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The empirical content of the notion of linguistic mental representations
Wolfram Hinzen


 Moderators: Adrianna Wozniak, Anne Reboul, Gloria Origgi
 

I

In using the term ‘language’, I shall be writing about the human language faculty – a set of mechanisms implemented in the brain and specific to our species, which generates expressions. These, intuitively speaking, are pairings of phonetic structures with semantic ones. This set of mechanisms, let us call it a generative algorithm, needs to exist: expressions are highly structured, and some procedure needs to generate that complexity.[1] We may think of the faculty as another ‘organ’ of the body, in the informal sense of a distinctive subsystem of our organism that interfaces with other such subsystems and emerges in ontogeny due to three factors: (i) genetic factors and laws of organismic development, (ii) external input, and (iii) general (e.g. physical) laws not specific to either language, our species, or the organic world (Chomsky 2005). A form of ‘nativism’ follows, albeit in a rather trivial sense, once the impact of (i) is non-negligible, which I will here take for granted for a trait such as language. I shall argue that there is no sufficient empirical basis for positing ‘referential relations’ between organism-internal representations generated in this ‘organ’, on the one hand, and external entities, on the other, if the relations and external entities in question are thought to determine or explain the meaning, ‘content’, or function of these representations. It is not the existence of mental representations that I will question – which, I will take it, simply follows from the fact that neither the parts of the relevant generated structures nor their combinatorial laws are physical (in any other than the trivial sense of belonging to nature – the one natural universe).

 

II

Human linguistic expressions form a system, in a similar sense as the natural numbers do. If there is one expression, there are innumerably many others, and understanding the former entails understanding the latter (Fodor and Pylyshyn 1988). If language consisted only of interjections, which are non-structured at the relevant levels of representation, this would not be the case: no interjection makes a prediction for the existence of any other interjection. Not so in the case of structured expressions. Thus, understanding the expression ‘John loves Mary’ is not to understand merely that some relation holds specifically between John and Mary. It is to understand that the very same relation can hold between any entities that form the subject and object of this expression, in the same way that a value can be inserted for an abstract variable. Similarly, the relation ‘plus 2’ in the equation ‘1+2=3’ is not a relation specifically between 1 and 3. It is a relation between any value that instantiates the relevant variables in the equation x+2=y. In the same way, then, understanding ‘John loves Mary’ is to understand algebraic relations between variables for which ‘John’ and ‘Mary’ are values. Hence, as a matter of algebraic fact, ‘Mary loves John’ is an expression, a part of the system, too. There is, moreover, no finite bound to the expressions that are part of the system in question, again not unlike the case of the natural numbers.

 

This is a tale, not merely of structures, but meanings. Meaning is systematically aligned with structure in this system, as a matter of contingent fact. The architecture of the language faculty might have been different – syntax and semantics could have been entirely independent computational modules with no implications of one for the other. But whatever human language we look at, the facts tell otherwise. Thus, in English, too, a decision over which variable the value ‘John’ instantiates has systematic consequences for how the resulting complex expression is semantically interpreted. Depending on where in the underlying hierarchical structure of the expression this lexical item is inserted, it comes out as either the agent or the patient of the event in question. That, if Mary loves John, Mary is in love, is not a conjecture, but a structural necessity. Any denial of this entailment is a violation of an algebraic law (not of logic, but) theta-theory, a module of Universal Grammar (UG). If the interpretation is to be different, the structure needs to be changed. By contrast, interpreting ‘Mary loves John’ to entail that John is in love is to draw a risky inductive inference: it is a conjecture that the structure does not license. In an older terminology, the first entailment is analytic; the latter is synthetic.  

 

This explanation of analytic entailment (structure-driven meaning facts in a biological organ) has not invoked any relation of representation or reference at any point (nor has it invoked truth). Whatever ‘John’ refers to, in particular, the fact that if that thing loves Mary, it is in love (and Mary is not necessarily), will hold. The explanation has invoked the structure of the language faculty, an organism-internal dynamical system that is not, apparently, experientially driven or stimulus-bound: excepting cases of pathology, the generation of an expression in a particular moment of time is not a function of what internal state we are in or which external state of the world we confront. As Quine (1960) put a related point, we cannot tell, from the features of the situations in which expressions are used, what they mean. A naïve objection might be that all normal children turn this trick when acquiring a language. But their accomplishment is wrongly described in these terms: what narrows down their search space when hearing unfamiliar sounds is what meanings they know; and as Lila Gleitman has shown, it is in fact the structures of expressions that their minds can generate which help with the mapping task (Gleitman 2005). 

 

By possessing the relevant generative algorithm, then, we can freely generate thoughts, merely by instantiating variables, and in doing so, we are moving around (mentally) in an infinitary system. Does that system represent anything? Its existence is due to the generative algorithm. Without it, there wouldn’t be any such system. The algorithm, as far as we know, exclusively exists in (is implemented in) one place in the universe, namely the human brain. Hence, without the human brain, there wouldn’t be any such system. The external environment, in particular, exhibits no traces of it. The sense in which language is external at all remains unclear: the written aspect of language is irrelevant for understanding the universal basis of our linguistic ability (most languages alive on this planet are not written). The acoustic aspect of language is close to irrelevant as well, as acoustics looked at as such, i.e. in physical terms, exhibits none of the features that we associate with language: morphological structure (words), syntactic structure (phrases), and semantic structure (meanings). If we wish to understand something about language, we don’t ask an acoustics expert or look at spectrograms, we ask a linguist.

 

What use then is the assumption that the system itself or any of its productions (structured expressions) represent the external environment, in some explanatory sense? Again, the linguistic environment described in physical as opposed to linguistic terms does not exhibit any of the algebraic structures that we find in the system and that systematically account for their semantic properties (to the extent that these are systemic: idioms or irony indicate that they need not be). Positing such structures out there, to then say linguistic structures ‘represent them’, seems circular. We need an empirical benefit for positing such ‘representation relations’. Saying mental representations in our head ‘represent’ some external content (referent, semantic value, etc.) is an empirical claim, not a philosophical hypothesis, and should be tested like other empirical claims. What is the relevant evidence?

 

III

One story is this. There is this generative algorithm, and it generates structures, but the CONTENT of these structures is something else (a worldly physical entity, perhaps an abstract entity). It’s what the structures relate to. This relation to an external object is what their MEANING consists in. Before they relate to it, there is no meaning. The structures in question are therefore, not just structures, but mental REPRESENTATIONS. They are relationally understood. Philosophy in the 20th century has largely been about the question of how this reference relation gets into place, and thereby determines the mystery notions I have here capitalized. Its perhaps deepest ‘anxiety’ has been to eradicate the case where meaning is plainly there but the external referent is missing, as in the case of the infamous current king of France. Russell’s method of eradication was to simply deny what is plainly the case from a linguistic point of view, namely that ‘the kind of France’ is a referential expression.

 

This externalist view runs counter to what is probably the most distinctive evolutionary design feature of human language: that reference in human language is intentional and free, and in particular physically unconstrained. Unlike in any other known animal communication system, the referent can be arbitrarily remote in space and time, it can be abstract, and it certainly need not exist. We have the privilege to refer to what we like. The meanings of any one in the infinity of complex expressions are not what they because these relate to anything external. They are strictly a function of the system’s internal combinatorics: ‘John loves Mary’ means that John loves Mary and entails that John is in love not because of the world but because of the expression’s hierarchical structure, its determining principles, and the lexical concepts it contains. An explanation of this meaning begins from items of the mental lexicon stored in long-term memory, each a pairing of a sound with a meaning (a mental concept, such as my concept of love). A retrieval procedure calls these items and inserts them into a derivation, which structures them in line with the laws of theta-theory and other modules of UG. The result of this process (all of it head-internal) is a complex expression with a new sound and a new meaning, which can then be externalized acoustically (though it need not). This meaning does not exist without the structure, I will assume – not in any Platonic heaven, nor in any external physical world (as far as we know). ‘Square circle’ means what it does, not because there are any, but because we have combined concepts in a particular way, generating a phrase structure of a particular kind. Combining concepts is free: we can do it to make worlds, rather than to mirror or represent the one that’s physically there.

 

On this view, given the structure, the meaning, if it’s systematic, will follow by necessity. Mapping this very structure to something else external to it – some physical conglomerate, some object posited in a non-physical realm – does not help to explain why it has the meaning it does. An appeal to the internal structure of the expression as revealed in linguistic analysis is needed to explain a semantic fact such as that if John loves Mary, John is in love but Mary not necessarily. Hence, whatever we map this expression with its internal linguistic structure to either needs to recapitulate this internal structure, in which case it is redundant, or it does not, in which case we need to ask why it is needed in the first place, since the linguistic structure does account for the meaning.

 

Here is an answer to the question of why the different structure is needed. Linguistic expressions do not just have a meaning which may follow from their internal structure. They are also true or false. And this indicates they relate to an environment – at least to a physical one (and one somehow hopes the idea carries over to abstract meanings). Features inherent to the expression could not explain that. Hence a different structure is needed, which does explain it. As I have indicated, that it could be the same structure would indeed be a very strange proposal: there are no verb phrases, relations of predication, subjects, lexical concepts, etc. out there in the physical world. But if it is a different structure, not isomorphic to the syntactic one that we find in the relevant production of the linguistic system (the expression), we don’t know how or by what principles we map the one to the other, or how the external would explain the internal one. A fully transparent mapping between a syntactic structure and the presumed semantic ‘correlate’ of it does not encounter this problem. Ideally, indeed, we would have an identity mapping here (Hinzen 2006). Be that as it may, let us turn to the proposal that truth and reference necessitate the idea that linguistic expressions intrinsically relate to the environment (as mind-independently and non-linguistically described), and that this accounts for their semantic properties.

 

IV

Some things we know: we know there is a word ‘true/truth’, which is associated lexically with a human concept stored in long-term memory, the concept of truth. We also know that all human languages exhibit a very special relation, the relation of predication. Predication is not quite like any other relation. It has been studied in linguistic terms for a long time (for recent accounts see Moro 2000; den Dikken 2005). Truth enters into this very special relation. Various other things can be predicated in this way, too, such as existence. If truth is chosen for purposes of this special relation, it is necessarily predicated of full (declarative) sentences as opposed to other kinds of syntactic structures, as (1) suggests, an ancient observation:

 

(1)

a. *[John] is true

b. *[the Eiffel tower] is true

c. *[my sister] is true

d. *[in the garden] is true

e. *[John nice] is true

f. *[walk quickly] is true

g. *[kill Bill] is true

h. *[John walk] is true

 

In each example of (1), truth is predicated of a syntactic object that is formally of the wrong kind to enter into such a predication: in (1a-c) the bracketed structures are Noun phrases (NPs), in (1d) it is a Prepositional Phrase (PP), in (1e) it is a ‘small’ (verbless, untensed) clause, as in ‘Mary considers [John nice]’, in (1f) it is a verb to which an adjunct has been adjoined, in (1g) it is a verb that as taken an argument (as opposed to an adjunct), in (1h) it is a clause with a non-finite verb. What do all of these various phrases have in common, structurally? The empirical answer is they are too impoverished to bear a predication of truth – in particular, they all lack finite Tense. Specification for tense, these data tell us, is something that truth needs. A syntactic object that has finiteness specified in it is a Complementizer Phrase (CP), as seen in (2):

 

(2) [CP That Caesar conquered Gaul] is true

 

Before we have reached that level of structural complexity, then, a CP, which necessarily contains phrases of the type bracketed in (1) and is more complex than any of them, truth is not an option. Similar claims hold for other second-order notions like existence, though existence is predicated of NPs. What (1-2) suggest, then, is that truth is inherently a structural phenomenon. It is woven into the architecture of the full human clause. ‘How we relate to the world’ explains nothing of this.

 

Quite the contrary: predicating truth is a very special way of relating to the world; and we are very likely alone at least on this planet in carrying out such mental feats. It would be surprising to be told that ‘relating to the world’ or a ‘causal relation of reference’ explains how this feat is possible. It appears to be the other way around: our mind builds a very specific and contingent kind of hierarchical structure: the rich fabric of the human clause (Hinzen 2003), with the verbal domain at the bottom, and the CP-TP (finiteness) layer on top. Once that structure is in place, a mental object exists that we can use to relate to the world in the specific way of carrying an alethic force. It provides what we may call a ‘challenge’ for how the world is. Is it that way? The answer we do not find out by building more structure in our minds, or by more thinking. We only find it out by leaving language behind, and doing experiments and interacting with the world instead. We go to a laboratory if we have one, or a mundane substitute for it in our more everyday truth judgements (Is this really Tom? Are these pants the best purchase?). Nothing of this necessitates or even suggests the empirical assumption that when we have predicated truth of a proposition, there is a structure out there, which is not quite that of the linguistic expression that contains our truth predication, but slightly different, and yet similar enough to relate to it inherently and explain it.

 

As far as I can see, the assumption is baseless. Different kinds of minds confront the physical world and its adaptive challenges. They meet them as good they can with the structures that they find in their minds. The structures that we find in some of these minds, in particular our own, are not predicted by the structures that we find out there, or the adaptive challenges they pose. Perhaps we are even alone in doing something as seemingly simple as asking a question, or what I called posing a challenge. Yet the physical environment is something that all minds share. Perhaps there is a ‘circle of causality’ where mental structures feed into an environment, which feeds back into these mental structures, and adaptivity is enhanced as a result (McGonigle&Chalmers 2001). None of this accounts for what I have emphasized here, the origin of structure, as a presupposition for judgments of truth.

 

V

The challenge posed remains, to show that we can or need to account for the productivity of human thought and the infinitary system of meanings in which we can move around at will when engaging in ‘thought’ by appeal to structures or entities outside the human organism. If it wasn’t met, where would this leave us? It means that while there are mental structures produced by some generative engine, they are not mental representations, in the relational sense commonly presupposed in philosophical discussions. As I suggested, though, the structures themselves need to exist. There is moreover all the justification in the world for calling them ‘mental’: for, at physical levels of descriptions, we can throw little light on them. If we could, we didn’t have to go to the linguists and listen to the abstract categories that they invoke to describe the brain’s processing of language. But we do. So we are stuck with all kinds of structures that need to be non-physically described, hence are non-physical, if we interpret, as we should, our best available empirical theories of the world realistically.

 

Calling mental structures that underlie human language use ‘unnatural’ on the grounds they are not describable in a physical vocabulary and share few if any of the features of physical objects, is as sensible today as it was for scientists in the 19th century do reject a realist interpretation of chemistry, on the grounds that the chemical could not be cashed out in physical terms. Science does not come with an ontology: it invents one. A ‘linguistic ontology’ is no less natural today than a chemical one should have been in the 19th century. But can mental structures enter causally into an act of language use in which a thought is conveyed in a physical medium (causing air vibrations)? The suggestion that they do is no more surprising than the suggestion that a material object can act where it is not – or the idea of non-physical action on a physical body. And yet, science has had to incorporate that very notion, that causation does not work mechanically, in terms of contact.   

 

So, we have, not merely structures, but mental ones. But are they representations? I have suggested they enter into the way we relate to the world, constitutively. They construct a human environment (or better, a number of possible worlds) more than they ‘reflect’ or ‘mirror’ one. Not even the phonological structures do: they relate to all kinds of acoustic external patterns for sure, but they do not represent them, in the sense that there are phonemes and prosodic contours out there (some concoction of molecules, perhaps) to which such internal structures which phonologists posit ‘relate’ or ‘refer’. As Chomsky (2000) emphasizes, such entities are not posited, and we expect this equally, or perhaps more so, on the semantic side. No doubt we do not want to say that a mental concept is some concoction of molecules outside. Again, no doubt there are various relations that connect the semantic underlying structure of an expression as generated in a human mind to physical structures in the environment. There is a myriad of causal connections in particular, in each and every case of creative language use. If I am right, none of this either explains what the internal structures mean or how they are used, nor why they have come into existence. The environment certainly doesn’t ‘cause’ such structures, nor do the regimes of adaptation enforce or explain them. The structures make great adaptive sense – they are usable. None of this means that their use explains why they have come to exist or how they work (can be put to use). Structure-building in the organism – organismic morphology and their laws of development, here at the level of abstract syntactic and algebraic structures processed by a brain – is an independent explanatory factor in evolution, interacting with the laws of adaptation yet not reducible to them (Müller and Newman 2005; Hinzen 2006).

 

The adaptive challenge that the evolutionary engineer is supposed to have ‘answered’ by fabricating language, on functionalist views, is usually identified as communication. As Pinker and Jackendoff (2005) put it: ‘language evolved for the communication of complex propositions’. But there is a radical difference, as noted above, between linguistic and non-linguistic communication. Any program explaining the features of human language from its use as a communication system will have to explain or predict its features, not from linguistic communication (which would be circular), but non-linguistic communication. But non-linguistic communication comes for cheap in evolutionary terms: every species does it, often more efficiently than we do, by some reasonable standards (for example, in the case of ants). Looking at its features (Hauser 1996) explains next to nothing about the structural features of human linguistic communication, or what makes this system unique.

 

As a natural object, language may only contingently relate to the communicative to which we put it: that we not only produce recursive structures in our thought, but also externalize them may well be a happy accident of evolution. The more we find quasi-linguistic structure-building processes in the non-human animal mind – hierarchical organization, categorization, perhaps recursion (McGonigle and Chalmers 2007) – the more in becomes clear that having a quasi-linguistic mind (a mind generating the abstract structures underlying spoken linguistic expressions) does not require an ability to externalize it.

 

VI

While I have mainly exploited the syntactic-structural aspects of language to draw these conclusions, I don’t think that the empirical study of meaning and reference of words would yield any other result. As I have argued elsewhere (Hinzen 2007), positing a ‘reference relation’ for words or the ‘parts of speech’ does not illuminate their meaning either. It presupposes them. It does not illuminate our ways of referring to a person or a city to say that there is a – perhaps causal – relation to ‘cities’ or ‘persons’. No standing in causal relations will explain why a creature that has a concept of a person has it, or a creature that lacks such a concept lacks it. No causal relation to a referent will explain why a child thinks a wizard (qua person) doesn’t change when he transforms himself into a lion, or a mouse; or why a city can stay the same, in our judgement, when it is destroyed and rebuilt elsewhere (Chomsky 2000). It is our concepts of persons and cities that determine these identities, or what the world can be like. Intentional reference needs to exploit the specific perspectives on the world that human concepts provide, just as a judgement of truth needs to exploit the configuration of a full proposition in abstract thought that the truth value is assigned to, in this judgement. Reference is a function of what concepts we possess, just as truth is a function of which structures our mind can generate (section 3). This cannot be so if reference explains concepts, or what they mean. It is the other way around. There might be a creature that has concepts, but cannot refer – probably most concept-using creatures on Earth are like this, if indeed intentional (as opposed to functional) reference is humanly unique and if at least non-human primates have a mental life as rich as current evidence suggests. There might even be a creature that can combine concepts recursively and compositionally at will (to generate ‘blue circle’, etc.), without ever intentionally referring or pointing to any one such thing (‘a blue circle’, or ‘this blue circle’), simply because it lacks the necessary computational resources: determiners such as ‘a’ or ‘this’, which localize a given, conceptually configured object in space.

 

VII

I have been defending a thoroughly ‘internalist’ perspective on the human faculty of language, opposing an externalist preference that is prevalent today (and has been so since the 1950s). I contend the deepest motive for positing a ‘relation of reference’, which I have argued is non-explanatory, or for individuating mental structures functionally, has been not empirical but metaphysical: physicalism has induced a pressure on eradicating mental entities as primitives of nature. If I am right, there is no such thing as a physical individuation of language anywhere in view; nor does science support in any way the underlying aprioristic ontological ideas. And the functional perspective on mental structures as ‘representations’ of an external environment does not sufficiently respect the most distinctive design feature of language, its freedom from external control, its lack of situation-specificity, and the apparent lack of physical constraints on its referential use.

 

Wolfram Hinzen

 

References

 

Chomsky, N.: 2000. New Horizons in the Study of Language and Mind, Cambridge University Press.

Chomsky, N.: 2005. ‘Three factors in language design’, Linguistic Inquiry 36:1, 1-22.

den Dikken, M.: 2006. Relators and linkers. Cambridge: MIT Press.

Fodor, J. and Z. Pylyshyn: 1988. ‘Connectionism and cognitive architecture: a critical analysis’, Cognition 28, 3-71.

Gleitman, L., K. Cassidy, R. Nappa, A. Papafragou, and J. C. Trueswell: 2005. ‘Hard words’, Language learning and development, (1), 23-64.

Hauser, M.D.: 1996: The evolution of communication. Cambridge: MIT Press.

Hinzen, W.: 2006: Mind design and minimal syntax. Oxford: Oxford University Press.

Hinzen, W.: 2007: An essay on names and truth, Oxford: Oxford University Press.

Moro, A.: 2000. Dynamic antisymmetry. Cambridge: MIT Press.

McGonigle, B., and M. Chalmers: 2001. ‘Circular causality comes to cognition’, in: Spatial schemas and abstract thought. Cambridge: MIT Press.

McGonigle, B., Chalmers, M.: 2007. ‘Ordering and executive functioning as a window on the evolution and development of cognitive systems’. Int. J. Comp. Psych., in press.

Müller G.B. and S.A. Newman: 2005. ‘The innovation triad: An EvoDevo agenda’
Journal of Experimental Zoology, MDE 304: 487-503.

Pinker, S. and R. Jackendoff: 2005. ‘What’s special about the human language faculty?’, Cognition 95, 201-263.

Quine, W.v.O.: 1960. Word and Object. Cambridge: MIT Press.

 



[1] A ‘generative’ grammar – an explicit theory of this algorithm – is for this very reason not a (controversial) theory, but a research programme.

Close Another reply to Rey  
John Collins
Jul 25, 2007 0:13 UT

Rey wants to insist on a distinction between, what we may call, causal externalism and constitutive externalism. He also insists on a distinction between weak and strong externalism. I think these pairs are useful in mapping the geography and I certainly didn’t intend in my fist reply to Rey to be conflating them. My contention, rather, was that while merely causal externalism clearly does some work for us in understanding how cognitive systems are embedded in a ensemble of other systems and, ultimately, the normal human environment, (see my examples of phonology and visual illusion) it remains unclear to me what explanatory work constitutive externalism is apt to perform, at least in the cases that are our present focus: the language faculty and human conceptuality more broadly.

One problem is just getting clear on what ‘constitutive’ means. Nomological dependence doesn’t seem enough, at least if we are after a naturalistic characterisation of intentionality. Anyhow, let us assume that what we are after is some property of concepts/lexical items that will, inter alia, gives us a meaning/belief distinction in the absence of an analytic/synthetic distinction. I take something like this to be the initial motivation behind Putnam’s twin earth story and it is certainly an animating reason for Fodor.

I suppose I’ve less animus for the a/s distinction than many. How about if we said something like this… we don’t want the a/s distinction to do serious epistemological work for us; or sole motive is simply that, on the face it, our concepts/lexical items carry inherent ‘perspectives’ (‘senses, if you like) on whatever we use them to talk about, i.e., atomism is out. The job of semantics is to figure out what perspectives go with which concept/lexical item and to capture whatever generalizations there are. Now, in perusing this endeavourer, it might well turn out that some of our concepts are, let’s say, externally orientated, perhaps even in ways Putnam suggested, others not, i.e., some concepts kinda include a ‘slot’ to be filled by the environment in some sense. The issue is empirical.

As I see it, this inquiry presupposes some stability via a revamped a/s distinction (the inherent ‘senses’), but just what stability obtains is to be discovered rather than pre-theoretically fixed. The issue of externalism, then, amounts to the question: How many of our concepts are externally orientated? I should say that few are, or at the very least, I don’t see why semantic inquiry as sketched should suppose that ALL concepts are.

So, as I see it, stability in the face of belief change is what we want, and we are only driven to externalism because of an undue suspicion of the a/s distinction. If we understand a/s aright, we can get stability (explain whatever stability there is to explain) without presupposing externalism. There is whatever externalism there is, but we have no reason to think it is a general characteristic of conceptuality at any level.

This, at least, is one take on our dispute.

Rey also suggests that a prime motive for an appeal to externalism is that it promises to account for how states of the brain can get to be about things – the long-standing problem of intentionality. I remain unmoved. I agree with Rey that externalism of some sort WOULD be some kind of answer to the intentionality problem, but I just don’t think it works. If we forego the atomism and think of a concept as a restricted cluster of senses/perspectives, then we really don’t want some label model of concepts, where the problem is to figure out how the labeling gets fixed. I prefer a model in which we deploy concepts to think about particular things, but there is no fixity in this relation outside of the uses to which we put our concepts. The concepts, thanks to their inherent features, restrict how we can use them, but that is all. I think one of the problems to seeing our way to this way of looking at things is the dominant idea that thinking is intimate with truth. I think that is wrong. But that is another story.

  0 replies to Another reply to Rey:
Open Hinzen's False Dilemma (4 replies)
Georges Rey, Jul 18, 2007 13:52 UT
Open Lacunae in a broadly true picture (1 reply)
John Collins, Jul 11, 2007 1:04 UT
 
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