The term “boundary” is rarely defined by philosophers who may call upon this term outside of mathematical contexts. Philosophers of science interested in specifying their domain of discourse take for granted that the concept of "boundary" makes sense, for example, when they rely upon boundary in arguments about a demarcation between science and other pursuits. And, pragmatists' approaches to the science/non-science distinction have been no exception. A close examination of how boundary concepts are involved in pragmatic instrumentalists' argument structures shows that the neglected concept of boundary can shed light on important foundational issues in the philosophy of science.


A Pragmatic strategy to defuse realist / anti-realist debate.


The following ideas are sometimes present in pragmatists' argument as assumptions, principles, goals or implications:

·        If there is to be progress in the philosophy of science, it is important that there be an area of common agreement neutral to distracting disagreements between realist and anti-realists.

·        It is, sometimes, useful to direct philosophical investigations according to an assumption of identity between an ideal of rationality and science at the limit.

The first of these ideas can be regarded as endorsing a kind of literary style or perhaps a negotiation strategy.   The second bulleted idea is about the merit in a particular way of implementing the first bulleted idea.  The various higher level disagreements are set aside to explore and concentrate on the utility of a historically interesting claim of identity between science and rationality.


Good pragmatists are careful not to claim too much.  One can explore the implications of identifying rationality with science without needing to commit either to the identity or taking sides in the realist anti realist debate.  For our purposes, what is important about the relationship of these two bulleted ideas is the degree to which application of the second may hinder or advance confidence in the first.


The strategic identification of rationality and science often ruffles a few feathers, particularly when it comes to an agreement on just what it is that is the same.  There is a suspicion voiced by some pragmatists, shared by historicists of science and sociologists of science, that the identification is not just false but even counter productive. The pragmatist may assert that the question of productivity should have some priority. For the pragmatist, there may be merit in following an argument with foreseeable impact even if the question of which premises are true has not yet been settled. She rejects the notion of foundational truths. She may site in defense the virtue, familiar to logicians, that unacceptable consequences down the line will weigh in convictions about the truth of premises that have been provisionally adopted along the way.   


 My interest, however, is not focused upon a particular outcome of efforts toward identifying science. Nor, do I have a positive way to identify rationality with science. Instead, I want to look at a particular kind of strategy used by pragmatists in the defense of the rationality of science. My purpose is to expose implications of shifting boundary concepts found in what I'll call the comparative move. This move in the pragmatist’ strategy draws upon insights from post positivist semantics and probability theory.  Whatever else its virtues, the preservation of a neutral zone between realism and anti-realism is valuable to the pragmatist to the degree that it coheres with the comparative move.  


The Comparative Move.


The comparative move requires two strategic prongs. The first prong seeks to bypass ontological puzzles imbedded in allegiance to Aristotelian categorization that could leave one committed to a particular side in the realist/anti-realist debate. The second prong is to provide some fulcrum with which to weigh competing ideas.


The comparative defense strategy for preserving a no foul zone path to the rationality of science begins by treating classification in non-Aristotelian terms.  While rejecting necessary and sufficient conditions of class inclusion, the pragmatist naturalizer suggests that we can get near to the same results using other criteria.[i] The pragmatist naturalizer relies on empirical evidential support for conjectures about cognitive structures thought to cause category specification rather than accepting that categories are simply imposed upon us by the nature of the world.  This contrasts sharply with the passive human activity for category specification suggested by Aristotle.   One considers, for example, epistemic, neuro-biological, evolutionary, or other constraints on human processes of class inclusion. This often results in treating the candidates for inclusion in science as having more or less a core and a fuzzy penumbra. We are led to believe that things are not so difficult in practice. As long as we can come to agreement on central cases, we'll carry on confident and rational discussion about what to count as science without much worry about the rest.  If we do run into a difficulty, we treat it as an exceptional case or anomaly to set aside and work out later.


The second important prong of the comparative defense strategy is to set a metric for determining what to count as science probabilistically. The appropriate pragmatic philosopher’s method for sorting out what's scientific is to go about things comparatively it's suggested.  On this basis, some pragmatists interested in a naturalist approach to sciences have defended the rationality of science against the many criticisms launched by historicists and sociologists of science. Exemplary is Larry Laudan's instrumental naturalism.  According to Laudan, identification of science is a fallible and comparative affair at the heart of which is a universal and rational metric called R1.


R1, simply put is a recommendation:   when choosing between two sets of methodological proposals, choose the set that has led to greater successful goal achievement, taking care that goals of past investigators do not differ from current goals. Putting the question of the rationality of scientists methodologies on a comparative and epistemic footing is supposed to be silent on questions about the ontology of the objects investigated by science and thus neutral to the realist anti realist debate.


          Although, diehards of the strong programme and old fashioned positivist oriented realists may still resist the modest claim for a middle ground between social pressures and a rational ideal, for the most part, this pragmatic naturalism has lately provided an uneasy truce between opposing positions. The anti-realist notices, approvingly that the comparative metric is fully epistemic and can be wielded without reference to Aristotelian categorization. They can adopt the strategy if only to use it in their campaign to show the bankruptcy of realist notions of science. The realist sees that the strategy has met criticisms of positivist approaches to the rationality of science without full scale surrender to the anti-realists. This strategy, thus, seems to provide a no foul zone for productive dialog.    But, even provided an agreement to set aside ontological worries to concentrate on epistemic issues, there is still left a lot of disagreement on the middle ground.




What merit is there in rehabilitating rationality?


          The perseverance of disagreement in the no foul zone, despite an ontological demurer, may lead some to wonder if there is anything left to be gained in continuing the investigation.  While others feel the interesting problems of rationality have all already been solved.  I will try to provide some motivation for continued effort to explore the rationality of science and suggest contexts within which the standard answers provided by instrumental naturalist approaches to science do not provide an easy answer.  Along the way I will move through some philosophical territory not usually associated with characterizations of science, but important to understanding rationality. One reason we may have difficulty stitching together the tattered bits or our notion of rationality is that we continue to rely upon a vestigial remnant of positivism found in the concept of boundary.


An internal tension of the comparative move is exposed by the link between positivism and boundary


When the twentieth century pragmatist W. V. O. Quine famously exposed the positivist dogma of analysity, he pointed out that there is nothing to be gained in reliance on synonymity, since synonymy can be understood only by a prior appeal to analyticity. What has not been noticed is that where synonymity is the conceptual marker of likeness, boundary is the conceptual marker of difference. So, the concept of boundary shares the same challenges. [ii]  And, finding a rational metric for boundaries is what the comparative move is all about.


This insight helps us to focus on and question the utility of the comparative move.  The motive for the first prong is now seen to be at odd with the second prong. Where formerly it seemed that comparing proposals for inclusion in science had no need of Aristotelian classification, we now see a covert link to a pre-Quinean notion of analysity that actually endorses an ontologically committed view of Necessity.


Science, Rationality, and the Knowledge Argument.


          Our evolving concept of rationality is intimately bound to our understanding of knowledge.  And, here is where we will find the most interesting involvement in boundary concepts, in the vicinity of the so called "knowledge argument".


          Frank Jackson provides one of the most discussed formulations of the knowledge argument in the famous case of Mary, a future scientist raised and tutored in a monochrome environment consisting of shades of gray. It is maintained that her scientific grasp of nature is absolutely complete and accurate including all that science could possibly contribute to knowledge of the colorful world outside of her environment.  Upon the fateful day that Mary ventures forth into that colored world we are informed by Jackson that she gains a new and significant bit of knowledge that could not be encompassed by the future complete science. Now, since by hypothesis Mary already knew all that there is to know about the material world and we intuitively feel that her experience of color constitutes a new and different (implicitly non physical) knowledge then, we are owed an explanation of how this is possible within a materialist theory.


          One supposed moral of this though experiment is that there is more to the world, e.g., epiphenomenal or non-physical qualia, than can be explained by materialism. Or, more boldly, materialism is false.


          Many commentators have argued for or against this intuition. I am primarily interested here with arguments that share confidence in the comparative schema discussed above in which they imbed their arguments. This comparative schema can be found in the philosophy of David Lewis, Larry Laudan and others. We will see how confidence in this comparative approach together with a robust pragmatism results in some puzzling conclusions about Mary's knowledge.


          Lewis argues that the story of Mary is flawed in a number of respects.  For example, our ability to imagine a complete and unfailing vision of possible future physics can mislead us into a hasty conclusion. Further, the supposed new knowledge gained by Mary is in fact accountable without reference to a non-material realm. Abilities to remember, imagine, and recognize constitute knowing what it is like to see colors in Lewis's view. Here too, Lewis calls upon our intuitions about counterfactuals. On the assumption that Mary's knowledge is of contingent facts, there is a possibility that acquiring the knowledge of what it's like to have colored vision could have arisen otherwise than is implied by the thought experiment.  “One might acquire abilities by some possible future neurophysiology or by magic,”  according to Lewis, "Maybe Mary knows enough to triangulate each color experience exactly in a network of resemblances, or in many networks of resemblance in different respects, while never knowing what any node of any network is like. (1990 p. 502)


Here is a regimented form of the knowledge argument given by Churchland interpreting a version attributed to Jackson.

For all x, if Hx & Px then Kmx

There is an x such that Hx & ~Kmx , i.e., what it is like to see red.


There is an x such that Hx & ~Px


Here m = Mary; Kyx = y knows about x; Hx = x is about persons; Px = x is about something physical in character, and x ranges over knowables.


Churchland claims that on this formulation there is a fatal ambiguity kmx in its two appearances. If one replaces K with a distinct letter, acknowledging the difference between informational or truth valuable knowledge and know-how, we see that the argument form does not lead to the anti materialist conclusion. Churchland, then, moves the argument beyond this simple division by providing a neuro-computational analysis of the situation.  I am inclined to agree with Churchland’s claims as well as the program of analysis he suggests. However, I am doubtful that such a program will not run afoul of the comparative move and no foul zone between realism and anti-realism. 


What has all this to do with "boundary"?


Churchland and others appeal to neuro-computational models in the explication of their position with regard to Mary. Part of the supposed appeal of such models is that they are within the scope of naturalism because modeling is an accepted scientific methodology. 


But can there be any hope of a naturalized scientific solution to the Knowledge argument? Those who would pin their hopes to such a solution are likely to appeal to the two pragmatic ideas with which this essay began either in the construction of their arguments or in efforts to compare the value of their position to other explanations on offer. Such meta-methodological comparison is one of the roles that is supposed to be filled by Laudan’s R1.


What if there is not a mere ambiguity between these but rather incommensurability?  Provided some x and some y, incommensurability is the lack of a co-measure i.e., some independent means by which anyone can come to see that x and y are the same.  Several new problems arise depending upon how we interpret incommensurability. Semantic incommensurability, Methodological incommensurability, and multi-domain incommensurability are three relevant types of incommensurability. (See Sankey and Chang for a survey of incommensurability).


Three versions of incommensurability


Incommensurability is not easily defined. Its root in the philosophy of science, borrowed from its use in mathematics, is found in Feyerabend (1962) and Kuhn (1962). Most simply, Incommensurability is captured by the slogan "having no common measure." Nearly fifty years of explication and modification of the common base found in this slogan have provided a rich tapestry of thought that is sometimes far removed from its origin. Howard Sankey (1994), as a first approach to his interpretation of semantic Incommensurability says,

to say that a pair of theories is incommensurable is to say that the theories do not share a common language or that the terms they employ do not have common meaning. . . . The languages of competing or successive theories in the same domain may differ with respect to the meaning, and even the reference, of their terms (p. 1).

 The result will be failure of intertranslatablity. [iii]   Such a result has been found to be unacceptable by commentators because it seems to make rational comparison of incommensurable theories impossible.  In part to meet such objections, Kuhn refined his semantic conception of incommensurability by localizing the phenomenon to taxonomic differences between competing vocabularies,


To the extent that I'm concerned with language and with meanings at all . . . it is with the meanings of a restricted class of terms. Roughly speaking, they are taxonomic terms, a widespread category that includes natural kinds, artificial kinds, social kinds, and probably others. . . . If different speech communities have taxonomies that differ in some local area, then members of one of them can (and occasionally will) make statements that, though fully meaningful within that speech community, cannot in principle be articulated by members of the other (1991 p. 315).

On this version of semantic incommensurability, a basis for dialogue and comparison between competing theories is still possible because there are possibilities of translation in unaffected areas of the respective languages. [iv]


          By contrast methodological incommensurability focuses upon the actions through which scientist acquire and maintain confidence in their theories.  The methodological incommensurability thesis is the thesis that alternative scientific theories may be incommensurable due to absence of common standards of theory appraisal.  In The Structure of Scientific Revolutions, Kuhn (1970) claimed that new theory acceptance is conditioned on preexisting methodological norms of evaluation, “There is no standard higher than the assent of the relevant community” (p.94).  Standards of theory appraisal depend on and vary with the currently dominant scientific paradigm.  Just in case methods of appraisal must vary between competing theories within a scientific domain such theories will have no common measure and thus be incommensurable.  The rationality of scientific theory acceptance, it seems, depends upon shared objective standards of theory appraisal. But, the goals and desires that motivate methods of appraisal may vary without restriction.  


If we consider incommensurability as a subject of scientific study, it’s easy to see that to solve for semantic incommensurability one provides an appraisal method to study the semantic phenomenon.  Churchland and others have opted for methods like logical analysis and neuro-computational modeling using parallel distributive processing.   But, we immediately see that the rationality of the undertaking is compromised by the problem of methodological incommensurability. The pragmatic instrumental naturalist would like to be able to point to comparative strategies like Laudan’s R1 to answer the threatened meta-methodological incommensurability.


Multi-domain incommensurability is a kind of incommensurability that is threatened when the terms and concepts used to solve semantic and methodological incommensurability are conflated at the meta-methodological level. And here is where we can find a specific example in the case of multi level uses of the term boundary.   If such incommensurability exists, it would not be responsive to comparative solutions like R1.


 What  are the consequences for the knowledge argument?


What are the consequences for the knowledge argument that differ from other versions of incommensurability?  On the multi-domain interpretation of incommensurability, it turns out that Mary knows less after seeing color than before!  By hypothesis Mary knows all there is to know about color.  Incommensurability would show that after certain experiences there would be less to know, in that what was formerly knowable included knowledge about color and afterwards the justification she formerly had for certain truths systematically failed even if the number of beliefs increased. What justifications can be offered and what shows that something has changed that rules out the prior justifications? If we had limited our investigation of incommensurability to standard versions, we would not see that the solutions to the standard versions were solutions only in virtue of looking beyond the scope of discourse allowed. But, multi-domain incommensurability has no outside place from which to place a fulcrum.


The case against multi-domain incommensurability.


The reticulating model says that there need be no outside place from which t o place a fulcrum. We simply need to make an assessment of where we stand, look about for a competing set of ideas, and hold on to the set that’s best supported.  We, can see that the reticulating model of the comparative naturalist approach is embarrassed by the fact that it cannot be applied to itself and gives no guidance in the important cases where all things are equally supported. This was the case for the question of boundary. It is the case for the case of Harry as we will se below, and it is the case for Mary.


On the pragmatic naturalist model we are not forced to accept incommensurability though.  It may simply be a matter of waiting for more data to interpret and so we wait.  Afterall, a simple solution to such problems is always on the horizon.


Even if multi-domain incommensurability fails to obtain, the residual ambiguity will not be simply resolved.


Ok. So, if there isn't incommensurability, then perhaps the ambiguity ought not be characterized as simple, because, it will require a new way of looking at boundary to resolve it: this will cause the appearance of a pragmatic truce forged between realism and anti realism to dissolve.


Let's try to do our best to stay within the constraints of our pragmatic no foul zone and instrumental naturalism to look at a similar case to Mary, the case of Harry. Harry learns the identity of fish by smell, chicken by sight.



==== dynamic connectionist representation ====*

       Is there something about Harry? 


We hypothesize that actions of the body, e.g. production of cortisol,                       adrenalin, etc., associated with affect, influence the activation of neurons and all this "AFFECTIVE influence".  We further hypothesize, contingently, that if there is an independent world, that world will influence the activation of neurons.                                     If there is no independent world, a story needs to be told about what source provides this degree of input.  Perhaps it is the influence of god or angels. We’ll call this "WORLD influence".


The model is silent on the ontological status of perceptions materialists may interpret in a topic neutral way.  Dualist and epiphenomenalists may see qualia here.  In any case, this collection of nodes is excited when instances of their corresponding object types are present,"available chicken perception-interface” and "available fish perception-interface"


Harry first learns about chicken only by smell and about fish only by sight.  

Consequently bundles of neurons are responsible for optical processing  are activated in response to each instance of an experience or thought associated with the relevant corresponding object type learned by way of sight,  "optical processing; learn fish by sight"


Harry first learns about chicken only by smell.  Consequently bundles of neurons responsible for aural processing are activated in response to each instance of an experience or thought associated with the relevant corresponding object type learned by way of smell, "arual processing; learn chicken by smell "


Linguistic, logical, and other conceptual representations are created and activated in other areas of the brain as a consequence of repeated experiences                                                   " re:'chicken' concept ", ” re:'fish' concept "


The Food class concept represents a quite complex neural bundle.  Not only does this bundle associate individual instances of the type 'food' but is an abstract sortal for hierarchical processing, "Food class concept"


The concepts fish and chicken compete as do the methods associated with each of these concepts.                                     



FISH SEEKING BEHAVIOR .... AND VICE VERSA. But, this does not mean that absence of one is evidence for the other.


The network also includes special nodes representing motivation for action "Moved toward ->”. Harry wants to do whatever will provide food                       


Harry comes toward the bar-b and begins experiencing. This excites his aural processing system neurons which connect with food concepts. He thinks, 'hmmmm food.' But because he has not learned all foods in the same way, only food concepts he had learned by smell get activated as a consequence of this initial experience.(However, Food concepts and categories may have already been established in connection with language learning via dthat.)  


Explanations are accounted for via links between nodes.                                                      


dthat is the neurology of ostension. dthat has two distinct roles, name-dthat and get-dthat.  Name-that is intimately connected to observation nodes.  get-that is intimately connected to methods nodes.  We use dthat to capture neuronal activations associated with tagging observations without attributing any properties to the observation except that the subject observation is self-identical 

and not another thing, "dthat ".


Name-dthat is accomplished via links between dthat, some observation, and concept nodes active in association with further retrieval of the name. The above captures the ambiguity between fish, chicken, and food.  


Get-that, is accomplished via links between dthat, some motor activating neurons such as move-towards, and observations.   


We will entertain three theories, food, fish, and chicken.       


Collapsed into the following neural bundles are motor neurons as well as complex strategies and procedural knowledge, "go method for chicken T1”, "go method for fish T2", "common go method for food T3".


If methods for investigating/consuming an observation compete greatly with other methods in the network, this will impact acceptance or rejection of nodes elsewhere in the network.                       


Here we mark neuronal bundles that may together represent theories that cohere together or compete. So, we mark concept nodes and methods nodes of the respective theories appropriately.           


Evidence nodes may contribute to the acceptance of one or more theories and so are not marked at belonging to a particular theory,"T1 chicken", "T2 fish","T1 chicken", "T2 fish", "T3 food"



Compare this to Mary.


On a neurocomputational analysis, Harry’s situation is not very different to Mary’s.  There are two time spans and two contexts of purported learning experiences. But, the clarity with which we are able to see the links between mental processes of individuation, names for observations, and the index of referents seems a bit clearer in the case of Harry. 


Compare the Churchland formalism of the situation for disambiguating Mary against a formalism of Harry's situation. Is this all decidable with out committing in the realism anti-realism debate? What does the ARU model tell us about this?


What part does a naive attitude towards boundary play in making answers easy answers? 


The unusual case of ‘boundary’ shows that when we naively look at the acceptance or rejection of a certain set of behaviors we may fail to see that our judgment of approval or disapproval of the behaviors can influence our identification and cognitive classification of the behaviors. This in turn may impact the syntactic as well as semantic force of the term. For example, we can be deluded into thinking that our judgment is simply a scientific enterprise followed by a moral judgment, when in fact the judgment is arrived at holistically in terms of coherence and meta-coherence that includes factors like emotion, utility, and propensities to act. 


Counting knowledge


The case of Mary gets its logic going by supposing that there is an easy way to count knowledge. In one column we stack the ‘bits’ of physical knowledge. In the other column we need to stack some other ‘bit’ and label the column, ‘other knowledge’.  As long as it looks like there is a possibility to fill the second column with something it won’t matter how we did the individuation and counting of what we’ve put in the physical knowledge column. No matter how we individuate, it seems, it will make sense to talk of there being more knowledge.  Our next step, on this picture, would be to ask if the ‘bit’ we’re considering for the second column is a justified, true, belief (+ ).  


But, this is an entirely misleading picture. Knowledge does not lay waiting in a stack of bits.  Suppose, as is supported by empirical evidence from neuro-psychology and is modeled in !ARU, that knowledge is matter of a continual processes of attention, and  interaction with the environment, involving both retrieval, and construction.  Surely, though, this alternative picture does not require the abandonment of a minimal ability to gauge some new information as either adding to physical knowledge or not? 


Looking at !ARU, we will make a first approach to this task by calling the sum of knowledge the number of stable positively activated neural bundles.  It is now easy to see how it will be possible for Mary to Know less after her introduction to the colored world. If it turns out that the addition of multiple inputs via the color receptor neurons suppresses neuronal bundles that were activated before the introduction of color experiences it should suggest that Mary knows less.











[i]    It is not necessary to hold a naturalist position to be a pragmatist. But, this is a popular position for contemporary pragmatism. So, it is worthwhile to see where it leads.

[ii]   The grammatical ambiguity which proved to be a fatal in the problem of synonymity is mirrored in comparative strategies of instrumental naturalist attempts to look for science non-science boundary for example.  When a single term such as “boundary” represents a theoretic object in one use and a methodological use as well, it can be destructively ambiguous.  This will be particularly acute if the ambiguity is between an entity and a property use. The model for a Grammatik basis of ambiguity is that a term may have two uses, either a singular term naming an entity or instead denoting a property. This kind of possibility arises for a whole class of terms. Examples include coherence, compatibility and boundary. This point deserves a full argument which space precludes providing here.


[iii]   Sankey maintains that on his interpretation "Incommensurability" is a non-denoting expression. That is while semantic incommensurability is a conceptually sound concept it is just that aren’t any examples (Personal conversation).


[iv]   In Dubbing and Redubbing Kuhn clarifies and revises his views in terms of their relation to the causal theory of semantics that his critics point to for solutions to puzzles of Incommensurability. He proposes a change to the standard Putnam/Kripke versions of causal historical semantics. In the standard versions, names rigidly designate the entity named through a process of naming that takes place at an original baptism. Normally, in standard versions of causal semantics, prototypical samples of the kind named are ostensively associated with the name. Once accomplished such a name rigidly designates that entity even in counter factual situations. The name refers to the very same entity ostended upon the baptism in any situation, in any possible world in which the entity exists. But on Kuhn's semantic theory rigid designation is for a limited time only. That time is limited by stipulation of a new taxonomic category together with introduction and acceptance of a new taxonomic system.