An entitative graph is an element of the
diagrammatic
syntax for
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...
that
Charles Sanders Peirce
Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism".
Educated as a chemist and employed as a scientist for t ...
developed under the name of qualitative logic beginning in the 1880s, taking the coverage of the
formalism only as far as the
propositional or sentential aspects of logic are concerned. See 3.468, 4.434, and 4.564 in Peirce's ''Collected Papers''. Peirce wrote of this system in an 1897 ''Monist'' article titled "The Logic of Relatives", although he had mentioned
logical graphs in an 1882 letter to
O. H. Mitchell.
The
syntax is:
* 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
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comp ...
are:
* The blank page denotes False;
* Letters, phrases, subgraphs, and entire graphs can be True or False;
* To surround objects with a cut is equivalent to Boolean
complementation. Hence an empty cut denotes Truth;
* All objects within a given cut are tacitly joined by
disjunction.
* 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.
Entitative graphs are read from outside to inside.
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 (or the complement thereof). Graphs that cannot be simplified beyond a certain point are analogues of the
satisfiable formulas of
first-order logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...
.
Peirce soon abandoned the entitative graphs for the
existential graphs, whose sentential (''alpha'') part is
dual to the entitative graphs. He developed the existential graphs until they became another formalism for what are now termed
first-order logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...
and
normal modal logic In logic, a normal modal logic is a set ''L'' of modal formulas such that ''L'' contains:
* All propositional tautologies;
* All instances of the Kripke schema: \Box(A\to B)\to(\Box A\to\Box B)
and it is closed under:
* Detachment rule (''modus po ...
.
The primary algebra of
G. Spencer-Brown
George Spencer-Brown (2 April 1923 – 25 August 2016) was an English polymath best known as the author of '' Laws of Form''. He described himself as a "mathematician, consulting engineer, psychologist, educational consultant and practitioner, co ...
's ''
Laws of Form
''Laws of Form'' (hereinafter ''LoF'') is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. ''LoF'' describes three distinct logical systems:
* The "primary arithmetic" (described in C ...
'' is isomorphic to the entitative graphs.
See also
*
Charles Sanders Peirce bibliography
This Charles Sanders Peirce bibliography consolidates numerous references to the writings of Charles Sanders Peirce, including letters, manuscripts, publications, and . For an extensive chronological list of Peirce's works (titled in English), s ...
References
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
*
Peirce, C. S., ''
Collected Papers of Charles Sanders Peirce'', Vols. 1–6,
Charles Hartshorne
Charles Hartshorne (; June 5, 1897 – October 9, 2000) was an American philosopher who concentrated primarily on the philosophy of religion and metaphysics, but also contributed to ornithology. He developed the neoclassical idea of God and ...
and
Paul Weiss (eds.), Vols. 7–8, Arthur W. Burks, ed., Harvard University Press, Cambridge, MA, 1931–1935, 1958. Cited as CP volume.paragraph.
* Peirce, C. S., "Qualitative Logic", MS 736 (c. 1886), pp. 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. 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. 372–378 in ''
Writings of Charles S. Peirce: A Chronological Edition, Volume 5, 1884–1886'', Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1993.
* Shin, Sun-Joo (2002), ''The Iconic Logic of Peirce's Graphs'', MIT Press, Cambridge, MA.
Charles Sanders Peirce
Diagrams
History of logic
History of mathematics
Mathematical logic
Philosophical logic