Abstract
I review and challenge the views on simplicity and its role in linguistics put forward by Ludlow (The philosophy of generative linguistics, 2011). In particular, I criticize the claim that simplicity—in the sense pertinent to science—is nothing more than ease of use or “user-friendliness”, motivated by economy of (cognitive) labor. I argue that Ludlow’s discussion fails to do justice to the diversity of factors that are relevant to simplicity considerations. This, in turn, leads to the neglect of crucial cases in which the rationale for simplification is unmistakably epistemic, as well as instances where simplicity is part of the content of substantive, empirical hypotheses. I illustrate these points with examples from the history of generative linguistics, such as: (a) the shaping influence exerted by simplicity, via its involvement in the notion of “linguistically significant generalization”, (b) its methodological and substantive contribution to the goal of explanatory adequacy, and (c) its central role in the Minimalist Program’s search “beyond explanatory adequacy”.
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Notes
Page references are to Ludlow (2011) unless otherwise noted.
There is no dearth of distinctions regarding simplicity in the literature, so I will only introduce those distinctions that are necessary for the purposes of this paper. My classification scheme has some commonalities with distinctions proposed in the literature (such as Rudner 1961; Bunge 1961, 1962; Hesse 1967; Baker 2011; Schulz 2012, among others), but given the different purposes and contexts, it is clearly different from them.
The range of entities for which simplicity may be a pertinent evaluation criterion is quite wide, and includes, inter alia, “theories”—and the kinds of things that go under this label are also diverse, ranging from very general conceptions about a subject matter to specialized systems of equations and computational models—as well as particular formulations of theoretical ideas, hypotheses, computational methods, data analysis techniques, notational systems, measurement systems, data-recording instruments and all sorts of artifacts associated with scientific research, regardless of their ontological status and epistemic role.
This is not to say that there aren’t alternative measures of parsimony of phylogenetic hypotheses—such as the number of parameters in a model—which, moreover, may yield incompatible results. Different measures may be appropriate for different purposes, or may incorporate different assumptions, but in any case they all aim to implement some version of Ockham’s Razor.
Nevertheless, the notions of formality and “theory-internality” and not identical. Simplicity criteria may be theory-internal to the degree that their applicability or relevance depends on certain theoretical assumptions, which may or may not be directly expressed in terms of formal characteristics or notational features.
It should be pointed out that the external–internal dimension must be to some degree relativized to particular theoretical contexts: “theory-external” does not necessarily mean external to or independent from any theory, but rather “external to the theory(ies) at issue”.
One can also find different aspects simplicity discussed under the various headings of (e.g.) “cohesiveness”, “elegance”, “economy”, “optimality” and “symmetry” (which are not always used everywhere in the same sense). Determining exactly what the members of the list are and how they are related to each other are interesting issues, but I won’t deal with them here.
I am using this term in a very general way to designate all sorts of entities, properties, processes or regularities comprising the subject matter of the field.
Derivability is the case to which philosophers of science have devoted the most attention—especially in the context of intertheoretical reduction—though not necessarily the only one.
Ockham’s Razor is usually stated as an injunction against multiplying entities beyond necessity. Some readings of the maxim emphasize its quantitative aspect (i.e. ‘do not multiply entities’), whereas in other readings the focus on the injunction against going beyond what is strictly essential. Relatedly, Barnes (2000) recognizes two different principles associated with Ockham’s Razor: the “anti-quantity” principle, and the “anti-superfluity principle”, corresponding to the two readings just mentioned. The type of theoretical move that is relevant for our purposes is the one that appeals, explicitly or implicitly, to the second principle. Also, notice that freedom from superfluous posits is different from sheer paucity of posits—even if the respective injunctions to eliminate superfluity and to reduce the number of posits often have identical implications. Thus, consider a theory A, containing n basic posits, all of which are essential, and another theory B with \(m ~\angle ~ n \) posits, some of which turn out not to be essential. There is one important sense then, in which A is more parsimonious than B (see Barnes 2000, 354ff).
See Lipton (1991).
Under which conditions can we said that an element is “superfluous”? First, a particular decision will depend on the relevant context, such as the purpose at hand. Suppose that the goal is to design a circuit. Then, given that the NAND operator is functionally complete (which is not true of the other truth functional connectives, except NOR) and that NAND gates are relatively easy or convenient to implement, then, in the Boolean (combinational) logic used to represent the circuit, all the other operators would be strictly speaking superfluous (you won’t gain any processing speed or reliability, or computational power by including them.) Now, if we have a very good psychosemantic theory that were committed to negation, conjunction and operation all being “psychologically real” irreducible, basic, operations, then if our goal is to provide a faithful characterization of human semantic competence they would not be superfluous. So, from an electronics perspective the system would have unjustified redundancies, but from the psychological one those redundancies would be warranted.
That is, a verb that does not take any objects, in contrast with ‘love’, that does take direct objects, as illustrated by 4.
Especially since quite general regularities in phrase structure can already be captured by X-bar theory, which will be discussed in Sect. 4.3.
This point has often been made by Nelson Goodman. For instance:
Nothing could be much more mistaken than the traditional idea that we first seek a true system and then, for the sake of elegance alone, seek a simple one. We are inevitably concerned with simplicity as soon as we are concerned with system at all [...] Thus simplicity [...] is not a consideration applicable after truth is determined but is one of the standards of validity that are applied in the effort to discover truth (Goodman 1958, p. 1064).
These kinds of changes are related to the ones mentioned by Whewell (1840/1984, 1858) in his discussion of the “colligation of facts”, such as those leading to the consilience of inductions effected by Kepler’s and Newton’s laws. Thus, in colligation:
Facts are not only brought together, but seen in a new point of view. A new mental element is superinduced; and a peculiar constitution and discipline of mind are requisite in order to make this Induction (Whewell 1858, p. 71).
Furthermore,
[T]he Facts that the planets revolve around the sun in certain periodic times and at certain distances, are included and connected in Kepler’s Law, by means of such Conceptions as the squares of numbers, the cubes of distances, and the proportionality of these quantities. Again the existence of thus proportion in the motion of any two planets, forms a set of Facts which may all be combined by means of the Conception of a certain central accelerating force, as was proved by Newton (emphasis in the original, Whewell 1840/1984, p. 206).
Correspondingly, a linguistic theory or theory of grammar is descriptively adequate if it makes “descriptively adequate grammars available for each language” (p. 24).
Taking a language L to be a set of finite strings (“grammatical sentences”), a grammar G is a set of rules that specifies the sentences of L, and assigns to each a structural description—that is, a full account of its elements and their organization.
This idea is clearly put forward in early writings:
[...] one of the considerations involved in setting up linguistic elements in a particular way, and consequently, in determining what are in fact the grammatical sentences, will be the total simplicity of the grammar in which these elements appear (MMH, p. 3).
It seems reasonable [...] to inquire into the possibility of defining linguistic notions in the general theory partly in terms of such properties of grammar as simplicity (LSLT, p. 114).
Thus, Chomsky points out that “[...] it is important to recognize that we are not interested in reduction of the lengths of grammars for its own sake. Our aim is rather to permit just those reductions in length which reflect real simplicity, that is, which will turn simpler grammars (in some partially understood pre-systematic sense of this notion) into shorter grammars (LSLT, p. 118, emphasis mine)”.
For reasons of convenience, I’ve been talking of grammars as if they were sets of rules. However, this is incorrect, since the same set of rules but with different order of application can constitute different grammars. Thus, they are more accurately characterized as sequences of rules (see LSLT, 125 ff).
“What lies behind a generalization or a regularity in a set of data is a pattern that permits a ‘compression’ in the description of that set, beyond a simple list of its members” (Berwick 1985, p. 225).
In Chomsky’s own summary of the role and nature of simplicity in the context of evaluation procedures:
The obvious means for selecting among grammars is in terms of the degree of significant generalization that they achieve. In the conventional sense of the term, a generalization is a single rule about many elements. Generalizing this notion, we might measure the degree of generalization attained by a grammar in terms of the formal similarity among its generative rules, the extent to which they say similar things about elements of various sorts.
And this in its turn required:
[...] a system of amalgamating similar rules, so that grammars with a greater degree of similarity among rules become, literally, shorter than others which express the same mapping from morphophonemic to phonetic representation. The system for amalgamating rules expresses a hypothesis as to the relations among rules that constitute linguistically significant generalizations (LSLT, pp. 26–27).
“[...] the evaluation procedure proposed in MMH (similarly, ATS, SPE and other work), constitutes an empirical hypothesis with regard to the “essence of human language”, specifically, with regard to the principles of organization that are taken to be fundamental in that the generalizations that express them are defined as “linguistically significant” and contribute to the selection of grammars” (LSLT, p. 28).
“Given criteria of adequacy for grammars of certain languages we can arrive empirically at notations with the property that the grammars meeting the criteria of adequacy are in fact the shortest, given these notations. In other words, we define simplicity so that, in certain clear cases, the simplest grammars are in fact the correct ones” (LSLT, p. 118). Furthermore:
[...] this procedure [i.e. developing notations that relate theoretical adequacy to simplicity] is no stranger than attempting to define “morpheme” in such a way that what we know to be morphemes in some language turn out to be morphemes when we apply the theory to a corpus of utterances in this language. This can be realized in a nontrivial fashion if we can give a general and abstract definition of “simplicity” (just as of “morpheme”) which in the case of particular languages leads to adequate grammars, and if the general theory of grammatical structure in which this definition appears meets certain considerations of significance that apply to any scientific theory (pp. 118–119).
The arrow means ‘rewrite as’.
The same point made in more cognitive terms:
It is clear, then, that choice of notations and other conventions is not an arbitrary or “merely technical” matter, if length is to be taken as the measure of valuation for a grammar. The criteria and notation are not matter of a priori, topic neutral methodological strictures, but make certain assumptions about the nature of human languages (as opposed to languages in general): human languages are such that the statement of their grammars can be considerably shortened by this particular set of conventions (we could imagine languages that do not yield to this treatment). Thus, when particular notational devices are incorporated into a linguistic theory of the sort we are discussing, a certain empirical claim is made, implicitly, concerning natural languages. It is implied that a person learning a language will attempt to formulate generalizations that can easily be expressed (that is, with few symbols) in terms of the notations of this theory [...] (Chomsky 1965, p. 45).
Simplicity can occasionally be an indicator of descriptive adequacy, via the notion of LSG, particularly in cases in which competing grammars don’t have the same level of descriptive adequacy. In these cases, descriptively adequate rule systems will tend to be more compact, since they capture certain patterns (“felt relations”) that would otherwise look accidental or would have to be accommodated in an ad hoc fashion.
Though a crucial goal of this strategy was a reduction in elaborateness and specificity of the transformations themselves (see Chomsky 1973).
‘N’, ‘V’ , ‘A’ and ‘P’ can be read as ‘noun’, ‘verb’, ‘adjective’ and ‘preposition’, respectively. ‘NP’ is ‘noun phrase’, and the same principle is applied to the other categories. Again, the arrow is to be read as ‘rewrite as’, or in the opposite direction as ‘is a’.
Another kind of position, not illustrated by the structures above, is what is called specifier, or spec.
Actually, the X-bar schema is a little more elaborate (X\(^{\prime }\) includes positions for adjuncts, and allows for recursion):
-
XP \(\rightarrow \) SPEC X\(^{\prime }\)
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X\(^{\prime }\) \(\rightarrow \) X\(^{\prime }\)
-
X\(^{\prime }\) \(\rightarrow \) X\(_{0}\) COMP
Chomsky (1970) and Jackendoff (1977) are the loci classici for X-bar theory.
-
Thus, it’s no surprise that Chomsky, in an early discussion of the role of simplicity, expresses the following:
Such considerations are in general not trivial or ‘merely esthetic’. It has been recognized of philosophical systems, and it is, I think, no less true of grammatical systems, that the motives behind the demand for economy are in many ways the same as those behind the demand that there be a system at all (Chomsky 1951).
Also, in the The Logical structure of linguistic theory (Chomsky 1975/1955):
It has been remarked in the case of philosophical systems that the motives for the demand for economy are in many ways the same as those behind the demand that there is a system at all [...] It seems to me that the same is true of grammatical systems, and of the special sense of simplicity that will concern us directly (Chomsky 1975/1955, p. 114).
As Crain and Pietroski (2006) put it.
Linguists often start by proposing a constrained grammar for a certain range of facts concerning adult competence. Then they try to abstract out regularities across lots of particular examples, across many languages. Then they try to explain these cross-linguistic phenomena in the simplest way. And so on (p. 65).
GB assumed what was called the “T model” of the architecture of the language faculty, which consisted in a series of levels of representation (four, in total), along with the constraints that they place on structures, the permissible operations, etc. The levels were comprised by two interfaces, called L(ogical)F(orm) and P(honetic)F(orm)—which interacted with the conceptual/intentional systems and the articulatory/perceptual systems, respectively—as well as two “syntax internal” levels, called D-structure and S-structure (earlier known as ‘deep’ and ‘surface’ structure). See Lasnik and Uriagereka (1988) and Haegeman (1994) for overviews of the GB approach.
Similar re-evaluations applied to other aspects of the theory, including its objects, operations and relations (see Hornstein et al. 2005).
The same considerations are relevant in cases where simplicity, in the relevant respect, is being played against other potentially conflicting desiderata—such as predictive accuracy, applicability in a certain context, or compatibility with a certain discipline or methodology.
Where such complexity involves “the extent to which constituents contain subconstituents, and the extent to which there is invisible structure” (Culicover and Jackendoff 2006, 414).
I.e., that an attribution of simplicity to an object x may be true when evaluated with respect to a given agent (e.g. a community) and false when applied to others, without x having undergone any change.
Understanding ‘tool’ in a sense broad enough to include, for instance, notational systems, experimental procedures and theoretical models.
E.g. “The questions in the exam were quite simple” (to answer, solve, etc.). Note that the adjective ‘simple’, when used in this sense, can be modified by an infinitival clause, so as to form complex (often hyphenated) adjectives, as in: ‘simple-to-follow instructions’, ‘simple-to-operate machinery’, etc. This is clearly not the case with other uses or senses of ‘simple’.
Though this might well be the case in other kinds of contexts, in which theories are employed as instruments in the pursuit of practical (as opposed to theoretical) goals.
See Hempel (1966).
There are many views and topics related to simplicity that we didn’t discuss here because they were not immediately relevant to our concerns. Among the excluded views are some which assign a global methodological import to simplicity, such as a fundamental part in induction (see Kemeny 1953; Harman 1999, increases prior probability (Jeffreys 1957; Hesse 1974) or promotes testability (Popper 1959). We also left out proposed simplicity metrics (such as those involving the number of free or adjustable parameters in a hypothesis), and we didn’t use curve-fitting as a central illustration of the role of simplicity in hypothesis testing and formulation, as many discussions of simplicity do. I have also left out of the discussion the possible role of uniformity as a precondition for the practice of induction (as in Newton 1687/1999, Principles 2 and 3, and Hume 1740/2000, book 1 part 3, sect 6 and Abstract), for instance, but only as a desirable outcome of theorization.
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Acknowledgments
I would like to thank Howard Lasnik and Paul Pietroski for discussion, as well as Matt Haber, Melinda Fagan, Ewan Dunbar and Shannon Barrios, for their help with parts of this paper.
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Barrios, E. Simple is not easy. Synthese 193, 2261–2305 (2016). https://doi.org/10.1007/s11229-015-0843-9
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DOI: https://doi.org/10.1007/s11229-015-0843-9