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The Laws of Thought and Thinking Machines

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The Laws of Thought and Thinking Machines AI MATTERS, VOLUME 5, ISSUE 1 5(1) 2019 The Laws of Thought and Thinking Machines Cameron 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 be of Thought on Which are Founded the Math- to help the general public, researchers, edu- ematical Theories of Logic and Probabilities cators, and practitioners to devise the truth of published in 1854 starts off with: the definition, meaning, applications, and im- plications of Artificial Intelligence. The pur- The design of the following treatise suit of that truth even if through an arbitrary is to investigate the fundamental laws of contrivance would be a noteworthy goal. The those operations of the mind by which rea- fact of the matter is whether any cosmologi- soning is performed; to give expression cal structure we have hinted at so far tracks to them in the symbolical language of a the underlying reality, we cannot escape that Calculus and upon this foundation to es- there is an underlying reality. At some point tablish the science of Logic and construct in time, we (humans) began the endeavor of method; to make that method itself the ba- trying to replicate the human mind with ma- sis of a general method for the applica- chines. There was first an effort to understand tion of mathematical doctrine of Probabil- the human mind, describe its inner workings, ities; and, finally, to collect from the var- and then build machines that could essentially ious elements of truth brought to view in duplicate the thinking process. Surely this the course of these inquiries some prob- point in time must mark or at least point to the able intimations concerning the nature of Cosmological “Big Bang” for AI. Right? the human mind. So far we have pondered whether the evolu- George Boole was not alone in suggesting tion of AI could be divided into epochs. We’ve that the operation of the mind or thinking pro- considered Machine Learning, Expert Sys- cess could be represented as a set of laws or tems, and Cybernetics as possible epochs fundamental axioms. Alfred Tarski in his On with each reaching back further in the AI time- Mathematical Logic and the Deductive Method line. But where did it all begin? What was which first appears in 1936 writes: the first epoch? When did we first try to dupli- cate the thinking and reasoning process within Complicated mental processes are en- a machine? When did we first try to repre- tirely reducible to such simple activities sent the inner workings of the human mind as as the attentive observation of statements a set of instructions? At what point did we try previously accepted as true, the percep- to replicate the human mind by non-biological tion of structural, purely external, connec- means? Would this point in time constitute the tions among these statements, and the beginning (Big Bang) of the evolution of what execution of mechanical transformations we now call Artificial Intelligence? We use the as prescribed by the rules of inference. Laws of Physics to describe structures, i.e., the beginning, evolution, and fate of the Uni- Gottfried Wilhelm Leibniz suggests that hu- verse. We call this structure the Cosmology. man reason can be reduced to fundamental Can the Laws of Thought play a similar role in logical calculation. In the Art of Discovery our quest for the real AI Cosmology? 1685, he writes in a letter to Philip Spener: If there are Laws of Thought, do we under- The only way to rectify our reasoning stand what they are? If there are laws for is to make them as tangible as those of the thinking process, how are they related to the Mathematicians, so that we can find what we currently call Artificial Intelligence? our error at a glance, and when there are George Boole’s An Investigation of the Laws disputes among persons, we can simply say: Let us calculate, without further ado, Copyright c 2019 by the author(s). to see who is right. 20 AI MATTERS, VOLUME 5, ISSUE 1 5(1) 2019 Logic Machines Epoch • Alfred Tarski (1933) Theory of Truth: Theory The idea that the operation of the mind and the thinking process could be represented as • Allen Newell (1955-1956,1957) mathematical logic and discrete structures in Logic Theory Machine and General Problem a finite form suitable for implementation by a Solver: Programs machine clearly predates the term “Artificial • Alan Turing (1948,1950) Intelligence”. In the AI Matters Volume 4 Issue Intelligent Machinery, Turing Test, ”Can Ma- 4 and Volume 4 Issue 2, we’ve presented the chines think?”: Theory, Program, Paper notions of AI epochs. We postulated that we • are currently in the Machine Learning Epoch, Allan Newell, Herbert Simon (1976) and that prior to that were the Expert System Physical Symbol System Hypothesis: The- and Cybernetics Epochs. Now we consider ory the Logic Machines Epoch that was powered by mathematical logic and discrete structures. Alan Turing is the second to last entry in The ultimate goal here is to possibly identify this list. He wrote his famous paper “Can A when and what were the first real attempts Machine Think?” in 1950. This is consid- at implementing the human thinking process ered by some as the beginning of the his- or the operations of the mind by a machine. tory of AI. But as you can see, the Logical Here is a listing of some examples of Logic Machines Epoch looks like the foundations of Machines. These Logic Machines reflect at- symbolic logic. Many AI systems have used tempts at developing a theory, framework, or a symbolic logic. Symbolic logic is based on mechanization of the operations of the mind. formal logic which represents propositions as symbolic structures. Inferencing is performed • Ramon Llul (1290) by mechanical manipulations of those struc- Ars Magna: Paper Machine tures. In this list, we see early attempts at de- signing comprehensive knowledge represen- • Thomas Hobbes (1651) tation languages, mechanical approaches to Leviathan Book:Theory reasoning, and devices/machines that utilized • Gottried Leibniz (1688-1689) these methods. Leibniz envisioned such a Calculus Ratiocinator: Machine Framework device or machine. He developed a frame- • Charles Stanhope (1775) work for the Calculus Ratiocinator or Calcu- Demonstrator: Device lus Reasoning machine. Its purpose was to perform logical deductions based on a frame- • Charles Babbage (1822-1833) work of Characteristica Universalis, a concep- Difference and Analytical Engines: Ma- tual language that was able to symbolically chines represents all human thoughts. These sym- • Semyon Nikoaivich Korsakov (1832) bols would then be manipulated mathemati- Comparing Ideas Machine: Machine cally by the Ratiocinator that would mechan- • Bernard Bolzano (1837) ically deduce all possible truths from a list of Wissenschaftslehre Book: Theory simple thoughts. He stated: • George Boole (1847-1854) Thus I assert that all truths can be Boolean Algebra and Laws of Thought: The- demonstrated about things expressible in ories this language with the addition of new • William Stanley Jevons (1870-1894) concepts not yet expressed in it N~ all such Logic Piano: Machine truths, I say, can be demonstrated solo • Friedrich Ludwig Gottlob Frege (1879) calculo, or solely by the manipulation of Second-order Logic and Axiomatic Predi- characters according to a certain form, cate Logic: Theories without any labor of the imagination or ef- fort of the mind, just as occurs in arith- • Bertrand Arthur William Russell (1910) metic and algebra. Principia Mathematica: Theory • Leonardo Torres y Quevedo (1911) Charles Stanhope developed his own version Chess Playing Machine: Machine of a “Ratiocinator”, not as ambitious, called 21 AI MATTERS, VOLUME 5, ISSUE 1 5(1) 2019 the “Reasoning Machine” or Demonstrator. Charles Stanhope worked on several logic machines 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 premises and probability problems with no more than two 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 constructed as to assist us in making demonstrations. I have termed it Demonstrator. It is so peculiarly contrived as likewise to exhibit symbolically those proportions or degrees of probability which it is the object of the Logic of Probability to discover. Figure 1: William Jevon’s Logic Piano William Stanley Jevons, an economist and lo- gician, was inspired by the Demonstrator and developed the Logic Piano in 1869. The Logic In each of these epochs, there were what Piano was a series of wooden boards with we now recognize as a hype cycle where it combinations of true and false terms. They was believed that we were at the veritable were arranged on a rack and a ruler used to precipice of duplicating human intelligence by remove certain excluded combinations. The a machine with all of the rewards and punish- faceplate above keyboard displayed the en- ments that achievement entails. There were tries of the truth table. The keyboard had differently misunderstood, misconstrued, mis- black-and-white keys like a piano used to en- used, sometimes ambiguous terminologies, ter the premises. The Logic Piano was the cul- e.g. ratiocinator, automata, cybernetics, and mination of a long series of inventions by Stan- artificial intelligence which all refer to the same hope that aided in the calculation of syllogisms underlying efforts. In the Logical Machines including a logical alphabet, slate, and stamp Epoch, Charles Babbage and his colleagues that would quickly produce the lines of a truth could be considered instigators of a hype cy- table in a logical argument.
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