Abstract
When IBM’s Deep Blue beat Kasparov in 1997, Bringsjord (Technol Rev 101(2):23–28, 1998) complained that despite the impressive engineering that made this victory possible, chess is simply too easy a challenge for AI, given the full range of what the rational side of the human mind can muster. However, arguably everything changed in 2011. For in that year, playing not a simple board game, but rather an open-ended game based in natural language, IBM’s Watson trounced the best human Jeopardy! players on the planet. And what does Watson’s prowess tell us about the philosophy, theory, and future of AI? We present and defend snyoptic answers to these questions, ones based upon Leibniz’s seminal writings on a universal logic, on a Leibnizian “three-ray” space of computational formal logics that, inspired by those writings, we have invented, and on a “scorecard” approach to assessing real AI systems based in turn on that three-ray space.
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Notes
- 1.
The authors are profoundly grateful to IBM for a grant through which the landmark Watson system was provided to RPI, and for an additional gift enabling us to theorize about this system in the broader context of logic, mathematics, AI, and the history of this intertwined trio. Bringsjord is also deeply grateful for the opportunity to speak at PT-AI 2013 in Oxford; for the leadership, vision, and initiative of Vincent Müller; and for the spirited objections and comments received at PT-AI 2013, which served to hone his thinking about the nature and future of (Weak) AI. Thanks are do as well to certain researchers working in the cognitive-computing space for helpful interaction: viz., Dave Ferrucci, Chris Welty, Jim Hendler, Deb McGuiness, and John Licato.
- 2.
Note that we say: “rational side.” This is because in the present essay we focus exclusively upon what Leibniz aimed to systematize via his “art of infallibility.” Accordingly, in short, we target systematic human thought. (In modern terms, this sphere could be defined ostensively, by enumerating what is sometimes referred to as the formal sciences: logic and mathematics, formal philosophy, decision theory, game theory, much of modern analysis-based economics (to which Leibniz himself paved the way), much of high-end engineering, and mathematical physics). We aren’t concerned herein with such endeavors as poetry, music, drama, etc. Our focus shouldn’t be interpreted so as to rule out, or even minimize the value of, the modeling of, using formal logic, human cognition in these realms (indeed, e.g. see Bringsjord and Ferrucci 2000; Bringsjord and Arkoudas 2006); it’s simply that in the present essay we adopt Leibniz’s focus.
- 3.
Such as those nicely presented in Russell and Norvig (2009).
- 4.
From “Letter to Galois,” in the year 1677, included in Leibniz and Gerhardt (1890).
- 5.
In Leibniz’s words:
One is obliged to admit that perception and what depends upon it is inexplicable on mechanical principles, that is, by figures and motions. In imagining that there is a machine whose construction would enable it to think, to sense, and to have perception, one could conceive it enlarged while retaining the same proportions, so that one could enter into it, just like into a windmill. Supposing this, one should, when visiting within it, find only parts pushing one another, and never anything by which to explain a perception. Thus it is in the simple substance, and not in the composite or in the machine, that one must look for perception. (§17 of Monadology in Leibniz 1991)
- 6.
Leibniz came strikingly close to grasping universal or programmable computation. But nothing we say here requires that he directly anticipated Post and Turing. This is true for the simple reason that Leibniz fully understood de novo computation in the modern sense, and also was the first to see that a binary alphabet could be used to encode a good deal of knowledge; and the properties he saw as incompatible with consciousness are those inherent in de novo computation over a binary alphabet {0, 1}, and in modern Turing-level computation.
- 7.
Bringsjord (1992) is a book-length defense of Weak AI, and a refutation of Strong AI.
- 8.
With apologies in advance for the pontification, Bringsjord maintains that there is really only one right route for diving into Leibniz on formal logic: Start with the seminal (Lewis 1960), which provides a portal to the turning point in the history of logic that bears a fascinating connection to Leibniz (since Lewis took the first thoroughly systematic move to intensional logic, anticipated by Leibniz). From there, move into and through that which Lewis himself mined, viz. (Leibniz and Gerhardt 1890). At this point, move to contemporary overviews of Leibniz on logic, and into direct sources, now much more accessible in translated forms than in Lewis’s day.
- 9.
Lewis (1960) asserts that the universal language, if true to Leibniz, would be ideographic pure and simple. We disagree. Ideograms can be pictograms, and that possibility is, as we note here, welcome—but Leibniz also explicitly wanted to allow UL to allow for traditional symbolic constructions, built out of non-ideographic symbols. We know this because of Leibniz’s seminal work in connection with giving us (the differential and integral) calculus, which is after all routinely taught today using Leibniz’s symbolic notation (e.g., \(\frac{dx} {dy}\), where y = f(x)).
- 10.
Axiomatic treatments of arithmetic, e.g., make use of this rule of inference, and then need only add modus ponens for (first-order & finitary) proof-theoretic completeness.
- 11.
The systems of modal logic for which C.I. Lewis is rightly famous are given in the landmark (Lewis and Langford 1932).
- 12.
An interesting way to see the ultimate consequences, for formal logic, of Leibniz’s infinitary reasoning in connection with infinitesimals and calculus, is to consider in some detail, from the perspective of formal logic, the “vindication” of Leibniz’s infinitesimal-based provided by Robinson (1996). Space limitations make the taking of this way herein beyond scope.
- 13.
The distinction is not always perfect. E.g., {} for the empty set is both iconic and symbolic.
- 14.
Infinitary logics are “measured” in terms of length not only of formulae, but e.g. number of quantifiers permitted in formulae. In the present paper, we leave aside the specifics. But we do point out to the motivated reader that Fig. 12.1, on the infinitary “ray,” refers to the infinitary logic \(\mathcal{L}_{\omega _{1}\omega }\), which, in keeping with the standard notation, says that disjunctions/conjunctions can be of a countably infinite length, whereas the number of quantifiers allowed in given formulae must be finite.
- 15.
- 16.
The primogenitor of the case for this series of events is Good (1965). A modern defense of the this original case is provided by Chalmers (2010). A formal refutation of the original and modernized argument is supplied by Bringsjord (2012). An explanation of why belief in the Singularity is fideistic is provided by Bringsjord et al. (2013).
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Bringsjord, S., Govindarajulu, N.S. (2016). Leibniz’s Art of Infallibility, Watson, and the Philosophy, Theory, and Future of AI. In: Müller, V.C. (eds) Fundamental Issues of Artificial Intelligence. Synthese Library, vol 376. Springer, Cham. https://doi.org/10.1007/978-3-319-26485-1_12
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