Name Strategy: Its Existence and Implications Mark D.Roberts August 11, 2004 Published: Int.J.Computational Cognition.3(2005)1-14. Abstract It is argued that colour name strategy, object name strategy, and chunking strategy in memory are all aspects of the same general phenomena, called stereotyping, and this in turn is an example of a know-how representation. Such representations are argued to have their origin in a principle called the minimum duplication of resources. For most the subsequent discussions existence of colour name strategy suffices. It is pointed out that the Berlin-Kay universal partial ordering of colours and the frequency of traffic accidents classified by colour are surprisingly similar; a detailed analysis is not carried out as the specific colours recorded are not identical. Some consequences of the existence of a name strategy for the philosophy of language and mathematics are discussed: specifically it is argued that in accounts of truth and meaning it is necessary throughout to use real numbers as opposed to bivalent quantities; and also that the concomitant label associated with sentences should not be of unconditional truth, but rather several real valued quantities associated with visual communication. The implication of real valued truth quantities is that the Continuum Hypothesis of pure mathematics is side-stepped, because real valued quantities occur ab initio. The existence of name strategy shows that thought/sememes and talk/phonemes can be separate, and this vindicates the assumption of thought occurring before talk used in psycholinguistic speech production models. Contents 1 Introduction 2 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Sectional Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Stereotypes Compared to Other Representations . . . . . . . . . . . . 5 1.5 Minimal Duplication of Resources . . . . . . . . . . . . . . . . . . . . . 6 2 Name Strategy in Colour Perception 7 2.1 Berlin-Kay Colour Ordering . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 The Sapir-Worf Hypothesis. . . . . . . . . . . . . . . . . . . . . . . . . 8 1 2.3 Name Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Remarks On Colour Perception . . . . . . . . . . . . . . . . . . . . . . 9 3 Name Strategy in Object Perception 9 3.1 Object Perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4 Memory Chunking 10 4.1 Recalling Re-coded Events . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.2 Memory for Chinese Words and Idioms . . . . . . . . . . . . . . . . . . 10 5 The Implications for Traffic Accidents 11 5.1 Colour Perception and Traffic Accidents . . . . . . . . . . . . . . . . . 11 6 Implications for Psycholinguistics 12 6.1 The Interaction Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6.2 Serial and Connectionist Models . . . . . . . . . . . . . . . . . . . . . 13 6.3 Language Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 6.4 Sememes and Phonemes verses Thought and Talk. . . . . . . . . . . . 14 6.5 Justification of Prior Thought . . . . . . . . . . . . . . . . . . . . . . . 14 7 Implications for the Philosophy of Language 15 7.1 Radical Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 7.2 Accuracy of Correspondence . . . . . . . . . . . . . . . . . . . . . . . . 16 7.3 Quantity of Transferred Information when in Re-coded Form . . . . . 16 7.4 Circuitous Correspondence . . . . . . . . . . . . . . . . . . . . . . . . 16 7.5 The Extralinguistic Assignment Problem . . . . . . . . . . . . . . . . . 18 7.6 Flagging by Countenance . . . . . . . . . . . . . . . . . . . . . . . . . 19 8 Implications for the Philosophy of Mathematics 20 8.1 The Continuum Hypothesis and the Segmentation Problem . . . . . . 20 8.2 Probabilistic and Fuzzy Tarski Truth Theory . . . . . . . . . . . . . . 22 9 Summary 22 9.1 Peroration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 9.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 10 Acknowledgements 24 1 Introduction 1.1 Motivation Name strategy is a type of deployment of a representation whose relationship to other and general representations is shown by the hierarchial diagram 1.2 below. Name strategy has particularly well-defined features clarifying the related properties of other entries in the diagram. Roughly the entries in the diagram can be explained as follows. Representation has no all-encompassing formal definition. In artificial intelligence it roughly means a set of conventions about how to describe things; it is a loose term to be kept in mind when creating 2 programs, languages etc., which entails keeping track of how knowledge or data or anything else is codified and whether this involves some condensation of the original material. It splits into two parts: 1. know-that representations usually these hold factual knowledge or data, and typically are the subject of information theory, 2. and know-how representations usually these hold inference knowledge in the form of programs and languages, and typically are the subject of instruction theory. For animals, as opposed to machines, representation again means the codified form of knowledge and data; again it splits into two parts: know-that representations which are stores of encyclopedic knowledge, and know-how representations which are essentially skills that can be deployed. Stereotyping loosely means collating information into a labeled set or template which can be readily (re-)used; properly this is cognitive stereotyping as opposed to social stereotyping, Stewart et al (1979) [45]. Examples of this are actions such as walking; an example which allows quantitative measurements is memory chunking, the existence of which has been readily demonstrated by many experiments. Name strategy means associating a given word with a stereotype. This splits into two types: 1. where the word activates a switch, the switch is perhaps innate, another example of a switch is pro-drop in linguistics, 2. where there is no switch. The paradigmatic, and best studied, example of the first of these is colour name strategy; in which the focal colours are progressively labeled by names as a culture advances until all eleven are named. Object name strategy is an example of the second. The purpose of the present paper is to describe the empirical justification for these representations and their implications for psychology, philosophy, and mathematics. 1.2 Diagram 1.3 Sectional Contents §1 establishes a framework which allows discussion of the nature of representations; it is advocated that there is minimal duplication of these. The existence of colour name strategy is discussed in §2. The similarity of the idea of adopting a name strategy and creating a representation discussed in §1.4. Colour name strategy is taken to be the paradigmatic case of stereotyping and the relationships of object name strategy and chunking to it are discussed in §3 and §4 respectively. Whenever colour name strategy is deployed it illustrates that thought can exist without words and in principle allows a qualitative measure of this. In §5 it is noted that the Berlin-Kay universal partial ordering for colours is similar to the frequency that traffic accidents occur for a car of a given colour. 3 N am e Strategy in the R epresentational H ierarchy R epresentations K now -how R epresentations K now -that R epresentations Stereotyping N am e Strategy C olour N am e Strategy O bject N am e Strategy M em ory C hunking Figure 1: The Representational Diagram 4 §7 continues, from Roberts (1998) [36], my approach to radical interpretation. This theory and how I differ from the traditional approach is summarized in §9.1. Name strategy suggests at least three problems with radical interpretation, they are: 1. the reduced accuracy problem, which is: Why have two colour names instead of one as this can reduce accuracy? 2. the segmentation problem, which is: How does a theory of meaning account for the real numbers, or why is the Continuum Hypothesis of mathematics justified? 3. the extralinguistic assignment problem, which is: traditional radical interpretation requires extralinguistic information in order to assign truth values to bivalent statements; the extralinguistic assignment problem asks: what is the correct concomitant label (or flag) associated with statements and how is it induced? In §6 it is pointed out that psycholinguistic speech production models require a-priori structure from which speech is produced. The example of an interacting speech production model is investigated, here the starting point is a word in quotation marks which represents the meaning of a word. It has long been argued by philosophers that a word in isolation has ambiguous meaning, so that there is the problem of why it is justifiable to start with the meaning of a word in isolation. It is here argued that the existence of name strategy indicates the independence of thought and talk, and thus vindicates the assumption of psycholinguistic speech models, namely that there is a starting point in production which is independent of words. §9.2 is the conclusion. 1.4 Stereotypes Compared to Other Representations The properties of colour name strategy are that it is a stereotype which in addition: 1. has eleven switches, see §2.1, 2. is culturally determined, see §2.1, 3. and is encapsulated. Encapsulation means that once the stereotype has been created it cannot be adjusted and that its modes of interaction are few and in principle determined: encapsulation results in a higher speed of processing. Object name strategy §3 and memory chuncking §4 are stereotypes which: 1. are not switched, 2. are determined by the environment, 3. are encapsulated. 5 How does what is here called a stereotype compare to other representations? Semantic representations, Shannon (1988) [42], are essentially codified and condensed information which is meant to encompass the "meaning" of a portion of language. Shannon argues that they are not a primary structure, this suggests that there is no switching and meaning (in the form of semantic representations) is stored in a similar way to object perception. Way (1991) [49] allows knowledge representations to be general enough to include metaphor. At this point what a representation is becomes entangled with what meaning is. My view is that "meaning" is too general and nebulous a term to pin down in this way, aspects of "meaning" must be involved in colour name strategy, the best thing to do is classify aspects of meaning and see what sort of representation they entail. Visual perception entails perceiving objects, and so contains object perception as discussed in §3; Farah (1988) [12] discusses whether visual imagery engages some of the same representations as used in visual perception. She finds neuropsychological evidence which suggests that some representations are used for both purposes. This dual purpose or multiuse of visual representations is similar to the multiuse of names in name strategy. Irrespective of whether representations are innate, the variety of use to which a given representation can be put suggests that there are general principles involving the creation and operation of representations. 1.5 Minimal Duplication of Resources Why do nervous systems in animals produce representations? An answer is that by holding a representation an animal does not have to do the same processing of information again and again. Indeed repeated information processing might be the method by which many representations are created; for example Jeannerod (1994) [22] repeated actions seem to improve motor control, in the words of Decety et al (1994) [9] "Mental practice involves rehearsal of neural pathways related to cognitive stages of motor control." Other examples which suggest that the representations used in imagination are the same as those received externally are: 1. the dual visual representations discussed by Farah (1988) [12], see the previous §1.4, 2. and the combined use of visual and auditory imagery when reading to oneself. The principle of minimum duplication stands in stark contrast to the ideas of modularity where for example there is no visual and auditory interaction until the information reaches the "cognitive center". Strict modularity is in any case unlikely for many reasons, three of which are: 1. the interaction of seeing and hearing words McGurk and McDonald (1976) [30], 6 w hite black green yellow yellow red green brow n blue pink orange grey purple Figure 2: The Berlin-Kay Partial Ordering 2. the orienting motor response which occurs at the third relay in human auditory processing Garman (1990) [14] p.62, 3. Frog "bug-perceivers" Garman (1990) [14] p.69, appear already to occur in the retina before any subsequent visual information processing occurs. The principle of minimum duplication is a minimality requirement in the same way as Ockam's razor (requiring the minimal explanation for scientific data) in the philosophy of science, however ultimately it might be possible to formulate it as a minimality requirement like the principle of least action in physics. 2 Name Strategy in Colour Perception 2.1 Berlin-Kay Colour Ordering The perception of colour often involves the deployment of a colour name strategy. The effect of this is to alter the way the colour is perceived. The five principles of colour perception have been given by Brown (1976) [4]: 1. The communicability of a referent in an array and for a particular community is very closely related to the memorability of that referent in the same array and for members of the same community. 2. In the total domain of colour there are eleven small focal areas in which are found the best instances of the colour categories named in any particular language. The focal areas are human universals, but languages differ in the number of basic colour terms that they have; they vary from two to eleven. 3. Colour terms appear to evolve in a language according to the Berlin-Kay (1969) [2] universal partial ordering: 4. Focal colours are more memorable, easier to recognize, than any other colours, whether the subjects speak a language having a name for the colour or not. 7 5. The structure of the colour space determined by multi-dimensional scaling of perceptual data is probably the same for all human communities and it is unrelated to the space yielded by naming data. 2.2 The Sapir-Worf Hypothesis. The five principles of colour perception can be used to test formulations of the Sapir-Worf hypothesis. This hypothesis is sometimes formulated Brown (1976) [4], and Kay and Kempton (1984) [23] as three separate hypotheses S-W.I Structural differences between languages will, in general, be paralleled by non-linguistic cognitive differences, of an unspecified sort, in the native speakers of the two languages. S-W.II The structure of anyones native language strongly influences the world view he will acquire as he learns the language. S-W.III The semantic system of different languages vary without constraint. 2.3 Name Strategy Kay and Kempton (1984) [23] p.75 define colour name strategy as follows: "According to the [colour] name strategy hypothesis, the speaker who is confronted with a difficult task of classificatory judgement may use the LEXICAL classification of the judged objects as if it were correlated with the required dimension of judgement even when it is not, so long as the structure of the task does not block the possibility." What this essentially means is that for colour judgement tasks the word for the colour may be deployed rather than the colour itself, provided that the nature of the task allows for this. This use of the word for a colour rather than the colour itself is a name strategy. The significance of name strategy from a cultural point of view is that it allows S-W.I to be tested. This can be done by using a language community in which all eleven focal colours have not been identified so that the language users do not have the option of deploying a name strategy. North American native languages have one word for blue and green, this is referred to as "grue" thus these speakers do not have the possibility of deploying the words "blue" and "green" in judgement tasks so that they can be used as controls. The scale of colour differences between focal blue and focal green, for the purposes of perception is measured not by wavelength, but by a previously ascertained difference scale. Kay and Kempton's experiments show that when the experiment involves the words blue and green, English speakers consistently and measurably assume colours near the blue/green boundary to be further toward the colour foci than they are; however when colour words do not occur this does not happen. They conclude that a naming strategy is involved which induces perceptual colour to move toward the colour foci. 8 2.4 Remarks On Colour Perception The existence of name strategy as discussed above can be interpreted as showing that thought can exist without words, but when words do occur they can influence thoughts in a quantifiable way. The effect of moving away from a difference boundary occurs not only in anthropology and psychology but in life science also: Lack (1947) [24] points out that two heavy billed finches Geospiza fortis and Geospiza fulinginasa, both have bills of approximately equal size when they are the only heavy billed finch on an island, however when they both occur on the same island the bill of one is much larger than the other. Brown (1976) [4] p.152 after noting the existence of colour foci universals and the above five properties of colour perception states "The fascinating irony of this research is that it began in a spirit of strong relativitism and linguistic determinism and has now come to a position of cultural universalism and linguistic insignificance." This suggests the possibility that there are universal perceptions and that it is the words superimposed upon them that enhance the cluster properties mentioned by Wittgenstein (1958) [51] p.31; such cluster properties are characteristic of concept formation, see for example Hampton (1979) [16] and Nuyts and Pederson (1997) [34], and occur not only for humans but also for other animals, for example pigeons have a concept of what a tree is, see for example Hernstein (1985) [17]. Note that, Scriven (1997) [39], Black, Brown, White, Grey, and Green are prevalent surnames, but Blue, Red, Yellow, and Purple are not; this seems to be also independent of the Berlin-Kay ordering. 3 Name Strategy in Object Perception 3.1 Object Perception It has been noted by Carmichael, Hogan, and Walter (1932) [6], that language has an effect on visually perceived forms. They constructed a number of experiments involving drawn figures that are midway between two clearly delineated objects, some of their examples include: a figure which is half way between a crescent moon and the letter "c", and a number which is half way between a two and an eight, etc . . . . They claim on p.83, that their experiments: "tend to substantiate the view that not the visual form alone, but the method of its apprehension by the subject determines, at least in certain cases, the nature of its reproduction." and their final conclusion on p.83, is that: "to some extent at least, the reproduction of forms may be determined by the nature of the words presented orally to the subject at the time that they are first perceiving specific visual forms." 9 An example of a similar effect is the ink-blot technique of making letters ambiguous, Lindsay and Norman (1972) [26], this involves part of a letter in a display of a word being obliterated by an ink-blot; the presence of the rest of the word disambiguates (i.e. removes the ambiguity in the choice of letter) the letter so that it is perceived as a letter which produces a word rather than a non-word. In other words object name strategy is often deployed in the apprehension of visual objects. In the view adopted here these are two examples of the similar phenomena to that found in colour perception; to wit when language is present it can adjust thought via a naming strategy. The difference is that these two object perception examples are not switched; and as they can be subject to subsequent adjustments they are not encapsulated either. 4 Memory Chunking 4.1 Recalling Re-coded Events Short term memory has a capacity to re-call about seven distinct elements of information, Miller (1956) [32]. Miller cites much evidence for this: from sound perception, where untrained people have the ability to recognize about six different pitches and five degrees of loudness; musically trained people can recognize a greater number of distinct pitches. There are similar results for the ability to recognize other uni-dimensional stimuli, which means a single stimuli without interference from other effects. For multi-dimensional stimuli, where there is more than one spectrum of features which distinguishes a stimuli, there is a relationship between the number of stimuli present and the number of objects that can be identified; inspection of Figure 6 in Miller (1956) [32] suggests that the number of objects that can be identified is proportional to the hyperbolic tangent of the number of stimuli present. Miller suggests that the mechanism by which this is achieved is by re-coding the sequence of information into chunks, and this is referred to as a chunking strategy; he says, Miller (1956) [32] p.93: "There are many ways to do this re-coding, but probably the simplest is to group the input events, apply a new name to the group, and then remember the new name rather than the original events." This re-coding strategy is chunking strategy in memory, which is here called memory chunking. Memory chunking is not encapsulated as it is possible for memories to suffer from subsequent interference. Memory chuncking is not switched. 4.2 Memory for Chinese Words and Idioms This mechanism seems to be related to the naming strategy of the previous sections, the connection between the two effects is illustrated by the study of short term memory capacity for Chinese words done by Zhang and Simon (1985) [53]. 10 Chinese written characters exist in two varieties, one type of characters has a name the other does not. Zhang and Simon asked some Chinese speakers to remember eight sets of the two sorts of characters. The subjects could immediately recall about six characters with names, but short term memory capacity for Chinese radicals not possessing common pronounceable names is about two or three items. Thus short term memory appears, on occasion, to adopt a name strategy similar to the name strategy of the two proceeding sections; however the new name referred to by Miller might not always be a specific word, it might be some other label. To see this consider short term memory in musical performance, where what is remembered may be specific notes, or a specific scale etc., chunking strategy is still involved but it is not now a name strategy. Therefore the term stereotyping is used to cover all three phenomena. 5 The Implications for Traffic Accidents 5.1 Colour Perception and Traffic Accidents Table: Rate of Involvement in Traffic Accidents of Cars by Colour. Number of Accidents per 10,000 Cars. Adapted from Table 7C.HMSO91. Black White Red Blue Grey Gold Silver Other Beige Green Yellow Brown 176 160 157 149 147 145 142 139 137 134 133 133 Two-colour cars are classified by their main colour. Other = Bronze,Pink,Orange,Purple, Maroon,Turquoise,Multi-coloured,&Unknown. The above table shows the rate, per 10,000 licensed cars, of accidents classified by colour. There is a striking resemblance of the three most accident prone colours namely black, white, and red to the Berlin-Kay diagram; and some resemblance among other colours, however accidents of blue cars seem to be anomalously high compared to green, yellow, and brown cars. Munster and Strait (1992) [33] note: "The data probably say more about differences in the types of car and driver represented in the colour groups than differences in the inherent safety of the car colours. It is possible that certain colours are more popular among groups of drivers with a higher risk of accident such as young drivers or company car users. Some colours may tend to be associated with particular makes and models of car. No doubt factors such as visibility also affect accident risk, but it would be difficult to distinguish their effects from those of the driver and vehicle, using the available data." 11 From the point of view presented in this paper, colours which have a greater propensity to be involved in a colour name strategy are more likely to coincide with the colour of a car involved in an accident. To put this another way: people who drive a car of a well-defined colour, are more likely to be involved in an accident. There have also been studies into the connection between personality type and car colour, Marston (1997) [28]. 6 Implications for Psycholinguistics 6.1 The Interaction Model There is evidence that the reception of speech is interactive, three examples of this are: 1) McGurk and McDonald's (1976) [30] demonstration that there is evidence that seeing the speaker speak influences the word heard, 2) McNeil's (1985) [31] demonstration that there is evidence that verbal speech production interacts with gesture, 3) Jacobson's (1932) [21] p.692 demonstration that various other physiological activities interact. These observations suggests that the verbal part of speech production is interactive. A model which allows both phonological and semantic influences to interact is the Stemberger (1985) [44] psycholinguistic interaction speech production model. In this model, when the word feather is activated a lot of other words are also activated with varying weights according to how closely they resemble feather. This can be described by the diagram in Stemberger (1985) [44] p.148 and text: "Semantic and phonological effects on lexical access. . . . an arrow denotes an activating link, while a filled circle is an inhibitory link. A double line represents a large amount of activation, a single solid line somewhat less, and a broken line even less. Some of the inhibitory links have been left out... for clarity. The exact nature of semantic representation is irrelevant here, beyond the assumption that it is composed of features; . . . a word in quotation marks represents its meaning." There is suppression (also called inhibition) across a level, and activation up or down to the next level. This model accounts for syntax by giving different weights to the different words so that words on the left come first. Speech errors come from the noise in the system. There are three kinds of noise. The first is that the resting level of a unit node is subject to random fluctuations; with the result that it is not the case that the unit nodes degree of activation remains at the base line level. A fluctuation could produce a random production of a part of a word. The second is that words that are used with a high frequency have a higher resting level, and therefore reach activation threshold, or "pop out", quicker. This implies that there should be less error for these high frequency words; furthermore it implies that when real words occur as an error, higher frequency words should occur as errors more often, and this does not happen. The third is the so-called systematic spread of activation; this means that the weights in the interaction allow an inappropriate activation of word. 12 6.2 Serial and Connectionist Models Serial models consist of a series of boxes arranged in strict order. These process a message into language and then articulate it. The evidence cited in §1.5 and at the beginning of §6.1 shows that serial language perception and production is unrealistic. Serial models begin with a "message level", Garret (1980) [13], and thus at the beginning requires thought, in the form of semantic content, to exist without talk, in the form of tangible language. In connectionist models of language and word production, for example Seidenberg and McClelland (1989) [40] p.527, the semantic aspects of the model are put in by hand. 6.3 Language Production The very words "model of language production" assume that some starting structure is metamorphosed into some finishing structure. In the present case it is clear that the finishing structure is speech and other forms of language, but it is not clear what the starting structure is. In other words, what language is supposed to be produced from. Now we consider how this appears to be done for serial, connectionist, and interactive models respectively. In serial models, Garret (1980) [13], the starting structure is the message level; here there are collections of amorphous thoughts which the production process crystalizes into language. Now this begs an assumption, because it implies that thought can exist prior to and/or independently of words. There appears to be a lot of scope as to how meanings of words can be accommodated within connectionistic models, for example Rumelhart and McClelland (1986) [38] p.99 say: "there is an implicit assumption that word meanings can be represented as a set of sememes. This is a contentious issue. There appears to be a gulf between the componential view in which meaning is a set of features and the structuralist view in which the meaning of a word can only be defined in terms of its relationships to other meanings. Later ... we consider one way of integrating these two views by allowing articulate representations to be built out of a number of different sets of active features." The componential view is a sort of correspondence theory of meaning, and similarly the structuralist view a coherence theory of meaning, for definitions of these terms see Roberts (1998) [36]. In interaction models the situation is a more complex than in serial models; here, according to Stemberger (1985) [44] p.148, the starting structure is a "word in quotation marks which represents its meaning". This cannot really be a starting point because it requires that a word has meaning in isolation, i.e. that context is irrelevant. It has been argued by Frege, Davidson, and others that not only the material context but also the context of a word in a sentence is necessary for an unambiguous assignment of meaning to a word. An example of an ambiguous word is "bank", what sort of bank is being referred to can be disambiguated by a sentence or perhaps some other source of information. An example of context ambiguity is: "1st speaker 13 to 2nd: Why don't you become a philosopher?" 2nd speaker: "Don't have anything to do with philosophers, they are underhand." 3rd speaker: "Why don't you become a philosopher." Sentence themselves are often ambiguous because they contain ellipses and indexicals, again they have to be dis-ambiguated by being put in the perspective of a wider context. This gives rise to a "holistic" view of the meaning of a word, this has been expressed by Davidson (1984) [8] p.22 as follows: "If sentences depend for their meaning on their structure, and we understand the meaning of each item in the structure only as an abstraction from the totality of sentences in which it features, then Frege says that only in the context of a sentence does a word have meaning; in the same vein he might have added that only in the context of the language does a sentence (and therefore a word) have meaning." Again it would appear that the starting structure is a thought; thus the models all assume that a thought occurs first and is processed into words, i.e. that thought and words are not identical, but are independent entities. Davidson (1984) [8] addresses this question, however he seems just to be concerned that if thought can occur without words, then this is also subject to radical interpretation, for example on p.157: "the chief thesis of this paper is that a creature cannot have thoughts unless it is an interpreter of the speech of another." this suggests to me that Davidson thinks that words and thoughts are concomitant simultaneously. 6.4 Sememes and Phonemes verses Thought and Talk. The preceding suggests that generally psychologists require sememes/thought to exist independently and prior to phonemes/talk; whereas philosophers are wary of thoughts existing independently. This is summed up by Wittgenstein's remark on where one cannot speak one cannot think. This is perhaps because of their different attitudes to studying communication. Psychologists are mainly concerned with explaining some particular aspect of language. Philosophers are most interested in accuracy and rigour of thought, if these are not written down they are hard to refute. 6.5 Justification of Prior Thought The assumption of the models, namely that thought can exist without words, is justified for at least five reasons. The first is because of Brown and McNeill's (1966) [5] demonstration of the existence of the tip of the tongue (TOT) phenomena. This occurs when people appear to be at a loss for the word that they are looking for. The second is because of the nature of musical instrument tuition, where it is possible to think about phrasing, etc . . . , without recourse 14 to words; this is contrary to Davidson's assertion, that a creature cannot have thoughts unless it is an interpreter, quoted at the end of §7.3, irrespective of whether musical conventions and performance are subject to radical interpretation, simply because notes are not speech. The third is that animals have brains and so are able, at least to some extent, to have something similar to thoughts, see for example Terrace (1985) [47] and Premack (1988) [35]. The fourth is semantic amnesia studies, DeRenzi et al (1987) [10]; their patient L.P. appears to have selective damage which suggests that semantics and phonetic are separable, for example on p.579: "The linguistic performance of L.P. was marked by a striking dissociation between impairment of semantic knowledge and the preservation of phonetic, grammatic, and syntactic rules." The fifth and clearest reason is because of the existence of name strategy, this not only shows that thoughts can exist independently of words, but furthermore colour name strategy allows quantitative statements of the degree of independence to be made; in colour name strategy there is a perceived movement away from the boundary between colours, and the amount of this movement could provide such a measure. There is the question of the temporal order of the independence, thought before talk seems to be the assumption of speech production models and seems to occur, but there is the possibility of the reverse which can be facetiously put as talking without thinking. In colour perception the existence of a switched focal colour word in a speakers repertoire adjusts the perception of colour, so that it appears that talk, in the form of name strategy, can occur prior to thought. 7 Implications for the Philosophy of Language 7.1 Radical Interpretation Philosophy of language is concerned with how language has meaning. Davidson's (1984) [8] view is that meaning is obtained through radical interpretation of sentences; or perhaps, Lewis (1974) [25], a larger structure. Radical interpretation optimizes the correspondence between language and the world and also the self-consistency (or coherence) of the language. I have given an outline of some aspects of my approach to it in Roberts (1998) [36] and this section follows on from there. In §2 it was shown that the existence of a colour name strategy reduces the correspondence between the true colour of a chip and its perceived colour; thus language does not help the mind in producing an accurate representation corresponding to the world, in fact in hinders it. In other words the use of a more polished language is obscuring truth. The assignment of truth values to statements is essential in the traditional picture of radical interpretation. Thus the question arises: is the existence of name strategy compatible with a modified form of radical interpretation, and if so exactly how is it necessary to change radical interpretation? 15 7.2 Accuracy of Correspondence A specific and neat illustration of the dilemma is posed by the question: Why have two words "Blue" and "Green" when all they achieve is a less accurate representation of the colours present? This is part of a question that can be successively generalized to include other colours; also it is related to why have memory chunking when this might cause a slight loss of accuracy, and furthermore as to why have stereotyping in general. A point to note is that usually these classifications are unconscious, and that this allows them to occur at great speed thus aiding swift communication. 7.3 Quantity of Transferred Information when in Re-coded Form The answer to the dilemma is that it allows a large amount of information to be communicated, even though there is a small cost in accuracy. It might be more accurate to not have separate words for blue and green, and then to indulge in lengthy comparisons every time a distinction between blue and green objects is required; but if large amounts of information is to swiftly communicated it is beneficial to have two separate words. For example, it is advantageous for a language community to be able to say: "Blue Gavagai are tasty, but Green Gavagai are poisonous" rather than: "Gavagai that are grue like the sky are tasty, but Gavagia that are grue like the grass are poisonous.". More formally, for a specific case of colour perception §2.1, the first principle, which states that the communicability of a referent is related to its memorability, illustrates the mechanism by which larger quantities of information can be more quickly communicated. A name strategy is chosen so that a large amount of information about the colour of an object can be easily remembered; and also be quickly and memorably communicated, despite the fact that it incurs a loss in the accuracy and truth of statements. Thus economy of expression accounts for the use of one word instead of two. There is still the problem of why there are the eleven switched colour perception centers. Why not have ten or fifteen switches colours, or none at all? These are human universals as given by the second principle of colour perception. A possible explanation is that the switched colours provide a framework within which a huge number of colours can be described. No switches would not give this framework. The reason that there are eleven of them might be that this is the maximum number that the brain can implement. 7.4 Circuitous Correspondence The foregoing presents a problem for the philosophy of language; because it shows that words are only in indirect correspondence with the world. This problem is approached by attempting to explain indirect correspondence by using standard techniques and seeing if these lead to a plausible explanation; the attempt consist of requiring that indirect correspondence is really a circuitous correspondence. By this is meant a pair {D,P}. D is a direct correspondence 16 and P a procedure with which the indirect correspondence I can be recovered. Notationally this could be expressed as D&P → I. The usual view of radical interpretation requires that sentences are bivalent, or two-valued; this means that the truth values "True" or the truth value "False" can be assigned to them. Here the possibility of assigning any quantity to (or labelling, or marking, or tagging . . . ) sentences is referred to them as being flagged. The existence of a name strategy, especially in colour perception, shows that there is no unique way of achieving this; for example, quantitative experiments could be constructed in which subjects would be required to state how blue or green a chip is, the quantitative results would depend on whether a name strategy was being deployed, then true or false sentences could be constructed to describe these quantitative differences, but these would have different truth values depending on whether a name strategy was being deployed. This ambiguity of truth values necessitates that a disambiguating procedure (i.e. a procedure which removes any ambiguity) be given. The form that such a procedure could take is the re-writing, hopefully in a bounded finite number of steps B, of the original sentences which are bivalent. An example of a re-writing procedure is what is here called a brittle re-write procedure. This can be described as follows: suppose that sentences can be given a single definite value, c.f. Urquhart (1986) [48], of say: U = {false, almostfalse, almosttrue, true}; (1) then the original set of sentences can be replaced by a larger set of sentences having just the values true or false, this can be done by posing the four additional sentences: "The previous sentence is False, Almost False, Almost True, True" all four of which are true or false. Another example, is to suppose that, instead of the sentences being bivalent it is possible to assign a set of labels or quantities Q to a sentence, for instance Q = {Happy and Good, Happy and Bad, Sad and Good, Sad and Bad}; (2) again for additional sentences, such as: "The previous sentence has the quality Q", can be constructed which are bivalent. This approach really falls under the scope of Davidson's program, (1984) [8] p.133, it is just the requirement that there should be a procedure for matching sentences without logical form (i.e. bivalent sentence) the gerrymandered part of a language where sentences do have logical form. It might be thought straightforward, for the circuitous correspondence of colours, to implement such a procedure; however first two problems have to be overcome. The first is that the re-write procedure would involve real variables, the parameters P to be adjusted, such as wavelengths, take values V on the real line < , i.e. V (P ) ε <; however it seems reasonable to assume that sentences and truth values can only be stated and assigned sequentially, so that the total number of truth values available N(T ) is an integer valued quantity, i.e.N(T ) ε Z; thus there is the problem of how to segment V (P ) so that N(T ) covers all cases, this is an example of the segmentation problem, discussed in §8.1. The second is that the re-write procedure has to be constructed post-hoc, after data about responses has been given, but extralinguistic assignment (or 17 flagging) of truth values to sentences is immediate; this is an example of the extralinguistic assignment problem discussed in §7.5. These two problems suggest that the traditional view of radical interpretation needs radical revision. 7.5 The Extralinguistic Assignment Problem In order for radical interpretation to work various principles, such as the principle of charity, have to be assumed. In Roberts (1998) [36] there is a version of this called cooperation dominance. These principles contain the idea that people communicate truthfully more often than not, and that details of their behaviour give indications of the truthfulness of their communication: hence it is possible to use extra-linguistic information to assign the truth values to sentences. Instead of just the bivalent assignment of B = {true, false}, (3) extra-linguistic information could assign different structure such as those of more complex logic, such as fuzzy logic, or alternatively a series of real numbers representing the probability that the sentence is true, its complexity and so on, see §8.2. However a problem arises because the existence of a name strategy shows that, at the time an apparently true statement is uttered the quantity of truth is not optimal; that the statement is apparently true is post hoc as it assumes that the listener posses the information, consciously or unconsciously, to transcribe it to the relevant true statement. A way that this could be accommodated in the usual theory is be requiring that the transcription process is contained in the passing theory of the language; but then it seems hard to justify referring to the extralinguistic information assigned as being "truth". A better description is to assume that the extralinguistic assignment is of relevant information, c.f. Sperber and Wilson (1987) [43]; the traditional case is a subcase of this, as most relevant information is true, but also it is possible to state irrelevant true statements. That truth is not the only quality needed for facility of communication has been noted by Church (1956) [7] p.2-3 "For purposes of logic to employ a specially devised language, a formalized language as we shall call it, which shall reverse the tendency of the natural languages and shall follow or reproduce the logical form [here having the restricted meaning that statements can be assigned bivalent truth values rather than be flagged by a formal system] at the expense, where necessary, of brevity and facility of communication." It is possible to quantify information, see the P-model of Roberts (1998b) [37], but quantifying relevant information presents problems: perhaps the vehemence or Fregian force with which a sentence is stated could lead to such quantification. Flagging by Fregian force is unrealistic as it implies that by shouting louder makes a statement more true, a better flag is relevant information. Relevant information is discussed in the commentary on Sperber and Wilson (1987) 18 [43]. The above relates meaning to relevant information, supposing that relevant information is frequently used in communication relates meaning to use, compare Wittgenstein (1958) [51] p.43 "For the word 'meaning' it can be defined thus: the meaning of a word is its use in the language." 7.6 Flagging by Countenance What is the nature of the concomitant flagging which occurs when a statement is uttered? The most important aspect of such flagging must be in the comparison with the passing theory of the language to preserve coherence (interior flagging); however at sometime exterior flagging must occur. Flagging occurs for purely auditory statements, for example a tape or telephone. This flagging is typically of the mood, age, and sex of the speaker, and seems to give information in addition to statements rather than be an aid to comprehension. The main component of flagging for comprehension is probably visual. Boyle, Anderson, and Newlands (1994) [3] show that having a visible speaker improves the efficiency of dialog and that this is more marked for young or inexperienced speakers. This suggests that the extralinguistic information required is at least in part conveyed by the visual acts of the speaker; as is it more marked for people learning the language more extralinguistic information is required here. Clearly some of visual information is in the form of demonstrable acts D = {pointing out left/right, up/down etc. . . .}, (4) and gesture emphasis. These could be used for flagging in the form Q = {degree of emphasis, spatial and temporal location, . . .}, (5) but it is not clear where this list would end or the relative importance of its components. A neater way is to note that one of the main components of visual communication are facial expressions, and these can be considered as contenders for the flags assigned. Of course it is possible to combine these with flags such as the above but with a loss of simplicity. The advantage of using facial expressions can be taken to convey the most relevant information is that Etcoff and Magge (1992) [11] find only five or six emotions that faces express: happiness, sadness, fear, anger, disgust, and perhaps surprise. Flagging using these five or six emotions produces an assignment of extralinguistic information called flagging by <6 facial countenance. Thus an alternative to sentences being assigned bivalent truth values or measures of unspecific relevant information, they can be assigned six real values Q = {happiness, sadness, fear, anger, disgust, surprise}. (6) These can be expressed in ascii smilies Q = { : −) , : −(, : −F, : −t, : −∗, : −s} = {+ happy smilie, sad smilie, bucked− tooth vampire with one tooth missing, cross smilie , ate something sour smilie, smilie after a bizzare comment}. (7) 19 Thus six real valued flags replace the one integer valued flag Q = {truth}. (8) This assignation taken to be the driving force behind the optimization of correspondence between language and the world and hence radical interpretation. 8 Implications for the Philosophy of Mathematics 8.1 The Continuum Hypothesis and the Segmentation Problem In mathematics there is an assumption: the Continuum Hypothesis see for example Maddy (1993) [27] and Hirsch (1995) [18], that mathematical objects can have continuous properties. A major place where this hypothesis appears is that real numbers cannot be constructed from rational numbers necessitating a new assumption for real number construction. An example of such an assumption is given by Dedekind's axiom of completeness, see for example Issacs (1968) [20]. Hirsch (1995) [18] p.146 notes as a possibility that "(b) Neurologists and psychologists learn enough about cell assemblies and cognition to make it scientifically certain that there could not possibly be any activity in the nervous system which would correspond to a truth value for the Continuum Hypothesis." What is about to be advocated here is something along these lines, essentially it is argued that both truth and meaning are intrinsically real valued. The segmentation problem is the problem of how to account for the existence of and meaning attributed to the real numbers. From the point of view of traditional radical interpretation the number of times truth can be assigned to natural language statements is integer valued, and so does not allow for real numbers. There are three parts to this problem: 1. how to account for the fact that real numbers as pure mathematical constructs have meaning, 2. how to account for the success, meaning, and use of real numbers in the physical world, 3. how to account for the success, meaning and use of real numbers in cognitive science. In the previous paragraph a simple example, which shows that the real numbers are necessary for assigning truth values, is given by colour name strategy. Similar problems arise with many other correspondences between languages and the world, for example consider the statement: 'Jones is six feet tall'. 20 This is unverifiable, the statement for which truth-values can be assigned is: 'Jones is six ± δ feet tall' where δ is some error, usually of a statistical nature. It is normally taken that physical measurements are real valued quantities with real valued errors, and therefore the real numbers are needed to describe the physical world. There is a chance that there is a theory of everything (TOE) and this has been reviewed by Taubes (1995) [46]. It could be argued that TOE would require that objects have only discrete properties, say by having length a multiple of the Planck length etc., but present quantum mechanics requires Hilbert spaces which in turn require properties of the real numbers, so that a requisite TOE would have to change this; in any case it seems unreasonable that philosophy of language and mathematics should legislate the nature of fundamental physics. A better reason for discarding the real numbers would be to assume that humans have only a finite number of integer valued brain states, so that the assignment of a finite number of truth values should suffice for the assignment of meaning as perceived by the brain. The indications are that real valued quantities are needed for describing cognition and hence brain states. Three examples of this are: 1. Wynn (1992) [52] p.323 describes the accumulator theory of how people learn to count, this requires that people can perceive temporal duration, a real quantity, and then when sufficient amount of this has accumulated set an integer valued quantity one higher, 2. a clock measuring real valued temporal duration is needed for many skills involving timing Shaffer (1982) [41], 3. and most perceptual models involve real valued quantities, see for example Massaro and Friedman (1990) [29]. These three examples suggest that real valued quantities should be used for describing brain states; however Hopfield (1984) [19] has shown that continuous neurons, which is what real neurons are, can often be described by two-state McCullock-Pitts neurons, suggesting that for psychological measurements bivalent quantities might suffice. The problem is in fact a worse than just requiring real numbers for physical and psychological measurements. Real numbers occur in pure mathematics and a general account of meaning should account for meaning in such a-priori languages, because apart from any other reason mathematics is good at describing the physical world, Wigner (1960) [50]. It appears that the segmentation problem does not have a solution involving only integers. The pure mathematical reason for this is that accounting for the meaning of the real numbers cannot be done by assigning an integer number of truth values, there is the requirement of a new axiom when constructing <. To put this another way having discrete truth values is not sufficient, even with brittle re-write procedures, for < to have meaning it must be possible to assign quantities Qε< to sentences. To put this another way sentences cannot be flagged by integer valued quantities, they have to be flagged by real valued ones. In traditional radical interpretation truth is an ab initio concept, for maximum compatibility 21 with this real valued generalizations of truth are required. Possible choices for real valued truth are probabilities or fuzzy truth values. 8.2 Probabilistic and Fuzzy Tarski Truth Theory Radical interpretation is in part motivated by Tarski's truth theory. Usually this applies bivalent truth values to formal languages. Church (1956) [7] p.25 seems to use the term "logical form" where "bivalence" has been used here. Davidson (1984) [8] p.19 appears to follow Church's usage. In other words they require integer valued flags, but here it is advocated that real valued flags are necessary. There are formalized languages which do not require that truth is bivalent but is real valued, examples of these are fuzzy logic and probability theory. As has been argued in the previous section real values should be used for describing truth in natural languages. There appears to be no reason why Tarski's truth theory cannot be modified to include statements which involve probabilities or fuzzy truth values, although this appears not to have been explicitly done in the literature. Instead of defining a relation: "Assignment a satisfies formula F in structure S: define a relation: "Assignment a gives formula F the value p in the structure S" in the probability case, p will be a real number between 0 and 1. 9 Summary 9.1 Peroration So what does a speaker take a sentence such as "Snow is white." to mean? Stripping away multitudinous provisos the essentially old view of radical interpretation would be along the lines: In a formal Tarski truth theory the truth of such a statement would be ascertained by comparison with the statement in another formal language. For learning a first natural language with no language to compare it to, the truth of a previously unheard statement is judged by seeing how well it matches the listeners previous model of the language and the external information available. The external information available is taken more often than not to be useful rather than misleading. Having judged a statement to be true the speaker then deduces that it is in accurate correspondence to the exterior world. Having information that accurately portrays the exterior world must entail knowing what it means; meaning is implicated by the above reasoning and is a derivative concept from it. So how does the picture of radical interpretation presented here differ? It differs in that truth is not a quantity that can be flagged to sentences. The two reasons are: 22 1. bivalent truth values could never account for the meaning of the real numbers < and the continuous properties that they describe throughout human experience, 2. there appears to be little psychological evidence that learners of a language flag sentences with truth values other real valued quantities seem more likely. There are three main consequences of this: 1. not only is meaning a derivative concept, truth is as well, 2. real numbers have to be introduced ab initio rather than be constructed from the integers, integers are thought of as being a derivative concept, 3. perhaps in principle mathematical or computational models, or psychological data could test aspects of the above; hopefully it moves the theory one step closer to being testable. 9.2 Conclusion In §2, §3, and §4 three distinct phenomena were discussed: in §2 the phenomena was colour name strategy, this occurs only for the eleven switched focal colours; in §3 the phenomena was object name strategy, this is not an identical phenomena to colour name strategy because there is nothing which directly corresponds to the fixed number of switched focal colours; in §4 it was mentioned that memory chunking is aided by the use of a name; these strategies are clearly related and it was argued that the relationship is that of the diagram 1.2 in the Introduction. It was argued in §1.1 and §1.4 that all of these should be considered representations, and that representations should be hierarchically classified according to their properties. In §7 and §8 some of the consequences of name strategy for problems in the philosophy of language and mathematics were outlined. These were summarized in §9.1. The technical results follow below: It was noted that having two colour words blue and green aids swift communication although there can be a loss in accuracy. The suggested solution to the segmentation problem was to require that real valued quantities (as opposed to the traditional view where a single bivalent quantity truth) should be assigned to sentences and used throughout in accounts of meaning. Thus the Continuum Hypothesis in mathematics is evaded as it is only possible to have real valued truth. 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