September 9, 2008
Chapter 3
Theory of Judgment Making and Its Consequences
1. Introduction
The starting point of the present research is the model of the Computational System (CS) put forth in Chomsky 1993. Taking the informants' linguistic intuitions to be a primary source of data for the evaluation of a theory of the CS and commiting ourselves to making our hypotheses empirically testable, we are led to adopt the Ueyama model of judgment making by the informant. In this chapter, I will elaborate on the Ueyama model and explore its consequences. This chapter will serve as a conceptual foundation for the empirical discussion in chapter 4.
In section 2, I will first review how the CS is embedded in the Ueyama model of judgment making by the informant. On the basis of the Ueyama model, I will then introduce a way to 'represent' the informant judgment, taking into consideration inherent difficulty with 'extracting' from essentially performance data (the informants' judgments) evidence for or against hypotheses about the properties of the CS. I will also note in section 2 two important attributes of the informants that can affect their judments. In section 3, I will address some consequences of what is suggested in section 2. Roughly put, one consequence can be summarized as follows: ungrammaticality always surfaces as unacceptability while grammaticality may or may not surface as acceptability. This asymmetry will serve as the underpinnings of the specific methodological proposals to be made in the rest of the chapter, most crucially, in regard to how we are to assess our hypotheses. I will also address a consequence of recognizing the informants' attributes mentioned in section 2. In sections 4 and 5, I will address the following, drawing in part from the discussion in sections 2 and 3: how to derive empirical consequences from hypotheses about the CS (section 4.1); how predictions are made and evaluated (section 4.2); and finally, how hypotheses are to be assessed (section 5). In section 6, I will address what could be done if our empirical predictions are not borne out, articulating, and in some respects revising, the view suggested in chapter 2 in regard to repeatability.
2. Theory of judgment making
2.1. Introduction
We understand the main goal of generative grammar to be the discovery of the properties of the Computational System (CS); see chapter 1.[1] Following Chomsky 1993, we consider that the input to the CS is a set of items taken from the mental Lexicon and the output is a pair of mental representations—one underlying 'meaning' and the other 'sounds/signs'.[2]
(1) The Model of the CS:
Numeration m / => / CS / => / LF(m)ß
PF(m)
Numeration m: a set of items taken from the mental Lexicon
LF(m): an LF representation based on m
PF(m): a PF representation based on m
Once we take informant judgments to be a primary source of data for hypothesis evaluation, we must recognize the following in regard to the relation between a theory of the CS (=(2a)) and a theory of how the informant's judgment obtains (=(2b)).
(2) a. a theory of the CS
b. a theory of how the informant's judgment obtains
(2a) cannot be empirically evaluated without (2b); considerations about (2b), on the other hand, could be revealing about the properties of the CS only if (2b) makes crucial reference to the CS properties. This is recorded in (3).
(3) a. (2a) cannot be empirically evaluated without (2b).
b. (2b) is useful to an empirical evaluation of (2a) only if (2b) makes crucial reference to (2a).
The relation between (2a) and (2b) can be established if we embed (2a) within (2b). One way to do so is to assume that the informant, upon seeing or listening to the presented sentence, forms a numeration, and compares the output of the CS with the presented sentence itself along with the relevant interpretation being considered. In the absence of alternative ways (known to us) of embedding (2a) within (2b), we will in fact pursue this possibility, following the recent works by A. Ueyama.[3]
Let us consider how the informants make their judgment on sentence a under interpretation g, focusing on experiments where questions such as those in (4) are part of the instructions to the informants.[4]
(4) a. Is sentence a acceptable under interpretation g?
b. How acceptable is sentence a under interpretation g?
'Interpretation g' in (4) is not meant to be the interpretation of entire a; it is instead meant to be part of the interpretation of sentence a. More in particular, what is intended by 'interpretation g' in (4) is an interpretation involving two linguistic expressions such as an anaphoric relation holding between two expressions. A more accurate way of stating the question in (4a) might therefore be something like "Is sentence a acceptable under an interpretation that includes g (a, b), where g (a, b) means a particular interpretation involving two expressions a and b?" In the ensuing discussion, I will however avoid using such a cumbersome way of phrasing the question and continue to use 'under interpretation g(a, b)' or simply 'under interpretation g' unless a more precise formulation is crucially needed.
In section 2.2, I will introduce the Ueyama model of judgment making by the informant. It will be maintained that its adoption is a consequence of (i) accepting Chomsky's (1993) model of the Computational System, (ii) committing ourselves to making our hypotheses about the Computational System empirically testable on the basis of the informants' acceptability judgments, and (iii) having the desire to ensure progress toward the goal of discovering the properties of the Computational System. The CS being embedded in a performance model poses inherent difficulty in accessing data that would be revealing about the properties of the CS and the difficulty will be addressed in section 2.2.2. Section 2.3 addresses what factors affect the informant's judgment on the acceptability of sentence a under interpretation g(a, b). What is proposed there is a consequence of the considerations in section 2.2. In section 2.4, we will recognize that the informant judgments are revealing about the properties of the CS only if the informants pay close enough attention to sentence a and interpretation g. We will further recognize in that section that the informants' resourcefulness may also affect their judgments.
2.2. The model of judgment making and the CS
2.2.1. How the theory of the CS is embedded in the model of judgment making
Consider again the model of the CS in (1), repeated here.
(1) The Model of the CS:
Numeration m / => / CS / => / LF(m)ß
PF(m)
Numeration m: a set of items taken from the mental Lexicon
LF(m): an LF representation based on m
PF(m): a PF representation based on m
A theory of the CS is concerned with questions like the following: what numeration gets mapped to what LF-PF output, what operations combine the items in the numeration in the derivation, what restrictions, if any, are imposed on such operations, etc. Neither a numeration nor an LF-PF output, however, is directly accessible to us. What is accessible to us is the informant's reported judgment on the presented sentence. Insofar as we take informant judgments to be a primary source of data for evaluating hypotheses about the CS, it seems natural, if not unavoidable, that ??? in (5) is (1).
(5) Presented Sentence ≈≈> ??? ≈≈> Judgment
In other words, if the CS plays the central role when the informant makes her judgment on an example sentence, it seems natural to assume that the CS is embedded in the model of judgment making by the informant, as schematized in (6).[5]
(6) Presented Sentence ≈≈> Numeration ==> CS ==>LF and PF ≈≈> Judgment
If we did not adopt this view, it would not be clear how the model of CS is related to the model of judgment making, which in turn would make it unclear in what sense informant judgments can serve as data for or against hypotheses about the properties of the CS.
According to this view, which has been advocated and articulated in recent works by A. Ueyama, the informant forms a numeration in part on the basis of the presented sentence and tries to determine whether the output of the CS is compatible with (i) the phonetic string of the presented sentence and (ii) the 'intended interpretation'.[6] If we choose informants who would always form a numeration that would end up yielding the PF that is compatible with the presented sentence (i.e., those who do not (consciously or unconsciously) 'alter' the presented sentence when judging it), we can be concerned only with the 'compatibility check' regarding the 'intended interpretation'.[7]
As to what 'mediates' the presented sentence and a numeration, I follow Ueyama to appear and take the presented presented to be an input to Parser, which, in part on the basis of word recognition, identifies the argument-predicate relations and the modification relations among the elements in the sentence. I furthermore assume, most crucially, that the output of Parser contributes to, or influences, the formation of a particular numeration.[8] We can thus modify (6) as in (7).
(7) Presented Sentence ==> Parser ≈≈> Numeration == CS ==>LF and PF ≈≈> Judgment
Assuming that a semantic representation (SR) obtains based on the LF representation and suppressing the PF output of the CS in our present discussion (assuming the string sensitivity of the informants; see above), the model of judgment making by the informancan be schematized as in (8).[9]
(8) The Model of Judgment Making by the Informant:
Presented Sentence ≈≈> Parser ≈≈> Numeration == CS ==>LF ==> SR ≈≈> Judgment
As noted above, what is intended within the box in (8) is that the input to the CS is a numeration and its output is an LF representation. The two arrows before and after CS in (7) (and (8)) thus represent the 'is the input of' relation and the 'yields as an output' relation, respectively. Similarly, what is meant by the arrow between LF and SR is that SR obtains based on LF. A numeration m thus results in LF(m) and eventually in SR(m). The other instances of the arrows in (8) are used more loosely, as indicated in (9).
(9) a. Presented Sentence ≈≈> Parser: ... is part of the input to ...
b. Parser ≈≈> Numeration: ... contributes to the formation of ...
c. SR ≈≈> Judgment: ... serves as a basis for ...
Let us review the model of judgment making adopted here. The informant is presented with sentence a and is asked a question such as (4a), repeated here.
(4) a. Is sentence a acceptable under interpretation g?
For example, the question can be "Is John thinks Mary loves himself acceptable under the interpretation that John and himself refer to the same individual?."[10] The presented sentence is part of the input to Parser since interpretation g as well as the informant's world knowledge might also help Parser identify the argument-predicate relations and the modification relations among the elements in the sentence; see (9a).[11] On the basis of such information, Parser helps the formation of a numeration; see (9b).[12] Once numeration m has been determined, the CS yields two output representations LF(m) & PF(m) by the application of some mechanical operations. SR(m) obtains on the basis of LF(m). Assuming that PF(m) is non-distinct from a, the informant's answer to (4a) is based on whether SR(m) is compatible with g. In that sense, the intended interpretation g as well as SR(m) serve as a basis for the informant's judgment on the acceptability of sentence a under interpretation g; see (9c).
Although this might appear to be a novel proposal, I maintain that the conception of Parser and its role in the model of judgment making suggested above is a direct consequence of the fundamental assumptions we adopt and the commitment we make for making our hypotheses about the CS empirically testable. Recall that according to the model of the CS adopted here, its input is a numeration (i.e., a set of items taken from the Lexicon, possibly along with some features) and its two output representations are LF and PF. Once we accept that the informant judgments are a primary source of data for the evaluation of the theory of the CS, it is necessary to embed the CS in the model of judgment making. Once the CS is assumed to be embedded within the model of judgment making, the presented sentence along with the 'intended interpretation' must contribute to the formation of the numeration, as also noted above; and what is responsible for the 'contribution' in question is called Parser. Hence the conception of Parser adopted here is also a consequence of the basic assumptions accepted here.
2.2.2. Difficulty in 'accessing' data about the CS
2.2.2.1. Difficulty
When presented sentence a and asked whether a is acceptable under interpretation g, as in (4a), repeated here, the informant tries to come up with numeration m such that m would serve as the input to the CS.
(4) a. Is sentence a acceptable under interpretation g?
As noted, we assume that as long as the informant pays close enough attention to the form of a, the PF(m) is necessarily non-distinct from a, if it does obtain. Given that LF is the 'basis' of 'meaning', it is reasonable to assume that the informant obtains the 'meaning' of a on the based on LF(m), and such a 'meaning' is referred to here as SR(m). Provided that PF(m) non-distinct from a obtains, what has to be determined, to answer (4a), is whether SR(m) compatible with g obtains.[13] If it does, the answer to (4a) is yes; and otherwise, the answer is no. The informant's answer to (4a) must therefore be based on whether or not the informant can 'come up with' numeration m corresponding to a such that SR(m) compatible with g otains. One might thus be tempted to conclude that the informant's judgment would therefore be revealing about properties of LF and hence of the CS, provided that SR(m) compatible with g(a, b) obtains only if LF(m) has a certain property.[14]