Contrariwise, if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.Through the Looking-Glass

Lewis Carroll (1832-1898)

On Tuesday night I made my second appearance on Science Café, BBC Radio Wales’ flagship weekly science and technology programme, which aims to explore the science and technology stories making the headlines and reveal the latest Welsh scientific research.

The topic of this week’s programme was **logic**: a two thousand year old system of reasoning and argumentation which (some) humans use every day, as well as being the foundation of computation and modern technology. I was joined on the panel by two distinguished colleagues, Professor John Tucker (Professor of Computer Science at Swansea University) and Professor Christopher Norris (Distinguished Research Professor in Philosophy at Cardiff University).

The discussion was driven by the expertise of the panel: starting from the development of “classical logic” as a formal system of the principles of inference and rational reasoning, all the way back to Aristotle and the classical trivium. Then moving into the mathematical logic of the late 19th century and early 20th century with Hilbert and his program to clarify the foundations of mathematics, how Gödel shattered Hilbert’s dream, and in particular, the significant contributions to philosophy, mathematics and logic of the Welsh-born Bertrand Russell. Logic cuts to the heart of computer science as it emerged as a discipline: Turing‘s work on the *Entscheidungsproblem* followed from Gödel’s work on the incompleteness theorems, with the notion of computation and general-purpose computers being of fundamental importance to the designers of the computer machinery in the 1940s. This rapidly moved on to a discussion of expressing human knowledge using logic with mathematical notation, developing “intelligent” thinking machines and the problems of artificial intelligence (especially so-called strong AI). This (briefly) touched upon my work using logic programming for real-world declarative problem-solving, particularly for provably optimal code generation and improving the efficiency of microprocessors.

In essence, the key point was made about how logic is pervasive in our modern technological society: in every piece of digital electronics and especially in software — a clear manifestation of logic. This led to an important education question: shouldn’t we be developing these important deductive reasoning, problem-solving and computational thinking skills at school? I certainly think so. Finally, in a move that may come back to haunt me in later years, I was asked to finish with a joke about logic…

The Science Café “Logic” programme is now available on iPlayer (but only for seven days after broadcast). You can also read about my week with the Science Café team in Wrexham in August 2011.

A little gem found via Twitter: “

Intelligent Machinery“, the seminal 1948 paper by Alan Turing.Also (mentioned above): “

On computable numbers, with an application to the Entscheidungsproblem” (1937).John von Neumann speculated about computers and the human brain in analogies sufficiently wild to be worthy of a medieval thinker and Alan M. Turing thought about criteria to settle the question of whether Machines Can Think, a question of which we now know that it is about as relevant as the question of whether Submarines Can Swim.Edsger W. Dijkstra (1984)