This paper is
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/explaining-possibility.html
A PDF version (possibly slightly out of date) is available here:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/explaining-possibility.pdf
This file was previously located at a different address, which is now being used
for a more complete discussion of requirements for construction kits able to
account for biological evolution:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/construction-kits.html
A partial index of discussion notes available from this web site is in
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/AREADME.html
Chapter 2 of the book -- now available online here -- claimed that explaining how something (or some class of things) is possible is a major function of science, and the rest of the book presented tentative examples illustrating how AI (including computational linguistics) advanced our ability to explain (and sometimes predict) possibilities, as theories in physics and chemistry had done previously. For example,
Many major past scientific advances were theories about what is possible and explanations of some possibilities in terms of more fundamental possibilities.
The chapter is included part of the new (slightly) revised, freely available,
online electronic edition of the book assembled in 2015, here:
http://www.cs.bham.ac.uk/research/projects/cogaff/crp/#chap2
Still being modified from time to time.
This is not intended to be a complete list.
NOTE: Some related ideas (Added 13 Mar 2016)
I have been aware for some time that there is an overlap between my ideas about
the role of explanations of possibilities, as opposed to laws, in science and
some of Stuart Kauffman's ideas, e.g. in his (1995).
I have now found much greater and more explicit overlap with this 2016 paper:
Longo, Montevil & Kauffman (2012)
Chapter 2 of Sloman (1978) was an attempt to extend the philosophy of science developed by Karl Popper (1934) (and revised/extended in his later publications) which distinguished between scientific statements or theories and non-scientific (e.g. metaphysical) statements. The former were required to be empirically falsifiable, since if no falsifiable empirical statement can be derived from a theory it was said to lack empirical content. Unfortunately this criterion has been blindly followed by many scientists who seem to be ignorant of the history of science. E.g. the ancient atomic theory of matter was not falsifiable, but was an early example of a deep scientific theory. Popper (unlike many scientists who promote 'falsifiability' as a criterion for scientific content) acknowledged that some metaphysical theories could be important precursors of scientific theories, but it is arguable that labelling them 'metaphysics' rather than 'science' is arbitrary, in view of their importance for science. For more on the ancient atomic theory see:
Popper's philosophy of science was extended by Imre Lakatos (1980), who proposed ways of evaluating competing scientific research programmes, based on the sorts of progress they made over time. This shifts the problem away from taking final decisions about which theory (or research programme) is best, allowing evidence to mount up in favour of one or another over time, though always allowing for the possibility that some new development will shift the balance of support. Emphasising evaluation over an extended period of time, Lakatos distinguished progressive and degenerating research programmes. Requirements were specified for deciding which of two progressive research programmes is better, though it is not always possible to decide while both are being developed. The history of science shows that what appears to be a decisive victory (like Thomas Young's evidence of diffraction of light, which was taken to disprove Newton's particle theory of light) can later be overturned (e.g. when light was shown to have a dual wave-particle nature).
My motivation, in 1978, for extending the work of Popper and Lakatos was based
on the observation that many important scientific discoveries are concerned with
what is possible, e.g. types of plant, types of animal, types of
reproduction, types of thinking, types of learning, types of verbal
communication, types of thought, types of mathematical discovery, types of atom,
types of molecule, types of chemical interaction, and types of biological
information-processing (a category that subsumes several of the other types).
Investigation of varieties of biological information processing and the
mechanisms (especially construction-kits) that support them is main focus of the
Turing-inspired Meta-Morphogenesis project, whose aims were first formulated
during the year of Turing's centenary 2012:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/meta-morphogenesis.html
A separate paper Sloman [DRAFT 2016] discusses in detail the ways in which specifications of "construction kits" provided by nature (e.g. physics and chemistry), including the mathematical properties and generative powers of those kits and space-time, can play a central role in answering questions about how various evolutionary processes are possible, thereby explaining how the products of those processes, namely enormously varied forms of life and the many biological mechanisms they use, all directly or indirectly products of natural selection, are possible.
NOTE ADDED 3 Mar 2016
I now think that one of the deepest and most interesting examples of a scientist trying to explain how something is possible is Erwin Schrödinger's attempt to answer the question "What is life?" (1944).
The rest of this paper focuses on the special properties of explanations of possibilities and why the important ideas of Popper and Lakatos about the nature of science have to be extended to accommodate them.
The answer given in the paper and book chapter had several components, namely: A theory purporting to explain how various objects, states of affairs, or processes are possible, should:
Often economy in science is taken to mean the use of relatively few concepts or assumptions, from which others can be derived as necessary. This is not always a good thing to stress, since great economy in primitive concepts can go along with uneconomical derivations and great difficulty of doing anything with the theory, that is, it can go along with with heuristic poverty. For instance, the logicist basis for mathematics proposed by Frege, Russell and Whitehead is very economical in terms of primitive concepts, axioms, and inference rules, yet it is very difficult for a practising mathematician to think about deep mathematical problems if he expresses everything in terms of that basis, using no other concepts. Replacing numerical expressions by equivalents in the basic logical notation produces unmanageably complex formulae, and excessively long and unintelligible proofs. The main points get buried in a mass of detail, and so cannot easily be extracted for use in other contexts. More usual methods have greater heuristic power. So economy is not always a virtue. This is also true of Artificial Intelligence models.
See
chapter 7 of CRP
and
McCarthy and Hayes, 1969,
for more on this:
"Some philosophical problems from the standpoint of Artificial Intelligence"
So a good explanation of a range of possibilities should be definite, general (but not too general), able to explain fine structure, non-circular, rigorous, plausible, economical, rich in heuristic power, and extendable (allow scaling out). It is not at all easy to produce explanations of possibilities that meet all these requirements. I think it can be shown that many highly regarded models/theories in AI, psychology, neuroscience, linguistics, and philosophy fail to meet them.
Features of a meccano set can be used to explain how a particular sort of toy vehicle or toy crane can exist, by showing how each can be assembled from the parts available, subject to the constraints of the kit. E.g. melting down metal parts and then re-shaping them is ruled out. Likewise features of a grammar and vocabulary can be used to explain how a particular sentence is possible by showing how the sentence uses words in a particular lexicon assembled in accordance with the rules of the grammar.
A specification of the components and assembly processes of each of Meccano and Lego sets can be used to explain how each can produce structures that the other cannot produce. A process of construction suffices to demonstrate that something is possible using a particular kit, e.g. a particular type of toy crane. Something deeper is required in order to explain why something is impossible for a particular kit, i.e. not included in the set of possible constructs supported by the kit.
For example a toy crane with a jib that is hinged at the bottom and can be raised and lowered is possible using meccano. Demonstrating that it is not possible using only lego-bricks can make use of a number of facts, such as that the processes of assembly of those bricks always produce only rigid structures, since there is no hinge mechanism and now means of creating a hinge mechanisms. A related argument is that the process of assembling a structure using lego bricks constrains each brick added to have edges with exactly three orientations (i.e. all edges can be divided into three classes where edges in each class are parallel, and edges in different classes are perpendicular to each other).
The idea of spaces of possibilities generated by different sorts of construction kits may be easier for most people to understand than the comparison with generative powers of grammars mentioned in the chapter. The idea of a construction kit is also more directly relevant to a host of types of scientific explanation, as well as theories in engineering.
This is a first draft attempt to spell out that idea, and will be expanded later.
For many scientific and engineering purposes we are interested not only in what can be built, but what the things that are built can do, e.g. how they can change shape, interact with other things, be extended, come apart, etc. etc.
Each kit, simple or combined, allows a space (domain?) of possible structures (and possible processes involving those structures). The spaces have different contents because of different mathematical features of the generating elements (parts and modes of composition).
Each explains possibilities in a domain without predicting which possibilities will be realised (which generally depends on external factors).
However there is an element of prediction insofar as the theory of a domain specifies constraints on ways in which complex instances can be extended.
For example, if you have already built some sort of structure using a kit, then, if the kit has not been exhausted, there will be alternative possible ways of extending that structure by adding one or more new parts. Each such extension will then normally remove some of the old possibilities for change and produce new possibilities for change.
To that extent there is predictive power in the theory of what the kit makes possible, though the predictions are not about what will happen after some change, but predictions about how sets of possibilities will be altered.
[I think Immanuel Kant had more than an inkling of this.]
There are also abstract construction kits such as grammars, axiomatic systems, computer programming languages, and programming toolkits. For more on varieties of construction kit see the discussion of concrete, abstract and hybrid construction kits Sloman [DRAFT 2016].
A1: The first answer is concerned with identifying the parts and relationships between parts that are supported by the kit, and how a crane of the sort in question could be composed of such parts arranged in such relationships.
A2: The second answer would describe a sequence of steps by which such a collection of parts could be assembled from the basic components provided by the kit. There may be many different sequences leading to the same result: identifying any one of them explains how the construction is possible, as well as how the end result is possible.
Both answers are correct, though A2 obviously provides more information than A1. Neither explanation presupposes that the possibility in question has ever been realised. This is very important for many engineering projects where something new is proposed and critics believe that the object in question could not exist, or could not be brought into existence using available known materials and techniques. The designer could answer sceptical critics by giving either an answer of type A1, or type A2, depending on the reasons for the scepticism. So from this point of view explanations of possibilities have much broader applicability than explanations of things that actually exist, since what actually exists is only tiny subset of what could possibly exist.
The associated document on construction kits subdivides explanations of type A2 into a variety of different sub-cases. (Work in progress.)
"How is X possible?" was a type of question raised for various cases of X by Immanuel Kant (e.g. how is knowledge of synthetic necessary truths possible?). In the early 1970s I wrote a paper about this, expanding on my 1962 DPhil thesis defending Kant's views of mathematical knowledge. The new paper attempted to show that claims about possibility and explanations of possibility are deeply connected with the most fundamental aims of science, and often require the current scientific ontology to be extended.
As far as I knew no philosopher of science had addressed such claims and explanations. Moreover they are counter-examples to many philosophical accounts of how scientific theories are, or should be, evaluated. E.g. the claim that X (or something of type X) is possible can never be refuted by experiment or observation. However it can sometimes be confirmed by observation of X, or of type X. So stressing the scientific importance of questions and theories about what is possible and how those things are possible required challenging major philosophies of science emphasizing prediction and refutation, including the work of two philosophers whom I greatly admired and had learnt from, Karl Popper and Imre Lakatos.
Moreover, explaining how X is possible seemed to be particularly relevant to some of the newest sciences, including theoretical linguistics, computer science, and artificial intelligence.
An exception could be a case where X is the - the Fundamental Construction Kit discussed in - since all concrete constructions must start from it (in this universe?). If Y is abstract, there need not be something like the FCK from which it must be derived. The space of abstract construction kits may not have a fixed "root". However, the abstract construction kits that can be thought about by physically implemented thinkers may be constrained by a future replacement for the Church-Turing thesis, based on later versions of ideas presented here. Although the questions about explaining possibilities arise in the overlap between philosophy and science (Sloman, 1978, Ch.2), I am not aware of any philosophers who explicitly address the theses discussed here, though there are examples of potential overlap, e.g. Bennett (2011); Wilson (2015).
There are many more examples of proofs of impossibility thousands of years old: Ancient mathematicians proved that it is impossible for the sum of the interior angles of a planar triangle to differ from half a rotation (180 degrees), as discussed in: http://www.cs.bham.ac.uk/research/projects/cogaff/misc/triangle-sum.html
(Extended: 30 Aug 2015)
It is worth noting that some proofs of impossibility depend on a set of
premisses that can be modified or extended without any mathematical error. For
example, there are "standard" proofs that it is impossible in Euclidean geometry
to trisect an arbitrary angle using straight edge and compasses. That proof
depends on limitations on uses of compasses and straight edge in Euclidean
geometry. However, anyone who understands those constraints can easily
understand a slight extension slight extension to its constructions by
permitting translations and rotations of a straight edge with two marked points,
known as the "Neusis" construction (known to Archimedes)
and with that extension trisection of an
arbitrary planar angle can be proved to be possible, as shown in:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/trisect.html
Turing proved that it is impossible for any Turing machine (TM) to be able to take in the specification of any arbitrary TM and derive a proof that it will, or will not, halt. If you understand what prime numbers are you may be able to construct a proof that it is impossible for any number of the form 7^{^m}-5^{^m} where m is a non-zero positive integer to be divisible by 5. (I have deliberately invented a theorem that is too specialised to be in any mathematical text book. You may prefer to try to prove a more general version that doesn't mention any particular numbers.)
Of course, any proof of an impossibility is a proof of some necessity, and vice versa, since the impossibility of P is the same as the necessity of Not-P, and the impossibility of Not-P is the same as the necessity of P. However, proof of possibility has a different character, though both proofs of possibility and proofs of impossibility start from prior knowledge about a "domain" that is under discussion (e.g. possible 2-D shapes in a plane surface). How to explain or model human knowledge about such domains remains problematic. The claim that logical reasoning abilities suffice was challenged in Chapter 7 of the 1978 book, and more recently in a collection of papers discussing various examples of mathematical reasoning, including this discussion of "Toddler Theorems" http://www.cs.bham.ac.uk/research/projects/cogaff/misc/toddler-theorems.html, and others on this web site: http://www.cs.bham.ac.uk/research/projects/cogaff/misc/AREADME.html.
A slightly revised version was published soon after as Chapter 2 of my (messy) 1978 book The Computer Revolution in Philosophy: Philosophy, science and models of mind (now freely available online here). The revised paper on explaining possibilities was Chapter 2, available here.
To my surprise, several readers whom I thought would share my views told me that they had found that chapter hard to understand, and could not see its relevance to the rest of the book, although I had previously been encouraged by approving comment from a theoretical physicist colleague with a philosophical background, who later went on to receive a Nobel prize for physics. He, and the founding editor of the Radical Philosophy Journal may, for all I know, be the only two people who understood and liked that chapter, apart from some of my students.
In November 2014, I stumbled across a 1981 review of the 1978 book, by Stephen Stich, which also made critical comments about Chapter 2, while approving of much else in the book -- though highly critical (and rightly so) of much of the style of presentation. The text of his review is available here (added 19th Nov 2014, with his permission).
This new document attempts to provide a clearer introduction to the idea of a set of possibilities and the concept of an explanation of how something is possible, based on the idea of a construction kit (e.g. Lego, Meccano, plasticine, paper+scissors, a programming language, and many more) as a generator of a set of possibilities. A first draft was written in November 2014, but it is likely to be clarified and extended later. The main idea is that the physical world provides a very powerful (mostly chemical) construction kit that was "used" by natural selection to produce an enormous variety of organisms on this planet, some of which have produced new sorts of construction kits as toys or as major engineering resources.
We still have much to learn about the powers of that construction kit, the details of how those powers came to be used for life on earth, and what sorts of potential it has that have not yet been realised.
Further discussion of requirements for such a construction kit and its powers can be found in a separate document still under active development: Sloman [DRAFT 2016]
This can be read as a contribution to metaphysics. A closely related document on 'Actual Possibilities' (published in 1996) is freely available online here.
REFERENCES
Construction Kits for Biological Evolution, 2017, in The Incomputable: Journeys Beyond the Turing Barrier, pp. 237--292,
Eds S. Barry Cooper and Mariya I. Soskova, Springer International,
http://www.springer.com/gb/book/9783319436678
The online version is still under development.
(Discussion note.)