Languages and genes: Can they be built up through random change and natural selection?
Can natural selection operating on random arrangements of material building blocks (i.e., subatomic particles, atoms, molecules, and larger collections and structures of matter), produce the genomes of all living things, the human language capacity, and all of the world's 6000 plus natural languages? There are two polar views on this question that are widely held by practicing scientists. At one extreme there is the neo-Darwinian claim that chance aided by natural selection can arrange dynamic information systems as they are now. At the other end there is the view that a transcendent Intelligence not limited by matter, space, and time is required. Here an argument is presented from logico-mathematical proofs developed in theoretical semiotics to show unequivocally that the known symbol systems seen in genomes and in human languages cannot be produced by chance arrangements of any kind of material building blocks. The argument is general. It applies to all possible symbol systems, though the emphasis here is o n the genetic system evidently underlying all living organisms and the human language capacity, which is manifested in the multitude of natural languages.
INTRODUCING CRUCIAL DISTINCTIONS
The argument to be presented refutes the proposition that symbol systems can be built up by chance from random arrangements of material particles (or any other objects, in the most logically general sense of the term "object") over a period of, say, 15 to 20 billion years as required by neo-Darwinian theory. The relevant logico-mathematical demonstration hinges on the distinctness of three kinds of sign systems: icons, indices, and symbols. It has already been shown, incidentally, that all possible sign systems can be built up from various combinations of these three types of sign systems (cf. Peirce, 1897). Hence, the argument to be presented is not one against constructive evolutionary processes, nor against chance per se as powerful mechanisms of change and risk. The argument centers on the kinds of signs known as symbols. It shows that the conventional aspects of symbols, their critical defining trait, cannot be built up out of icons or indices in any conceivable combination or multitude. The central demo nstration has the power of a logico-mathematical proof - which in its turn is grounded in a whole family of related proofs generated by the strictest form of mathematical logic.
To comprehend the argument, it is necessary to understand the foundational difference between icons, indices, and symbols, and it is essential to apply a fully mathematicized (stricly necessary) variety of logic. In the next few paragraphs these critical elements will be introduced -- icons, indices, and symbols along with the logico-mathematical basis for the argument. It is important throughout the entire presentation to keep in mind that the term "object" (or "thing") is always used in its most general sense - to mean any material thing, particle, grain, or clump of matter, any substance, gas, or relation between such things or substances, or any relation between relations between such things to any conceivable degree of complexity. This definition of the term "object" bears no weight in the argument, but it is useful to enable comprehension of the method of reasoning. In fact, all the definitions in this section can be, and have elsewhere been built up by strictly necessary logico-mathematical reasoning ( cf. published writings of C. S. Peirce [1839-1914] in Hartshorne & Weiss, 1931-35; see also Burks, 1957-58; Fisch et al., 1982-present; Houser, 1986; Ketner, 1992; Nagel, 1959; and more recently Oller, 1993, 1996a, 1996b; Oller & Giardetti, 1999). Although the definitions do not sustain the argument, they are useful to enable its comprehension; therefore, only the essential elements are discussed.
An icon, as the term is commonly used, is an image of something else. In its more technical application in theoretical semiotics (i.e., in the science that deals with all kinds of signs and systems of meaning) an icon is the sort of sign that gets its meaning by resembling its object. Every object is intrinsically an icon of itself and incidentally of whatever else it may resemble. Herein lies the difficulty in interpreting icons on account of the fact that all of them more or less resemble each other, as seen in three-dimensional transformations of images in advertisement. For example, the placid surface of a lake is transformed smoothly into a rolling Goodyear tire.
An index, in the common sense of the term, is a list of some sort that points to a list of another sort (e.g., a list of topics attached to page numbers at the end of a book). In theoretical semiotics, however, the term index is applied to the kind of sign that connects with its object through some kind of action or movement. An example would be the act of turning to a particular page in a book, or moving to a certain location. An index has meaning only to the extent that it connects with its object. A pointing finger that merely waves around in all directions is not a well-formed index. Only when the pointing is directed towards and connected with a particular object, say a plane flying over head, does it acquire meaning as an index. It does so by connecting one or more sign user/interpreters with the object pointed at. In the technical sense of the term, an index is like an electrical cord that provides power, a pipe that transports some material, or a road that connects distant points.
By contrast, a symbol, according to theoretical semiotics, is the sort of sign that only gets its meaning through a conventional (usually an entirely arbitrary) association with its object. For instance, the fact that my parents named me "John" and not "Randolph," or "Victoria" illustrates and defines the nature of a convention. The defining trait of symbols, their conventionality utterly distinguishes them from mere icons and indices. Whereas symbols can represent other symbols (enabling synonymy, paraphrase, and translation), icons, and indices, the reverse is not true. Icons and indices cannot, without the presupposing the conventions of symbols, represent or otherwise generate the conventions upon which symbols are based.
The heart of the logico-mathematical argument against neo-Darwinism is summed up in the fact just stated. This material and logically demonstrable fact is the key to the simplicity and power of the entire argument. The argument itself is rooted in the method that Peirce called "exact logic"--by which he meant fully mathematicized, strictly necessary logical reasoning. It was Peirce's goal, by such a method, to uncover the logical conditions necessary to the possibility of there being any semiotic (i.e., meaning) systems. It is the point of this paper to apply certain more recent developments from the logico-mathematical variety of theoretical semiotics (a generalized variety of Peirce's method) to neo-Darwinian theory. Whereas mathematical reasoning is necessary reasoning in the abstract, without referring to any material objects (excepting notational symbols and their associated abstract concepts), the brand of theoretical semiotics applied here is necessary reasoning applied to abstract symbols that are in fact associated with the objects of experience. Therefore, exact logic is more concrete than pure mathematics but not less necessary. The method is summed up in a single caveat: begin with nothing that is doubtful and proceed from there only by taking steps already shown to be necessary.
A Summary of the Neo-Darwinian Theory
The Darwinian theory is familiar to all educated persons (Eldredge, 2000; Pennock, 2000). Its underlying story is told in the public schools, the media, the universities, the scientific institutions, and even in most of the theological seminaries of the present day. Kitcher (1982) sums it up:
The earth was formed about 4.5 billion years ago. Biologically significant molecules appeared relatively quickly. From a primitive atmosphere, rich in simple molecules (hydrogen, nitrogen, water, methane, and ammonia), organic compounds were generated. Eventually, self-replicating molecules--like DNA--appeared, along with amino acids and proteins, The first simple organisms, probably unicellular organisms, without a nucleus were made from these basic constituents. (p. 27)
From there a theoretical series of transitions occurred leading up to the mammals from which "one line of descent" led "to the great apes--and their close cousin, Homo sapiens" (Kitcher, 1982, p. 28). Arguably, the most difficult transition in the series was the one leading up to the human language capacity.
D. K. Oller (2000) speculates that "in scaling Mount Improbable [i.e., climbing up to the human language capacity], that huge feature of the evolutionary landscape that would seem impossible to conquer in a single leap (Dawkins, 1996), humans may have found ways to move up in stages to plateaus of improved capability" (p. 337). The still sketchy story concludes with the hope that "eventually ancient humans may have reached a final plateau from which the scaling of the linguistic peak could proceed" (Oller, 2000, p. 338). The question remains whether this occurred suddenly in a single leap or in minute steps over a relatively long period of time.
Binford (1981), White (1989), Dawkins (1996), Leakey (1994), and Pinker (1994) have found it useful to hypothesize "a single leap from a vocal system resembling that our near relatives, the apes, to one of full-fledged speech" (D. K. Oller, 2000, p. 364). The orthodox neo-Darwinian narrative, by contrast, requires that a gradual series of steps must have occurred. Bickerton (1981), Deacon (1997), and Tobias (1996) subscribe to that view and propose that ape-like ancestors progressed through a long series of now extinct (highly simplified, pidgin-like) communication systems "superior in power and presumable survival value to that of each prior stage" (D. K. Oller, 2000, p. 27). The question to be addressed here is whether either of these options can be developed in a logically coherent form. It will be argued that they cannot.
Explaining the Transition(s) Leading to Genes and Languages
It is the transitions that require examination in the neo-Darwinian narrative. D. K. Oller sums up the problematic nature of these transitions: "The pattern of paleontological results suggests the existence of capabilities that changed discontinuously at key points" (2000, p. 337). It is difficult to overestimate the problematic nature of these transitions within the neo-Darwinian theory. Perhaps the most extreme attempt to explain them is the notion of "punctuated equilibrium" as suggested by Gould and Eldredge (1972). It involved the revival of the "hopeful monster" theory -- the notion that great genetic changes can accumulate over a period of time and then suddenly express themselves in a whole new phyletic line. In fact, the purpose of the whole Darwinian enterprise can be construed as nothing more, nor less than an attempt to explain all of existence as a series of transitions. It is, however, the discontinuities that demand attention within any such theory.
Although Darwin set aside the problem of how matter itself came into being (Pennock, 2000, p. 161), many present-day evolutionists subscribe to the Big Bang theory (Eldredge, 2000) to explain the origin of matter ex nihilo (i.e., from nothing) in the first moment of time. From the logico-mathematical point of view, there is an essential problem inasmuch as the bursting into being of the universe requires a host of unjustified mathematical assumptions--all of them associated with the fundamental discontinuity between nothing and something. Then, there is the problem of how the matter came to be systematically distributed as we now find it in stars, galaxies, our solar system, and on the earth (Hoyle, 1983). More critically, how did it come to be arranged so as to enable the existence of the biosphere? How did the genetic basis for life come about (Crick, 1981)? From there, how did speciation occur? To explain all these transitions, and others, the neo-Darwinian orthodoxy has focused attention on the syntactic, indexical relations between various iconic elements--that is, indexical arrangements of molecules of matter whose existence must be presupposed.
For instance, Robert T. Pennock illustrates this kind of reasoning by explaining how speciation can occur in the neo-Darwinian perspective. The building blocks of DNA consist of the sugar bases Thymine (T), Adenine (A), Guanine (G), and Cytosine (C). These may be construed as foundational icons, a kind of alphabet, of the genetic system. Pennock says "some additions, deletions and rearrangements of those Ts, As, Gs, and Cs" and "you have the genome of a different species" (Pennock, 2000, p. 157). According to him, the diversity of the whole biosphere, leading right up to the human language capacity, can be accounted for in this way: by random changes in syntactic (indexical) arrangements of the basic building blocks (the icons) assisted by the power of natural selection.
Among the discontinuities that this approach is supposed to account for is the well-known "Cambrian explosion" of living forms: the profusion of algae, bacteria, and protozoans. From there forward, by rearranging indexical associations of icons, the neo-Darwinian theory proceeds to account for the generation of plants, fish, reptiles, birds, dogs, dolphins, and apes eventually leading up to what Deacon (1997) calls the symbolic species. The final, and arguably the greatest leap to be explained--the greatest discontinuity on which we focus attention here--is the one leading to the language capacity. For a quarter of a century, this problematic "transition" has commanded attention (Binford, 1981; Chomsky, 1975; Dawkins, 1996; Deacon, 1997; D. K. Oller, 2000; J. W. Oller, 1981b, 1982, 1984a, 1984b, 1988, 1997, 2000; Oller & Omdahl, 1994; Pennock, 2000; Pinker, 1994; Tobias, 1996).
Deacon (1997) supposes that the first symbols were formed from "indexical associations," which came to be understood as relations "between words and associated objects" (p. 301). Counterposed to his view, there is the long-standing theoretical argument capped off by a famous mathematical proof of Miller and Chomsky (1963) showing that "statistical associations" (i.e., indexical ones arising by chance) of the sort hypothesized by Deacon cannot generate the known complexity of any natural language (also see Chomsky, 1956, 1957, 1959, 1965, 1980, 1993; Chomsky & Fodor, 1980).
The special difficulty faced by the neo-Darwinian orthodoxy with respect to the language discontinuity almost comes into view with respect to the difference D. K. Oller (2000) notes between the indexical relation seen in the act associated with the actor producing that act, as contrasted with the relation seen in any meaningful use of a conventional symbol. He writes, "Words are radically different [from actions associated with their actors] ... Instead of indexing conditions obligatorily [as the sound of coughing necessarily indexes the actor who performs that act], they [i.e., words and symbols] make reference arbitrarily, yielding a kind of value that is different in both content and in the process by which it is derived" (D. K. Oller, 2000, p. 200). Yet, he does not go so far as to deny Deacon's thesis that symbols can be accidentally built up from indexical associations. But that is the essential question here. Can symbols be constructed from indexical associations of icons?
The Plausibility of the Neo-Darwinian Theory
It is possible to arrange species in a hierarchy, more or less, and to suppose a line of descent pointing backward from man to algae (or some other simpler life form). In fact, countless scenarios for lines of descent have been proposed and uncountably many are conceivable. It is true that embryology, genealogy, and development unfold over space and time. Learning itself seems to follow a pattern not unlike the one Darwin proposed for the development of all species. Microevolution is commonly observed (e.g., the increasing abundance of dark colored Peppered Moths [Biston Betularia] during the industrial revolution in England as noted by Kettlewell [1955a, 1955b] is a frequently cited example). From evidence that natural and artificial selection work within limits, it is an easy leap of inference to the supposition that the whole universe, including genetics and languages, can be explained by random mutation and natural selection. Why couldn't material icons come to be arranged by chance into the meaningful p atterns that are found, for instance, in the sequence of letters on this page? In fact, why couldn't such events also explain the ability to read and make sense of these words?
The answer is not simple, but it is grounded in the power to reason and to apply reasoning to itself. This is the key problem for the neo-Darwinian orthodoxy in all its varieties. Without presupposing symbols that are already abstract, the gaps between material objects in space and time and those between the species are not bridgeable at all. Darwin's story is not merely incomplete, but it is false from the logico-mathematical point of view. Incidentally, a related theme in one of the empirical applications of theoretical semiotics, especially in psychometric research, shows that intelligence is at the heart of language and reasoning (J. W. Oller, 1981a; Oller, Kim, & Choe, 2000a, 2000b; Oller, Scott, & Chesarek, 1991). However, the neo-Darwinian orthodoxy supposes that purely material relations, without any necessary intervention by prior intelligence of any kind, can in fact generate abstract, arbitrary symbol systems and the intelligence that those systems necessarily presuppose. The logico-mathematical a rgument sketched in the next section shows why the neo-Darwinian orthodoxy cannot possibly be correct in these claims. The argument shows the neo-Darwinian scenario not merely to be unlikely, but to be necessarily (in the purely logico-mathematical sense) impossible.
Can Icons and Indices Evolve by Chance into Symbols?
With all of the foregoing in mind, the question is, how can the material icons and their indexical relations, formed only by chance and assisted by natural selection, have been guided across the void that separates them from intentional, abstract, general, and fully conventional symbol systems? To clarify the nature of the problem, let us next consider more closely the logical peculiarities of symbols. In particular, it is essential to consider more closely the logical properties of icons, indices, and symbols as well as their dependency relationships. Omitting details that can be found in J. W. Oller, Jr. (1996a), what follows is a sketch of the perfectly general and self-consistent logico-mathematical argument.
First, consider icons. To be an icon of a cup, or a car, or a DNA molecule, or the word the, or the book titled The Emergence of the Speech Capacity, the icon itself must resemble the cup, or the car, or the DNA molecule, or the word the, etc. To take an icon as a sign of some other object (which can only be an icon of itself and also of the other icon) by saying that the one resembles the other in the manner of an icon is to require the service of, in addition to the icons that resemble each other, one or more indices. Indices involve connections between icons and are the only way of showing connections between them in space, time, or in any fiction construed by imagination. If no connection is made, no meaningful index can appear between any icons. To serve as an indexical sign of a relation between any pair of things (invariably shown as icons) that may be selected, it is necessary for the index to actually connect the things (icons) related. Thus, indices can be shown to be utterly dependent on the prior existence of icons. If there were no icons at all to be connected, there could be no indices to connect them. This is a strict logical necessity.
To achieve a well formed index, at a minimum a connection between two icons is necessary. For instance, at its limit of near meaninglessness, the minimal structure of an index can be illustrated by drawing a line segment on a sheet of paper. As an act, the index connects the pencil and paper and the points on the line segment. Materially the act also connects the paper with the surface that holds it up and that surface with what lies beneath it, and so forth. It connects the manipulator of the pencil with the pencil, and so forth, and so forth, ad infinitum at both ends of the index. Thus, if analyzed closely, any index (and this conclusion is logically necessary, i.e., strictly provable as has already been shown by Peirce  and by J. W. Oller [1996a]) points to a countless number of possible icons at both of its ends.
An index is like a line segment, or a movement, with one or more icons at its beginning and at its end. From the perceptual point of view, indices cannot be formed without one or more movements of some icon within a larger space. But it is universally difficult, especially if the index is produced by some other sign-user, for any other sign-user to say exactly where either one or both of the ends of any index lies. For instance, an index relating a cup to the person drinking from it, must connect the cup with the person, but can as easily connect the person with the liquid in the cup, with the drugs put into the liquid by someone else, with that other person who poisoned the liquid, etc., ad infinitum.
Thus, it is necessary in addressing the claims of neo-Darwinian theory, to keep in mind the universal difficulty of saying exactly where any index points to or from. It is precisely because of this universal logical incompleteness of indices-what Peirce (1902/1932) called their "reactional degeneracy"-that no index can ever form a satisfactory basis for sharply determining the meaning of even one single symbol. When more than one index is brought to bear on any given icon or pair of icons, the indeterminacy problem is merely increased by the number of added indices. Therefore, indices cannot serve to produce those fully arbitrary, regular, or conventional symbols that are found in every human language and in the genetic code as well. While the argument can be constructed in excruciating detail as a strict proof, its essence has already been given in the preceding lines.
Defenders of the neo-Darwinian orthodoxy might hope that icons could make up for the logical poverty of indices. However, it turns out that every icon (treated as a sign and not merely an undetermined object) invariably suffers from the same lack as every index on account of the fact that every icon depends on one or more indices to locate it in the first place, and also to associate it with whatever else it may be an icon of. If sign-users, genes, genomes, or organisms are to make use of any icon as a sign for something else, it is essential first to find and identify the icon of interest (e.g., the one to be fitted into a sequence of icons, say, in a strand of RNA, or in a protein under construction). Therefore, every icon suffers from the logical incompleteness that Peirce called the reactional degeneracy, which is universally associated with indices. Also, every icon has a certain logical incompleteness of its own that only makes things more difficult for the neo-Darwinian theory. Every icon not only res embles whatever it may be taken (through some index) to be an icon of, but it also, unfortunately, tends to resemble more or less everything else in the whole universe. This peculiar problem with icons results in what Peirce (1902/1932) called the qualitative degeneracy of icons. Peirce's mathematical proof of this logical incompleteness of icons was dramatized by the T1000 that transforms itself into a cop and chases Arnold Schwarzenegger in Terminator 2. The image of the cop melts into a tile floor in one scene and into the pavement in another scene only to regather itself and resume the chase in both instances. Because every icon resembles every other icon more or less, any icon, if taken as a sign, can be transformed into any other icon. This too is strictly provable in the logico-mathematical way. It is a necessary consequence of the logical nature of icons.
As a result, from an icon alone, it is impossible to determine just what it is a sign of on account of the fact that it more or less resembles everything. Add to this the logical problem of the natural indeterminacy associated with the ends of any index and the difficulty of transforming icons and indices into well-formed and relatively determinate symbols comes into view. It turns out that the only way to remove the logical indeterminacy associated with every icon and index is by appeal not merely to a symbol, but to a whole system of symbols meeting certain logical requirements in advance. To bring the problem into a sharp focus, it is useful to take the argument to a higher level of abstraction.
The Adinity of Predicates
It can be seen that icons are essentially monadic (to borrow a word from Peirce  who followed Leibniz [1691/1953]). That is, if we think of a sign as a sort of predicate that takes one or more arguments (in the sense of modern linguistic theory) to fill it out, an icon is the sort of predicate that can be filled up with just one argument. Indices, by contrast, are essentially dyadic. They are predicates of a different kind and they involve at a minimum, two iconic arguments to fill them up. It can be seen that the dyad we are speaking of here is constructed by relating two of the former monads. To express the idea of the logical valence of predicates (what is now called argument structure in linguistics), Peirce proposed the term ad-inity. Thus, a predicate (or any sign used as a sign) that is strictly limited to one argument (a monad) has an adinity of 1, and a predicate requiring 2 arguments (a dyad) has an adinity of 2, and so forth.
Logico-mathematical reasoning shows that any well-formed index can have neither more nor fewer than two icons, one at each of its ends. Logically, it is contained within a larger icon that embraces both of the icons at its ends, but that larger icon is not taken into consideration by the index itself (i.e., it does not have a third end to point to the larger scene in which it is located). Also, we have already seen that the principal trouble with any icon is that none of them can be entirely unambiguous if we try to make it out to be a well-determined conventional symbol. Every icon, unfortunately owing to its very nature, resembles everything in existence. Neither can this universal ambiguity be removed from any particular icon by merely pointing at it with the assistance of an index. No index can fully disambiguate and thus identify any particular icon on account of the logical indeterminacy of every index. Indices cannot remove the logical incompleteness of any particular icon on account of the fact that i ndices have the peculiar indexical indeterminacy that has already been pointed up. That is, every index tends to capture in its purview anything that lies along the logical line that connects it with its intended object. As a result, there are always potentially infinitely many objects pointed to, and or from, by any given index. The illusion that this is NOT so (e.g., we really know exactly who is writing these lines as distinct, say, from the person reading them) involves appeal to a well-formed symbol system without which no such determination can be made at all.
Relatively Perfect Signs--True, Narrative Representations
It is not until we get to the level of a symbol that we find the type of sign that can solve the dual problems of the indeterminacy associated with icons in their separateness combined with the special indexical indeterminacy associated with all indices. It can be strictly proved and it is relatively easy to illustrate that only a situated symbol of the kind that I have elsewhere termed a true narrative representation (TNR; J. W. Oller, 1993, 1996a-b) can fully disambiguate and, thus, determine the identity of any particular icon. A representation is any sign or object taken as a sign of some other sign or object. A narrative representation is the type of sign that is situated in a real or imagined space-time context so that its reported elements unfold over rime, as in the telling of a tale. A true, narrative representation is merely one where the actual facts of some space-time context are correctly associated with the conventional uses of the signs making up the narrative so that the events actually unfold ing in space and time fit the representations of those facts.
This is nothing more, nor less than the simplest and most commonplace idea of what truth is. TNRs at their basis are what Lakoff and Johnson (1987) call simple central truths. TNR-theory can be construed as an elaboration of Tarski's logical proof that all meaning can be reduced to reference (Tarski 1936, 1944; see also Field, 1972; Kitcher, 1993, p. 133). Owing to the fact that TNR-theory and its logical corollaries (cf. proofs given in J.W. Oller, 1996a; Oller & Giardetti, 1999) depend on nothing but logical consistency, they can only be defeated by showing an inconsistency in their development. Anyone who could do so would be doing a service in the interest of science, but if no inconsistency can be shown, it would appear that the logical consequences of TNR-theory must be taken seriously. Certain highly specialized hypotheses deriving from TNR-theory have been explored in several empirical domains including psychometrics (Oller, Kim, & Choe, 2000a, 2000b; Oller, Kim, Choe, & Jarvis, 2001; Xiao & Oller, 1 994;), studies of language processing and acquisition (Al-Fallay, 1994; Taira, 1993;), communication disorders (Oller & Rascon, 1999; Smith & Damico, 1996;), and in the field of visual and verbal interpretations in education, advertising, marketing, and political campaigns (Giardetti, 1992; Giardetti & Oller, 1995; Oller & Giardetti, 1999). In all these cases, the theory generates hypotheses that have stood up to careful empirical scrutiny.
TNR-theory shows that any well-formed symbol brings into view an entirely different sort of sign-system than can be found in any complex of icons joined into an index or complex of indices. No complex of icons, or of indices can manufacture the crucial conventional logical property necessary to every well-formed symbol. Although every symbol most certainly employs both icons and indices to the extent that the said symbol may appear in any material context, in order for the symbol to be attained, it must be grounded in a richer system of symbolic relations that enables the determinacy that is missing in icons and indices to be attained. This is not obvious to mature human beings on account of our pervasive and nearly complete dependence on well-formed symbols to make sense of our world. Yet, the peculiar nature of symbols becomes increasingly evident in the abstractive processes of a normal human infant acquiring a language (Oller, 1996b, Oller & Rascon, 1999). For a symbol to serve as such it requires all of the following properties, which can be shown to lead to a host of others not unlike these: A symbol must be abstracted from the local context(s) of its instantiation, it must be recombinable with other symbols in unaccountably many contexts, and it must be generalized to all possible contexts like any one of those that may instantiate the meaning of the symbol.
TNR-theory shows that the simplest well-formed symbols take the triadic form of the symbols in a true story. For instance, suppose that it is truly reported that during a certain period of history the famous Greek named Socrates married a woman named Xanthippe, or Socrates married Xanthippe. The reference to either Socrates, or Xanthippe, or the marriage of these two to each other, if the story is true, can serve to exemplify a TNR. Although nothing hinges on this assumption, for the sake of the illustration, let it be supposed that the proposition that Socrates married Xanthippe is a TNR. Now, consider the simplest case of a TNR contained within the statement in question to be the reference to the man SOCRATES by the name Socrates.
We notice that there are at a minimum three elements here, which must be the case for all TNRs (a strictly necessary logical proposition). First, there is the material element, the person SOCRATES (supposing that the report is merely true in the most mundane and least semantically burdened sense of the word "true"). Second, there is the surface-form of the representation (e.g., the name shown here as a sequence of letters, Socrates). It turns out that this second element is a special kind of icon for an indexical act of referring to the bodily person, SOCRATES. And, third, there is the dynamic act itself constituted by the TNR that links the surface-form of the symbol, Socrates, with the material object, SOCRATES. The element most apt to be neglected is this indexical linking, the act, which is crucial to making the proposition out to be a TNR. This link is an index that establishes an indexical relation between both the bodily SOCRATES, on the one hand, and the surface-form of the word, Socrates, on the oth er. It also establishes an indexical relation between each of these elements and the distinct symbols with which they are associated syntactically in the utterance, semantically (in general) by convention, and pragmatically by the reference to SOCRATES through a correct use of the name Socrates. Upon closer inspection, it turns out that each of the three elements just spelled out consists of at least three more, though we will not iterate these here, and each of these additional elements is both entailed by and entails all the others.
TNRs as Well-Formed Signs
Oller and Collins (2000) have proved in the logico-mathematical way that TNRs have a kind of a trinitarian perfection (in the grammatical sense of the term perfect, as in the perfect tenses, or in the logical sense, as in a perfect, i.e., well-formed structure). In a TNR structure, each of the three main parts (the material element, the linking act, and the surface form of the representation) entail the other parts and the whole. That is to say, TNRs are not merely triadic structures, like the three corners of a triangle, but they are holistically interrelated. In fact, an acquaintance with any of the major parts of a TNR entails (i.e., logically guarantees) an acquaintance with the other parts and with the whole. Without reproducing the technical proofs of this claim we can nonetheless illustrate them. If the name Socrates is truly related to the bodily person SOCRATES through the truthful and competent ACT linking these elements into a TNR (supposing only for the sake of illustration that the statement that Socrates married Xanthippe is both a truthful and competent representation), it comes out upon examination that every one of the three separate parts of the TNR can itself be shown to be a triad of triads where each of the separate triads entails all of the others. And where, thus, it follows by the strictest logic that all of the main parts of the TNR at any level of the structure must meet all of the logical requirements pertaining to any well-formed symbol. That is, each of the three parts of the structure entails the others. On account of the fact that it has been proved (Oller & Collins, 2000) that all of the logical perfections of TNRs are entailed by any one of them, nothing essential is lost if we restrict attention here to the set of logical perfections that fall into the category of pragmatics (i.e., those having to do with the practical, material world). The pragmatic perfections of TNRs include the fact that only TNRs among all possible sign structures are (a) determinate with respect to their me aning, (b) connected through well-formed references with the space-time continuum, and (c) generalizable to all similar contexts such as the one(s) instantiated in the TNR (J. W Oller, 1993; 1996b).
TNR-theory proves that no mere icon or indexical relation has any of the logical perfections associated with symbols. No icon is determinate with respect to its meaning, nor is it well connected with respect to any particular bit of material in space and time, and neither can any icon (in and of itself) be generalized so as to take note (or single-handedly to enable any sign-user to take note) of its resemblance with all of the possible objects that it may resemble. The generalization, if attempted, is assured of going completely over the top and reaching all possible objects on account of the universal qualitative degeneracy of icons (Peirce, 1902/1932). As for determinacy or connectedness with a particular location in space and time, an icon without the assistance of one or more indices has no determinacy whatever. The raw icon, a monad in separate singleness, has no more power to determine its location in space and time than a billiard ball can tell its identity by recounting its history. An icon cannot ev en tell the time and place of its present appearance. It cannot give its coordinates.
But what of an index? It also cannot determine a particular object on account of its universal logical incompleteness (what Peirce [1902/1932] called its "reactional degeneracy") and thus lacks the determinacy perfection. It cannot show the connection of any undetermined icon with a particular location in space and time on account of its indeterminacy, and it cannot be determinately generalized for the same reasons. It would not be possible to tell what meaning was being generalized from any given index owing to the universal indeterminacy of all indices.
What, therefore, makes well-formed symbols--TNRs being the simplest and archetypical cases--utterly different from icons and indices is that well-formed symbols inevitably have all the properties of TNRs. The conventional aspect of symbols may be thought of as a rule, habit, or even a whim, but what is perhaps most amazing about symbols is that for any convention to serve in the formation of a symbol, the convention itself must be taken in a distinctly symbolic way. It must meet all the logical requirements of a symbol a priori--before the fact. The logical properties associated with every well-formed symbol include general applicability to all possible similars, complete abstractability from any context that might instantiate its conventional uses, and combinability with other symbols so that it can be distinguished from those other symbols and yet be recognized for the individual symbol that it is itself (i.e., it has to have a distinct and determinate identity in order to function as a symbol).
A Simple Logical Demonstration (i.e., a Proof)
The most damaging fact about well-formed symbols for the orthodox theory of evolution is that none can ever be established, discovered, or created from anything but a symbol of the same kind. This last point has been strictly proved in a variety of ways (J.W. Oller, 1993, 1996a, 1996b, 1998; see also Peirce, 1897, 1908). The simplest form of such a proof is the demonstration that a monad, as shown, say, in a dot or a circle (e.g., like this one, O) if thought of as a relational system (i.e., a representation), is really an incomplete (Peirce would say degenerate) triad in the first place. We normally think of any icon (always a kind of monad) as consisting of whatever it contains within its boundary, or edges, or beneath its surface, or within its scope. Consider the monadic circle or dot more intensively, however, and it will invariably be found out to have three distinct parts only one of which is represented in the icon itself. There is the included area within it, the excluded area outside the icon, and t he boundary (or other coloring) that marks them as distinct.
Ordinarily, all that we perceive of an icon is its surface, edge, or boundary. But any way you slice it, the icon considered as the sign of anything, turns out to be a qualitatively incomplete (i.e., degenerate) triadic structure. Nor is there any conceivable way with icons alone to generate anything other than a monadic icon. Cut an icon in half, or take any fraction of it you like, and all that remains is an icon, or more than one of them. However, without an index, an iconic sign can only represent one object at any given time and indeterminately at that on account of the logical incompletenesses associated with both icons and indices. If an icon is included within another icon, owing to the monadic nature of every iconic predicate, all that can be represented is the complex unity consisting of the whole. The relationship of inclusion cannot be separately acknowledged or represented without the assistance of an index.
Next, consider the representational power of an index. If it is a connection between two icons, as shown say in the diagram, O -- O, where the circles are taken as the ends of the index and the line segment as the connection, we see that the index is necessarily a triadic relational structure. Yet, logically speaking, inasmuch as it connects one end point to the other and the reverse, if we were to extend the line through either of the end points or by joining two indexical relations at their ends--on account of the indeterminacy of every index in the first place--then the new end points would still express only two distinct arguments (i.e., the icons at the ends of the index). As a result, Peirce showed in the "logic of relatives" that joining pairs of indices never produces any predicate with an adinity higher than 2. Thus, owing to their very nature--considering nothing but their adinity-it can be seen that indices alone are sterile and cannot generate relations of any higher adinity.
Symbols, however, as we have seen invariably have at least a triadic adinity. Such a logical structure seen as a sign (predicate) relation can be diagrammed as a "Y" where each of the end points consists of a distinct iconic element and each of the lines leading to it consists of a special kind of index linking that argument into the predicate. Now we have, as Peirce showed (1897), finally arrived at a relatively well-formed kind of logical relation from which adinities of any higher level can be achieved. For instance, by joining any one of the ends of one Y (e.g., imagine circles representing icons on the ends) with any end of another similar structure, an adinity of 4 will be achieved. The ends that are joined no longer point to distinct arguments, but the remaining ends will require 4 arguments to fill them up. By repeating the same operation (i.e., joining another triad with the 4-ended one in hand), relations of any adinity can obviously be achieved. Thus, from a system of symbols with triadic complexit y (adinity) all higher systems of actual relations can logically be attained.
On account of the logical relations of monads, dyads, and triads to polyads of all higher adinities, it is possible to see why any human language that can get up to the number 3 can easily reach all the natural numbers. What may not be so easy to see is that the idea of continuity can be made explicit in signs of an adinity of 3 and higher, but not in icons (with an adinity of 1) or indices (with an adinity of 2). This last fact is made fairly explicit by noting that the continuous space connecting any pair of icons in any index whatever cannot be represented without graduating to a relational dynamic with at least an adinity of 3. While the idea of continuity (which Peirce proved to be the same as that of generality; cf. Peirce, 1902/1932; Ketner, 1992) may be implicit in an icon, and in an index, it cannot be made explicit without signs at an adinity of 3 or higher.
With all of this in mind, the logical impossibility of an ape, or porpoise, or parrot, or what-have-you stumbling to the idea of a symbol from the mere observation of indexical relations is already proved. But the force of the argument may be made clearer still in relation to a thought experiment originally proposed by Searle.
The Chinese Room Experiment
Searle (1980, 1992), Deacon (1997), Pennock (2000), and essentially all who embrace the neo-Darwinian orthodoxy in any of its variants assume that accidental indexical associations between randomly distributed icons can somehow be transformed by natural selection into fully general, abstract, and recombinable symbol systems. No one expresses this idea more clearly than Deacon (1997) who describes the problem in terms of Searle's (1980, 1992) "Chinese Room" experiment. Searle asks us to imagine that inside a box a brute force computer that does not know a word of a certain language, call it Chinese (or any Language-X), receives strings of symbols fed through a slot on one side of the box, and through another slot feeds out strings in Language-X. Searle supposes, and Deacon agrees, that, in principle, it would be possible to match up input and output strings so deftly that persons on the outside of the box would be unable to detect the mindless basis by which the process on the inside was linking the input str ings with the output strings. Just as Searle construes the analogy as showing how learning might proceed without intelligence, Deacon accepts the same metaphor as showing how neo-Darwinian evolution can generate the symbol systems of the genetic code eventually leading up to the human genome and thence to the human language capacity. He paraphrases Searle in supposing that "mind is a physical process, and physical processes can be copied whether we understand what we are copying or not" (Deacon, 1997, p. 460).
Is this claim true and are such pairings of symbols actually possible in principle in the material world? Can language acquisition (and also neo-Darwinian progress) be emulated by a mindless computer relying on nothing but brute force memory and stored associations? Deacon (1997) claims: "In principle, given enough data from prior interviews between real people and enough computing power to store and search through them, it will always be possible to fool even the most sophisticated questioner and yet so without any semblance of consciousness or sentience" p. 460). In other words, Deacon supposes that the Chinese speakers on the outside will think that the person, or computer, on the inside is a Chinese speaker, when in fact the system knows nothing of Chinese. Thus, Deacon agrees with Searle and concludes that human language acquisition, and the whole problem of the human brain and the language capacity, can be explained mindlessly. Deacon says, "I have no doubt that nonbiological devices with nonbiological minds can, and probably will, be built. Nature itself produced minds by blind trial and error" (1997, p.460).
Let's examine the foregoing argument and the "storage" problem. It ought to be noted immediately that the experiment is a poor analogy for human language acquisition or the supposed evolution of species on account of the fact that it appeals to speakers of Chinese to provide the associations to start with. How could the interviews be conducted if the interviewers did not already speak Chinese? More to the point, how could the interviews be conducted if there were as yet no speakers of any language on the planet? Hence, the experiment cannot address the essential question it claims to be about. The question is this: Can random indexical associations between icons be, naturally selected (without knowing the language or symbol systems in advance) to, produce the desired complexities we find in languages and genes?
Ignoring the crucial design flaw in the experiment, suppose the language is English and that the person outside the box asks the computer to please count the characters in this sentence, excluding spaces and other marks of punctuation, and then repeat them up to the 100th letter. Suppose that the computer inside the box can receive inputs in a typed format and can associate them with other inputs in a typed format. What are the chances that the computer would be able (without ever consulting anyone who knows English, for that would be cheating) to generate the desired response? How long would an observer have to wait for the appropriate response to emerge from the output slot?
The reader will note that the required response is relatively simple for anyone who speaks English and who can count to 100. Ignoring spaces, capital letters, numbers, and marks of punctuation, as instructed, there would be 1 chance in [26.sup.100] or 1 chance in 3.14 X [10.sup.141] of finding the requisite answer. To bias things toward an outcome favorable to neo-Darwinian theory suppose that there were 3 billion computers inside the box. This number is chosen somewhat arbitrarily because it is the approximate number of base pairs in the human genome as shown in the human genome project (Human Genome Project, 1992). Somewhere and somehow in that lengthy sequence the human language capacity is accounted for. Next, suppose that these 3 billion computers (imagined to be analogous to an equal number of pre-biotic oceans) were set to work producing a random sequence of 100 letters every thousandth of a second for 4.5 billion years (the estimated age of the earth according to Kitcher, 1982, p. 9). To generate the desired string just once would require, on the average, 7.36 X [10.sup.110] tries. In other words, the age of the earth would need to be longer than 4.5 billion years by a factor of 7.36 X [10.sup.110] in order for us to expect to be able to generate the desired sentence just once on the average (as if such an experiment could be conducted and replicated 7.36 trillion trillion trillion trillion trillion trillion trillion trillion trillion billion times). The difficulty is enhanced by the supposition of the Darwinists that the indexical associations can all be stored in the computers in advance so that by brute force, the computer in the box can find the desired string by matching the one from the input with the requisite one for the output. Clearly the odds against the success of the Chinese Room experiment are evidently insurmountable from a statistical point of view, but we can set the statistics aside on account of the fact that the transformation of any number of indexical associations of icons into just one symbol grounded in an arbitrary convention has already been shown to be logically impossible.
No Solution by Chance
While neo-Darwinists, and all other varieties of evolutionists, must suppose that the symbol problem can be solved by chance, they have not shown how any single step in the vast series of steps needed can be taken by an accumulation of chance events that might subsequently be selected. Above, it has been shown by strict Peircean logic that the problem of forming symbols from icons and indices cannot be solved by chance at all. It cannot be solved without appeal to a fully developed, abstract, general, recombinable symbol system that is known a priori. In other words, the intelligence underlying symbol systems is a pre-requisite, not an outcome of language acquisition, nor a developmental process as seen in genetic systems.
Contrary to claims commonly made by evolutionists, it is not enough to point to living organisms and assert (as Darwin did) that evolution must have occurred on account of the resemblance of organisms. To do so is to ignore the universal logical imperfections of all icons. All icons without exception resemble all the rest. To suppose that a continuous history can be inferred from iconic resemblances can be called the iconic fallacy of neo-Darwinism. To recover from it, evolutionists such as Deacon (1997) appeal to indices. However, in doing so, the iconic fallacy is compounded with the false assumption that indexical associations formed by chance can cause symbol systems (and thus life and languages) to arise. This is the indexical fallacy of the neo-Darwinian theory.
The evidence that a genome sequence, such as that found in any living species, is meaningful (i.e., a symbol rather than something less) is the fact that it specifies the architecture and functions of a viable organism. Each instance of the genome is itself a symbol meeting all the logical requirements for a symbol. The genome is generally applicable to all the cells of the organism and to all of its possible offspring insofar as the genome can be shared by reproduction. The genome is abstracted from the particular cell, which it happens to be part on account to the fact that the same symbol appears in each and every one of the cells dependent upon that genome. The genome, as such, is therefore discretely combinable (not merely blended, so as to meet requirements spelled out by Pinker, 1994; also cf. Kako, 1999) with other entities -- this is so with respect to proteins, to the body, and to the whole eco-system inhabited by that living body.
What is the likelihood that a single symbol consisting of hundreds of thousands or even billions of linked signs could be produced by an accumulation of accidental changes (e.g., copying errors, chemical insults, radiation induced errors in the sequence, or the like)? The hill to be climbed by random mutation and natural selection is higher and steeper than can be suggested by the human genome alone because all the genomes of all organisms must be discovered and expressed by chance (assisted by natural selection) in such a way as to generate the entire biosphere. That is, the genetic code itself, the underlying meaning basis of the symbol system, which enables the existence of the biosphere, must be generated by chance. Crick (1981) was among the first to observe that this construction cannot be done piecemeal, but must be produced all at once. The capstone of the whole problem is the unique human language capacity, which enables us to discourse meaningfully about all of these questions.
From all of the foregoing, it can be seen that if we were dependent on neo-Darwinian evolution to engage in this present discourse, the chances of its occurring would be zero. As we saw in the Chinese Room experiment above, there is nothing in existence small enough to serve as a suitable analogue for the vanishing likelihood of getting just 100 letters of the alphabet into a particular pre-determined sequence by chance. Never mind the difficulty, without any symbol systems, of trying to say in advance how it would be possible to tell if the result had been achieved or not. The latter difficulty is far greater than the former. The difficulty faced by neo-Darwinian theory, and equally by punctuationist variants of evolutionary theory, in generating any symbol system whatever is not merely to produce the symbol in the manner of a Xerox machine producing a copy of a page of text, but to produce a meaningful string of biological symbols arbitrarily and conventionally associated with their meanings. The problem i s not just one of syntax and pragmatics, which might conceivably be solved by chance given an eternity of time to accomplish the desired results, but the problem transcends time in the realm of pragmatics where syntax connects with pure semantics (i.e., with the fully abstract and general meanings of well-formed symbols).
That is, it is not only necessary to produce certain meaningful genetic and linguistic sequences, but their generative basis - their conventional meaningful systems of correspondence to the material world. As shown above, the simplest symbol systems of the requisite kind are those found in true stories that correctly represent the facts of which they happen to be true. Such stories cannot be generated at all by random arrangements of icons and indices, nor can they be found and identified by natural selection. Both of the latter outcomes, as was proved above, would require the presupposition of symbols, which is precisely what neo-Darwinian theory cannot presuppose.
Intelligence Is Required Before the Fact
The world's most distinguished linguist and one of the 10 most often cited scholars of all time, and the only one of those still living (according to Pinker, 1994, p. 23), Noam A. Chomsky concluded that:
some intellectual achievements, such as language learning, fall strictly within biologically determined cognitive capacity. For these tasks, we have "special design," so that cognitive structures of great complexity and interest develop fairly rapidly and with little if any conscious effort. (1975, p. 27)
With reference to this remark and others along the same lines, Patterson and Linden (1981) accused Chomsky of "a creationist view of the universe" (p. 204). Actually, Chomsky's sympathies lie with Gould's theory of "punctuated equilibrium" (Gould & Eldredge, 1972). Still, Chomsky is difficult to ignore on account of the fact that his claims about the human language capacity are evidently true. The gap that separates humankind from other species, and human speech from those systems specially taught to apes by human beings, really is as Deacon said "a yawning chasm" (1997, p. 412).
Pennock (2000), interestingly asserts that linguistics is on the side of the Darwinian orthodoxy. He says that the universal fact that languages change over time and evolve into distinct and mutually unintelligible new languages provides a microcosm of evolution showing it to be true. In fact, the change we see in languages over time is exactly analogous to the process that Michael Denton (1986; see also J. W. Oller, 1988) called microevolution, which can be defined as natural drift within limits. We start out with an efficient, general abstract system of combinable symbols and that is exactly what we end up with. It is just the sort of change we see in the famed case of the Peppered Moth, Biston betularia. We start with a moth and end with a moth. Lateral drift within the genome is seen, but we do not see the moth becoming a mouse, or a man, or any higher species. Neither does any language modify itself so as to become something other than the kind of language it was at the start.
As Michael Denton (1986) noted neo-Darwinian theory and its competing evolutionary rivals are not only logically imprecise, but also incoherent upon close examination. Consider, for instance, the supposition of Deacon (1997) in the "imaginative" story of the hypothetical "co-evolution" of the brain and language. Deacon asserts that language can evolve "thousands of times faster than the human brain" (p. 110). But, if A (the human brain) is necessary in order for B (the language capacity) to exist, how is it possible for B to arise thousands of times faster than A? Or, if God has not "put eternity in their hearts" how is it possible that every natural language of human beings, but no other communication system among all the other species, contains anything resembling the notion of generality, continuity, abstractness, infinity, zero, negation, or eternity? Where in all of natural experience, as represented exclusively by perceivable icons and indices (without symbols) can the concept of infinity be found? Whe re is nothingness manifested in icons or indices? What manifest index or icon can show the negation of any abstract predicate? How is it possible to point unambiguously with an index to what is not there when it is not possible to point unambiguously to what is there? Or how can what is not done (or found) in any perceivable context be depicted unambiguously without symbols?
The idea of eternity--which invariably entails, continuity, generality, abstractness, conventionality, and the infinite combinability of symbols--can only be attained by a sign-user who already possesses the language capacity. Only the human species has that capacity, and neither it nor the genetic basis for it can be constructed by random arrangements of icons and indices operated on by natural selection. While these abstract ideas, and many more, can be found in normal children somewhere between 3 and 7 years of age, it is clear that such ideas cannot arise from random indexical associations between icons. Nor is there any possibility of their being selected by purely material means as supposed in the neo-Darwinian principle of natural selection. The foundational premise of neo-Darwinian theory (and of its materialistic rivals) is false.
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OLLER, JOHN W, JR.. Address: University of Louisiana at Lafayette, P.O. Box 43170, Lafayette, LA 70504-3170.
Title: Professor and Head, Department of Communicative Disorders; Director, Doris B. Hawthorne Center for Special Education and Communicative Disorders.
Degrees: Ph.D. Linguistics, University of Rochester. Specializations: Linguistics, language proficiency and nonverbal intelligence, autism, and the theory of abstraction.
I want to thank Barry Ancelet, Eric Johnson, Stephen D. Oller, and Jack L. Omdahl for comments on this article. They all helped to make it better but are not responsible for the end result. Correspondence concerning this article may be sent to John W Oller, Jr., University of Louisiana at Lafayette, P.O. Box 43170, Lafayette, LA 70504-3170.
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|Author:||Oller, John W. Jr.|
|Publication:||Journal of Psychology and Theology|
|Date:||Mar 22, 2002|
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