Complexity and Syntactic Simplicity
in Ockham's Mental Language
(Comments on Yiwei Zheng: 'Ockham's Connotation Theory and Ontological Elimination', Eastern APA Meeting, Washington DC, December 30, 1998)
In these comments I am going to argue that Yiwei Zheng's paper, by postulating an imaginary mental language in a proposed new interpretation of Ockham's conception of mental language, provides us with an imaginary solution to what turns out to be an imaginary problem. Having said this, however, I hasten to add that the paper has undeniable merits in pointing us in the right direction for revealing the imaginary character of the problem.
Since the paper does not quite spell out the problem it intends to solve, let me begin by reconstructing the problem itself. As we shall see, a careful exposition of the problem will already hold the key to its solution, or rather its elimination.
The paper lays down three conditions to be met by a "good interpretation" of Ockham's theory:
(a) [every] connotative term has a semantically equivalent, fully expanded nominal definition [the "synonymy thesis"]
(b) there is no synonym[y] in mental language[, that is, synonymous spoken phrases are subordinated to one and the same concept]
(c) [there are] simple connotative terms in mental language
I am not entirely convinced that these three conditions jointly constitute absolutely necessary desiderata of a "good interpretation", but this is not the issue I wish to address here. Instead of this primarily philological issue, I would rather deal here with the primarily philosophical issue of whether it is possible to provide a consistent interpretation of these three points in accordance with Ockham's tenets.
Conditions (a) and (b) clearly entail the claim that
(d) every spoken connotative term is subordinated to the same concept as its nominal definition.
However, since a nominal definition is a complex phrase, it has to be subordinated to a complex concept; that is to say,
(e) every nominal definition is subordinated to a complex concept.
But these claims (namely, (d) and (e)) entail that
(f) every spoken connotative term is subordinated to a complex concept;
which is just another way of saying that
(g) every concept corresponding to a spoken connotative term, that is, every connotative mental term, is complex.
This conclusion, however, obviously contradicts condition (c).
The paper attempts to resolve the resulting contradiction by eliminating the crucial assumption in this argument, namely, the assumption that since a nominal definition is a complex phrase, it has to be subordinated to a complex concept. (That is, the assumption backing premise (e) above.) Indeed, the paper intends to show further that according to Ockham no concepts can be complex, given his claim that all concepts are simple, indivisible qualities of the mind. Thus, all complex phrases of our spoken languages would have to be subordinated to simple concepts.
However, this claim seems to be in conflict with the obvious compositionality of our complex phrases. For a complex spoken expression can have compositional meaning only in virtue of the compositional meaning of the concept it is subordinated to, since no spoken phrase can have any meaning whatsoever other than the meaning it has from the corresponding concept. But then, how could a simple concept have compositional meaning, if it cannot be composed of any parts, and so its meaning clearly cannot be a function of the meanings of its parts?
The paper argues that one can show that it is possible to provide a recursive semantics for simple connotative concepts without assuming their syntactic complexity. However, according to the paper, to this end we need to posit an imaginary mental language in which imaginary complex concepts do semantic duty for real simple concepts.
(1) In what follows, I am going to argue that it is indeed possible to provide a recursive semantics for simple concepts without assuming their syntactic complexity. But in order to see this, it is sufficient to realize the importance of a distinction implicit in Ockham, but quite explicit in the work of John Buridan, namely, the distinction between semantic vs. syntactic complexity. [I described the distinction in these terms in my "Latin as a Formal Language: Outlines of a Buridanian Semantics", Cahiers de l'Institut du Moyen-Âge Grec et Latin, Copenhagen, 61(1991), pp. 78-106. Buridan draws the distinction by distinguishing between a term's being complex from the grammarian's point of view (syntactic complexity) and from the logician's point of view (semantic complexity). Cf. SD 1.1.6; 1.2.1; Sophismata, c. 1, conclusion 10.] The point of the distinction is that these two do not always have to go hand in hand, and thus it is possible to have semantically complex, but syntactically simple signs in any language, be it written, spoken, or mental.
(2) Secondly, I will argue that with this distinction at hand we clearly can provide a recursive semantics for syntactically simple concepts without any need of positing an imaginary mental language, which is a solution Ockham would certainly find preferable.
(3) Finally, I will argue that any interpretation, including Zheng's, which is based on the distinction between semantic and syntactic complexity will not render conditions (a)-(c) consistent, unless we are talking about the complexity of concepts equivocally, in which case, however, the problem is merely imaginary.
Pro 1o. Following the suggestions of Buridan, let us call a sign syntactically complex if and only if it has parts which are separately meaningful, and which determine the meaning of the whole they constitute by the meanings they separately have. By this criterion, for example, the word 'fireman' is not syntactically complex, for even if it has separately meaningful parts, those parts do not determine the meaning of the whole by the meanings they separately have (for a fireman is not something that is both a fire and a man). By contrast, the phrase 'a man whose job is to extinguish dangerous fires' is syntactically complex in this sense, as is obvious.
On the other hand, let us call a sign semantically complex if and only if its meaning is a function of the meanings of other signs, regardless of whether those other signs are its constitutive parts in an ontological sense or not. Thus, by this criterion, the inscription 'fireman' is semantically complex, provided we take the inscription 'man whose job is to extinguish dangerous fires' to be its nominal definition, stipulating the meaning of this term. (In case someone does not like this nominal definition of 'fireman', I might just introduce the new term 'biltrix' into our conversation by this nominal definition.) But then it is obvious that the inscription 'fireman' (or 'biltrix', if you prefer) is both syntactically simple and semantically complex in the sense just defined. So, it is clearly possible to have a sign in a language which is syntactically simple, but semantically complex.
With this distinction in mind, it is easy to establish my second point.
Pro 2o. As we could see, a sign, indeed, any sign, will be semantically complex if and only if its meaning is a function of the meanings of other signs, but those other signs may or may not be its constitutive parts in an ontological sense. Thus, we may have any number of semantically complex signs, which, however, need not contain any constitutive parts that are meaningful in themselves, indeed, they need not contain any constitutive parts at all. Therefore, ontologically they may be indefinitely simple, and thus, they may not have any spatio-temporal parts, just as Ockham claimed concerning mental propositions.
But then it is perfectly possible to have a recursive semantics for ontologically, and so also syntactically, simple connotative concepts without any need of positing an imaginary mental language. All we need to realize in this connection is that by the complexity of a concept corresponding to a spoken complex expression we should understand its mere semantic complexity: that the concept in question is complex means only that its semantic values are functionally dependent on the semantic values of the concepts corresponding to the separately meaningful parts of the spoken expression subordinated to it, but the concepts corresponding to these parts need by no means be the constitutive, ontological parts of the concept corresponding to the whole expression. [As Buridan says: "… if a word has been imposed to signify a complex concept consisting of several simple concepts, then it needs an interpretation by means of several words that signify separately those simple concepts, of which the complex one consists." 8.2.4.] Therefore, with this understanding of the purely semantic complexity of complex concepts, there is clearly no need for positing an imaginary mental language to account for the compositionality of semantically complex but syntactically simple concepts. But then, such an imaginary mental language is doomed to fall prey to Ockham's Razor.
Pro 3o. It is also easy to see, however, that acknowledging the ontological, and hence syntactic simplicity of semantically complex concepts will still not yield the desired consistent interpretation for conditions (a)-(c), provided in the argument proving their inconsistency we talk about simplicity or complexity always in the relevant, semantic sense. For according to that argument, conditions (a) and (b) entail the semantic complexity of all connotative concepts on account of their corresponding to both semantically and syntactically complex nominal definitions. But condition (c), stating the simplicity of at least some connotative concepts, taken again in the sense of claiming semantic simplicity, clearly contradicts this conclusion. (In fact, this is precisely why Buridan rejected the claim that all connotative terms have nominal definitions, given his explicit endorsement of certain semantically simple connotative terms, such as non-substantivated adjectives.)
On the other hand, as we have seen, insisting on the syntactic simplicity of all mental concepts need not entail anything concerning their semantic simplicity. Thus, if we interpret condition (c) as claiming mere ontological, and hence also syntactic simplicity to some connotative terms, then the contradiction is merely apparent, and the problem it seems to generate is obviously imaginary.
This last point is important because Zheng's solution also turns on the distinction between semantic and syntactic complexity, which he quite clearly indicated in his distinction between recursive semantics and compositional syntax, but eventually failed to exploit in his solution. In fact, a careful exposition of the problem of the inconsistency of conditions (a)-(c) could already have shown the sufficiency of this distinction for the elimination of the problem. Nevertheless, Zheng's paper, by calling our attention to the importance of this distinction, effectively points us in the right direction for revealing the merely imaginary character of this problem.
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