Tuesday, March 16, 2010

Change and contradiction

When reading about dialectics, one repeatedly hears that change and contradiction are intimately and necessarily connected, even for the simplest forms of change.

For example, Engels writes that "Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both... in one and the same place and also not in it."[1] I don't want to examine this particular physical case too closely, because it is entangled with quantum mechanics (via the quantization of space and time), and this is a whole question in itself.[2] But Engels' statement is nevertheless interesting.

Engels' claim relies on the obviousness of one kind of "contradiction" - that which results from change. A body is in one place; later it is not in that place but in another place. Thus a statement which was once true is no longer true, and we have two true but incompatible statements - a "material contradiction", perhaps? Trotsky finds the same kind of "contradiction" in a pound of sugar: "All bodies change uninterruptedly in size, weight, colour, etc. They are never equal to themselves."[3]

But this kind of contradiction is trivial and uninteresting. Any change involves an entity or process moving from one state to a different state. We have already rejected the idea that literally everything changes, and Trotsky concedes that even when things do change, if the changes are "negligible for the task at hand", we can ignore them, and speak of coherent, "self-identical" entities.[4] So if this is all there is to the relationship between contradiction and change, talk of "contradiction" adds nothing, and we are left with nothing more than an admonition not to assume that things are static when it is not safe to do so.

Engels' non-trivial claim is that change "can only come about through" a contradiction which already exists, embedded in reality at a given instant. Bertell Ollman puts the same point clearly: "Dialectical thinkers attribute the main responsibility for all change to the inner contradictions of the system or systems in which it occurs."[5] This claim, that change necessarily results from contradiction, is the one that seems like it might have really interesting implications.

To evaluate it, we first need to define "contradiction", or material contradiction specifically, more precisely.

One approach would be to start with the relatively clear definition of a logical contradiction - "a proposition, statement, or phrase that asserts or implies both the truth and falsity of something"[6] - and say that a material contradiction is simply a logical contradiction which is true. This is not promising, for two reasons.

The first is that for any of the examples we have used so far, one can disentangle them so that there is no actual logical contradiction. "Capitalism has both an inherent drive to expand and an inherent tendency to crisis which restricts expansion." "Capitalism both empowers its bourgeois rulers and, ultimately, leaves them helpless before their natural enemies, the working class." We are not actually asserting simultaneously the truth and falsity of any proposition in these rhetorical oppositions - we are merely looking at different aspects of the situation.

The second reason not to claim that logical contradictions can be true is the principle of explosion: from a true contradiction, one can derive anything. (And not in a useful way, contra XKCD.)

For example, say that a pound of sugar is itself, and it is not itself. Then it is itself - that is one half of what we have just asserted. Then either the pound of sugar is itself, or Santa Claus exists - to any true statement, one can add "or [whatever]", and the whole, the disjunction, will remain true. But then let us remember the second half of the original contradiction: the pound of sugar is not itself. With this, we can reject the first half of our disjunction. And since we have shown that the disjunction as a whole is true, that means the second half must be true. In other words, we have just proven that Santa Claus exists.

Suspect a trick? Of course, this reasoning isn't valid. But that's because the premise wasn't valid. Each step thereafter used a rule of propositional logic which we rely on all the time and would be very difficult to do without.[7]

So let's abandon the idea of true logical contradictions and look for another definition of a material contradiction.

We could try to retreat a little, without changing direction, and say that material contradictions occur whenever two statements which are somehow contrary or in tension, without being strictly contradictory, are both true. This, however, is almost as bad an option, because there is no good way to define this kind of propositional tension - it will likely come down in each case to rhetoric, whether English offers a way to phrase the two statements so that they sound contradictory.

A more promising approach, I think, is to view a material contradiction as the existence of opposing forces or tendencies. Ollman gives a good definition of a contradiction along these lines: "The incompatible development of different elements within the same relation."[8] Ollman's phrase "incompatible development" is nice because on the one hand we can use the strict sense of "contradiction" - the outcomes towards which various forces tend are genuinely incompatible, that is, they could not occur simultaneously without logical contradiction - and on the other hand we do not have to claim that a logical contradiction is ever actually true, but rather that contradictory forces must result in a change in the system before the state of logical contradiction is reached.

Let us provisionally accept this definition, then, and go back to our original question: does all change result from this kind of contradiction?

Our definition of contradiction excludes one semi-intuitive rationale for the "change requires contradiction" thesis - the notion that change requires some sort of "lack", or imperfection, in what exists.[9] The idea is that a truly complete and self-consistent reality would necessarily be static - from perfection can flow only constant perfection. But given the idea of contradiction as the existence of incompatible tendencies, there is no need to try to explore and clarify this rationale - a "lack" is not by itself a contradiction.

Losing one possible rationale, however, is not necessarily a problem for the original thesis. So let's consider what it implies.

It is at least plausible that all change requires some sort of pre-existing tendency, or else it would be uncaused. The only counter-example I can think of is if there is true randomness, as in some interpretations of quantum mechanics, but even there we might describe the probability distribution which governs the quantum state as an existing tendency, and so preserve our claim.

It is also plausible that all change occurs within some system. Now, certainly all change within any given system does not necessarily stem from a cause internal to that particular system. If the geologists are right, Earth's ecology in the era of the dinosaurs was transformed from the outside in about as dramatic a way as might be imagined - by the impact of a gigantic meteor. And there are many other similar examples, phenomena for which I like the term "Excession", following Iain Banks. But there is always a larger, enveloping system, to which any given cause of change is internal, up to the scale of the universe.

In any case, that still leaves one more step before we have a positive answer to our question - does all change, that is caused within a system, stem from multiple, contradictory tendencies or developments? Or, equivalently, since we have admitted a necessary connection between tendency and change - is every tendency in reality matched by one or more opposing tendencies within the same process?

I think not. Take Engels' simple object in motion - for it to travel in a straight line, there need be no tendency other than its inertia. Or at a more abstract and social level, take the tendency for scientific knowledge and technology to advance. Certainly that does not have only positive effects, or even necessarily advance the average person's knowledge. But is there a counter-tendency for technology to regress?

For any example I can name, I am sure someone can come up with some contrary tendency somewhere. But remember that we are not merely seeking a contrary tendency, we are seeking one within the same system, the same process of change. That, I do not think it is always possible to provide.

One more example: a computer running a sort algorithm on a list of numbers in its memory, say merge sort. There is a tendency, as this process runs, for the list to become sorted - a tendency which is in fact mathematically provable, and can be quantified in various ways (for example, we can find the number of comparisons which must be done in the worst case for a list of any given length). Here we have a well-defined process - in fact, "process" could be a technical term here as well as a philosophical one - which not only contains a well-defined development, but apparently excludes any possibility of a counter-development.

Remember also the dilemma posed in the previous post - in relating dialectics to science, we want to avoid either Lysenkoism or mere mysticism. Now that we have made the question of whether change always stems from contradiction more concrete, we can see that the same dilemma applies here. Either dialectics commands scientists to find opposing tendencies in every system, or it asserts their existence without allowing any concrete conclusions to be derived from this assertion. Neither option is satisfactory.

At best, then, if a conception of dialectics as a set of laws or facts about the world is defensible, its defense requires losing content. We cannot sustain at the same time two universal propositions; that change is always caused by tendencies which are 1) united and internal to a single process, and 2) contradictory. To make either proposition universal we must abandon the other, and doing so would leave dialectics with little to say.

Can this problem be solved by narrowing dialectics' domain? Perhaps we can retain the idea of dialectics as a set of truths about the world, if we speak only of a part of the world - human history, or capitalism. Or do we have to abandon dialectics' claim to describe reality, in favor of a conception of dialectics as method, or form, or critique? These questions still have to be answered.

[1] Anti-Duhring, chapter 10.
[2] One can certainly view something like Schroedinger's cat as a case of a material contradiction. But I think it is more useful to view it as an indication that we should not try to think of quantum mechanical particle as analogous to macro-scale objects like cats.
[3] "
The ABC of Materialist Dialectics", in A Petty Bourgeois Opposition in the Socialist Workers' Party.
[4] ibid.
[5] Dance of the Dialectic, p. 18.
[6] Merriam-Webster's Online Dictionary. (Yeah.)
[7] A few mathematicians have tried to develop logics which allow contradiction while avoiding explosion, most commonly logics which take more values than "true" and "false". But if consistent, they tend to end up adding complexity without having any actual advantages in terms of conceptual power. Timothy Williamson's book Vagueness has a persuasive section on this.
[8] Dance of the Dialectic, p. 17.
[9] Hegel uses the term "deficiency": "Internal self-movement proper... is nothing else but the fact that something is, in one and the same respect, self-contained and deficient, the negative of itself." Cited in Rees, Algebra of Revolution, p. 51.

Sunday, March 14, 2010

Dialectics as a "general science"

In Marxist writing about dialectics, one often finds very general assertions. "The various seemingly separate elements of which the world is composed are in fact related to one another."[1] "The whole world, natural, historical, intellectual, is... a process, i.e., as in constant motion, change, transformation, development."[2] "All reality is constantly changing."[3] "As soon as we consider things in their motion, their change, their life, their reciprocal influence on one another... we immediately become involved in contradictions."[4] "Real change must result from any contradictory system."[5]

If we take statements like these literally, the implications are very strong.

Take the claim that "all reality is constantly changing." Does that mean that the value of pi changes? Perhaps we should exclude it from the proposition, since we cannot really even conceive of what it would mean for pi to change. (Or at least I can't; maybe some mathematician has.)

But what about a more material number, the fine structure constant - which is related, among other things, to the speed of light? Physicists know more or less what it would mean for it to change, but from what I understand, most believe it doesn't. Or take protons. Does dialectics imply that they decay, rather than existing indefinitely? Some physical theories predict proton decay, but there is no experimental evidence for it.

Lastly, what about the laws of physics themselves? Rees quotes the biologists Levin and Lewontin to the effect that one of dialectics' key insights is that "the laws of transformation themselves change" - for example, the laws which govern economic dynamics under capitalism will themselves be different in another historical epoch.[6] Does dialectics then imply that, say, if the equations of general relativity are valid today, they were not yesterday and will not be tomorrow?

I am not taking dialectics anywhere new by asking these questions. Engels' writing on dialectics is full of examples from biology, chemistry, and math. But his examples appear mostly intended to illustrate, and are picked to be easy. If you look instead for hard cases like these, where change, contradiction, etc., are at the very least non-obvious, dilemmas begin to arise.

I can see four ways of approaching the question of what dialectics might say about proton decay.

The first approach is the most straightforward - to embrace the scientific implications. Yes, one might say, protons must somehow transform themselves under the impulse of their own internal contradictions;[7] even if dialectics cannot by itself give us a complete physical theory, it can give us certain assertions, like the inevitability of change, as a starting point.

I find this implausible on its face; it would imply a much closer relationship between physics and philosophy than we usually see in real life. One can list plenty more physical examples which at least seem to contradict dialectics in this interpretation - and in the best case, the theory could be no more certain than its contrarian implications for physics. Experiments which extend what we know about the minimum lifespan of the proton would, in challenging one premise of dialectics, thereby challenge even dialectical arguments about capitalism.

A second approach would be to re-describe the propositions of dialectics as tendencies rather than absolute laws. So, one could say, while we should expect everything to change, including elementary particles, we must allow for exceptions when evidence or reason requires them.

This is not very satisfying. It makes dialectics something much less useful than Engels' "science", Rees' "algebra", or Novack's "logic". It is basically impossible to disprove, since there is no way of quantifying the proportion of exceptions across physics, biology, philosophy, and history. And, it would make it strange to even speak of a coherent subject called "dialectics". If dialectics is a mere set of rules-of-thumb - "don't expect things to be static", "look for connections between parts and larger wholes", "look for internal causes of change" - what makes these tendencies special? There doesn't seem to be anything to distinguish these, as rules-of-thumb, from others, like one I once heard from a professor: "If a statement is true for the first three random, non-trival examples you check, it's probably always true."[8]

A third approach to the problem would be to say that in expecting protons to decay, one would be drawing too specific an implication, and looking for the wrong kind of change. Dialectics tells us - one might argue - that everything in the world is in some way involved in a process of change, without telling us that any individual part of the world must change in any particular way. So - the argument might go - protons do change: they move in space and time, they gain and lose energy, they join and leave nuclei. Thus they accord with the predictions of dialectics. Why ask more?

The problem here is subtler, but equally fatal for the original claim of universality. It is that we no longer know exactly what dialectics does imply or even suggest about any particular question; if things must change only in some aspect or in relation to some given system, this does not tell us anything much in practice. And it is not merely a question of needing to use a materialist method, to always apply dialectics to concrete reality. If we say that dialectics only applies to some aspect of any given entity, situation, process, or structure, and we cannot in advance tell which, that is functionally equivalent to admitting that dialectics only applies sometimes, and we cannot in advance tell when.

The third approach thus collapses into the fourth and last approach, which is to admit that dialectics does not give us laws which really apply to everything, even as tendencies, and in particular that it has nothing to tell us about proton decay.

Can the collapse be avoided? I can think of one more distinction which an advocate of the third approach might try to make. That is to say that, while not every true way of describing something must be dialectical, the dialectical way of approaching something will always be more fruitful, getting at a dynamic which is somehow more crucial. So, while dialectics might not tell us whether or not a proton will ever decay, that inapplicability itself tells us that understanding proton decay is not the best way to begin understanding particle physics. Decay is a particular prediction, not the heart of the theory.

That argument may be plausible for the example we have been using, but it does not hold up in general. Take another case: gravitational orbit, e.g. the orbit of the Earth around the Sun.

One way to describe an orbit is to say that it is the result of two balanced opposing forces. Gravity pulls the Earth inward, while centrifugal force pulls the Earth outwards, so in the end it travels in an ellipse. This seems like a classical dialectical triad - two contradictory forces impelling motion in a new, third direction. But in fact, centrifugal force isn't real in the same way that gravity is, even in Newtonian physics. The Earth is not pulled outwards; rather, absent any external force, it would travel in an inertial straight line, and gravity merely bends its path. Inertia is not really a force. Moreover, according to the theory of relativity, even gravity is not really a force. Instead, space-time itself is bent. So the first "dialectical" view is accurate on the surface, but misleading from the perspective of a deeper theory.

I have focused so far on just one universal claim that dialectics might make, the claim that everything changes. There are other claims available to the theory. But without discussing them individually, let's note what's already been established, if, like me, one finds the modest fourth approach the most plausible.

A defensible version of dialectics will be a theory not about everything in the universe, but at most about processes of change, where we have already established that they exist. This isn't necessarily that much of a retreat, and it gives us a handy, non-circular definition of a dialectical "totality": not merely any arbitrary collection of nouns, but a coherent process of motion, development, or transformation - in the maximalist interpretation, any such process. The key question then becomes the concept of "contradiction", and its relationship to change and causality.

That question is worth its own post. But already in this one, we have not just slightly narrowed the territory dialectics might claim. We have also noted a dilemma that any conception of dialectics will have to face. Does the dialectic have specific implications for scientific theory, in any field, or not? Either answer is problematic; on the one hand, we risk an idealistic if not Lysenkoist attempt to make science answer to a 19th-century philosophical theory, and on the other hand, we risk reducing dialectics to a vague and insubstantial mysticism. As we explore what might be valuable in the dialectic, we will have to chart a course between these twin rocks.

[1] Rees, Algebra of Revolution, p. 5
[2] Engels, Socialism: Utopian and Scientific, chapter 2. More specifically, Engels says that it is the "great merit" of Hegel that he "represents" the world in this way.
[3] Novack, Logic of Marxism, p. 66. See also Marx's slightly different formulation: "The dialectic... regards every historically developed form as being in a fluid state, in motion" (cited in Rees, p. 100-1).
[4] Engels, Anti-Duhring, chapter 10.
[5] Rees, p. 118.
[6] ibid., p. 78.
[7] Protons are, after all, internally differentiated totalities; they are made up of quarks.
[8] Applied to statements about the natural numbers in a class on discrete math.

Monday, March 8, 2010

Dialectics and formal logic

In exploring the dialectic, I plan to examine conceptions of it one by one, and consider whether they can be sustained. The goal is to move more or less from the broadest to the narrowest, until we find a core that is true.

So, let's start with a very broad conception of dialectics: as a successor to mathematical formal logic, which "arose out of the criticism of formal logic, overthrew and replaced it as its revolutionary opponent, successor and superior," in the words of George Novack.[1] The idea is that dialectics has a relationship to conventional logic which is analogous to the relationship between the theories of Einstein and of Newton, or between an obsolescent tool and a state-of-the-art one.[2]

This is so immediately problematic that I do not even know how to present it more fully before abandoning neutrality.

Mathematical logic allows the mechanical deduction of results - one can start with an expression like "(A OR B) AND (NOT A OR C) AND (B OR NOT C)" in terms of Boolean (true or false) variables A, B, and C, and then use a computer to determine, given values for the variables, whether the expression is true or false. Or one can even use a computer to check whether the expression is valid - whether it is true for all possible values of A, B, and C - or satisfiable - whether it is ever true given any values of A, B, and C - using an algorithm like resolution which does not require plugging in any specific values for the variables at all.[3]

One cannot do anything like this for dialectics. As Rees writes, dialectics is "not a calculator into which it is possible to punch the problem and allow it to compute the solution."[4] But calculability is precisely what distinguishes logic as logic. It is not an incidental benefit. The reason we can use mathematical logic in a calculator is that mathematical logic, given whatever premises, can tell us unambiguous conclusions which follow necessarily. If the "laws" of dialectics were laws in the same sense that commutativity is a law of Boolean logic, we could tell computers how to obey them, and so use them in programs. We can't.

Logic enables us to go from one or more true statements to another equivalent true statement without the need for additional empirical verification. If I see, say, one protest result in a victory, I know that it is not the case that all protests are defeated, without having to check any additional protests, thanks to a basic equivalence in first-order logic. And when we go beyond single-step deductions, very often logic will take us to non-obvious conclusions.

But deduction of this kind is not available with dialectics. Rees concedes that "once we are sure we have made an accurate abstraction", that does not mean "we can also be sure that any further categories that emerge as a result of contradictions which we find in our concept will necessarily be matched by contradictions in the real capitalist world. This... is only a safe assumption on the basis of constant empirical verification."[5]

So dialectics' non-calculability is not merely a question of a missing formalization. Logic is a mathematical way of examining a process that is essential to reasoning, where we place our knowledge and beliefs into relationship with one another in order to draw conclusions and form a coherent whole, without any necessary mediation by new or additional experience. Dialectics, whatever it is, is a different kind of beast.

Engels writes, "Even formal logic is primarily a method of arriving at new results, of advancing from the known to the unknown — and dialectics is the same, only much more eminently so."[6] But if we are to set dialectics up against formal logic, as an alternate method of deduction, then if it is more "eminent", that is only in the sense that the Pope is more eminent than a subway conductor. The latter does practical work herself, while his eminence has subordinates for that.

Of course, why should one set dialectics up as a rival to logic as studied by mathematicians and computer scientists? Why disparage formal logic with dishonest word games - like Novack's attempt to slide from "A = A", to "A always equals A", to "A cannot be non-A", to "a man cannot be inhuman, democracy cannot be undemocratic", without the reader noticing a non-equivalence, in order to cast doubt on the "law of identity"?[7]

This kind of rhetorical trick has nothing in common with science, but is necessary if dialectics needs to conquer logic's territory in order to have living space. So why not abandon the attempt?

We should. The only problem is that if you do not view dialectics as a logic like Boolean logic or first-order logic, you do not get universality for free. Engels describes dialectics as "the science of the general laws of motion and development of nature, human society and thought."[8] But if dialectics cannot take over logic's universal applicability, and if it cannot be formalized and studied in isolation independent of topical content, there is no clear reason why we should assume it is so general. We will have to reconsider how universally its principles really apply.

[1] Logic of Marxism, p. 28.
[2] The Einstein/Newton analogy is used by John Rees, Algebra of Revolution, p. 271. Of course, he says in the same place that dialectics is not an "alternative" to formal logic, but this seems to be just a confused retreat from the full implications of the original idea. Einstein's theory was, of course, an alternative to Newton's, which is a mere low-energy approximation.
[3] Of course, for general expressions checking satisfiability is NP-complete, and so infeasible in practice, but that's off topic.
Algebra of Revolution, p. 271.
ibid., p. 110.
Anti-Duhring, chapter 11.
Logic of Marxism, p. 18. This is a truly awful passage, which stands out even in a very bad book. On top of the idiotic hackery of the claim that "man cannot be inhuman" follows from the law of non-contradiction, Novack asserts that this law follows "logically and inevitably" from the law of identity, and in turn "flows logically" to the law of the excluded middle. Of course, not only are these three axioms not derivable from one another (or they would not be axioms), there are in fact consistent logical systems which deny the law of the excluded middle, used in constructivist math. And then there's the fact that the three laws Novack discusses are archaic and do not constitute the complete axioms of any modern logical system...
Anti-Duhring, chapter 11.

Saturday, March 6, 2010

The dialectic

I plan to write a series of posts on the Marxist notion of "dialectics" or "the dialectic", with the goal of answering the following questions: What is the dialectic? What is it good for? Is it defensible, or ultimately just mysticism?

I'm no expert - I haven't read Hegel's Logic, nor, except for bits, even Engels' Anti-Duhring. I am not qualified to write a history of ideas - what did Marx himself really think? - nor do I find that question very interesting. But I do think I have read and heard enough arguments on the topic to begin to judge their substance.

John Rees* gives the following definition of the "essentials" of the dialectic:
  1. The world is a constant process of change;
  2. The world is a totality; and
  3. This totality is internally contradictory.
The idea is that the dynamics of change in the world should be examined by seeing it as composed of parts which are in tension with one another but which which are nevertheless united in a systematic way, and that this tension is what propels the system as a whole.

Per Rees, the triadic "thesis"/"antithesis"/"synthesis" pattern which is commonly associated with the dialectic, where the contradictory existence or validity of thesis and antithesis results in a new state or idea, the synthesis, which subsumes and transforms both, is then simply one form taken by such dynamic, contradictory totalities. The phrase "unity of opposites", also associated with dialectics and sometimes called a "law", describes the relationship between thesis and antithesis in this kind of triad. The "negation of the negation", another "law", is a yet more specific version of the triad, in which the thesis comes first, then is apparently defeated or subordinated by the antithesis, which finally is defeated or subordinated by a new synthesis that contains elements of the original thesis. The last common "law", the "transformation of quantity into quality", is, on the other hand, a characteristic of how dialectical transformations more broadly take place: a contradictory set of forces will push a system in one direction without fundamentally changing its character for some time, but eventually the changes will add up to a new and fundamentally different configuration.

Some more-concrete examples of dialectically contradictory totalities, in Marxist theory: The interdependent relationship between the economic "base" of society and the political and cultural "superstructure". The class struggle between bourgeoisie and proletariat under capitalism and the possibility of socialism as its result. The relationship between productive forces and the mode of production, where capitalism at first advances production and then begins to weight it down through crises. The role of a revolutionary party as both an element of working class consciousness and an actor upon it.

According to a dialectical interpretation, each of these systems is a totality in that its parts are inseparable from one other and can have no independent existence, but are rather aspects or "moments" of one coherent whole, abstracted and treated as separate only in thought, as a means of systemic analysis. (There can be no base without a superstructure, no party without a class.) Each system is contradictory, either containing some kind of struggle, or described by multiple propositions which are somehow opposite but are simultaneously true. (The bourgeoisie and proletariat are at war, the party both acts and is acted upon by the class.) Finally, the contradictions are what propel the system forward - if not for the contradictions, the system would be static, but they give it the possibility of becoming something new. (Capitalism may become socialism not because someone had an idea which wins out in a side-by-side comparison but because it creates its own gravediggers.)

I do think there is something to these examples - their "dialectical" aspects as just described are real and important. But that leaves many questions unanswered.

The key terms, "totality"/system/process, "contradiction"/opposition, and change/motion/transformation, have not been defined. How broadly does the dialectic apply - to nature, to society, or merely to elements of capitalism? Are its laws akin to those of logic and math, to those of physics, or to the more-or-less approximate generalizations of, say, biology - or are they simply rules-of-thumb, useful pointers? Is the dialectic a set of connected theses, propositions about the world as a whole, or is it a structure which things may take, which implies certain properties, or is it a grab-bag of fundamentally unrelated adjectives which sometimes apply together but only coincidentally?

I want to try to answer these questions, at least to my own satisfaction, in following posts.

* The Algebra of Revolution, p. 114. This is an interesting and useful survey of Marxist thinking about dialectics despite Rees' tendency to elide hard questions.