Difference between revisions of "Continuous predicate"
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* [[Charles Sanders Peirce|Peirce, C.S.]], "Letters to Lady Welby", pp. 380–432 in ''Charles S. Peirce : Selected Writings (Values in a Universe of Chance)'', [[Philip P. Wiener]] (ed.), Dover, New York, NY, 1966. | * [[Charles Sanders Peirce|Peirce, C.S.]], "Letters to Lady Welby", pp. 380–432 in ''Charles S. Peirce : Selected Writings (Values in a Universe of Chance)'', [[Philip P. Wiener]] (ed.), Dover, New York, NY, 1966. | ||
| − | == | + | ==Resources== |
| + | * [http://vectors.usc.edu/thoughtmesh/publish/147.php Continuous Predicate → ThoughtMesh] | ||
| + | |||
| + | ==Syllabus== | ||
| + | |||
| + | ===Focal nodes=== | ||
| + | |||
| + | {{col-begin}} | ||
| + | {{col-break}} | ||
| + | * [[Inquiry Live]] | ||
| + | {{col-break}} | ||
| + | * [[Logic Live]] | ||
| + | {{col-end}} | ||
| + | |||
| + | ===Peer nodes=== | ||
| + | |||
| + | * [http://beta.wikiversity.org/wiki/Continuous_predicate Continuous Predicate @ Beta Wikiversity] | ||
| + | * [http://mywikibiz.com/Continuous_predicate Continuous Predicate @ MyWikiBiz] | ||
| + | * [http://www.netknowledge.org/wiki/Continuous_predicate Continuous Predicate @ NetKnowledge] | ||
| + | |||
| + | ===Logical operators=== | ||
| + | |||
| + | {{col-begin}} | ||
| + | {{col-break}} | ||
| + | * [[Exclusive disjunction]] | ||
| + | * [[Logical conjunction]] | ||
| + | * [[Logical disjunction]] | ||
| + | * [[Logical equality]] | ||
| + | {{col-break}} | ||
| + | * [[Logical implication]] | ||
| + | * [[Logical NAND]] | ||
| + | * [[Logical NNOR]] | ||
| + | * [[Logical negation|Negation]] | ||
| + | {{col-end}} | ||
| + | |||
| + | ===Related topics=== | ||
| + | |||
| + | {{col-begin}} | ||
| + | {{col-break}} | ||
| + | * [[Ampheck]] | ||
| + | * [[Boolean domain]] | ||
| + | * [[Boolean function]] | ||
| + | * [[Boolean-valued function]] | ||
| + | * [[Differential logic]] | ||
| + | {{col-break}} | ||
| + | * [[Logical graph]] | ||
| + | * [[Minimal negation operator]] | ||
| + | * [[Multigrade operator]] | ||
| + | * [[Parametric operator]] | ||
| + | * [[Peirce's law]] | ||
| + | {{col-break}} | ||
| + | * [[Propositional calculus]] | ||
| + | * [[Sole sufficient operator]] | ||
| + | * [[Truth table]] | ||
| + | * [[Universe of discourse]] | ||
| + | * [[Zeroth order logic]] | ||
| + | {{col-end}} | ||
| + | |||
| + | ===Relational concepts=== | ||
| + | |||
| + | {{col-begin}} | ||
| + | {{col-break}} | ||
| + | * [[Continuous predicate]] | ||
* [[Hypostatic abstraction]] | * [[Hypostatic abstraction]] | ||
| − | |||
* [[Logic of relatives]] | * [[Logic of relatives]] | ||
| − | * [[ | + | * [[Logical matrix]] |
| + | {{col-break}} | ||
| + | * [[Relation (mathematics)|Relation]] | ||
| + | * [[Relation composition]] | ||
| + | * [[Relation construction]] | ||
| + | * [[Relation reduction]] | ||
| + | {{col-break}} | ||
* [[Relation theory]] | * [[Relation theory]] | ||
| + | * [[Relative term]] | ||
| + | * [[Sign relation]] | ||
| + | * [[Triadic relation]] | ||
| + | {{col-end}} | ||
| + | |||
| + | ===Related articles=== | ||
| + | |||
| + | * [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, “Propositional Equation Reasoning Systems”] | ||
| − | + | * [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, “Differential Propositional Calculus”] | |
| − | * [http:// | + | * [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, “Differential Logic : Introduction”] |
==Document history== | ==Document history== | ||
Revision as of 15:06, 29 April 2010
A continuous predicate, as described by Charles Sanders Peirce, is a special type of relational predicate that arises as the limit of an iterated process of hypostatic abstraction.
Here is one of Peirce's definitive discussions of the concept:
When we have analyzed a proposition so as to throw into the subject everything that can be removed from the predicate, all that it remains for the predicate to represent is the form of connection between the different subjects as expressed in the propositional form. What I mean by "everything that can be removed from the predicate" is best explained by giving an example of something not so removable.
But first take something removable. "Cain kills Abel." Here the predicate appears as "— kills —." But we can remove killing from the predicate and make the latter "— stands in the relation — to —." Suppose we attempt to remove more from the predicate and put the last into the form "— exercises the function of relate of the relation — to —" and then putting "the function of relate to the relation" into another subject leave as predicate "— exercises — in respect to — to —." But this "exercises" expresses "exercises the function". Nay more, it expresses "exercises the function of relate", so that we find that though we may put this into a separate subject, it continues in the predicate just the same.
Stating this in another form, to say that "A is in the relation R to B" is to say that A is in a certain relation to R. Let us separate this out thus: "A is in the relation R¹ (where R¹ is the relation of a relate to the relation of which it is the relate) to R to B". But A is here said to be in a certain relation to the relation R¹. So that we can express the same fact by saying, "A is in the relation R¹ to the relation R¹ to the relation R to B", and so on ad infinitum.
A predicate which can thus be analyzed into parts all homogeneous with the whole I call a continuous predicate. It is very important in logical analysis, because a continuous predicate obviously cannot be a compound except of continuous predicates, and thus when we have carried analysis so far as to leave only a continuous predicate, we have carried it to its ultimate elements. (C.S. Peirce, "Letters to Lady Welby" (14 December 1908), Selected Writings, pp. 396–397).
References
- Peirce, C.S., "Letters to Lady Welby", pp. 380–432 in Charles S. Peirce : Selected Writings (Values in a Universe of Chance), Philip P. Wiener (ed.), Dover, New York, NY, 1966.
Resources
Syllabus
Focal nodes
Template:Col-breakTemplate:Col-breakTemplate:Col-endPeer nodes
- Continuous Predicate @ Beta Wikiversity
- Continuous Predicate @ MyWikiBiz
- Continuous Predicate @ NetKnowledge
Logical operators
Related topics
- Propositional calculus
- Sole sufficient operator
- Truth table
- Universe of discourse
- Zeroth order logic
Relational concepts
Related articles
Document history
Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.
- Continuous Predicate, MyWikiBiz
- Continuous Predicate, Beta Wikiversity
- Continuous Predicate, NetKnowledge
- Continuous Predicate, PlanetMath
- Continuous Predicate, SemanticWeb
- Continuous Predicate, ThoughtMesh
- Continuous Predicate, GetWiki
- Continuous Predicate, Wikinfo
- Continuous Predicate, Textop Wiki
- Continuous Predicate, Wikipedia
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