255 research outputs found
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
Predicativity and parametric polymorphism of Brouwerian implication
A common objection to the definition of intuitionistic implication in the
Proof Interpretation is that it is impredicative. I discuss the history of that
objection, argue that in Brouwer's writings predicativity of implication is
ensured through parametric polymorphism of functions on species, and compare
this construal with the alternative approaches to predicative implication of
Goodman, Dummett, Prawitz, and Martin-L\"of.Comment: Added further references (Pistone, Poincar\'e, Tabatabai, Van Atten
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Inventing Intelligence: On the History of Complex Information Processing and Artificial Intelligence in the United States in the Mid-Twentieth Century
In the mid-1950s, researchers in the United States melded formal theories of problem solving and intelligence with another powerful new tool for control: the electronic digital computer. Several branches of western mathematical science emerged from this nexus, including computer science (1960s–), data science (1990s–) and artificial intelligence (AI). This thesis offers an account of the origins and politics of AI in the mid-twentieth century United States, which focuses on its imbrications in systems of societal control. In an effort to denaturalize the power relations upon which the field came into being, I situate AI’s canonical origin story in relation to the structural and intellectual priorities of the U.S. military and American industry during the Cold War, circa 1952 to 1961.
This thesis offers a detailed and comparative account of the early careers, research interests, and key outputs of four researchers often credited with laying the foundations for AI and machine learning—Herbert A. Simon, Frank Rosenblatt, John McCarthy and Marvin Minsky. It chronicles the distinct ways in which each sought to formalise and simulate human mental behaviour using digital electronic computers. Rather than assess their contributions as discontinuous with what came before, as in mythologies of AI's genesis, I establish continuities with, and borrowings from, management science and operations research (Simon), Hayekian economics and instrumentalist statistics (Rosenblatt), automatic coding techniques and pedagogy (McCarthy), and cybernetics (Minsky), along with the broadscale mobilization of Cold War-era civilian-led military science generally.
I assess how Minsky’s 1961 paper 'Steps Toward Artificial Intelligence' simultaneously consolidated and obscured these entanglements as it set in motion an initial research agenda for AI in the following two decades. I argue that mind-computer metaphors, and research in complex information processing generally, played an important role in normalizing the small- and large-scale structuring of social behaviour using mathematics in the United States from the second half of the twentieth century onward
On the Semantics of Intensionality and Intensional Recursion
Intensionality is a phenomenon that occurs in logic and computation. In the
most general sense, a function is intensional if it operates at a level finer
than (extensional) equality. This is a familiar setting for computer
scientists, who often study different programs or processes that are
interchangeable, i.e. extensionally equal, even though they are not implemented
in the same way, so intensionally distinct. Concomitant with intensionality is
the phenomenon of intensional recursion, which refers to the ability of a
program to have access to its own code. In computability theory, intensional
recursion is enabled by Kleene's Second Recursion Theorem. This thesis is
concerned with the crafting of a logical toolkit through which these phenomena
can be studied. Our main contribution is a framework in which mathematical and
computational constructions can be considered either extensionally, i.e. as
abstract values, or intensionally, i.e. as fine-grained descriptions of their
construction. Once this is achieved, it may be used to analyse intensional
recursion.Comment: DPhil thesis, Department of Computer Science & St John's College,
University of Oxfor
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