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Digital infinity

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123:, who was the first scientist to argue that a man-made machine might truly be said to 'think'. But his often forgotten conclusion however was in line with previous observations that a "thinking" machine would be absurd, since we have no formal idea what "thinking" is — and indeed we still don't. Chomsky frequently pointed this out. Chomsky agreed that while a mind can be said to "compute"—as we have some idea of what computing is and some good evidence the brain is doing it on at least some level—we cannot however claim that a computer or any other machine is "thinking" because we have no coherent definition of what thinking is. Taking the example of what's called 'consciousness,' Chomsky said that, "We don't even have bad theories"—echoing the famous physics criticism that a theory is "not even wrong." From Turing's seminal 1950 article, " 209:
vibrating air, to electricity in a wire, to charges in silicon, to flickering light in a fibre optic cable, to electromagnetic waves, and then back again in reverse order. ... Likewise, a given programme can run on computers made of vacuum tubes, electromagnetic switches, transistors, integrated circuits, or well-trained pigeons, and it accomplishes the same things for the same reasons. This insight, first expressed by the mathematician Alan Turing, the computer scientists Alan Newell, Herbert Simon, and Marvin Minsky, and the philosophers Hilary Putnam and Jerry Fodor, is now called the
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be ignored. Strictly speaking, there are no such machines. Everything really moves continuously. But there are many kinds of machine which can profitably be thought of as being discrete-state machines. For instance in considering the switches for a lighting system it is a convenient fiction that each switch must be definitely on or definitely off. There must be intermediate positions, but for most purposes we can forget about them.
337:' as described in Randy Allen Harris's 1993 publication by that name. The linguistic wars attracted young and ambitious scholars impressed by the recent emergence of computer science and its promise of scientific parsimony and unification. If the theory worked, the simple principle of digital infinity would apply to language as a whole. Linguistics in its entirety might then lay claim to the coveted status of 318:—hoped to explore the extent to which similar principles might be applied to the various sub-disciplines of linguistics, including syntax and semantics. If the phonological component of language was demonstrably rooted in a digital biological 'organ' or 'device', why not the syntactic and semantic components as well? Might not language as a whole prove to be a digital organ or device? 213:. It is one of the great ideas in intellectual history, for it solves one of the puzzles that make up the 'mind-body problem', how to connect the ethereal world of meaning and intention, the stuff of our mental lives, with a physical hunk of matter like the brain. ... For millennia this has been a paradox. ... The computational theory of mind resolves the paradox. 92:, Galileo describes with wonder the discovery of a means to communicate one's "most secret thoughts to any other person ... with no greater difficulty than the various collocations of twenty-four little characters upon a paper." "This is the greatest of all human inventions," Galileo continues, noting it to be "comparable to the creations of a Michelangelo". 333:. The underlying assumption here is that the requisite conceptual primitives—irreducible notions such as 'animate', 'male', 'human', 'married' and so forth—are genetically determined internal components of the human language organ. This idea would rapidly encounter intellectual difficulties—sparking controversies culminating in the so-called ' 270: 26:. Alternative formulations are "discrete infinity" and "the infinite use of finite means". The idea is that all human languages follow a simple logical principle, according to which a limited set of digits—irreducible atomic sound elements—are combined to produce an infinite range of potentially meaningful expressions. 303:. The basic idea was that every phoneme in every natural language could in principle be reduced to its irreducible atomic components—a set of 'on' or 'off' choices ('distinctive features') allowed by the design of a digital apparatus consisting of the human tongue, soft palate, lips, larynx and so forth. 325:'—the proposal that the speaker generates word and sentence meanings by combining irreducible constituent elements of meaning, each of which can be switched 'on' or 'off'. To produce 'bachelor', using this logic, the relevant component of the brain must switch 'animate', 'human' and 'male' to the 'on' 598:
It has the advantage of maintaining the integrity of linguistics, as within a walled city, away from the contaminating influences of use and context. But many have grave doubts about the narrowness of this paradigm's definition of language, and about the high degree of abstraction and idealization of
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OCLC summary: "When it was first published in 1957, Noam Chomsky's Syntactic Structure seemed to be just a logical expansion of the reigning approach to linguistics. Soon, however, there was talk from Chomsky and his associates about plumbing mental structure; then there was a new phonology; and then
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Information and computation reside in patterns of data and in relations of logic that are independent of the physical medium that carries them. When you telephone your mother in another city, the message stays the same as it goes from your lips to her ears even as it physically changes its form, from
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It remains for us to examine the spiritual element of speech ... this marvelous invention of composing from twenty-five or thirty sounds an infinite variety of words, which, although not having any resemblance in themselves to that which passes through our minds, nevertheless do not fail to reveal to
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used to encode signals then have no effect on the message conveyed. 'Off' (or alternatively 'on') remains unchanged regardless of whether the signal consists of smoke, electricity, sound, light or anything else. In the case of analog (more-versus-less) gradations, this is not so because the range of
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The digital computers considered in the last section may be classified amongst the "discrete-state machines." These are the machines which move by sudden jumps or clicks from one quite definite state to another. These states are sufficiently different for the possibility of confusion between them to
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there was a new set of goals for the field, cutting it off completely from its anthropological roots and hitching it to a new brand of psychology. Rapidly, all of Chomsky's ideas swept the field. While the entrenched linguists were not looking for a messiah, apparently many of their students were."
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and so forth. Take the consonant , for example, and switch voicing to the 'off' position—and you get . Every possible phoneme in any of the world's languages might in this way be generated by specifying a particular on/off configuration of the switches ('articulators') constituting the human vocal
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This way, digital computation and communication operates independently of the physical properties of the computing machine. As scientists and philosophers during the 1950s digested the implications, they exploited the insight to explain why 'mind' apparently operates on so different a level from
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rose to prominence as one of the most audacious champions of this 'cognitive revolution'. Language, he proposed, is a computational 'module' or 'device' unique to the human brain. Previously, linguists had thought of language as learned cultural behaviour: chaotically variable, inseparable from
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Just as Bloomfield's mentalism was one way of keeping meaning away from form, by consigning it to psychology and sociology, so Chomsky's performance is a way to keep meaning and other contaminants away from form, by consigning them to "memory limitations, distractions, shifts of attention and
133:, Chomsky provides the example of a submarine being said to "swim." Turing clearly derided the idea. "If you want to call that swimming, fine," Chomsky says, repeatedly explaining in print and video how Turing is consistently misunderstood on this, one of his most cited observations. 204:—light, sound, electricity or whatever—chosen to transmit the corresponding signals. Note that the Cartesian assumption of mind's independence of matter implied—in the human case at least—the existence of some kind of digital computer operating inside the human brain. 155:'. No physical mechanism can be intrinsically 'digital', Turing explained, since—examined closely enough—its possible states will vary without limit. But if most of these states can be profitably ignored, leaving only a limited set of relevant distinctions, then 85:
as perhaps the first to recognise the significance of digital infinity. This principle, notes Chomsky, is "the core property of human language, and one of its most distinctive properties: the use of finite means to express an unlimited array of thoughts". In his
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was generally considered the most rigorously scientific branch of linguistics. For phonologists, "digital infinity" was made possible by the human vocal apparatus conceptualised as a kind of machine consisting of a small number of binary switches. For example,
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Turing did not claim that the human mind really is a digital computer. More modestly, he proposed that digital computers might one day qualify in human eyes as machines endowed with "mind". However, it was not long before philosophers (most notably
314:—to apply distinctive features theory to the study of kinship systems, in this way inaugurating 'structural anthropology'. Chomsky—who got his job at the Massachusetts Institute of Technology thanks to the intervention of Jakobson and his student, 310:. During the 1950s, he became inspired by the prospect of extending Roman Jakobson's 'distinctive features' approach—now hugely successful—far beyond its original field of application. Jakobson had already persuaded a young social anthropologist— 187:
matter which particular medium is being employed: equating a certain intensity of smoke with a corresponding intensity of light, sound or electricity is just not possible. In other words, only in the case of
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impossible. Neither animals nor machines can think, insisted Descartes, since they lack a God-given soul. Turing was well aware of this traditional theological objection, and explicitly countered it.
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An implication is that 'digits' don't exist: they and their combinations are no more than convenient fictions, operating on a level quite independent of the material, physical world. In the case of a
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science. No part of the discipline—not even semantics—need be "contaminated" any longer by association with such 'un-scientific' disciplines as cultural anthropology or social science.
196:'matter'. Descartes's celebrated distinction between immortal 'soul' and mortal 'body' was conceptualised, following Turing, as no more than the distinction between (digitally encoded) 59:
others all of the secrets of the mind, and to make intelligible to others who cannot penetrate into the mind all that we conceive and all of the diverse movements of our souls.
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computation and communication can information be truly independent of the physical, chemical or other properties of the materials used to encode and transmit messages.
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Language is, at its core, a system that is both digital and infinite. To my knowledge, there is no other biological system with these properties....
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For Chomsky, the only channels of communication that are free from such ideological contamination are those of genuine natural science.
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Today's digital computers are instantiations of Turing's theoretical breakthrough in conceiving the possibility of a man-made
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interest" as well as to "the physical and social conditions of language , use" (1965 :3; 1977:3)—to psychology and sociology
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digital machine, the choice at each point is restricted to 'off' versus 'on'. Crucially, the intrinsic properties of the
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Translated by J. Cottingham, R. Stoothoff and D. Murdoch. Cambridge: Cambridge University Press, Vol. 1, pp. 139-141.
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mechanism of 'digital infinity', Chomsky promised to bring scientific rigour to linguistics as a branch of strictly
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Noam Chomsky, 1991. Linguistics and Cognitive Science: Problems and Mysteries. in Asa Kasher (ed.),
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otherwise 'messy' (non-digital) brain. This conception of human cognition—central to the so-called '
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is a digital computer, or at least that certain mental "modules" are best understood that way.
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social life and therefore beyond the remit of natural science. The Swiss linguist
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Previously the idea of a thinking machine was famously dismissed by
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possible settings is unlimited. Moreover, in the analog case it
578:. Longman Linguistics Library. London: Longman. p. 250. 200:
on the one hand, and, on the other, the particular physical
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This led some of Chomsky's early students to the idea of '
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7th International Conference on the Evolution of Language
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Rene Descartes, 1985 . 'Discourse on the Method.' In
119:' of the 1950s and 1960s—is generally attributed to 410:Antoine Arnauld and Claude Lancelot, 1975 (1660). 100:'Digital infinity' corresponds to Noam Chomsky's ' 329:position while keeping 'married' switched 'off' 501:. New York and Oxford: Oxford University Press. 295:apparatus. This approach became celebrated as ' 206: 161: 56: 39: 273:The human speech apparatus in sagittal section 529:(4). London, UK: Academia Europaea: 581–603. 435: 433: 393: 391: 8: 286:" could be switched 'on' or 'off', as could 159:the machine may be considered 'digital': 104:' mechanism, conceived as a computational 425:The Philosophical Writings of Descartes. 387: 487:Cambridge, MA: MIT Press, pp. 64-127. 7: 637:'Honest fakes' and language origins. 442:Computing Machinery and Intelligence 401:Oxford: Blackwell, pp. 26-53, p. 50. 125:Computing Machinery and Intelligence 474:London: Allen Lane, Penguin, p. 24. 33:Frontispiece and title page of the 14: 640:Journal of Consciousness Studies, 642:15, No. 10–11, 2008, pp. 236–48. 485:Aspects of the Theory of Syntax. 96:The computational theory of mind 626:'Unravelling digital infinity'. 306:Chomsky's original work was in 16:Term in theoretical linguistics 624:Knight, C. and C. Power 2008. 1: 574:Leech, Geoffrey Neil (1983). 414:The Hague: Mouton, pp. 65-66. 497:Harris, Randy Allen (1993). 211:computational theory of mind 632:(EVOLANG), Barcelona, 2008. 677: 149:universal thinking machine 535:10.1017/S1062798704000493 576:Principles of pragmatics 458:10.1093/mind/LIX.236.433 628:Paper presented to the 599:data which it requires. 412:The Port-Royal Grammar. 24:theoretical linguistics 22:is a technical term in 514:Knight, Chris (2004). 440:Turing, Alan (1950). " 356:Generative linguistics 274: 227: 172: 151:—known nowadays as a ' 108:inserted somehow into 76: 55: 37: 470:Steven Pinker, 1997. 272: 252:Ferdinand de Saussure 32: 499:The Linguistics Wars 361:The Library of Babel 323:generative semantics 297:distinctive features 117:cognitive revolution 472:How the Mind Works. 399:The Chomskyan Turn. 312:Claude LĂ©vi-Strauss 230:A digital apparatus 70:and Claude Lancelot 516:"Decoding Chomsky" 483:Chomsky, N. 1965. 366:Origin of language 275: 38: 661:Cognitive science 635:Knight, C. 2008. 102:universal grammar 668: 612: 608: 602: 601: 571: 565: 564: 559: 557: 552:on 14 April 2021 551: 545:. 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Index

theoretical linguistics

Antoine Arnauld
Noam Chomsky
Galileo
Dialogo
universal grammar
module
cognitive revolution
Alan Turing
Computing Machinery and Intelligence
Mind
René Descartes
Turing machine
medium
computational theory of mind
Hilary Putnam
Noam Chomsky
Ferdinand de Saussure
semiotics

phonology
voicing
palatisation
nasalisation
distinctive features
Roman Jakobson
morphophonemics
Claude LĂ©vi-Strauss
Morris Halle

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