An entitative graph is an element of the diagram

Diagram

A diagram is a two-dimensional geometric symbolic representation of information according to some visualization technique. Sometimes, the technique uses a three-dimensional visualization which is then projected onto the two-dimensional surface...

matic syntax

Syntax

In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....

  for logic

Logic

In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

 that Charles Sanders Peirce developed under the name of qualitative logic beginning in the 1880's, taking the coverage of the formalism

Formal system

In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...

 only as far as the propositional or sentential

Propositional calculus

In mathematical logic, a propositional calculus or logic is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules and axioms allows certain formulas to be derived, called theorems; which may be interpreted as true...

 aspects of logic are concerned. See 3.468, 4.434, and 4.564 in Peirce's Collected Papers.

The syntax

Syntax

In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....

 is:

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

The semantics

Semantics

Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....

 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 "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

Tautology (logic)

In logic, a tautology is a formula which is true in every possible interpretation. Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense...

 (or the complement thereof). Graphs that cannot be simplified beyond a certain point are analogues of the satisfiable formula

Formula

In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language....

s of first-order logic

First-order logic

First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...

.

Peirce soon abandoned the entitative graphs for the existential graph

Existential graph

An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, and continued to develop the method until his death in 1914.-The graphs:...

s, whose sentential (alpha) part is dual

Dual

Dual may refer to:* Dual , a notion of paired concepts that mirror one another** Dual , a formalization of mathematical duality** . . ...

 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

First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...

 and normal modal logic

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\toand it is closed under:...

.

The primary algebra

Laws of Form

Laws of Form is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy...

 of G. Spencer-Brown

G. Spencer-Brown

George Spencer-Brown is a polymath best known as the author of Laws of Form. He describes himself as a "mathematician, consulting engineer, psychologist, educational consultant and practitioner, consulting psychotherapist, author, and poet.".-Life:Spencer-Brown passed the First M.B...

 is isomorphic to the entitative graphs.

See also

• Charles Sanders Peirce
• Charles Sanders Peirce bibliography
  Charles Sanders Peirce bibliography
  This Charles Sanders Peirce bibliography consolidates numerous references to Charles Sanders Peirce's writings, including letters, manuscripts, publications, and Nachlass...
  
  
• Existential graph
  Existential graph
  An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, and continued to develop the method until his death in 1914.-The graphs:...
  
  s
• Laws of Form
  Laws of Form
  Laws of Form is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy...
  
  
• Logical graph
  Logical graph
  A logical graph is a special type of diagramatic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic....
  
  s