An entitative graph is an element of the

diagram A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three- ...

matic

syntax In linguistics, syntax () is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure ( constituency) ...

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 premises ...

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 Formalism may refer to: * Form (disambiguation) * Formal (disambiguation) * Legal formalism, legal positivist view that the substantive justice of a law is a question for the legislature rather than the judiciary * Formalism (linguistics) * Scient ...

only as far as the

propositional In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...

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

is: * The blank page; * Single letters, phrases; * Dashes; * Objects (subgraphs) enclosed by a

simple closed curve In topology, the Jordan curve theorem asserts that every ''Jordan curve'' (a plane simple closed curve) divides the plane into an " interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior ...

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 Philosophy (f ...

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 In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor S ...

. * 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 In mathematical logic, a formula is ''satisfiable'' if it is true under some assignment of values to its variables. For example, the formula x+3=y is satisfiable because it is true when x=3 and y=6, while the formula x+1=x is not satisfiable over ...

formula In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship betwee ...

s 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 graph An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote on logical graph, graphical logic as early as 1882,Peirce, C. S., " n Junctures and Fractures in Logic (ed ...

s, whose sentential (''alpha'') part is

dual Dual or Duals may refer to: Paired/two things * Dual (mathematics), a notion of paired concepts that mirror one another ** Dual (category theory), a formalization of mathematical duality *** see more cases in :Duality theories * Dual (grammatical ...

to the entitative graphs. He developed the existential graphs until they became another formalism for what are now termed

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 Ch ...

'' is isomorphic to the entitative graphs.

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

See also

References

Bibliography