The Laws of Thought and Thinking Machinesat implementing the human thinking process or the operations of the mind by a machine. Here is a listing of some examples of Logic Machines.

AI MATTERS, VOLUME 5, ISSUE 1 5(1) 2019

The Laws of Thought and Thinking MachinesCameron Hughes (Northeast Ohio ACM Chair; [email protected])Tracey Hughes (Northeast Ohio ACM Secretary; [email protected])DOI: 10.1145/3320254.3320263

The ideal value of an AI Cosmology would beto help the general public, researchers, edu-cators, and practitioners to devise the truth ofthe definition, meaning, applications, and im-plications of Artificial Intelligence. The pur-suit of that truth even if through an arbitrarycontrivance would be a noteworthy goal. Thefact of the matter is whether any cosmologi-cal structure we have hinted at so far tracksthe underlying reality, we cannot escape thatthere is an underlying reality. At some pointin time, we (humans) began the endeavor oftrying to replicate the human mind with ma-chines. There was first an effort to understandthe human mind, describe its inner workings,and then build machines that could essentiallyduplicate the thinking process. Surely thispoint in time must mark or at least point to theCosmological “Big Bang” for AI. Right?

So far we have pondered whether the evolu-tion of AI could be divided into epochs. We’veconsidered Machine Learning, Expert Sys-tems, and Cybernetics as possible epochswith each reaching back further in the AI time-line. But where did it all begin? What wasthe first epoch? When did we first try to dupli-cate the thinking and reasoning process withina machine? When did we first try to repre-sent the inner workings of the human mind asa set of instructions? At what point did we tryto replicate the human mind by non-biologicalmeans? Would this point in time constitute thebeginning (Big Bang) of the evolution of whatwe now call Artificial Intelligence? We use theLaws of Physics to describe structures, i.e.,the beginning, evolution, and fate of the Uni-verse. We call this structure the Cosmology.Can the Laws of Thought play a similar role inour quest for the real AI Cosmology?

If there are Laws of Thought, do we under-stand what they are? If there are laws forthe thinking process, how are they related towhat we currently call Artificial Intelligence?George Boole’s An Investigation of the Laws

Copyright c© 2019 by the author(s).

of Thought on Which are Founded the Math-ematical Theories of Logic and Probabilitiespublished in 1854 starts off with:

The design of the following treatiseis to investigate the fundamental laws ofthose operations of the mind by which rea-soning is performed; to give expressionto them in the symbolical language of aCalculus and upon this foundation to es-tablish the science of Logic and constructmethod; to make that method itself the ba-sis of a general method for the applica-tion of mathematical doctrine of Probabil-ities; and, finally, to collect from the var-ious elements of truth brought to view inthe course of these inquiries some prob-able intimations concerning the nature ofthe human mind.

George Boole was not alone in suggestingthat the operation of the mind or thinking pro-cess could be represented as a set of laws orfundamental axioms. Alfred Tarski in his OnMathematical Logic and the Deductive Methodwhich first appears in 1936 writes:

Complicated mental processes are en-tirely reducible to such simple activitiesas the attentive observation of statementspreviously accepted as true, the percep-tion of structural, purely external, connec-tions among these statements, and theexecution of mechanical transformationsas prescribed by the rules of inference.

Gottfried Wilhelm Leibniz suggests that hu-man reason can be reduced to fundamentallogical calculation. In the Art of Discovery1685, he writes in a letter to Philip Spener:

The only way to rectify our reasoningis to make them as tangible as those ofthe Mathematicians, so that we can findour error at a glance, and when there aredisputes among persons, we can simplysay: Let us calculate, without further ado,to see who is right.

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[email protected]

http://dx.doi.org/10.1145/3320254.3320263


Logic Machines Epoch

The idea that the operation of the mind andthe thinking process could be represented asmathematical logic and discrete structures ina finite form suitable for implementation by amachine clearly predates the term “ArtificialIntelligence”. In the AI Matters Volume 4 Issue4 and Volume 4 Issue 2, we’ve presented thenotions of AI epochs. We postulated that weare currently in the Machine Learning Epoch,and that prior to that were the Expert Systemand Cybernetics Epochs. Now we considerthe Logic Machines Epoch that was poweredby mathematical logic and discrete structures.The ultimate goal here is to possibly identifywhen and what were the first real attemptsat implementing the human thinking processor the operations of the mind by a machine.Here is a listing of some examples of LogicMachines. These Logic Machines reflect at-tempts at developing a theory, framework, or amechanization of the operations of the mind.

• Ramon Llul (1290)Ars Magna: Paper Machine

• Thomas Hobbes (1651)Leviathan Book:Theory

• Gottried Leibniz (1688-1689)Calculus Ratiocinator: Machine Framework

• Charles Stanhope (1775)Demonstrator: Device

• Charles Babbage (1822-1833)Difference and Analytical Engines: Ma-chines

• Semyon Nikoaivich Korsakov (1832)Comparing Ideas Machine: Machine

• Bernard Bolzano (1837)Wissenschaftslehre Book: Theory

• George Boole (1847-1854)Boolean Algebra and Laws of Thought: The-ories

• William Stanley Jevons (1870-1894)Logic Piano: Machine

• Friedrich Ludwig Gottlob Frege (1879)Second-order Logic and Axiomatic Predi-cate Logic: Theories

• Bertrand Arthur William Russell (1910)Principia Mathematica: Theory

• Leonardo Torres y Quevedo (1911)Chess Playing Machine: Machine

• Alfred Tarski (1933)Theory of Truth: Theory

• Allen Newell (1955-1956,1957)Logic Theory Machine and General ProblemSolver: Programs

• Alan Turing (1948,1950)Intelligent Machinery, Turing Test, ”Can Ma-chines think?”: Theory, Program, Paper

• Allan Newell, Herbert Simon (1976)Physical Symbol System Hypothesis: The-ory

Alan Turing is the second to last entry inthis list. He wrote his famous paper “Can AMachine Think?” in 1950. This is consid-ered by some as the beginning of the his-tory of AI. But as you can see, the LogicalMachines Epoch looks like the foundations ofsymbolic logic. Many AI systems have usedsymbolic logic. Symbolic logic is based onformal logic which represents propositions assymbolic structures. Inferencing is performedby mechanical manipulations of those struc-tures. In this list, we see early attempts at de-signing comprehensive knowledge represen-tation languages, mechanical approaches toreasoning, and devices/machines that utilizedthese methods. Leibniz envisioned such adevice or machine. He developed a frame-work for the Calculus Ratiocinator or Calcu-lus Reasoning machine. Its purpose was toperform logical deductions based on a frame-work of Characteristica Universalis, a concep-tual language that was able to symbolicallyrepresents all human thoughts. These sym-bols would then be manipulated mathemati-cally by the Ratiocinator that would mechan-ically deduce all possible truths from a list ofsimple thoughts. He stated:

Thus I assert that all truths can bedemonstrated about things expressible inthis language with the addition of newconcepts not yet expressed in it N all suchtruths, I say, can be demonstrated solocalculo, or solely by the manipulation ofcharacters according to a certain form,without any labor of the imagination or ef-fort of the mind, just as occurs in arith-metic and algebra.

Charles Stanhope developed his own versionof a “Ratiocinator”, not as ambitious, called

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the “Reasoning Machine” or Demonstrator.Charles Stanhope worked on several logicmachines for 30 years in the late 18th century.The Demonstrator was a device to solve me-chanically:

• traditional syllogisms,• numerical syllogisms,• elementary probability problems

It could process no more than two premisesand probability problems with no more thantwo independent events. Due to these limita-tions and the fact that it could not solve ’real-life problems’, Stanhope called it the Demon-strator.

As the instrument is so constructedas to assist us in making demonstrations.I have termed it Demonstrator. It is sopeculiarly contrived as likewise to exhibitsymbolically those proportions or degreesof probability which it is the object of theLogic of Probability to discover.

William Stanley Jevons, an economist and lo-gician, was inspired by the Demonstrator anddeveloped the Logic Piano in 1869. The LogicPiano was a series of wooden boards withcombinations of true and false terms. Theywere arranged on a rack and a ruler used toremove certain excluded combinations. Thefaceplate above keyboard displayed the en-tries of the truth table. The keyboard hadblack-and-white keys like a piano used to en-ter the premises. The Logic Piano was the cul-mination of a long series of inventions by Stan-hope that aided in the calculation of syllogismsincluding a logical alphabet, slate, and stampthat would quickly produce the lines of a truthtable in a logical argument. Stanhope’s logicalmachines used the generate-and-test proce-dure where all the possible combinations aregenerated and the impossible conclusions areremoved. The results are the broadest con-clusions that could possibly be produced fromthe premises. The truth table was more likea spreadsheet representing all of the logicalcombinations. His machine could only pro-cess four-terms but he planned to developa 10-term engine which would have requiredenough space to display 1,024 combinationsof its logical alphabet. Figure 1 is an image ofJevon’s Logic Piano.

Figure 1: William Jevon’s Logic Piano

In each of these epochs, there were whatwe now recognize as a hype cycle where itwas believed that we were at the veritableprecipice of duplicating human intelligence bya machine with all of the rewards and punish-ments that achievement entails. There weredifferently misunderstood, misconstrued, mis-used, sometimes ambiguous terminologies,e.g. ratiocinator, automata, cybernetics, andartificial intelligence which all refer to the sameunderlying efforts. In the Logical MachinesEpoch, Charles Babbage and his colleaguescould be considered instigators of a hype cy-cle in their time. He invented several mechan-ical devices that he proposed could computemathematical and logical functions. The Dif-ference Engine (in the 1820s) was to calcu-late and print various kinds of logarithmic andtrigonometric tables and the Analytical Engine(in the mid-1830s) was to extend its rangeinto logic and employ abstract symbolic alge-bra. Neither of these machines was ever com-pleted. Although Babbage’s intentions werefor his machines to perform mathematical andlogical functions, his colleagues were allowedto associate mental powers to the AnalyticalEngine. Babbage allowed his colleagues to

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do so, creating hype in order to obtain financialand public support as well as political attentionfor his projects. Babbage also made claimsabout his engines. In his 1832 book, Onthe Economy of Machinery and Manufactures,Babbage claimed that his Difference Enginecould replace the third section of De Prony’swork division scheme for producing mathe-matical tables. The third section was made upof 60 or 80 people who could add, subtract,and perform computations and return the re-sults to the second section for checking. Be-cause his Difference Engine was not able toproduce complete tables, it was impossible forhim to get financial support for his Analytic En-gine.

Different time periods, different cultural trends,different geographical locations, but generallythe same basic motivation, i.e, build a ma-chine that can duplicate, or simulate the op-eration of the human brain and mind. Per-haps this realization can inform our mission todevelop a standard model that identifies andclarifies what we as researchers, educators,engineers and practitioners mean by the termArtificial Intelligence. Figure 2 shows a Venndiagram of the various disciplines that defineAI.

Figure 2: Venn Diagram of the Disciplines that de-fine AI.

Benefits of a Standard Model for AI

Is it possible that there is a single standardmodel that describes the intersection shownin Figure 2? If we had such a standard modelwould that make it easier to inform and ed-ucate the public with respect to AI? Would astandard model of AI make the recruitment ofstudents and future researchers more straightforward? Would that standard model supportthe notion of a single AI Cosmology? Couldsuch a model really capture George Boole’sintention to codify the Laws of Thought, or re-alize Leibniz’s dream of reducing human rea-son to logical calculation? How far back intime do the epochs of imbuing machines withthe operations of the brain/mind extend? Isthere a physics of knowledge that underlies asingle standard model for AI? Stay tuned!

References

Aspray, W. (1990). Computing Before Com-puters. Iowa State University Press.

Babbage, C., Babbage, H.P. ed. (1889).Babbage’s Calculating Engines. A CollectionPapers Relating To Them; Their History, andConstruction. London. E. and F.N.

Babbage, C. (1832). On the Economy ofMachinery and Manufactures. Cambridge,Cambridge University Press.

Gardner, M. (1958). Logic Machines andDiagrams. New York. McGraw Hill Book Co.

Green, C.D. (2005). History of Psychol-ogy: Was Babbage’s Analytical EngineIntended To Be A Mechanical Model Of TheMind? Educational Publishing Foundation.Vol. 8, No. 1, p. 35D 45.

Jevons, W.S.(1869). The Substitution ofSimilars, The True Principle of ReasoningDerived From a Modification of Aristotle’sDictum. Macmillan.

Sieg, W. (2008). Handbook of the Philosophyof Science. Philosophy of Mathematics: OnComputability. North Holland p. 535.

Wiener, P.P. ed.(1951). Leibniz Selections. C.Scribner’s Sons.

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Cameron Hughes is acomputer and robot pro-grammer. He is a Soft-ware Epistemologist atCtest Laboratories wherehe is currently working onA.I.M. (Alternative Intelli-gence for Machines) andA.I.R (Alternative Intelli-gence for Robots) tech-nologies. Cameron isthe lead AI Engineer forthe Knowledge Group atAdvanced Software Con-

struction Inc. He is a member of the advisoryboard for the NREF (National Robotics Edu-cation Foundation) and the Oak Hill RoboticsMakerspace. He is the project leader of thetechnical team for the NEOACM CSI/CLUERobotics Challenge and regularly organizesand directs robot programming workshops forvarying robot platforms. Cameron Hughesis the co-author of many books and blogson software development and Artificial Intelli-gence.

Tracey Hughes is a soft-ware and epistemic visu-alization engineer at CtestLaboratories. She isthe lead designer for theMIND, TAMI, and NO-FAQS projects that uti-lize epistemic visualiza-tion. Tracey is also amember of the advisoryboard for the NREF (Na-tional Robotics EducationFoundation) and the OakHill Robotics Makerspace.

She is the lead researcher of the technicalteam for the NEOACM CSI/CLUE RoboticsChallenge. Tracey Hughes is the co-authorwith Cameron Hughes of many books on soft-ware development and Artificial Intelligence.

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The Laws of Thought and Thinking Machinesat implementing the human thinking process or the operations of the mind by a machine. Here is a listing of some examples of Logic Machines.

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