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{{Английская Википедия/Панель перехода}}
{{short description|Element of the diagrammatic syntax for logic}}
{{More inline citations needed|date=November 2022}}
{{Confusing|reason=the syntax and semantics seem arbitrary/unmotivated and not fully explained|date=November 2022}}

An '''entitative graph''' is an element of the [[diagram]]matic [[syntax]] for [[logic]] that [[Charles Sanders Peirce]] developed under the name of '''qualitative logic''' beginning in the 1880s, taking the coverage of the [[formal system|formalism]] only as far as the [[propositional calculus|propositional]] or sentential aspects of logic are concerned. See 3.468, 4.434, and 4.564 in Peirce's ''Collected Papers''.{{Full citation needed|date=November 2022}} Peirce wrote of this system in an 1897 ''Monist'' article titled "The Logic of Relatives", although he had mentioned [[Logical graph|logical graphs]] in an 1882 letter to [[O. H. Mitchell]].{{Sfn|Hawkins|1975|p=129}}

The [[syntax]] is:{{Why|date=November 2022}}

* The blank page;
* Single letters, phrases;
* Dashes;
* Objects (subgraphs) enclosed by a [[simple closed curve]] called a ''cut''. A cut can be empty.

The [[semantics]] are:{{Why|date=November 2022}}

* The blank page denotes '''False''';{{Cn|date=November 2022}}
* Letters, phrases, subgraphs, and entire graphs can be '''True''' or '''False''';
* To surround objects with a cut is equivalent to Boolean [[Complement (order theory)|complementation]].{{Sfn|Hawkins|1975|p=129}} Hence an empty cut denotes '''Truth''';{{Cn|date=November 2022}}
* All objects within a given cut are tacitly joined by [[disjunction]].{{Sfn|Hawkins|1975|p=129}}{{Verification needed|date=November 2022}}
* A dash is read "everything" if it is encircled an even number of times, and read "something" if it is encircled an odd number of times.{{Sfn|Hawkins|1975|p=129}}
Entitative graphs are read from outside to inside.{{Sfn|Hawkins|1975|p=129}}

A "proof" manipulates a graph, using a short list of rules, until the graph is reduced to an empty cut or the blank page. A graph that can be so reduced is what is now called a [[Tautology (logic)|tautology]] (or the complement thereof). Graphs that cannot be simplified beyond a certain point are analogues of the [[satisfiable]] [[formula]]s of [[first-order logic]].{{Why|date=November 2022}}

Peirce soon abandoned the entitative graphs for the [[existential graph]]s, whose sentential (''alpha'') part is [[duality (mathematics)|dual]] to the entitative graphs.{{Why|date=November 2022}} He developed the existential graphs until they became another formalism for what are now termed [[first-order logic]] and [[normal modal logic]].

The primary algebra of [[G. Spencer-Brown]]'s ''[[Laws of Form]]'' is isomorphic to the entitative graphs.{{Cn|date=November 2022}}{{Why|date=November 2022}}

==See also==
* [[Charles Sanders Peirce bibliography]]

==References==
{{Reflist}}

=== Bibliography ===

* {{Cite journal |last=Hawkins |first=Benjamin S. |title=The Existential Graphs of Charles S. Peirce |url=https://www.proquest.com/docview/1303699159 |journal=Transactions of the Charles S.Peirce Society |volume=11 |issue=2 |date=1975 |pages=128–139 |jstor=40319733 |id={{ProQuest|1303699159}} |via=ProQuest}}

* [[Charles Sanders Peirce|Peirce, C. S.]], ''[[Charles Sanders Peirce bibliography#CP|Collected Papers of Charles Sanders Peirce]]'', Vols. 1–6, [[Charles Hartshorne]] and [[Paul Weiss (philosopher)|Paul Weiss]] (eds.), Vols. 7–8, Arthur W. Burks, ed., Harvard University Press, Cambridge, MA, 1931–1935, 1958. Cited as CP&nbsp;volume.paragraph.
* Peirce, C. S., "Qualitative Logic", MS 736 (c. 1886), pp.&nbsp;101–115 in ''The New Elements of Mathematics by Charles S. Peirce, Volume 4, Mathematical Philosophy'', Carolyn Eisele (ed.), Mouton, The Hague, 1976.
* Peirce, C. S., "Qualitative Logic", MS 582 (1886), pp.&nbsp;323–371 in ''Writings of Charles S. Peirce: A Chronological Edition, Volume 5, 1884–1886'', Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1993.
* Peirce, C. S., "The Logic of Relatives: Qualitative and Quantitative", MS 584 (1886), pp.&nbsp;372–378 in ''[[Charles Sanders Peirce bibliography#W|Writings of Charles S. Peirce: A Chronological Edition]], Volume 5, 1884–1886'', Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1993.
* [[Sun-Joo Shin|Shin, Sun-Joo]] (2002), ''The Iconic Logic of Peirce's Graphs'', MIT Press, Cambridge, MA.

[[Category:Charles Sanders Peirce]]
[[Category:Diagrams]]
[[Category:History of logic]]
[[Category:History of mathematics]]
[[Category:Mathematical logic]]
[[Category:Philosophical logic]]
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