For the extension of a predicate, see extension (predicate logic).
- For the extension of a field, see field extension.
- For the extension of a bounded linear operator, see continuous linear extension.
- In model theory, a model B is an extension of a model A (and A is a submodel of B) if and only if the universe of A is a subset of the universe of B and the interpretations of the nonlogical symbols of A are the restrictions of the interpretations of the same symbols of B to the universe of A.
- In anatomy, extension is one of the movements of a joint such as the knee.
- Extension (geology)
- Extension (telephone)
- In computing:
- For the programming concept, see extension (computing).
- For the Apple Mac OS implementation of operating system extensions, see Extension. For problems with same, see extension conflict.
- For the last part of a filename, see filename extension.
- For the addons for the Firefox Web Browser, see Extension (Mozilla)
- In community development, extension involves the building of community capacity by outsiders. Examples are health or agricultural extension. See extension agency.
- Electricity and electronics: Extension cable.
- Hair extensions are strands of human hair placed onto a persons hair in order to elongate or thicken existing hair.
- In education, an extension course, program, or school is continuing education.
- Extension, BC is a small former coal-mining village near Nanaimo, BC, Canada.
- In cheerleading, an "extension" is a stunt comprising of a flyer being held in the air by the bases' fully extended arms.
- In music, an extension is a set of notes that fit outside the standard range.
Computability Logic - Wikipedia (free encyclopedia) article.
Infinitary Logic - Article in the Stanford Encyclopaedia of Philosophy by John L. Bell. Infinitary Logic is a branch of formal logic where finitary formulae are replaced by potentially infinitary mathematical entities.
Logic System Interrelationships - Shows how a number of representative logics fit together. The interrelationships usually given as something of the form: System X is system Y plus the axiom Z. By John Halleck.
Non Standard Logics - A comprehensive listing of flavours of non-standard logic with brief descriptions and references, compiled by Peter Suber.
What are Weak Arithmetics - Notes defining the subject. Available in HTML and PS formats.
| Google I/O 2009 - Even Faster Websites | |
| Next Video | |
