Some references that I’ve found helpful when ‘reasoning about reasoning’.
Design for a brain 1960. (Ed. 2 has significant improvements.) A cybernetic classic. Ashby notes the correspondence to game theory (and thus to Whitehead). In simpler case Cybernetic language is considerably more accessible than Whitehead.
With Conant: Every Good Regulator of a System must be a Model of that System, 1970. It claims that:
“The theorem has the interesting corollary that the living brain, so far as it is to be successful and efficient as a regulator for survival, must proceed, in learning, by the formation of a model (or models) of its environment.” [My italics.]
The notion of a regulator is an objective mechanism which is required to maintain pre-defined objective criteria: i.e., keep some output within a ‘good’ domain. It may also have other functions, e.g. optimising something. The theory shows that in so far as a system to be regulated conforms to some model, it will need – in effect – to be modelled to be regulated effectively. It does not explicitly consider feed-back from output to input. Where this is present on could apply the theory to short-term regulation, within the delay of the feed-back. Alternatively one could apply it at the level of strategy rather than base events and activities. In this case one needs to model ‘the game’, including the ‘board’, the players and their motivations.
Risk Society: Towards a New Modernity, 1992. Argues that the application of modern rationality, methods and technologies has had unfortunate unintended consequences, spreading risk proper and wasting effort on fixing the problems created. ‘Modern management’ becomes reflexive. Beck sees signs of this very widely and points to further problems ahead.
[U]ncalculable threats add up to an unknown residual risk which becomes the industrial endowment for everyone everywhere.
A popular and influential Green author on complexity and holism, marking modern (post-war) interest in these subjects. He draws on Bateson and Bohm, but appears unaware of Smuts and his impact on modern Physics etc.
The Tao of Physics, 1975.
The Turning Point, 1982.
The Web of Life, 1996.
D Fudenberg and DK Levine
The Theory of Learning in Games, 1998. A mainstream account, favoured by sensible economists.
Turing’s statistical specialist at Bletchley Park and subsequently a controversial statistics guru. Good developed Keynes notions of likelihoods and fusion.
Good Thinking: The Foundations of Probability and Its Applications, 1983. A good summary of Good’s work on ‘weight of evidence’ etc.
Charles Handy is one of ‘the’ British management gurus.
The Age of Unreason, 1989. Argues that in developed countries like Britain, ‘top-down’ management is no longer viable in the face of various trends, and that in future ‘work’ needs to be more knowledge-based and hence learning and federated. Handy emphasises the need for people to show Keats’ ‘negative capability’ and show initiative and discretion. Handy notes how this will lead to greater short-term efficiencies and hence widespread competitive pressure for all aspects of life to follow his model. But, he notes ‘market forces’ will not take account of longer-term needs (e.g. of global warming), continuing ‘the tradition that it makes good economic sense to borrow from [our] grandchildren to boost our standard of living today’. Hence there will be a greater need for people to ‘value’ longer-term issues. [Handy’s predictions have largely come about, but we still lack the longer term thinking. Presumably some insightful de-facto ‘institution’ would be needed that is not shaped or driven by market values, to identify and explain risks and opportunities.]
Kant is a key figure of ‘the enlightenment’.
Critique of Pure Reason, Ed. 2 1787. Kant extensively catalogues different types of reasoning, showing the need for ‘synthetic a priori’ reasoning, as in mathematics. Kant shows how reasoning is typically a ‘work in progress’, which goes wrong when it claims a certainty or finality that is not justified. He is equally critical of dogmatism, misplaced ‘mathematical’ (i.e. formal) and ‘practical’ or ‘pragmatic’ reasoning.
Kant’s 12 ‘pure concepts of the understanding which apply to objects of intuition’ include ‘Of Community (reciprocity between agent and patient (sic))’. ‘This is a quite different kind of connection from that which is found in the mere relation of cause and effect’ and plays a key role in Kant’s concept of a ‘whole’. Most of Kant’s examples of the mis-use of reason are when reasoning has been confined to mundane objects and causality, but leaps to make groundless deductions about community.
Kant has a corresponding notion of the structure of possible knowledge. This includes partial orders for space and time, of bounded, nested and inter-related communities, wholes and systems whose ‘ways of existing’ may persist or periodically ‘alter’
Kant also distinguishes between scientific and technical reasoning. The former is always uncertain and striving, whereas the latter may be pragmatic. Kant made a significant contribution to modern notions of science. More …
Keynes was a mathematician student of Whitehead, employed by the treasury during the war, who worked with JC Smuts on the transition to peace. The Prime Minister (Lloyd George) supported Keynes in producing the first two references as ‘lessons identified’ from the war.
Treatise on Probability 1919. Keynes’ critique of ‘standard’ (numeric) probability theory, together with some useful generalisations. Refers to Whitehead (Keynes’ tutor). Underpins subsequent work. More …
The Economic Consequences of the Peace 1919. Keynes shows that although depressions are impossible according to the then classical economics, based on standard probability, ‘animal spirits’ introduced the greater uncertainties, of the kind described in his treatise, made a crash and a sustained impression virtually certain. Thus whereas the conventional view was that economies were inherently buoyant, so that recessions could occur as a result of ‘exogenous events’, such as war, a depression could actually occur endogenously – due to ‘market failures’.
The General Theory of Employment, Interest and Money 1935. The master work on economics. It explains how crises such as those of 1929 and 2007/8 occur, and suggests some remedies. Underpinned by the treatise on probability, but this is not widely appreciated. ‘Keynesian’ economics means the application of stock remedies whatever the cause. In this sense, Keynes was not a Keynesian. Rather he developed a theory as a way of looking at economies. His approach was to follow where theory led, taking account of residual uncertainties.
Prigogine is known for his work on dissipative structures, for which he won a Nobel prize.
From Being to Becoming: Time and Complexity in the Physical Sciences, WH Freeman, 1980. (Monograph)
With I Strengers: Strengers Order out of Chaos: man’s new dialogue with nature Heinemann 1984. (Popular account, with a foreord by Alvin Toffler.)
An account of dissipative structures (away from equilibrium) and the implications for entropy, emergence and time, based on a model consisting of operators that act on operators. It shows how one can not only get order degrading into chaos, but how order can emerge from chaos, one many scales, cyclically. It fits within the framework of Whitehead. Order out of Chaos emphasises the need for a new approach to science and the use of science. More …
Smuts worked with Keynes on economics.
Holism and evolution 1927. Smuts’ notoriously inaccessible theory of evolution, building on and show-casing Keynes’ notion of uncertainty. Although Smuts and Whitehead worked independently, they recognized that their theories were equivalent. More …
The Scientific World-Picture of Today, in ‘British Association for the Advancement of Science, Report of the Centenary Meeting’. London: Office of the BAAS, 1932. Smuts’ presidential address, outlining the new ideas in ‘Holism and evolution’ and their import. (Also available from JAMA.)
Ian has done more than most to explore, develop and explain the most important parts of qualitative mathematics.
Life’s Other Secret: The new mathematics of the living world, 1998. This updates D’Arcy Thompson’s classic On growth and form, ending with a manifesto for a ‘new’ mathematics, and a good explanation of the relationship between mathematics and scientific ‘knowledge’. Like most post-80s writings, it’s main failing is that it sees science as having achieved some great new insights in the 80s, ignoring the work of Whitehead et al, as explained by Smuts, for example.
On Contradiction 1937. Possibly the most popular account of Whitehead’s ideas.
Whitehead was Russell and Keynes’ tutor.
Process and Reality 1929. Notoriously hard going, it formalises some of Kant’s ideas on the structure of knowledge, linking it to Keynes’ work on uncertainty.
American civil-war thinker and poet. Part of the inspiration for the Beat movement.
Leaves of Grass 1855. Part of Smuts’ inspiration.
ABACI – a consultancy who offer to tailor solutions.