A logical machine is a

tool A tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates ba ...

containing a set of parts that uses energy to perform

formal 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 ...

operations. Early logical machines were mechanical devices that performed basic operations in

Boolean logic In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denote ...

. Contemporary logical machines are computer-based electronic programs that perform proof assistance with theorems in mathematical logic. In the 21st century, these

proof assistant In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor ...

programs have given birth to a new field of study called

mathematical knowledge management Mathematical knowledge management (MKM) is the study of how society can effectively make use of the vast and growing literature on mathematics. It studies approaches such as databases of mathematical knowledge, automated processing of formulae an ...

Origins

The earliest logical machines were mechanical constructs built in the late 19th century.

William Stanley Jevons William Stanley Jevons (; 1 September 183513 August 1882) was an English economist and logician. Irving Fisher described Jevons's book ''A General Mathematical Theory of Political Economy'' (1862) as the start of the mathematical method in ec ...

invented the first logical machine in 1869, the logic piano. In 1883, Allan Marquand invented a new logical machine that performed the same operations as Jevons' logic piano but with improvements in design simplification, portability, and input-output controls.

References

Bibliography

* * Marquand, Allan ** (1883), "A Machine for Producing Syllogistic Variation" in C. S. Peirce, ed., '' Studies in Logic'', pp. 12–15, along with "Note on an Eight-Term Logical Machine", p. 16. Google Book
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Book reprinted 1983 with introduction by Max Fisch. ** (1886), "A New Logical Machine", ''Proceedings of the American Academy of Arts and Sciences'' 21: 303–07. Google Book
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* Peirce, C. S. ** (1886 letter), Letter, Peirce to A. Marquand, 1886 December 30, published 1993 in Kloesel, C. et al., eds., ''Writings of Charles S. Peirce: A Chronological Edition'', Vol. 5. Indiana Univ. Press, pp. 421–3. Google Book
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** (1887), "Logical Machines", ''The American Journal of Psychology'' v. 1, n. 1, Baltimore: N. Murray, pp. 165–70. Google Book
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Reprinted in (1976) ''The New Elements of Mathematics'' v. III, pt. 1, pp. 625–32; (1997) ''Modern Logic'' 7:71–77, Project Eucli
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and (2000) ''Writings of Charles S. Peirce'' v. 6, pp. 65–73. * Baldwin, Mark James (1902), "Logical Machine", ''Dictionary of Philosophy and Psychology'', pp. 28–30 Google Book
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''Classics in the History of Psychology'

* Ketner, Kenneth Laine (1984), "The early history of computer design: Charles Sanders Peirce and Marquand's logical machines", with the assistance of Arthur Franklin Stewart, ''Princeton University Library Chronicle'', v. 45, n. 3, pp. 186–211. PUL
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* Dalakov, Georgi (undated), "Charles Peirce and Allan Marquand", ''History of Computers and Computing''

Mathematical logic {{mathlogic-stub

Origins

See also

References

Bibliography