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age that we theoretically identify as being that of a paramecium this image is publicly accessible as is made evident by the possibility of hooking the microscope up to an arrangement that projects the image on a screen for all to see that image is an observable phenomenon on his scheme therefore it is this image to which biological theory is accountable not as any biologist would insist the appearance and behavior of observed paramecia themselves for an alternative view consider an example from modern astronomy to which van fraassen indirectly refers 168 during the 1990s nasa published images produced by the compton gamma ray observatory one of four instruments aboard this satellite based observatory was tuned to detect gamma rays of roughly 51 mev and pointed at the center of the milky way earlier observations had suggested that there might be particularly interesting gamma ray sources in this energy range and indeed a plume of such sources was recorded protruding at a right angle from one side of the center of the galaxy since 51 mev is the energy of each of two gamma rays produced by the annihilation of an electron positron pair it was concluded that a plume of positrons is being emitted asymmetrically from the center of the milky way no theoretical explanation for the existence of such a source of positrons was then known van fraassen also characterizes phenomena as what we use theories to explain 97 101 in ordinary scientific discourse astronomers would say that in detecting the plume of positrons being ejected from the center of the milky way they had discovered a new phenomenon for which they had no current theoretical explanation they might also say that this phenomenon first appeared in the images produced by the compton observatory but the primary object of their theoretical investigations is to explain the plume of positrons not merely the phenomenon appearing on their computer monitors describing the not humanly observable plume of positrons as a phenomenon to be explained is well justified by scientific practice the existence of electron positron annihilation is historically a theoretically and experimentally well established physical phenomenon as van fraassen would say it is part of historically stable physics 122 that such annihilation produces a pair of 51 mev gamma rays is also accepted physical knowledge so the inference that what is ultimately producing the appearance on their computer screens is gamma rays from electron positron annihilation is well justified how the positrons are being produced is a question to be investigated and any proposed theory of stellar formation in the center of galaxies etc will have to provide an explanation of this process of course there must also be an account of how the images are produced but that is more a matter of engineering and computer science than theoretical physics it requires models of the experiment in addition to models of the fundamental physical processes in van fraassen s picture by contrast explaining the images which for him are the observable phenomena is the goal of theory this is not a mere verbal dispute over the use of the word phenomenon the above example suggests that it is more representative of contemporary scientific practice to think of science as indeed discovering new phenomena but describing those phenomena in an ever expanding theoretical vocabulary rather than confining descriptions to the realm of the truly humanly observable even here however van fraassen does have a reply though in the context of ordinary rather than scientific language i n any ordinary way of speaking in is not correct to say that we have the experience of seeing a paramecium image in ordinary language the correct report is that we have the experience of seeing a paramecium as long as ordinary discourse is not filtered through some theory it does not imply that those are objects 110 but scientific discourse one would think is rightly filtered through some theory so the implication that those are objects should be legitimate van fraassen s insistence that science is responsible only to what is humanly observable has been the most criticized aspect of his philosophy of science since the scientific image his continuing commitment to empiricism comes out clearly when he writes if appearances are what appear to us then by definition we never do see beyond the appearances this insight clear enough in locke and berkeley could be the slogan for our entire discussion 99 and remember appearances for van fraassen are appearances of phenomena locke and berkeley of course were sensationalists for them appearances were of internal mental entities van fraassen will have no truck with such things his appearances are public nevertheless they function very much like sense data sense data are ontologically homogeneous they have no depth so they provide a stable epistemological base for all empirical claims the realm of humanly observable things is not so homogeneous including as it does everything from a grain of sand to the sun but it is still a relatively stable base ironically computer technology has turned van fraassen s scientific phenomena which now consist mostly of two dimensional computer images into public analogs of sense data at one point he concedes that one might draw a line for example at the outputs of electron microscopes rather than optical microscopes the empiricist point is not lost if the line is drawn in a somewhat different way from the way i draw it the point would be lost only if no such line drawing was to be considered relevant to our understanding of science 110 and this point is generalized in response to the physicist steven weinberg s distinction between the hard and soft parts of scientific theories van fraassen issues the challenge if you are going to distinguish between a hard and a soft part of science in some such way tell us how you draw the line 111 the response of a moderate realist such as myself is that no such line drawing is relevant to our understanding of science my question now is whether van fraassen has a deeper motivation beyond a general commitment to empiricism for drawing a line and for drawing it where he does empiricist structuralism if there is to be a line drawn for van fraassen s phenomena what is on the other side structure structuralism in the philosophy of science is the view that our theoretical knowledge is knowledge of structure only van fraassen presents his empiricist version of structuralism in two theses i science represents the empirical phenomena as embeddable in certain abstract structures theoretical models ii those abstract structures are describable only up to structural isomorphism 238 this represents a major departure from his earlier views assuming a standard reference and truth based semantics his earlier view was that theoretical claims may or may not be true of things referred to but science can remain agnostic so regarding unobservables he was a semantic realist but an epistemological agnostic having abandoned standard semantics for a usage based view of scientific representation he is free to abandon this view as well empiricist structuralism is closer to skepticism than agnosticism it says we cannot theoretically distinguish for example vibrations in a diatomic gas molecule from vibrations in electromagnetic radiation such as visible light structurally both are instances of harmonic motion and that is as far as our theoretical knowledge can go this remains a serious i think fatal objection for scientific realists who would be structuralists but it is no problem for an empiricist structuralist there does remain a major problem for empiricist structuralism which van fraassen recognizes and faces head on as he insists theoretical models are abstract structures and all abstract structures are mathematical structures 238 this emphasis on abstract mathematical structures fits with his endorsement of the mathematization of the world picture which he sees as having culminated in the twentieth century 237 the problem as he himself presents it is this how can an abstract entity such as a mathematical structure represent something that is not abstract something in nature 240 now van fraassen had already dealt at length with a version of this problem earlier in the book under the title the problem of coordination a theory would remain a piece of pure mathematics and not an empirical theory at all if its terms were not linked to measurement procedures but what is this linkage 115 on van fraassen s telling reichenbach set himself the problem of identifying coordinating definitions for length and time without the use of geometric or kinematic terms 119 but asks van fraassen how can such coordinating definitions be meaningfully introduced except in a historical context where there are some prior coordinations already in place i submit that they cannot 121 according to van fraassen we have no problem understanding what is measured from two perspectives from within the historical process in which measurement procedures are created and from above when there is a stable theory that deals with the measured property 122 in general the rules or principles of coordination that can be introduced to define particular sorts of measurement cannot even be formulated except in a context where some forms of measurement are already accepted and in place there is no presuppositionless starting point for coordination 137 the solution to what might be called the empirical representation problem for empiricist structuralism follows similar lines in his own words t he theory to phenomena relation is an embedding of one mathematical structure in another for the data model or more accurately the surface model which represents the appearances is itself a mathematical model 252 but there is nothing in an abstract structure itself that can determine that it is the relevant data model to be matched by the theory 253 nevertheless a particular data model is relevant because it was constructed on the basis of results gathered in a certain way selected by specific criteria of relevance on certain occasions in a practical experimental or observational setting designed for that purpose 253 in other words t he phenomenon what it is like taken by itself does not determine which structures are data models for it that depends on our selective attention to the phenomenon and our decisions in attending to certain aspects to represent them in certain ways and to a certain extent 254 this is indeed as he describes it a sea change in our thinking about structuralism inspired by the move to a usage based understanding of scientific representation 254 my question now is this once we have adopted an agent based account of representation why do we ever need to pass from the physical to the purely mathematical and in particular why do we need to make this transition just at the point where we might go beyond the realm of the truly humanly observable returning to my earlier example why cannot our practices be rich enough that we can meaningfully report appearances on a computer monitor as revealing a plume of positrons being ejected from the center of the milky way to go beyond these rhetorical questions consider a very simple example of van fraassen s invoked for a slightly different purpose a table top the table top he says is metrically isomorphic to a euclidian square 249 but that cannot be no real table has perfectly straight sides or perfect right angle corners since the edges are not perfectly sharp it would require a judgment just where to begin and end a measurement of its width which would likely not be the same in both directions what we should say i think is that the table top is metrically similar to a euclidian square it s area is roughly the square of the average length of a side so we are never dealing with an abstract mathematical object or to put it in old fashioned linguistic terms we never get to an uninterpreted claim about the table it is always the edge of a table not the edge of a euclidian square with which we are concerned the language of science is throughout an interpreted language or is it enter quantum mechanics stage left the quantum mechanics challenge 297 the suggestion that the language of science is thoroughly physically interpreted is a realist suggestion it implies that there is no fundamental divide between what is humanly observable and what is not for contemporary humans positrons are ontologically though not epistemologically on a par with planets this is not metaphysics but a realism in practice remember after all that we are not discussing criteria for god s creation nor for the structure of reality our concern is with completeness criteria for the sciences in practice which evolve within the resources humanly available 297 the completeness criterion in question here is what van fraassen calls the appearance from reality criterion roughly science must explain how appearances are produced in reality 281 noting that this completeness condition has been honored since the scientific revolution he argues that it has now been rejected in scientific practice that is practice which includes quantum mechanics this is one place the argument of the book becomes a bit technical for those who are not philosophers of physics but the import is clear the requirement is that scientific theories explain in theoretical terms how particular appearances are produced for quantum theory it is not just that what is predicted are probability distributions over a range of possible outcomes that in itself is not an obstacle for satisfying a liberalized version of the criterion the question is does this scientific theory specify explicitly or implicitly a process whether deterministic or stochastic by which this appearance is produced 299 the answer is no a theoretical description of any measurement process does not seem to provide a place for the specific outcome in question 300 the criterion cannot be fulfilled so in the end it seems van fraassen s insistence on the centrality of the humanly observable and the purely mathematical nature of theoretical structures stems from his conviction that this is how things are in fundamental physics that is quantum theory there are echoes here of nils bohr s view that the language of experiments involving quantum phenomena is a classical language a language of middle sized objects and indeed van fraassen s own empiricist interpretation of quantum mechanics has a bohrian flavor taking quantum theory as a touchstone for the philosophy of science is not an idiosyncratic position in the first part of the twentieth century hans reichenbach championed the view that the philosophy of science must reflect the major new developments in the physics of that time especially quantum mechanics van fraassen reichenbach s intellectual heir via carl hempel and adolf gr ű nbaum endorses this sentiment saying that our...