The Four Causes Revisited

Previously I abbreviated my account of book capital Alpha of the Metaphysics, focusing mainly on Aristotle’s own remarks about the “knowledge being sought”. The other main content of this book is a discussion of what his predecessors had to say about this question. The bulk of it concerns the pre-Socratics, with mention of the poets who preceded them.

I tend to regard serious philosophy as starting with Plato. By comparison, even though they have interesting things to say, the pre-Socratics seem mostly to just make dogmatic pronouncements in a simplistic way. As Aristotle says, “[W]hile in a certain way all the causes have been spoken of before, in another way they have not been spoken of at all. For the earliest philosophy about everything is like someone who lisps [sic], since it is young and just starting out” (ch. 10, Sachs tr., p. 28).

But Aristotle’s remarks on his predecessors here — including a brief mention of Plato — also give insight into his perspective on what was most original in his own thought.

These remarks are superficially structured around Aristotle’s claim that no one before him made use of all four causes. But implicitly, this historical critique is preparing the way for a much more fundamental point about the overall leading role of that for the sake of which, which parallels his more developed argument about the nature of explanation in Parts of Animals. The treatment here could also be seen as an anticipation of related conclusions about the nature of the first cause, which will not be made explicit until book Lambda.

The very way in which he briefly introduces the four causes here at the beginning of the Metaphysics already has several important nuances:

“[One cause] is thinghood [ousia or “substance”], or what it is for something to be [what it is] (since the why leads back to the ultimate reasoned account, and the first why is a cause and source), another is the material or underlying thing, a third is that from which the source of motion is, and the fourth is the cause opposite to that one, that for the sake of which or the good (since it is the completion of every coming-into-being and motion” (ch. 3, p. 6).

“Causes” are reasons why. The what-it-is (ti esti) of things is their form, but notably he does not use the word “form” here. The word that Plato had used for form (eidos) had a more common usage for the “look” or visible form of a thing, which is nearly opposite to the sense of essence and deeper truth that Plato and Aristotle give to it.

(Hegel’s remarks on the intangibility of truth suggest a relation between this more ordinary usage of eidos and a weakness of the specifically Platonic notion of form, in which the open-ended nature of essence that Plato so well represents in his depictions of Socratic inquiry is compromised by Plato’s conflicting tendency to sometimes suggest that the form of a thing is something that could be simply known once and for all.)

The material or “underlying thing” answers to the superficial sense of “substance” (ousia) as a logical “sub-ject” of properties in the Categories. But Aristotle has already here associated ousia with the form rather than the material. This could be seen as anticipating the argument of book Zeta on the what-it-is of things, in which the “underlying thing” sense of ousia is eventually superseded by that of the what-it-is.

Pre-Socratic philosophy arose in the relatively cosmopolitan environment of the thriving trade centers of Ionia in Turkey. The Ionians formulated various theories positing a material first principle (water for Thales, air for Anaximenes, fire for Heraclitus, “the Unlimited” for Anaximander).

“Of those who first engaged in philosophy, most thought that the only sources of all things were of the species of material” (ibid). “[B]ut as people went forward in this way, their object of concern itself opened a road for them, and contributed to forcing them to inquire along it. For no matter how much every coming-into-being and destruction is out of some one or more kinds of material, why does this happen and what is its cause? … [But since sources of this kind] were not sufficient to generate the nature of things, again by the truth itself, as we say, people were forced to look for the next kind of source. For that some beings are in a beautiful or good condition, or come into being well or beautifully, it is perhaps not likely that fire or earth or any other such thing is responsible…. So when someone said an intellect was present, just as in animals, also in nature as the cause of the cosmos and of all order, he looked like a sober man next to people who had been speaking incoherently beforehand…. Those, then, who took things up in this way set down a source which is at the same time the cause of the beautiful among things and the sort of cause from which motion belongs to things” (pp. 7-9).

This may seem like a very “Hegelian” kind of argument: “their object of concern itself opened a road for them”. But in reality it is Hegel who is being Aristotelian.

“So these people, as we are saying, evidently got this far with two causes out of those we distinguished in the writings about nature, the material and that from which the motion is, but did so dimly and without clarity, rather in the way nonathletes do in fights; for while dancing around they often land good punches, but they do not do so out of knowledge, nor do these people seem to know what they are saying. For it is obvious that they use these causes scarcely ever, and only to a tiny extent. For Anaxagoras uses the intellect as a makeshift contrivance for cosmos production, and whenever he comes to an impasse about why something is necessarily a certain way, he drags it in, but in the other cases he assigns as the causes of what happens everything but the intellect” (ch. 4, p. 9).

He applauds Anaxagoras for bringing intellect into the discussion, but criticizes him for using it mainly as what Brandom would call an “unexplained explainer”. To the extent that Anaxagoras has an implicit theory of the way in which intellect affects other things, Aristotle regards him as treating it as a “source of motion”. But Aristotle notes that it is completely unclear in Anaxagoras how intellect is supposed to be a source of motion. The same goes for Empedocles’ principles of love and strife.

Aristotle will retain an important role for intellect (and love too) as well as the notion of sources of motion, but he decouples these, and develops a different account of each. In both the Physics and the Metaphysics, he ends up tracing sources of motion to potentiality. But meanwhile, the source of motion is also what the Latin scholastics and early moderns called the efficient cause.

It is again vitally important to recognize the order of explanation that Aristotle employs. He explains the operative aspects of “efficient causality” in terms of the more fundamental notion of developed potentiality. He does not explain “potentiality” in terms of efficient causality, and he most especially does not explain potentiality in terms of some passive role in what the scholastics and early moderns understood by efficient causality. Once again, when he is being careful, Aristotle makes it clear that the primary model for this kind of cause is something like the art of building as a developed potentiality, not something immediate like the hammer’s blow or the carpenter’s arm.

Chapter 5 is devoted to the Pythagorean school’s teaching that mathematical things are the sources of all things. This chapter also incorporates remarks on the Eleatic school’s teaching that the One or Being is the source of all things. He treats both of these as partial anticipations of Plato, grouping them together as “the Italians”, since both of these schools were centered in the Greek colonies in Italy.

“After these philosophic speculations that have been mentioned came the careful work of Plato, which in many ways followed the lead of these people, but also had separate features that went beyond the philosophy of the Italians. For having become acquainted from youth at first with Cratylus and the Heraclitean teachings that all sensible things are always in flux and that there is no knowledge of them, he also conceived these things that way later on. And since Socrates exerted himself about ethical matters and not at all about the whole of nature, but in the former sought the universal and was the first to be skilled at thinking about definitions, Plato, when he adopted this, took it up as applying to other things and not to sensible ones, because of this: it was impossible that there be any common definition of any of the perceptible things since they were always changing. So he called this other sort of beings forms, and said the perceptible things were apart from these and all spoken of derivatively from these” (ch. 6, pp. 14-15).

“In a curtailed way, then, and hitting the high spots, we have gotten hold of who happens to have spoken about origins and truth, and in what way” (ch. 7, p. 16). “But about what it is for something to be, and thinghood, no one has delivered up a clear account, but those who posit the forms speak of it most” (p. 17).

Aristotle thinks that Plato came closer to what is needed than any of his predecessors.

“That for the sake of which actions and changes and motions are, they speak of as a cause in a certain way, but they do not say it that way, nor speak of what is so by its very nature. For those who speak of intellect or friendship as good set these up as causes, but do not speak as though anything that is either has its being or comes into being for the sake of these, but as though motions arose from these” (ibid, emphasis added).

We saw that Aristotle understands Anaxagoras as claiming that intellect is a source of motion, in some direct but unexplained way. Aristotle maintains on the contrary that intellect is a cause in what he above called the “opposite” sense of that for the sake of which.

He continues, “And in the same way too, those who speak of the one or being as such a nature do say that it is the cause of thinghood [i.e., of things being what they are], but not that it either is or comes about for the sake of this; so it turns out that they both say and do not say that the good is a cause, since they say it is so not simply but incidentally” (ibid, emphasis added).

Parts of this remark apply to the Pythagoreans (the one) and the Eleatics (the one or being). All of it, including the part about the good, applies to the Platonists. For Aristotle, neither “the one” nor “being” is in its own right a true cause, because neither gives us a specific why for anything. Aristotle’s own notion of the first cause is to be identified neither with Thomistic Being nor with the neoplatonic One. On the other hand, the good is a true cause, because it does give us specific reasons why. These are expressible in terms of that-for-the-sake-of-which. But he also delicately implies that even Plato treats the Good more like a source of motions than a grounding for explanations in terms of that-for-the-sake-of-which. Elsewhere, he says that Plato treats the Good as a formal cause, rather than as that-for-the-sake-of-which. In any case, he clearly thinks that Plato treats the Good as affecting things in some other way than as that-for-the-sake-of-which. The neoplatonists explicitly represent the One or the Good as producing all things. But at this level, the specificity of reasons why things turn out some particular way is completely left behind.

Without a reason why things turn out as they do, for Aristotle there is no true cause. That-for-the-sake-of-which is more preeminently and properly a why than any of the other causes, and for Aristotle this makes it more preeminently and properly a cause than any of the other causes. That is why it seems reasonable to him that the first cause of all should be purely a cause in the sense of that for the sake of which.

The scholastics and the moderns tend to reduce all causes to the notion of efficient cause that they put in the place of Aristotle’s “source of motion”. But for Aristotle, a source of motion is principally a means to the realization of an end, to which it is subordinated. Aristotle ultimately subordinates all other causes to the operation of the good as that for the sake of which. The result is not a total determination or absolute necessity, but rather various hypothetical necessities that can each be realized in more than one way, and that therefore still allow room for genuine contributions to the outcome from secondary causes.

Aristotle’s association of that-for-the-sake-of-which with completion in the earlier quote recalls the way that he elsewhere associates it with actuality, which in the Barnes-edited Collected Works edition of the Physics is translated as “fulfillment”, and which Aristotle closely identifies with entelechy, which also implies completion. Thus, although I don’t recall him ever explicitly saying it, both potentiality and actuality are represented among the four causes, which we could now alternatively list as form, material, potentiality, and actuality. This particular conclusion is new to me, but based on the argument sketched here it seems pretty solid. This has a number of interesting consequences.

For example, with these identifications in hand, we can apply the priority of actuality over potentiality in Aristotle as an alternate reason why that-for-the-sake-of-which is prior to the source of motion.

We can also see another reason why although there is a kind of analogy between the actuality/potentiality and form/material relations, the distinction between actuality and potentiality cannot be reduced to that between form and material. Otherwise, there would be only two distinct kinds of causes, and not the four on which Aristotle insists. This distinction between the two distinctions fits perfectly with Aristotle’s other insistence that nonsensible as well as sensible things can have being in potentiality, whereas only sensible things are properly said to have material.

Next in this series: Infinity, Finitude, and the Good

Toward Potentiality and Actuality

With the discussion of independent things, the saying of what they are, and the provision for deriving sayings in the other categories from this, we have taken simple saying in the various senses of Aristotle’s Categories about as far as it can go. Although higher dialectical aspects will emerge in what is yet to come, I think the main results of Metaphysics book Zeta (VII) are qualified well enough to be counted by Aristotle as a permanent acquisition that will still be enhanced, but never rolled back.

Aristotelian saying is far from exhausted by saying in the syntactic senses of the Categories, however. We have yet to touch upon its all-important normative aspect, and the corresponding saying of things with an additional modal dimension of potentiality or actuality. This will be intimately involved with that-for-the-sake-of-which (see also Aristotle on Explanation). Book Eta (VIII), treated here, serves as a transition to the main discussion of potentiality and actuality that lies ahead in book Theta (IX).

For Aristotle (and Hegel as well), to say that something is actually X is to judge that it has achieved and is stably continuing to achieve a full expression of what it is to be X, which means it is actively fulfilling that for the sake of which X’s do what they characteristically do (see also Entelechy). In thinking about this, it is important not to set the bar too high — Aristotle thinks it is true of many things.

Then for something to be potentially X, at least within itself it has to be fully “ready” to undergo whatever is required by the process of becoming an actual X, though its becoming an actual X in fact will usually depend on conditions external to it, and in particular on the activity of some other actual X — parents in the case of offspring, and something like a Platonic “model” of the thing in the case of artificial things.

Book Eta begins with a summary of book Zeta, so here it is evident from the text itself that the two are intended to develop one continuous argument. Then book Theta will begin with a very short summary of both Zeta and Eta.

“Now one ought to reckon up the results of what has been said, and, putting them all together, to set out the final point to which they come. And it has been said that the causes, sources, and elements of independent things are being looked for” (ch. 1, Sachs tr., p. 155).

Here again we have a more refined statement of the goal of the inquiry. He then cheerfully points out what is in fact the big new impasse reached in the previous book, concerning the impossibility of defining independent things:

“But in one way it follows from the discussions that what it is for something to be, and what underlies something, are kinds of thinghood, and in another way that thinghood is the general class, more than the specific one, and the universal more than the particulars; and the forms are also connected with the universal and the general class (since it is by the same argument that they seem to be independent things). And since what it is for something to be is thinghood, and the articulation of that is a definition, for that reason distinctions were made about definition and about what something is in virtue of itself; and since a definition is a statement, and a statement has parts, it was also necessary to know about the parts — which sort are parts of an independent thing and which not, and if these are the same ones that are parts of the definition. And further, in the course of this, it turned out that neither the universal nor the general class is thinghood” (ibid).

He highlights the discussion of definition, saving till the end the major issue that the independent thing itself is a particular that cannot be the direct subject of a definition. The subtle cue that there will be something problematic in what is said is his “in one way it follows”.

It is typical of both Aristotle and Hegel to appear to endorse an argument for a while, only to eventually overturn it. This can be seen as preliminarily giving each current argument the benefit of the doubt, rather than attempting to anticipate its future refutation. Both Aristotle and Hegel consider it essential for learning to go through the process of an argument’s dialectical development, and not just anticipate ultimate conclusions, as if out of nowhere.

The last statement — that universals do not directly characterize substance-essence-thinghood, which is always particular — is one of the most important conclusions of the Metaphysics. It means that for Aristotle, knowledge (episteme) also will not apply to independent things, since independent things are particulars. This implies that for independent things, we have to rely on something like the practical judgment cultivated for ethical practice, which is directed at particulars.

Those who have wanted to treat “metaphysics” as a “science of being” are going in the opposite of Aristotle’s direction. First he characterizes “being” as having to do with what things are and what can properly be said about them. Then he says the inquiry is really about the causes of independent things. Then he eventually concludes that knowledge does not apply to independent things, because they are particulars. What he is after here is a kind of practical wisdom, not scholastic “science”.

“But now let us go over what concerns the acknowledged independent things. And these are the perceptible ones. And all perceptible independent things have material. And what underlies something is its thinghood, and in one sense this is the material (and by material I mean that which, while not being actively a this, is a this potentially), but in another sense what underlies something is its articulation and form, which, being a this, is separate in articulation; and a third sort of underlying thing is what is composed of these, of which alone there is coming into being and destruction, and which is separate simply. For of the independent things in the sense that corresponds to the articulation, some are separate simply, while others are not” (pp. 155-156).

Here he explicitly generalizes the notion of an “underlying thing”. In the previous book, he started with the accepted view that this must be some kind of material. Then he adopted a Platonic lesson that the form or articulation of things better characterizes what they are. Then he diverged from the Platonists and concluded that independent things are even more important than form.

He certainly discussed all three cases, but my reading of the previous book was that only the composite of both form and matter ended up fully and properly qualifying as an independent thing. In part, he is being extra generous here to his former colleagues in the Platonic Academy, as well as to common-sense views of material. But he is also setting the stage for a new conclusion we will see shortly.

At this point, I am a little mystified by the implication that both all composites and some forms (presumably, some forms of non-perceptible things, which have been mentioned in passing but not discussed yet) will turn out to be in the same way “separate simply”. His only developed argument about the applicability of “separateness” to forms so far has been against the separateness of the Platonic forms, at least in any context involving perceptible things.

However, it is also true that the previous book does in passing seem to defer discussion of the possibility that there are non-perceptible independent things. To anticipate, it does seem true that any first cause of all, analogous to the first cause of motion he argues for in the Physics, must also be independent, for by definition, “first” means having no dependencies.

“[I]t remains to say what the thinghood of perceptible things is in the sense of being-at-work. And Democritus seems to think there are three ways things differ (for he thinks that the underlying body, the material, is one and the same, while what differ are design, which is shape, twist, which is position, and grouping, which is order). But it is obvious that there are many differences; for instance, some things are spoken of by reference to the composition of their material, as are all those made by mixing, such as milk blended with honey; others by way of a binding-cord, such as a bundle, others by means of glue, such as a book, others by means of bolts, such as a box, others by more than one of these, others by position, such as a threshold and a capstone (since these differ by being placed in a certain way), others by time, such as dinner and breakfast, others by place, such as the winds, and others by the attributes of perceptible things such as hardness and softness, density and rarity, or dryness and fluidity, some things differing by some of these, some by all of them” (ch. 2, pp. 156-157).

As this passage makes clear for non-independent perceptible things, in no case does what he calls the “being-at-work” or “actuality” of things involve what we ordinarily think of as work (which is why I still guardedly use “actuality”). In the case of non-independent perceptible things, the “being-at-work” has to do with whatever makes a unified thing out of material components.

“So one must grasp the kinds of differences (since these will be the source of being)…. So it is clear from these considerations that if thinghood is the cause of each thing’s being, it is among these differences that one must look for what is responsible for the being of each of these things. None of these examples is an independent thing, but still there is an analogous structure in each of them” (p. 157).

As we saw in the previous book, Aristotle sees definitions not in the modern formalist sense of characterizations we simply posit in isolation, but as built up from an ordered series of essential differences that progressively distinguish something from other things. To define something for Aristotle is to clarify its relation to classifying distinctions from other things.

“Now it is clear from these examples that the being-at-work and the articulation are different for different materials” (p. 158).

Kinds of materials are a sort of universals, so we do expect their distinctions to be fully articulable. From his examples above, what is responsible for the unity of material things that are not independent living things is itself something material. What kind of thing this source of material unity will be varies according to the case.

“One must not ignore the fact that it sometimes escapes notice whether a name indicates a composite independent thing or its being-at-work and form” (ch.3, p. 158).

“[W]hat it is for something to be belongs to the form and the being-at-work” (p. 159).

Form establishes a what, though it is a universal what and not a particular what. So far we have only seen examples of the somewhat non-intuitive being-at-work of material, non-independent things, which I just called the “source” in Aristotle’s sense for their material unity.

“Now it is obvious to those who inquire about it that a syllable is not made of its letters plus combination, nor a house out of bricks plus combination…. Nor indeed is humanness animalness plus two-footedness, but there has to be something which is apart from these, since these are its material, and that something is neither an element nor derived from an element, but since people leave this out, they describe its material” (ibid).

Here he continues his dispute with Plato’s other students. Combination is not a material ingredient of anything, even in the sense of purely logical or “intelligible” material.

“But whether those things that are the thinghood of destructible things have being separately is not at all clear yet, except that it is clear for certain things at least that this is not possible, as many as are not capable of being apart from the particulars, such as a house or a piece of furniture. So presumably these things themselves are not independent things, nor is any of the other things that are not composed by nature, for one may posit that nature alone is the thinghood in destructible things” (ibid).

I find the above a bit perplexing. The previous book clearly seemed to assume that there are perceptible independent things, and that at least all earthly perceptible things are destructible, though he seems to assume the stars and planets are indestructible, since he sees no evidence to the contrary. But it seemed that animals and plants were implied to be independent things, and to have their own distinctive substance-essence-thinghood. He definitely said that “the soul of an animal… is its thinghood disclosed in speech”. Isn’t an animal a destructible thing?

“[I]t does not belong to an independent thing to be capable of a definition” (p. 160).

This again was a major conclusion of the previous book.

“[E]ach independent thing is a complete being-at-work-staying-itself [entelechy], and a particular nature” (pp. 160-161).

Here he explicitly associates the independence of independent things with the teleological notion of entelechy.

“[W]henever one is inquiring after what is responsible for something, one must state all the causes the thing admits of” (ch. 4, p. 162).

I silently passed over his discussion of his predecessors in book I, but his main argument there was that none of them took all the causes into account. In particular, even Plato resorted to treating the Good as a formal or efficient cause. Aristotle regards interpretation by that-for-the-sake-of-which as his own major innovation.

“And what is the cause in the sense of form? What it keeps on being in order to be. And what is the cause for the sake of which it is? Its end, though presumably both of the last two causes are the same. And one must state the nearest causes: What is the material? Not fire or earth but the material peculiar to the thing” (ibid).

I just pointed out that Aristotle regards the distinction of that-for-the-sake-of-which from a formal cause as of major importance. His identification of the two here therefore must be intended as less than fully general. Form has senses that do not primarily emphasize any normative component, such as the form of triangularity. But as we have seen, Aristotle also speaks of the souls of animals as forms.

One might say that the soul is the entelechy (literally, “in [it] end having”) of a living body. Entelechies may come in layers. More precisely, the soul would be a name for the “first entelechy” of the body, or its achieved and continuing organic functioning. For Aristotle, this is intrinsically a normative concept. To speak of the entelechy of a body implies that it is not only functioning, but functioning well in relation to its intrinsic ends. Higher ongoing functions — just insofar as they are well realized — involve higher entelechies.

He makes an important point about material. What is usually most relevant is “not fire or earth but the material peculiar to the thing“, such as an organic body or a particular mineral. The more specific a material is, the more form-like it is. We will see shortly that Aristotle takes this to the point of identity between the most specific material and the form of a material thing.

“[T]here will not be material in those things that are or are not without changing” (ch. 5, p. 163).

In the Physics, the material cause was originally developed as part of the explanation of change.

“[A]ll things that have more than one part, and of which the sum is not like a heap, but a whole that is something over and above the parts, have something responsible for them…. But a definition is one statement not by being bundled together like the Iliad, but by being of one thing” (ch. 6, pp. 163-164).

A form is normally treated as an integral whole. A definition implicitly refers to an integral whole.

“Now it is clear that, for those who approach defining and explaining in this way that they are accustomed to [crudely adding specifications together, as in “animal plus two-footed”], it is not possible to give an account of it and resolve the impasse. But if, as we say, there is one thing that is material and one that is form, and the former has being as potency and the latter as being-at-work, the thing sought after would no longer seem to be an impasse” (p. 164).

I think what he is saying here is that the definition applies to the form only, not to the composite. That is probably why he earlier mentioned the ambiguity between a name’s referring to the form, and its referring to the composite. This does resolve some of the earlier puzzles about the applicability of definitions (a definition applies to a form). It is important to recall, though, that he just said again that there is still no direct applicability of definitions — which are expressed in universal terms — to independent things, which are particulars.

“But as many things as do not have either intelligible or perceptible material, are each of them some very thing that is one, just as also some very thing that is, a this, an of-this-sort, a so-much (and this is why neither being nor one is included in definitions), and what it is for something to be is immediately a particular one and a particular being. Hence there is no other thing responsible for the being-one of any of these, nor of the being-a-being of each, since each is immediately a certain being and a certain one, not in the sense of being in a class of beings or ones, nor of being among things that have being apart from particulars” (pp. 164-165).

Now he begins to speak in general about things that have no material. What this will apply to is as yet unspecified.

“But as was said, the highest level of material and the form are one and the same thing; the former potentially, the latter actively, so that looking for what is responsible for their being one is like looking for a cause of one thing; for each of them is a certain one, and what is in potency and what is in activity are in a certain way one thing. Therefore there is nothing else responsible, unless in the case of something that moves it from potency to being-at-work, but everything that does not have material is simply something that is itself one” (p. 165).

Back again to things that do have material, here he makes a point I alluded to earlier. One aspect of Aristotle’s hylomorphism is this identity of the most specific material with the form (for things that have material). Each independent thing has its own entelechy that is the primary cause of its being what it is.

Finally, he reiterates that things without material do not require anything external to give them unity.

Next in this series: The Innovation of Potentiality-Actuality

Formal and Material Interpretation

Human reasoning has two sides, that could be called formal and material. Any reasoning applicable to the real world necessarily involves the “material” side that is concerned with actual meaning “content”. It may also involve the “formal” side, which aims to express reasoning in terms of mechanically repeatable operations that are completely agnostic to the actual meanings they are used to operate on. Reasoning in some abstract contexts may rely entirely on the formal side.

Aristotle is usually credited with inventing formal logic, but he paid a lot of attention to the material side as well. In the Latin middle ages both sides were recognized, but the formal side was generally emphasized.

Formal mathematical logic underwent an immense development in the 20th century, somewhat like the earlier success story of mathematical physics. The syntactic devices of mathematical logic seemed so powerful that its rise led to a great neglect of the material, interpretive side of logic. Husserl was one of the few 20th century authors who questioned this from the start. More recently, Brandom has argued that Kant and Hegel were both fundamentally concerned with the material, interpretive side of logic, and that this is what Kant meant by “transcendental” logic (and what Hegel meant by “dialectic”).

Generally when I mention interpretation here, I have the material side in mind, but there is also such a thing as formal interpretation. Formal interpretation or “evaluation” of expressions in terms of other expressions is the most fundamental thing that interpreters and compilers for programming languages do. As with material interpretation, formal interpretation makes meanings explicit by expressing them in terms of more elementary distinctions and entailments, but it uses purely syntactic substitution and rewriting to do so.

Material interpretation can always potentially go on indefinitely, explaining real-world meanings by relating them to other meanings, and those in terms of others, and so on. In practice, we always cut it short at some point, once we achieve a relatively stable network of dependencies.

Formal interpretation on the other hand is usually engineered to be decidable, so that it actually does reach an end at some point. The fact that it reaches an end is closely related to the fact that precise formal models are always in some sense only approximations of a determination of reality that is actually open-ended. Formal models are a sort of syntactic reification of open-ended material interpretation. We may think we have taken them as far as they can go, but in real life it is always possible that some new case will come up that requires new detail in the model.

We also use a kind of formal interpretation alongside material interpretation in our spontaneous understanding of natural language. Natural language syntax helps us understand natural language meaning. It provides cues for how different clauses are intended to relate to one another. Is what is meant in this clause an exception? A consequence? A presupposition? A fact? A recommendation? Something being criticized? (See also Formal and Informal Language.)