When a scientist complains about a philosopher

1.   1.   Philip Anderson (which I think one can say safely that he knows something about how Physics is done http://en.wikipedia.org/wiki/Philip_Warren_Anderson) “screams” against Nancy Cartwright in

Anderson, P. W. (2001). Science: A ‘dappled world’or a ‘seamless web’?.Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 32(3), 487-494.

To me the “dappled world” Anderson has Cartwright believe in is very much like the world of sciences against the world of Science that Latour speaks about.

Indeed Anderson takes a strong position:

He claims that Cartwright holds  “a very common misconception…. [that] the primary goal of science is prediction, prediction in the sense of being able (or at least wishing) to exactly calculate the outcome of some determinate set of initial conditions.

Against this Anderson states that the primary goal of science is:

“to achieve an accurate, rational, objective, and unified view of external reality.”

In the spirit of negotiations let us see in the article what he really cares about.

Let us concentrate on what he says about BCS theory (http://en.wikipedia.org/wiki/BCS_theory) since this is the example he chooses.

I think that what he especially cares about is the generative and expandable nature of scientific models, both within the domain that the models first appear and as connectors between different domains. Anderson speaks about sciences being strongly interconnected, being a web.

Let us see what he says about BCS:

a)      First within solid state physics: “between the original BCS paper, which indeed proposed a ‘model’, and the approximate end of the verification and validation process which made the model into what physicists properly call the‘theory’ of phonon-mediated (ordinary, or BCS) superconductivity.” “in 1957 BCS may have been describable as a ceteris paribus model, with no adequate account of a wide range of phenomena, or of its own limitations. It was made, by 1965, into an enormously flexible instrument with a high degree of a priori predictive power, and even more explanatory power.” “The theory is no longer confined to its ‘cocoon’ but deals well with all kinds of messy dirt effects.”  

b)      Then outside solid state, in elementary particles, in nuclear physics etc “Far from being an isolated ‘model’ applying only in its shielded cocoon …it was an explosive, unifying, cocoon-breaking event.”

Now  negotiation can work I think along the following lines. One can perceive the interconnectedness of sciences as expressing  the gradual revealing of a seamless common picture that underlies everything. But this is a very high demand and we do not have a binary choice between solipsistic “sciences” with small s and common Science, with big S.

However if one wants to extract the values that the moderns care for, one cannot ignore what is said here by Anderson.  My opinion is (following the Latourean approach) that one should respect the sense of indignation that the practitioner feels.

 I think that he line of [REF] need to be supplemented by the concern for bundles of [REF] trajectories.  “dealing with dirty effects” and being an instrument of exploration and prediction in a broader sense , is a property of bundles of [REF] trajectories and not a property just of each one.

Even when one speaks about passages from representation to representation ([REF] trajectories) , each “mean of representation” in the ladder from the material and the instrument to the scientific paper, or from the prediction of the theorist to the gathered data and then towards their interpretation , is stabilized, has a recognized form and use thanks to some homomorphisms that must connect the trajectories themselves.

Somehow each mean of representation had been proven as a “successful mean of representation”.

What also comes in my mind is the following comment from the book Axiomatic Method and Category Theory (http://arxiv.org/pdf/1210.1478v1.pdf) of Andrei Rodin (pg 287)

 “the proponents of Fregean logical objectivity and proponents of more liberal structuralist objectivity agree that the key to objectivity is invariance. Then the controversy reduces to questions about different kinds of invariance: some people defend the invariance of Form, some other defend the invariance of Substance, etc..”

vs

“thinking about objectivity in terms of functoriality (i.e., co- and contravariance) rather than invariance.” “This approach sublates the debate about invariance and refuses the Platonic viewpoint (taken by Nozick as a matter of course) according to which the most objective things are those, which are the most stable and the lest capable for change. The functorial objectivity amounts to the coherence of changes rather than to the lack of change.”

These comments sound to me close to the spirit of MOE and AIME in general. However, especially in understanding science I wander if the transport of “immutable mobiles” along [REF] trajectories is very close to an emphasis on “invariants” or whether scientific practice is closer to that other approach suggested by Rodin (I continue this line of thought later on)

I want also to add here that Anderson is also concerned with (what I think is) the [POL] and [ORG] dimension of sciences. He says:

“To me, the epistemology of modern science seems to be basically Bayesian induction with a very great emphasis on its Ockham’s razor consequences, rather than old-fashioned deductive logic.”

Bayesian logic (http://en.wikipedia.org/wiki/Bayesian_inference) is , if I understand well, a calculating device, especially designed to deal with the cognitive shortcomings of us humans when we have to deal with various options that have different “weight”. However it is just an aid. Inside Baysean calculus there are points where there need to be put “probability estimates” coming through experts, or rather through a college of experts.

So perhaps the Bayesian logic of which Anderson speaks is a calculating support for the functioning of the [POL] cycle in scientific communities gathered around their own issues.

2.   2.     Now I want to draw a similarity between what is described in the Modes of Existence Book as “a bifurcatory view of reality” and the book’s position against this view on the one hand and what seems to me (who am an amateur, I confess) to be a similar reaction towards a bifurcatory view in Mathematical Logic. The reason why I turn to math is because as a Physicist I find very difficult how one can deal with Science or the sciences  without treating Mathematics very seriously.

I use as my guide the book of Andrei Rodin Axiomatic Method and Category Theory (http://arxiv.org/pdf/1210.1478v1.pdf). I rough lines this is a picture I get:

In mathematics, as perceived by the Formal Axiomatic Method (as worked out especially by Hilbert) there is a distinction between “real” mathematical constructions (which are purely symbolic) and “ideal” mathematical constructions which describe any interpretations of the symbolic constructions. The symbolic constructions  are manipulated following a Universal logic and in this sense they produce a huge warehouse of mathematical constructions. So the symbolic formulas are the real, distilled mathematical reality, while the specific applications are in a sense ways to help our thinking in concrete ways.

However

a)      “ in practice “mathematicians in their actual practice generally do not tend to reduce mathematical constructions to symbolic constructions. they develop a mathematical notation called by some philosophers (but rarely by mathematicians themselves) informal or semi-formal. This latter sort of notation just like the traditional geometrical notation helps one to describe mathematical constructions in terms of certain symbolic and diagrammatic constructions and does not, generally, require making difference between “real” and “ideal” mathematical objects”

b)      Rodin claims that mathematicians like Lawvere and Voevodsky develop approaches to mathematical logic (categorical logic, in the case of the former) in which logic is locally developed at the same time that local mathematical theory is developed. The practice of mathematics is not distinguished between a Universal logic (running on the mind of the mathematician) and the specific mathematical concepts “in front of him” but somehow (I am not a mathematician myself)  logic and mathematical content coexist and codevelop locally and indeed one may chose to interpret what one writes either leaning more heavily towards logic or leaning more heavily towards the local mathematics themselves (this is how I understood the general argument). I get the same feeling in this article of Rodin: “Unlike Hilbert, Lawvere does not use logic as a ready-made tool (recall Hilbert’s “unalterable laws of logic”) for sorting out certain informal geometrical concepts. Instead Lawvere’s analysis reveals a specific logical framework within the given geometrical concept. This internal logical framework remained wholly unnoticed by Grothendieck and his collaborators when they first developed the topos concept “(http://arxiv.org/pdf/1408.3591v3.pdf) Moreover Rodin goes on towards the end of the book to delineate the characteristics of such a new Axiomatic Method for mathematics.

Rodin : “The main philosophical dilemma that I consider is, roughly, this: either (i) logic is fundamental in the sense that it gives us an independent access to an ideal space of logical possibilities where the actual world exists side-by-side with plenty of other possible worlds, which can be explored only mathematically, or as Cassirer insists in the above epigraph, (ii) logic and mathematics must stick to the actual world as we know it through empirical sciences, and by all means must avoid producing possible “metaphysical worlds of thought” even if these appear more logically coherent and more mathematical beautiful than our actual world. With many important reservations that this rough formulation requires I shalldefend the latter view.”

“In my suggested approach logic is designed along with the rest of conceptual construction rather than used as a ready-made foundation for making further mathematical constructions”

There are other  points also that make this mathematical effort to look like a brethren of the MOE book.  For example, a comment by Lawevere himself:

(Lawvere in Rodin page 103)

“In my own education I was fortunate to have two teachers who used the term “foundations” in a common-sense way (rather than in the speculative way of the Bolzano-Frege-Peano-Russell tradition). [..] The orientation of these works seemed to be“concentrate the essence of practice and in turn use the result to guide practice”. I propose to apply the tool of categorical logic to further develop that inspiration.

Foundations is derived from applications by unification and concentration, in otherwords, by the axiomatic method. Applications are guided by foundations which have been learned through education. ( [158], p. 213, italic is author’s)”

Then Rodin’s  comments about how the Formal Axiomatic system is unproductive in the practical sense:

“As far as we want to continue to develop the Galilean science (and the technology connected this type of science) our mathematics must provide for it forms of possible empirical interaction rather than just forms of propositions. In other words it must provide forms appropriate for doing   various things in the world but not only forms for talking about this world and showing how the world looks like in a mathematical representation. Since formal axiomatic theories are not appropriate for this job we need to learn how to build mathematical theories differently.”

“Scientists make up mathematical models of their experimental systems, manipulate both with the models(theoretically) and with the experimental systems (in real experiments) and see whether the manipulations of the two sorts work coherently. This is, of course, an oversimplified picture of the scientific experiment (for more details see [57]) but it is sufficient for seeing that the possibility to establish a correlation between mathematical manipulations, on the one hand, and experimental manipulations, on the other hand, remains essential in today’s mathematically-laden experimental science.”

“In order to design an experiment one needs a mathematical model (representation) of a given physical environment itself but not of formal propositions interpretable in terms of this environment; mathematical manipulations (i.e. some further constructions) with a model of the former sort may serve as a guide for real experimental manipulations within the given environment, mathematical manipulations with amodel of the latter sort cannot be directly used for this purpose”

If I get it right what he says is that upon working in a domain there gradually is built a local logic interconnected to local content and this “logic” is not disconnected in a high above level but it is interwoven with the practicalities of the specific situation

My feeling is that there is here a strong resonance between these two different programs

A.      The mathematical program might offer to the MOE or AIME project   the mathematicians' immense experience with varieties of construction

B.      MOE or AIME may offer to the mathematical project a very sophisticated approach to subjectivity that helps the working logicist or philosopher of mathematics to get more blood and bones on their work through their own progress in self understanding 

P.S. Rodin's comments on Lawvere's understanding of logic seem very relevant to what, in my opinion, anderson really cares about
pg 123
“While Tarski thinks about logic in a traditional vein as an invariant structure over a given universe of discourse, Lawvere’s categorical logic is a device that allows one to translate a proposition meaningful in a given universe Y into another proposition meaningful in another given universe X taking into account the relationship between the two universes expressed by morphism f : X → Y”

pg 124
 “Logic is understood here no longer as a system of universal forms of thought, nwhich are not sensitive to differences between various domains of its application, but rather as a universal translational protocol, which allows one to navigate between different domains.”

pg120
“Lawvere’s philosophical understanding of logic as a conceptual tool (calculus ratiocinator) rather than the characteristica universalis, i.e., the “universal medium” ([113], p. xi).”