There is an interesting passage within the second introduction of The Creative Mind, where Bergson discusses the nature of problems. Problems, we are told, are, in a sense, solved the moment they are stated, and thus it is the stating of problems that is the crucial activity, rather than the solving of them. Bergson seemingly holds that the solution of problems is trivial compared to their stating. Furthermore, of this stating, Bergson tells us it is a matter of ‘inventing’ not discovering. We don’t find problems, through an uncovering, but invent them, through positing.
Here I want to unpack Bergson’s position – taking the above introduction as schematic: firstly, in what sense problems are solved the minute they are stated. Secondly, how the stating of problems is to take priority over solving them. And lastly, what goes into the invention of a problem, if it is not to be a question of discovery, but of creation.
This final point appears, on the surface, to be at odds with the second, concerning priority – if the posing of problems is a creative, rather than investigative (in the sense of ‘uncovering’) enterprise, by what rights does it assert its priority? Another way to put this is if problems are created, then why are they so troublesome? Why create them at all? In fact, as Deleuze notes in Bergsonism, Bergson can be seen as applying the division of the true and the false to problems themselves. However, this division, that appears to secure an objectivity for problems, cannot be made in the style of ‘fabricated, false problems’ and ‘objective, real problems discovered in the heart of things’ – in fact, the opposite seems to hold better, if we want to correlate true-false with created-discovered: false problems are uncovered, true problems created1placeholder. But, let’s start at the beginning.
Solutions are given when the problems are stated
In what sense are problems solved the minute they are posed? This seems to fly in the face of all of our intuitions concerning problems: if their solutions are given with them, then why would we have to suffer problems at all?
“But the truth is that in philosophy and even elsewhere it is a question of finding the problem and consequently of positing it, even more than of solving it. For a speculative problem is solved as soon as it is properly stated. By that I mean that its solution exists then, although it may remain hidden and, so to speak, covered up: the only thing left to do is to uncover it. But stating the problem is not simply uncovering, it is inventing.” (Bergson, p. 57)
What Bergson is getting at here is that once we have put the problem in a certain way, couched in particular concepts that come along with the words we use for stating it, what counts as a solution has been heavily demarcated. Often, only a handful of potential candidates remain for solutions, the only thing left to do is try them on one by one, perhaps engaging various heuristic methods to speed up this process. If we know the key to open the door is one of the keys on the chain, then the problem is solved, all that needs to be done is to try each in turn, focussing on keys that seem roughly the right size first. The solving, then, forms a mere denouement.
Problems provide the conditions for their solutions. They establish the diction, the grammar, and the possible objects of any and all solutions – the solutions play on the terms set for them by the problems they are responses to. We see this most clearly in simple examples. Recall the little puzzle of trying to transport a fox, a chicken, and a bag of grain2placeholder across a river with a boat that can only fit you and one member of your menagerie, leaving the other two behind, where their appetites create all kinds of chaos if left unsupervised. With the problem posed as it is, the solution is either ‘some finite number of defined trips’ or ‘it is impossible’3placeholder. Of course, the actual solution is one of these finite number of defined trips, but all of the possible strings of defined trips share a stifling resemblance and proximity, based on how tightly the problem defines the entities involved, and their possibilities. The ‘solution space’ is so tightly constrained by the problem, that you would be able to recognize even a partial fragment of an attempted solution should you find it scrawled on a piece of paper.
The fox-grain-chicken-boat problem is, like tic-tac-toe, a problem that is perfectly stated to a fault: seemingly arbitrary constraints provided by the terms of the problem press the solution down very thin lines. Any deviation from these lines is not a solution to the problem at all, but a refusal to take part in the hypothetical it sets up. Given this we might feel that problems of this playful and hypothetical variety constrain and determine by their very nature. It’s part of the exercise of such recreational problems that possible solutions are determined tightly in advance, and the vast majority of possible responses ‘outlawed’ by the hypothetical (One cannot just throw the chicken across the river, or leave the fox at one’s brother-in-law’s house). Hence, the immanent solvability could just be a product of the posing of certain kinds of artificial problems.
There is no doubt a sense in which these ‘recreational’ puzzles possess something artificial, cut off from the real problems we face and must suffer, but this is more a question of degree, and not type. That is, the immanence of the solutions to the stating of the problem is not merely a product of artificial constraints placed on a hypothetical, the statement of any problem has something of this hypothetical character, this ‘presumptive’ movement where certain things become fixed, and certain responses ‘outlawed’ by the terms. One difference between problems lies in how amenable the problem is to be restated or affected by these seemingly outlawed responses. The fox-grain-chicken problem is very rigid here, only open to ‘inspiration’ that fits tightly within the mould (once one realizes that it is ‘legal’ to take items back across the river, then the solution emerges quickly). However, inspiration always needs to be chained to the terms of some problem or other, just for the simple fact that it must answer to a problem in order to be an inspiration at all.
The stating of problems matters more than their solutions
Now we can see what Bergson has in mind when he reserves ‘uncovering’ for solutions, and ‘inventing’ for problems. Insofar as problems provide the conditions for their solutions, they organize them. The work of uncovering solutions, then, is the work of extrapolating out what the problem makes possible. In a sense, we dig in the wake left by the formation of the problem. Absent a problem to organize them, solutions are senseless, and not even solutions to anything.
But, if we extend this out to all positive propositions (as Deleuze eventually does in the Logic of Sense), then all propositions depend on some problem or other for their sense. This feature was also noted by Collingwood, who argued every assertion presupposes a question to which it is a response which determines it (1940). Ultimately, the image is of various ‘wakes’ left by problems, in which we not only dig to uncover solutions, but also the positive character of thought in its power to assert propositions.
However, to think that problems too are uncovered is to reduce what is distinct between problems and solutions to a single level. The conditioning power of problems over their solutions, then, would only be explicable in terms of an arbitrary adopting of the interrogative attitude. But what would this interrogative attitude be but a ‘problematizing faculty’? That is, a faculty for inventing problems. However we look at it, we discover that the posing of a problem is of a different order than the presentation or demonstration of solutions. The work of demonstrating solutions is conditioned by how a problem has been stated, and obviously must wait for such a statement for it to begin. Accordingly, there’s always something ‘ex nihilo’ about the arrival of a problem, and the activity it inaugurates and presides over. This is the work of invention:
“Discovery, of uncovering, has to do with what already exists actually or virtually; it was therefore certain to happen sooner or later. Invention gives being to what did not exist; it might never have happened. Already in mathematics and still more in metaphysics, the effort of invention consists most often in raising the problem, in creating the terms in which it will be stated. The stating and solving of the problem are here very close to being equivalent; the truly great problems are set forth only when they are solved.” (Bergson, p.58)
Accordingly, problems take priority. The work of developing them, of fixing their terms and defining their scope, establishes the space over which solutions, as propositions, become meaningful. A ‘false problem’ is not one that is unsolvable – it will have its solution waiting there to be uncovered in its wake. The issue will be that this solution will only have the sense its problem allows. And if the problem itself is meaningless, poorly posed, at its moment of invention, the mere fact that it has a solution does not redeem it, nor make it significant. These ‘false problems’ might, owing to this deficiency, be ‘unstable’, and result in endless circularity. Or, they could be simply solvable, but just not matter. To understand how problems can go astray, we need to look to how they are invented in the first place.
How we invent problems
So, the crucial question becomes the ‘how’ of this invention.
Let’s return to our chicken and grain and fox and boat problem. This problem is obviously ‘invented’, in that we can trace its lineage back to some specific moment where it was developed, in the form of a game, by some author (perhaps Alcuin of York, who seems to be the first to have written it down in the 8th century4placeholder, but it may predate this). Earlier we mentioned that the ‘artificial’ nature of this problem did not depend on it having a finite set of solutions tightly bounded by the way it is posed, because this is a feature of any problem. It is the business of problems to bound a ‘solution space’, and determine its meaning. It’s not its hypothetical nature that makes it artificial, but, rather, the construction of the objects that make the problem work. The animals in the story are simplified to the point of being mere tokens, their mutual relations are absolute and exhaustive. Absent here is the fleshy depth of an actual chicken, the caprice of an actual fox, the husks and heft of actual grain. It’s at this point where the ‘artificial’ character of the problem emerges: at the level of how the terms or elements are constructed.
But, if, again, we search here for a difference of type between this artificial problem and the problems of life, we’ll again be frustrated. It might very well seem that the problems we must suffer in life are composed of empirical terms that are irreducibly ‘thick’, but we need to recall that problems require positing, and are always thus couched in some terms or others, even if these ‘terms’ are perceptual in character (i.e., ‘things’ or ‘properties’). That is, in order to pose a problem, we need to define and delimit a number of terms, which determines their possible interactions. It’s the business of language, or ‘general ideas’, to perform such carving, and in a language we discover an entire lexicon that carves up the world, grouping and delimiting clusters of phenomena.
Bergson dismisses the question of the ‘general idea of general ideas’: the definition is easy enough to give5placeholder. The question he raises is of the origins of these general ideas, which will form the structure of terms that can organized into a problem:
“the important question for the philosopher is to know by what operation, for what reason, and especially in virtue of what structure of the real, things can thus be grouped [by a given general idea], and this question does not admit of a unique and simple solution.” (Bergson, p.60)
It does not admit of a unique solution, because the origins of general ideas are multiple, their histories and trajectories distinct and varied. And not only the ideas, but also our capacity to entertain them at all. If an idea presents a way of grouping or carving out the world in a certain way, our analysis of its origins is going to take us back to our inherent capacities to perceive, to think, and to act such that such a grouping or carving could have developed. It would be nice if each, seemingly clear, concept called up by a word mapped onto a region of the world with the precision and regularity of a chess board, that each word in a natural language only had one respondent, but what reason do we have to think that either the concept, or our neurological faculties for apprehending and manipulating it, would be so fortuitously tuned?
“It really seems, to listen to certain theorists, that the mind fell from heaven with a subdivision into psychological functions whose existence simply needs to be recognized: because these functions are such, they will no doubt be used in such a manner.” (Bergson, p.60)
Bergson here seems to have in mind the Kantian division of the mind into faculties, each of which take their form from the recognition of a particular capacity of the psychological subject. For example, we have the capacity to be affected by objects. Kant gives the name ‘sensibility’ to this capacity, and inaugurates a faculty whose function is to be affected by objects. We continue and map out the faculties in this way, discovering all of the offices and regulations of the experiencing and thinking subject. But each of these faculties has sprung from a capacity. This is not a true ‘reverse engineering’ of the constituents and limits of experience, but merely its redescription. Bergson thinks in order to give a proper account of the faculties, and the general ideas associated with them, it is not enough to ‘read them off’ a supposedly self-evident experience; one must additionally inquire into their reasons for their being the way that they are:
“I believe on the contrary that it is because they are useful, because they are necessary to life, that they are what they are: one must refer to the fundamental exigencies of life to explain their presence and to justify it if need be, I mean in order to know if the ordinary subdivision into such or such faculties is artificial or natural, and if in consequence we should maintain it or modify it.” (Bergson, p.60)
That is, it’s not enough to infer from our capacity to use general ideas that we must have a ‘faculty of general ideas’ that does whatever we can do with general ideas, and then legislate, in the Kantian manner, legitimate and illegitimate exercises of this faculty. We additionally need to ask what function this faculty (if it is, in fact, only one) served and serves, why we or any other organism can group experiences into generalities to begin with. We will not be able to determine legitimate and illegitimate uses of general ideas (in the posing of problems) if we don’t reveal the motivated forces that went into their development. For Bergson, biology is the constant thread we must always refer back to.
In line with this focus, Bergson offers us a genetic account of general ideas:
“we shall find that every living being, perhaps even every organ, every tissue of a living being generalizes, I mean classifies, since it knows how to gather, in the environment in which it lies, from the most widely differing substances or objects, the parts or elements which can satisfy this or that one of its needs; the rest it disregards. Therefore it isolates the characteristic which interests it, going straight to a common property; in other words, it classifies, and consequently abstracts and generalizes.” (Bergson, p.61)
Here generalizing is nothing more than a form of ‘classification’ that emerges in the order of life through the most basic functional features of simple organisms. Relatively closed systems defining territories and environmental features. When we consider this ‘differentiation’ of nutrient matter occurring in simple cells or tissues, we are considering practically mechanically structured functions. It’s the physical structures of the membranes that are ‘doing’ the differentiating here. But, here is the beginning of ‘generalities’ as such.
Bergson needn’t be suggesting that our cells generalize, and so we, as a bundle of cells, can do it too. It’s merely that we need to look to the actually existing biological world of life for possibilities and origins to understand how human faculties work, through analogy, or direct causation, chasing our faculties back to their roots, and naturalizing them.
Let’s consider something more human and familiar. “Red” is an oft cited example of a general property. Many things are red, when we see them we can see they ‘share’ this common property. To understand the generality ‘red’ we need to look at ourselves as organisms. We can infer, in the basic Kantian manner, that we have a biological ‘red’ detector. A kind of abstract machine that groups together a number of neurological and nervous assemblages. We move from the conditioned to the condition (red perceptions to ‘red detectors’). The Bergsonian step is to then ask what use is this detector, what is it for? In the exigencies of life, why should this detector emerge from the processes of evolution? Which then leads us to the question: what is it a detector of? To know what ‘red’ is, we need to be able to give an account of what properties it groups together, and just why we should group these properties into a single perceptual category.
Dennett gives a useful discussion of this in Consciousness Explained6placeholder. His point there is that colour and colour vision most probably emerged interdependently. We live in such colourful environments that it’s easy to forget that out in the natural world, most coloured things are themselves organisms (plants and other animals). That is, the evolution of seeing colours was co-dependent with an evolution of ‘being colourful, being seen’. The brightness of ripe fruit, and the fantastic colouring of flowers were not sad secrets existing in the darkness prior to organisms that could see these displays, but are the way they are because of an evolution alongside organisms who could ‘appreciate’ them. Flowers evolve to signal to bees and other flying insects who themselves evolve to discriminate these signals. Evolutionary pressures push on both organisms, in both directions: the sender and receiver. Similar stories can be told for other evolutionary lineages of colour vision. We get better at differentiating certain colours alongside other organisms who get better at broadcasting information using this difference, just insofar as this difference ‘makes a difference’ to the two sets of organisms.
Now, the important part here is that the whole colour enterprise takes advantage of a number of the physical properties of light, but not all of the physical properties of light, and, not only the physical properties of light. The physical properties of various compounds, biological and mineral, and their interactions with light waves, nerves and neurons and other structures, are all implicated. Here is a big tangle of interconnected causal forces, across different scales, tempos, and levels of description. A mess of properties that share no intrinsic common measure, but are there as a subset of all the ‘happenings’ in the concatenation of matter. And insofar as they are there, they exist as material for evolutionary exploration. A certain, scrappy, signifying system begins to emerge by strapping together a number of material properties and processes, which, owing to its proliferation through successful reproduction, becomes refined: brighter red apple skin and better rods and cones.
Now, we have, as a kind of ‘virtual machine’ (to paper over the biological complexity for a minute) a ‘red detector’. This ‘sensor’ is sensitive to a particular cluster of physical properties in the world. We shouldn’t be seduced by the appealing picture that our colour vision dispassionately tracks a single physical quantity: the wavelengths of light. The story is more complex than this (there’s more to our perceiving red than just reading a precise frequency), but also when we consider the origins of this ‘faculty’ we should realize that it may track faithfully a single physical property, but it much more likely would not. Why would it? Why would this biological system, emerging from the forces of evolution with its principle of ‘good enough/whatever works’ have such an upstanding epistemic character? It might, but it needn’t. Much more likely is there is a whole variable grab bag of physical properties that have been ‘gerrymandered’ (Dennett, 1991) by the interests of this discriminating sensor/detector, and the explorations of signifying potentials of organisms evolving to be better seen (for pollination, for seed dispersal, for warning). In this strange cooperation between organisms with nervous systems and the organisms who want to communicate to them, ‘red’ emerges as a signal, out of whatever bits and pieces of the physical reality that will get the job done. And with red, then also green, then also blue and orange and pink and so on.
The key point is we have a stable generality; red, but when we look into the origins of this generality, we discover it gerrymandering together a potential number of different processes and properties. When we add language to the picture, we see that the stability of the generality allows us to use a single word ‘red’ to refer to it. But then this word’s extension is not a single physical property in the world, but a tangle of them that have been carved out during the long processes of evolution.
“If some creature’s life depended on lumping together the moon, blue cheese, and bicycles, you can be pretty sure that Mother Nature would find a way for it to “see” these as “intuitively just the same kind of thing”” (Dennett, 1991, p.381, fn).
For Bergson language maintains this unstable relationship to the world that can only be stabilized by a careful examination of what precisely is being carved out by a term with reference to how it emerged from the exigencies of life, with no assurance in advance that some idea will cleanly ‘carve nature at its joints’. Bergson notes a perennial issue in philosophy is that words, and the general ideas that they call up, have often been accepted readymade – their upstanding epistemic character assumed. The analysis of their origins is painstaking work, and often increases complexity that must be dealt with rather than abate it…
“The philosopher has not always this patience. How much simpler it is to confine oneself to notions stored up in the language! These ideas were formed by the intelligence as its needs appeared. They correspond to a cutting out of reality according to the lines that must be followed in order to act conveniently upon it. Most frequently they distribute objects and facts according to the way they can be turned to account, throwing pell-mell into the same intellectual compartment everything which concerns the same need.” (Bergson, p.40)
This is why the inquiry into the ‘general idea of general ideas’ is secondary to the inquiry into particular general ideas: the ones that are activated in the positing of a problem. In each case the result may be different, as we disentangle the cultural and historical and biological layers involved in the terms, hence the need for patience.
Conclusion
To tie this all together, when we pose a problem, it must be couched in these or those terms. We have no assurance in advance that the problem thus posed gets at any significant categories, any significant ridges or folds in the concatenation of things. This needs to be worked out separately. A thousand solutions could have their meaning animated by a problem stated in such a way that is unmoored from the structures of the real, and thus a thousand meaningful but insignificant solutions are cast to the wind. Absent this work of determining the terms of the problem, and taking care of its statement, the eventual solution of a problem is of little import. Of course a problem will warrant the solution it deserves, in the terms it is couched, but the more crucial question is whether or not the problem itself is legitimate, which we can now see involves a case-by-case attention to the origins of the general ideas it mobilizes, and the faculties through which these are engendered. Insofar as it must make use of some general ideas or others, and these general ideas mostly always have a functional, gerrymandered character, then all problems are constructed relative to a ‘milieu’ – a particular carving out of being by the developing exigencies of life. Thus, for Bergson, it would seem all problematizing takes place within life, within the order of living.
So what of the ‘artificial’ character of the fox-grain-chicken problem? There’s nothing artificial about it, except for the ‘cartoon’ layer that transparently narratives it. Excluding the possibility that someone might take it to concern an actual issue of agricultural logistics, the grasping of the problem turns us over to these curious terms: the (x) that will subsume (y) but be subsumed by (z). Seen in this way, their generality goes far beyond food chains (which they represent only poorly) and instead pull together a particular class of functions. This is precisely why, now, if you pay attention, no doubt in the next week or two you will encounter a problem that is re-stateable in just these terms. When you do, just remember you have to keep the fox with the grain, and bring that middle chicken, that links the whole chain of relations, back and forth across the river, whatever the term ‘river’ collects together in your present encounter of the problem.
Works Cited
Bergson, H. (1946). The Creative Mind. New York: The Philosophical Library.
Collingwood, R. (1940). An Essay On Metaphysics. Oxford: Oxford University Press.
Deleuze, G. (1991). Bergsonism. New York: Zone Books.
Deleuze, G. (1990). The Logic of Sense. London: Athlone.
Dennett, D. (1991). Consciousness Explained. New York: Back Bay Books.
Because, a false problem that is merely an ‘effect’ of concepts is the kind of thing you can uncover by playing with them. A real problem requires a creative insight – it actively ‘glitches’ the smooth surface, and creates new concepts. This will make more sense after we look at Bergson’s take on general ideas.
Or a wolf, a goat, and a cabbage.
Defining that finite series, the possible combinations, is ultimately the ground of the mathematical field of combinatorics.
“Homo quidam debebat ultra flavium transferre lupum, capram, et fasciculum cauli. Et non potuit aliam navem invenire, nisi quae duos tantum ex ipsis ferre valebat. Praeceptum itaque ei fuerat ut omnia haec ultra illaesa omnino transferret. Dicat, qui potest, quomodo eis illaesis transire potuit.”
PROPOSITIONES ALCUINI DOCTORIS CAROLI MAGNI IMPERATORIS AD ACUENDOS JUVENES, 18 – PROPOSITIO DE HOMINE ET CAPRA ET LUPO [Link]
“Doubtless one can easily keep the general idea of general idea, if one insists. It is enough to say that we agree to call general idea a representation which groups an indefinite number of things under the same name: most words will thus correspond to a general idea.” (Bergson, p.59-60)
This is not the first time I’ve had occasion to remark on the complementary nature of Bergson and Dennett. My theory for this is they share affinities owing to how both thinkers bring biology to bear on metaphysics, and end up deriving many similar conclusions, in vastly different registers.