A summary of Logic and information by Keith Devlin

Logic and Information attempts to set the foundation for a framework for the characterization and science of meaning and information. Devlin approaches information as a logician and doesn’t rely upon Claude Shannon’s classic Information Theory.

This books seems to have been generally dismissed or discounted as an over ambitious attempt to formulate information flow without any hard science or mathematics. However the books ambition and original approach does bring light to some interesting concepts.

The books states the following about itself.

  • “It is a mathematics book, or at least a “pre-mathematics” book that covers issues of crucial importance to philosophers, linguists, computer scientists, and cognitive scientists. Accordingly, it has been written in areas, and possibly other fields as well. It is applied mathematics. More precisely the book describes an instance of the important (applied) mathematical activity of modeling. It is a ‘research monograph’ in the spirit of mathematical theory, a piece of mathematics. And very much in the spirit of present-day mathematical research, little (in fact no) attempt has been made o turn it into a work of scholarship.

    The overall goal is to provide the mathematics required for a science of information. I start the process of fleshing out a mathematical framework that will (I hope) form the backbone of such a science in the same way that parts of present-day mathematics support, say, physics.

    It is a challenge. By sending this volume out into the world at this early stage in the development, I hope that others will be able to progress still further.”

  • The referencessituation theory which is “… the fact an agents’s world divides up into a collection, or succession, of situations: situations encountered, situations referred to, situations about which information is received..
  • Situation Theory

    Situation theory was first coined by Jon Barwise and John Perry. It is the idea that all communication comes in the context of a situation. An example given in the book is of two people watching a San Francisco 49ers football game. If one person say to the other “Rice is great”, in that situation the message has meaning because both know that Rice is referring to Jerry Rice the wide receiver on the 49ers.

    Situation theory may seem obvious and unnecessary but it is not without precedent in traditional Shannon information theory. It could be pointed out that when a message is transmitted in English that it is part of “the situation” that both sender and receiver understand the English alphabet.

    The Infon is Born

    Infon vs Bit

    Meet the Info the more abstract cousin of the bit.

    Logic and information is presumably the inventor of the term infon and infonic.

    What is an Infon? A single piece of information the who, what, where, when, and why within a “situation”.

    An Infon is a bit with context in the situation.

    Conclusion

    Logic and information is an ambitious and flawed attempted to bring about a more contextual mathematics of information. Devlin alludes to the fact that the book had to be finished at a different university from were it started. This was because it was considered “undesirable”.

    Einstein’s space is no closer to reality than Van Gogh’s sky. … The scientist’s discoveries impose his own order on chaos, as the composer or painter imposes; an order that always refers to limited aspects of reality, and is biased by the observer’s frame of reference, which differs from period to period, as a Rembrandt nude differs from a nude by Monet.
    –Arthur Koestler
    The Act of Creation