Excerpts from Sounding Out Semantics

"In this book, I will attempt to show that the semantic/pragmatic distinction is illegitimate, and that whole enterprise of semantics is ill founded and fallacious. The conventional account of what we humans do with words is founded on an ancient analysis that has evolved and mutated, but not eliminated the basic premise that words are signs or symbols that stand for, express, signify, represent, encode, designate, denote or refer to semantic content: their lexical meanings and referents. I will try to provide a persuasive argument that spoken words are not signs or symbols that encode semantic content. I will try to demonstrate that this semantic premise in all of linguistic theory is fallacious and distorts all attempts to explain how words function in human behavior. I hope to persuade you that spoken words, i.e. vocal utterances, have a multitude of uses in context, but no stable meanings or referents that are context neutral. Nor do they represent or express anything in the speaker’s mind. That is, human languages are not representational symbolic systems. I hope to persuade you that all human speech is conditioned verbal behavior that has consequences and is sensitive to time, location, context broadly construed, and the speaker’s speech history.
If you accept this hypothesis, it has enormous ramifications for our understanding of the acquisition and use of language by humans. Along with the ramifications on language acquisition and use, this new hypothesis of language impacts all other areas of human knowledge and behavior." pg. 6

“Across the pond in America, scholars Edwin Sapir and Benjamin Whorf made a revolutionary and highly controversial claim about language in the late 1930s. After extensive field research into the culture and language of the Hopi Indians of North American, Whorf concluded that their language shaped their thinking to such an extent that it provided them with a world view quite different from people who spoke what he called “standard average European” (SAE) languages. Whorf claimed that the structure of human thought processes was non-trivially influenced by the structure of a speaker’s native language. In the trivial sense, of course, people are influenced by what others say and write. That is how we humans acquire much of our knowledge. However, Whorf claimed that people who spoke different languages may see reality in quite different non- trivial ways and that those differences would have profound effects upon their very basic thought processes and their non-verbal behavior.” pg. 15-16

“Speech was a unique form of behavior exclusive to the human race, but a behavior none the less. For Skinner, there was no need to cloak the analysis of this behavior in the usual dualist garb of thoughts, ideas, and concepts in human minds that were encoded, represented or expressed by word symbols and then transferred to other minds. There were no mental entities or processes mentioned or implied by Skinner. Word meanings were neither in the minds of speakers nor abstract speaker-neutral entities encoded in the word symbols. “The meaning of an utterance is either some feature of the occasion upon which it is uttered or some effect upon a listener.” Skinner (1969: 11.) This was a complete break from the traditional semantic assumptions about word symbols and their alleged semantic content and was quickly discounted by psychologists, linguists and philosophers alike.” pg. 21-22

“I hope to show that TCS theorists, and all other semantic theorists, are badly mistaken. I contend that the semantic paradigm of words that have lexical/literal meanings, i.e. semantic content, is based on a number of mistaken assumptions. In the following chapters, I hope to outline those mistakes and show why they are mistakes. I hope to persuade you that not only is TCS a fatally flawed theory, all of semantics is fatally flawed because words have no lexical/literal meanings. I hope to persuade you that the sounds emanating from humans do not stand for, express, signify, represent, encode, designate, denote or refer to other things. I hope to persuade you that these word sounds are not signs or symbols or semantic designators and that all of traditional language theory is based on fallacies, the semantic fallacies, and these fallacies have extreme consequences.” pg. 46-47

“The formalism begun with writing has led language theorists down the garden path of semantics. Never-the-less, to make the semantic claim that words have literal or lexical meanings which are separate and distinct from their use in context is unsupported by the data, i.e. human speech. In fact, all human speech is behavior conducted by a human with a history of word- sound use that affects any future speech behavior with acoustic devices conducted at a time and place with innumerable presuppositions and contextual elements that are indispensable to interpretation of the behavior.” pg. 59

“The non-semantic perspective I am proposing rejects all three of these semantic assumptions and the concomitant dualism necessary for semantic theory to succeed. In spite of the widespread belief that the symbolic nature of human speech behavior is obvious, theorists are making a huge and fateful error with this claim. It is neither obvious nor self-evident that human vocal behavior is a system of signs or symbols with consistent speaker-neutral lexical meanings and referents, or that speaking represents peculiar non-physical entities and processes in the speaker's head. In fact, spoken words, phrases and sentences are gerrymandered units of grammar, some of which have variable independent functionality when used by various speakers at various times in various contexts.” pg. 60

“Speakers learn the functional value of acoustic devices and syntax from others in their speech community. What counts as a word, a phrase, a clause or a sentence makes no difference whatsoever to an infant learning to speak or an accomplished speaker in a preliterate society.” pg. 64

“Meanings give certain words semantic content in formal semantic theories, but they are inexplicable and completely superfluous in the analysis of human verbal behavior. So, let us join J.L. Austin, Donald Davidson, Willard V.O. Quine, B.F. Skinner, the radical pragmaticists et al., and dispense with individual word meanings altogether.” pg. 69

“This rule-bound recommended speech behavior has been taught to generations of literate human speakers. Thus, many of the regularities witnessed in various speech communities are a result of these prescriptive rules which are inculcated in speakers and passed on from generation to generation.” pg. 73

“To analyze the symbolic written representations of speech behavior, i.e. text, out of context, is a fool’s errand. It is a fool’s errand in which philosophers and linguists have been engaged for millennia. Language scientists and theorists alike must listen to the data in context. The vocal behavior is the subject to be studied, not written recordings of such behavior outside of any context.” pg. 74

“This functional interpretation of language acquisition in children is completely contrary to the current compositionality or lexical syntax theories where the meaning of a complex expression is determined by the meanings of its constituent words and their grammatical relationships. Such lexical syntax theories are after the fact reconstructions presupposing grammatically correct complete sentences composed of words with stable consistent lexical meanings. But these theories cannot be reconciled with the observed speech behavior of humans. Human speech simply cannot be deconstructed into words with meanings; it must be parsed into multipurpose acoustic devices of many kinds based on their functional value when all contextual elements, including relevant presuppositions and the speaker’s speech history are recognized and accounted for.
Among competent adult speakers, counterexamples to lexical syntax theories are too numerous to count. Consider the much-used idiom, “kicked the bucket”. (Sound it out.) In contemporary America the use of that utterance is not dependent upon knowing the theoretical meanings of the sounds “kicked”, “the” or “bucket”. Even non-English speakers can learn to use the idiom when and if they have heard it used in context in lieu of the word sound “died”. They can learn how to use that holistic three-word lexeme and utilize it without regard for the dictionary meanings of its constituent terms or the grammar of the English language.” pg. 81

“Some contemporary philosophers still maintain that there is a complete language of concepts, etc., viz. mentalese or LOT (language of thought) that is represented or expressed by public languages. By their account, all languages are translatable, where identical non-symbolic concepts are clothed in the various symbols of public speech and, in effect, childhood language acquisition is learning a second language, the first language being mentalese, or LOT.” pg. 105

“So, you cannot simply declare an end to dualism and go about using the same words you have been using. If you are to explain how language works, you must change your word usage as well as the theoretical foundations of linguistic analysis. To break the grip of semantics and dualism you must change your verbal behavior about your verbal behavior.” pg. 111

“This dualism in its many forms has been a critical component of European American (EA) speech and thinking for centuries. The human body has been variously juxtaposed with the spirit, the soul, the mind, the self, the psyche, or subtle variations of these immaterial entities which reside in human bodies yet are distinct from the bodies. They are distinct and separate components of humans which enjoy a different type of existence; mental existence. The prominence of this mind/body dualism or one of its permutations in Western thought over the past centuries is undeniable.” pg. 149

“Consciousness is said to be the medium in which private mental entities exist, e.g thoughts, ideas, concepts etc., and mental activities, e.g. thinking, believing and knowing etc., take place. Moreover, the consciousness itself is said to be ontologically unique; it cannot be reduced to observable physical phenomena or accounted for with current physical laws. Rather than outdated spirits, souls, or minds, consciousness is now said to exist within the human body.
However, while consciousness is described, it is also said to contain or consist of other mental phenomena: the raw feel of pain, the experience of sunset red, the taste of broccoli, the sound of high C, the smell of a rose. These are all said to be personal, subjective, existentially unique, irreducible private sensations. They are elementary sense data or qualia that are insubstantial yet exist in consciousness, consist of consciousness, or are functions of consciousness.” pg. 150

“The third consistent theme in discussions about the EA self is the self as the director in control of its corporeal container. Human bodies are the receptacles wherein the self resides, if only on a temporary basis for many, and that self is the agent that controls its physical embodiment. As Socrates argued in the Phaedo, the self is the seat of personal responsibility and moral accountability where decisions are made regarding the body’s behavior. It is the initiator of human action, the causal origin of most human behavior. The self, not the body, is the seat of free will. The self decides what to do and drives the intentional behavior of every fully functional human.” pg. 153

“This command and control function of the conscious internal self provokes one of the most baffling questions in all of philosophy: how can this immaterial conscious entity, the self, interact with the material body? How does the human spirit, the soul, the mind, the ego, the psyche, or the self control the human body? For instance, my self decides to move my right leg right now and, voila! It moves. One can describe all the physical processes of nerve endings, electrical impulses, synapses in the brain, etc., but that does not tell me how my conscious self, that non- physical agent within my body, controls my very physical leg. What I want to know is how my thoughts and ideas and intentions, mental things residing in consciousness, get my leg to move?
How can we bridge this causal barrier between consciousness and the body? If you assume that you have a soul, a spirit, a psyche, an ego, a mind, or a conscious self, how do you explain the control that it has over your body? If physics is causally complete, i.e. all physical effects have physical causes, how can a non-physical agent be the cause of physical effects? How can you explain the interaction of two types of entities and processes existing in two different ontological realms? Something has to give.” pg. 154

“For instance, the problem of other minds has been a bugaboo for legions of philosophers that has been ongoing for millennia. In brief, how can people justify their claims to know that other people have minds or internal selves? I know that I have a mind supposedly because of the introspective evidence. However, other minds and their constituents are simply unknowable for me because they are undetectable by me. What I observe about other people are their bodies and their behavior, not their minds or the mental processes. Even though other people talk about their own minds and mental activity within those minds, they could be zombies. There is absolutely no direct evidence available to me that people, other than me, have minds.” pg. 158

“These other minds are the intentional agents that direct the behavior of the other bodies. These other minds have the knowledge, the beliefs, the false beliefs, the desires and the intentions which cause the observed behavior of their bodies. These other minds experience the sensations. They exercise free will and decide what their bodies will do next. All of these inferences about humans and their behavior are a result of conditioned English verbal behavior and its foundations in the mind/body dichotomy. Dualist assumptions about other bodies with other minds and free will arise because the habitual verbal behavior of English speakers has incorporated those assumptions.” pg. 160

“Still, the intentional stance gives humans the same unreliable predictions about their behavior that the alignment of the planets, ghostly ancestors, demons, spirits, or gods gave them prior to the advent of intentional explanations. That is because they are all ill-founded. Without assuming all the metaphysical accoutrements required by intentionality and the intentional stance, human beings are controlled by amazingly complex internal physical processes and a history of interactions with the environment. The fact that intentional explanations are much more economical and widely used is not sufficient grounds for accepting them as adequate explanations. And the theoretical background required to justify these intentional explanations is brimming with paradoxes.
On the other hand, J.B. Watson and B.F. Skinner, provided the framework for non- teleological, non-intentional explanations for all animal behavior, including human verbal behavior. Their non-teleological explanation is consistent with Darwin’s theory of descent with modification and the empirical evidence thus far discovered.14 It relies on stimulus-response- reinforcement (S-R-R), molecular biology and ultimately physics to explain the behavior of all organisms. It is an historical explanation, as is evolution, in which the entire history of an organism’s reinforcement and punishment explain future behavior. It should not be abandoned in favor of metaphysical speculation about contemporaneous mental or psychological states and processes as the causes of human behavior.” pg. 187

“Skinner claimed that human verbal behavior could be explained within the stimulus-response- reinforcement paradigm of behaviorism. People could infer whatever they wanted about psychological states and forces within the human organism. The only data available are the history of the organism, the stimuli, the response of the organism, and the reinforcement or lack thereof, and that is enough to explain the behavior, any behavior.
To have an intention, or purpose, need not be framed within the usual dualistic psychological paradigm. Intentions can be framed as predilections to act in a certain way based on genetic inheritance, a history of previous S-R-R conditioning, and the stimuli to which an organism is exposed. All the future behavior of an organism, including verbal behavior, is shaped by the previously reinforced behavior. The behavior evolves over the history of an organism.” pg. 191

“Utilizing word sounds such as “mental phenomena”, “consciousness”, “qualia”, “sense data” “sensations”, “phenom”, “existence” et al. as they are currently being used and producing new philosophical arguments will not breach the ontological barrier. The use of these word sounds creates and sustains the ontological barrier. The change required of philosophers is a change in their verbal behavior. They must stop using words that have the embedded mind/body dualism or some alternative third ontological status implied or inferred. Philosophers’ intuitions and their thinking will change with the change in their verbal behavior. The mythical mental phenomena, consciousness, qualia, sense data, phenom etc. will disappear when theologians, philosophers, psychologists, teachers and truck drivers stop speaking about themselves the way they currently do.” pg. 208

“Propositions are linguistic acts, not psychological entities floating around in human minds as Intentional objects. Humans have innumerable inclinations to behave vocally, including utterances of declarative propositional statements based on neural recordings of the states of affairs they observe and remember. “Mental content”, “propositional attitudes” and “psychological propositions” themselves are entirely misleading characterizations of what all animals, both human and non-human, have in their heads. Unfortunately, the way SAE speakers talk about these hypothetical epistemic states of believing, knowing, hoping, doubting etc. easily leads some philosophers to assert that the stored forms of such beliefs, knowledge must be propositional. The consequence of this characterization is, as Daniel Dennett said: “... one can easily be misled into thinking that it is obvious that beliefs and desires are rather like sentences stored in the head.” Chalmers (2002: 559 Dennett)
Dennett then expounds on “serious belief attribution” to distinguish those systems that “really” have beliefs and desires. He makes the distinction when there is none to be made. If you presuppose dualism and utilize current English speech behavior, you will think that some organisms “really have beliefs and desires” while others do not. Then the debate begins over what things “really have beliefs and desires”. Does Norman Malcolm’s dog really have beliefs?” pg. 216

“Whereas dumb machines can exhibit purposeful behavior, i.e. humans can see the purpose of the machines, humans refuse to allow them purpose or intentionality. In the robotic assembly of autos, for example, the output of robots is dictated by the input and the architectural design of the robots. The decision making is not in the machines; it has been put there by their human designers. As mentioned previously, John Searle dubbed it “derived intentionality” as opposed to the “original intentionality” in people. The machines do not really decide amongst different courses of action. The human-derived if-then architecture of machines along with the contemporaneous input from the assembly line enables the robots to select which of the diverging branches of action to utilize. This is the same ability humans have and refer to as free will.” pg. 224

“Without free will, rules and the intentional stance, humans become nothing more than stimulus-response “protein robots” in the words of Daniel C. Dennett. Human societies, built upon rules, have a huge stake in free will, rules and the intentional stance. They are part and parcel of our social and political philosophies and are deeply imbedded in our speech behavior. In spite of that, it is all part of the ghost in the machine legend. What will it take to give up dualism, the intentional stance and the myth of the internal agent with free will who chooses whether or not to obey rules? It will take an epiphany on the scale of that of Copernicus’, Newton’s, Darwin’s, Einstein’s, Whorf’s, and Skinner’s.” pg. 226

“Given human hubris, it is not surprising that for many of them the standard for artificial intelligence (AI) is claimed to be the ability of a computer to think as a human would think. The Turing Test is often said to be a test for AI. Computer engineers would build a Turing machine in a room and have someone ask it questions. That person could also ask questions of a human in the same room. If the inquirer could not determine whether the answers are from the machine or from the human, theorists must grant that the machine in the room is intelligent.
Reasonable follow-up questions might be: if the machine is intelligent, does it believe certain things and know other things? Can it truly think? Would humans endow the computer with a thinking mind? The answers to these philosophical questions are quite simple. No, machines are not intelligent. They do not believe or know things. Nor do they engage in mental activity or have minds, not because of the limits of current technology, but rather because of the limits of current conditioned English verbal behavior which has the ontological barrier firmly in place. If you are a competent English speaker, you will not say or think that machines can believe or know things or engage in mental activity. You will refuse to say or think that machines can have minds or consciousness existing in them.” pg. 233

“Deutscher provides numerous insights on the origins and evolution of word sound function in many languages. He presents this unfolding process as a pervasive metaphorical movement whereby acoustic units make transitions from very down-to-earth concrete applications to more general uses. This analogical or metaphorical process is quite simple. Humans recognize the functional value of physical tools and acoustic devices. They then use the same tools and acoustic devices to do new work in a new frame of reference. Humans see how something works and they transfer that utility to a novel arena. This one-way path toward expanding utility is evident in tool use and word use everywhere. It continues unabated.” pg. 251

“The basic questions in linguistic theory these days are not so much whether language evolved, but how it evolved, and whether a more generalized improvement in intelligence produced speech, or vice versa. (See Language Evolution by Morton H. Christiansen and Simon Kirby.) The field of language evolution has produced some remarkable research in an attempt to answer these questions. Researchers from many disciplines have contributed, but there is no consensus on how human speech evolved. Yet there seems to be agreement that three adaptive systems contributed to the adoption and growth of human verbal behavior: individual learning, cultural transmission and biological evolution.
Of course, the development of such language theorizing has created schisms. For instance, certain features of human communication are lacking in animal communication. Some theorists have concluded that this apparent gap between animal communication and human communication must be bridged if they are to prove that human languages could have evolved. Some try to account for the gap by producing theories of gradual transition. Others speculate about a sudden mutation in the human brain which allowed for the use of a protolanguage. The work of Bickerton, Carey, Desalles, Deutscher, Hurford and many others are part of the ongoing dispute between continuity theorists and discontinuity theorists. (Darwin was a continuity theorist, 1859) In spite of this academic kerfuffle, evolution is the only way to explain the development of language, unless one accepts the creationist’s account of the origins of human language or treats it “... as if it had sprung from Jove’s brow—one, entire, unique and indivisible”, as Bickerton (1995: 50) put it. Treating speech as conditioned behavior would greatly ease theorist's efforts in doing so.” pg. 257-258

“Language theorists of the nativist variety, such as Noam Chomsky and Steven Pinker, claim that the acquisition of human speech behavior cannot be entirely accounted for by behaviorists. They claim that operant conditioning alone or iterated learning cannot be responsible for certain observed linguistic phenomena. These nativists have concluded that humans have more than a general cognitive ability that can manifest itself in the ability to use language. This group of Neo-Platonists or Neo-Rationalists, if you prefer, suggest that there is a language domain-specific innate Universal Grammar that every person is born with. This universal grammar underlies the variety of surface grammars acquired by people worldwide.
However, after more than four decades of extensive research and theorizing, a universal grammar has yet to be described or discovered. A rule-based system that captures all of the observed phenomena of the multitude of surface grammars has not been produced. After a half century of research, the evidence for a rule-based universal grammar or “deep structure” is non- existent. In fact, most of the evidence has suggested just the opposite. For example, the childhood acquisition of irregular verbs and plurals in English has been shown to be a simple matter of rote learning. There is no system of rules which can account for their acquisition and use. Grammars are as diverse and pliable as phonemes, morphemes, lexemes and all the other grammatical units of human speech that have been parsed by linguists. And the arguments against any such universal grammar provided by the human genome are manifold. The leading proponent of the innate Universal Grammar (UG) theory is Noam Chomsky. His central argument for a UG is that language is generative, i.e. people can generate an infinite number of possible sentences from the limited sample of sentences they hear.” pg. 260

“This theoretical rule-based UG is the offspring of rule-based speech theory in philosophy of language. It assumes that some grammatical rules are innate, and some are learned or “internalized”. (This sounds suspiciously like operant conditioning.) Moreover, none of these rules are said to be conscious rules. Competent, mature speakers are unable to articulate these rules, yet they adhere to these rules in the formulation of grammatically well-formed sentences.
This view has brought about considerable debate about what a rule is. On that there is no consensus because the word sound “rule” has no fixed literal meaning either.” pg. 260

“Language is heritable, not genetically, but behaviorally, and when we inherit a language from our predecessors, we inherit their phonetics, their grammatical constructions, their metaphors, their idioms, etc. We also inherit the metaphysics built into the use of their language. The metaphysics of our forebears has deep footings in the intellectual edifice of Occidental thinking and word sound usage in the Western world. The linguistic behavior of SAE-speaking people has an intrinsic mind/body dichotomy that manifests itself whenever we use that verbal behavior to discuss our verbal behavior. However, there is no evidence to support the contention that word sounds stand for non-physical entities that are located in a non-physical container in your head, none. Nor is there any evidence that your head contains a rule based Universal Grammar.” pg. 271

“The word “deixis” derives from the Greek word for “pointing”. Within descriptive linguistics, deixis is a pragmatic phenomenon considered to be outside the purview of semantics. Linguists claim that many word sounds stand for, represent, encode, signify, denote, designate or refer to different things depending upon the circumstance in which they are uttered. It does not appear that these words have a literal content or constant semantic referents. The meanings and/or referents of these word sounds vary with the speaker and the time and place of their utterance. Deixis within linguistics establishes a boundary between semantics and pragmatics, between words with fixed referents supposedly, and those with shifting referents depending upon the circumstances in which they are used. The referents of word sounds such as “i”, “here”, “it”, “tomorrow”, “these days”, “ours”, “my dog”, for example, are completely context dependent and speaker centric. There are no stable lexical meanings for these words.
In an effort to sort through the deixis phenomenon, linguists have categorized deictic words and expressions in many languages. Many deictic word sounds are dependent upon who is the speaker, for example: “i”, “me”, “mine”, and “we” in English. It is said that the referents of those words shift with the speakers who utter them.” pg. 282

“Morphology, the study of word formation, is one branch of semantics. Many words consist of two or more morphemes. Morphemes are considered minimal linguistic signs, grammatical units where a connection between sound and meaning can be made. The word sound “undesirable” is claimed to have two morphemes, or units of meaning, “un” and “desirable”. “un” also appears in numerous other words and has similar morphemic meaning for each of them it is claimed: “unlikely”, “unhappy”, “unbelievable”. “un” has a meaning that modifies the meaning of the stem word. So we are told by linguists.
Likewise, the morpheme “phon” in “phonetic”, “symphony”, “telephone”, “euphonius”, is said to have the same meaning. Many polymorphemic words are said to be composed of smaller meaningful units like “phon”. Becoming a proficient speaker of any language is said to consist in part, in learning its morphology, in being able to deconstruct the meaning of larger words into smaller units or vice versa. Having this ability supposedly enables proficient word users to construe word meanings from morpheme meanings, and amazingly, we can do this unconsciously, according to experts.” pg. 285

“Explaining metaphors has been a formidable obstacle in the path to discovering how language works. Metaphor, metonym, hyperbole, understatement, satire, irony and euphemism are all recognized as word uses that flout literal meanings. They are tropes (figures of speech) that prove useful. Yet when linguists analyze these uses of language, they cannot reconcile meaning with use, semantics with pragmatics. How is it that speakers and writers can take words that mean one thing and use them to mean something different? Regarding the above epigraph, obviously, no man is an island. But that is not what the speaker meant in the that metaphor. Well then, how do we know what the speaker meant if he’s not using the words’ ordinary meanings?
In conventional analysis there are a number of theories which try to explain the metaphorical use of words: the comparison theory, the interaction theory, the substitution theory and the network theory. Other than the network theory, they all assume that there is a stable literal meaning encoded in words and a computational process whereby speakers and listeners determine the figurative meaning being used in the metaphor. The insinuation is that there are hidden meanings in metaphors which can be determined by following certain procedures. However, there is little if any evidence to suggest that language learners or well-educated speakers go through any computational process to learn and use metaphors. On the other hand, the network theory proponents and the radical pragmaticists propose that we give up on the notion of meaning altogether, including figurative meanings.” pg. 289

“Human speech can often be misinterpreted because of vagueness or ambiguity. Hearers only have an accurate interpretation of an utterance when they properly recognize the use of the utterance in context. They must recognize when an utterance is being employed humorously, sarcastically, cynically, etc. Even so, vagueness and ambiguity are natural and unavoidable effects of human speech behavior. Unique, stable, fixed, precise meanings and referents for semantic designators are pipe dreams for logicians and professors of semantics.” pg. 299

“Morris Kline goes on to chronicle the development of Greek mathematical thinking. That history blossoms during the classical period of Plato and Aristotle. For Plato, human bodies only occupied the earth for a brief period. The human souls, however, pre-existed their embodiment here on earth. It was during this pre-existence that the souls were endowed with necessarily true mathematical knowledge, a priori knowledge about mathematics and geometry. The Pythagoreans influenced Plato, but Plato and his successors were the philosophers who firmly enshrined numbers and geometrical shapes in their metaphysical pantheon. For Plato, numbers existed independently of the humans who used them. They were ideal forms. Numbers contrasted with physical numerals, the symbols, were entirely different entities enjoying a separate ontological status.
Aristotle differed from Plato in that he thought that numbers existed as ideas in human minds, or impressions on the soul, not as independent ideal objects. Numbers were mental in nature and did not exist outside of the human minds that held them. Like Plato, numbers enjoyed a separate ontological status. For Aristotle, these numbers were entities existing in the mental realm and had numerals to represent them in the physical realm.” pg. 316

“However, during the late Middle Ages the Crusades brought back the works of the Greeks from their Arab fiduciaries. Access to Greek writings began a slow revival in intellectual curiosity and inquiry. A renewed interest in mathematics was inspired by the belief that God’s design principles were to be found through mathematical analysis. An ordered universe, designed by God, could be made comprehensible by understanding mathematics. To study mathematics was to look into the mind of God.” pg. 320

“Other sciences and mathematical science became inextricably bound. Advances in math produced advances in science. Calculus and coordinate geometry were powerful tools in ballistics, optics, hydro-dynamics, celestial mechanics and other branches of the new physics of Newton. Advances in science then inspired more advances in mathematics. The explanatory power of mathematics was questionable, though the predictive power was undeniable. When combined with precise measurement, mathematical equations yielded precise, accurate answers that gave clear evidence of the validity of the new math, even though the new types of numbers being used were not understood in the way that counting numbers were understood.” pg. 321

“By using symbols for zero, negatives and irrationals, the Hindus had unshackled algebra from counting numbers and measurement, but they had not freed it from Greek metaphysics. Hindus and Arabs had been able to use mathematics without any metaphysical misgivings. Europeans, on the other hand, confronted the metaphysics of mathematics head on. They were unabashed dualists. Human beings had bodies and minds. Numerals were clearly symbols that represented mental things: number concepts, number ideas, and number abstractions, just as word symbols represented concepts, ideas and abstractions. That much was clear.
Real numbers and rational numbers were no problem for the European philosophers of the age. Rationalists and empiricists alike vouched for the conceptual nature of numbers.” pg. 323

“Many of these new number symbols would have been anathema to the Greeks. The numbers these symbols represented were not constructible, commensurable or conceivable, yet somehow the symbols worked. There is no geometric projection for ‘√-1, √-4, √2 or 24.’ What possible concepts or abstractions could be in the mind of a mathematician who uses these symbols in their calculations? Yet there they were, the number symbols ‘√-1, √-4, √2 and 24’ representing unfathomable, ungraspable, unimaginable, inconceivable numbers. The Greek philosophical moorings of mathematics had to be abandoned. No longer were number symbols required to represent constructible numbers, commensurable numbers, or conceivable numbers.” pg. 329

“The use of number sounds precedes recorded history. Consequently, the origin of numbers is lost in the fog of the past. None-the-less, philosophers of mathematics speculate that early man needed a method of recording and keeping track of animal herds. It is suggested that before the advent of tally sticks, primitive men kept track of animals by matching them with pebbles. After a night full of wolf howls, a herder could find reassurance in the fact that his bag of pebbles could still be matched with the animals in his herd. That matching process did not require the use of number sounds. Establishing a correspondence between two sets of objects does not require counting, or the counting number sounds. Well before knowing how to count with word sounds, humans knew how to match two sets of objects in a one-to-one correspondence. They still do, as reported in the epigraph for this section.
The first evidence of matching was tally sticks which have been recovered by archeologists. Rather than pebbles in a bag, marks on a stick provided an easy, visible method of recording herd census. As with pebbles, it is quite possible to know you have the same quantity of animals in the morning that you had the night before without knowing how many you have. Whatever the size of his herd last night, the herder knew that the wolves did not eat any of his sheep the previous night if the marks on a tally stick could be matched with the animals again in the morning. He could watch his sheep move by and take pebbles out of a bag or move his finger down the tally stick saying: “sheep”, “sheep”, “sheep” until he removed the last pebble or his finger reached the last tally mark on the stick. By thus establishing a one-to-one correspondence, he knew that he did not lose any sheep. Matching would have been very useful; it could have confirmed equivalent quantities for the shepherd without him knowing how many sheep he had.” pg. 340

“How is it that we have machines that can do math much better than we humans can? Yet, we have no machines that can carry on a conversation. So why is it that five-year-olds can speak competently, but not do math without special training? How is it that children learn to use words so easily and numbers only with much effort? Could it be that we need symbols and rules to do math but we do not need them for language acquisition and use? Could it be that the use of numeric symbols is rule-bound behavior while the use of word sounds is not rule-bound. Yes, that is precisely why we observe the discrepancy between the acquisition of math skills and the acquisition of language skills. In fact, mathematics is a rule-governed system of procedural knowledge that requires formal education to learn; language is not.” pg. 351

“All numbers are simply conventional symbols that can be manipulated by rule to provide theoretical and/or practical results. All those number symbols represent sounds; nothing more and nothing less. ‘-1’ represents the sound “negative one”. ‘√-1’ represents “the square root of negative one” (sound it out—spoken numerals). If you can perform a math (most likely decimal), perform an algebra (most likely linear), or a geometry (most likely Euclidian) you have procedural knowledge. You have learned how to use number sounds and symbols for those sounds within the respective algorithms. Mathematicians have a skill that has taken three millennia to develop and years to teach each one of them. They have learned useful rule-bound conditioned behavior.” pg. 354

“In their search for undeniably true declarative knowledge, analytic philosophers and logicians recognized different types of propositional statements, the basic atomic units which made up all of declarative knowledge. These propositional statements could be categorized and organized in such a way as to be less confusing. This process would also facilitate the development of general methodologies for determining the truth of these statements based on the categories. In that way, all human declarative knowledge could be grounded in true propositional statements based on accepted standards of truth for the various forms of such statements.” pg. 371

“More theories for truth were put forth by numerous philosophers. The criteria for the truth of propositions were variously: correspondence, coherence, convention, performatory, intuition, pragmatism, self-evidence, authority et al. Was truth a property of sentences or was it a property of the psychological proposition represented by the sentence? Or was truth a property of a speaker neutral independent fact encoded by the literal meaning of a sentence? What is the meaning of truth? How can truth be defined? How could philosophers analyze the concept of truth? The questions and contradictions were abundant. Yet, philosophers needed to agree on truth before they could agree on what constituted knowledge. The nature of truth remained a mystery, and as a result, so did the nature of knowledge.” pg. 377

“We humans store our declarative propositional knowledge (know-that) internally the same way we store our non-propositional procedural knowledge (know-how), in neurological connections. There are no great controversies when theorists explain how people remember how to manipulate pliers or how to play the piano, often generating novel behavior. Remembering small units of such behavior and producing novel combinations in response to stimuli is a result of conditioned muscle movement and the combinatorial capacity of the human brain. Declarative propositional knowledge is no different, unless we make dualist assumptions about minds and bodies. When we recall knowledge claims, we recall behavior. We perform our speech acts with word sounds either vocally or sub-vocally. We behave in ways which have been previously reinforced.” pg. 389

“Eventually, the search for unassailable knowledge led Western theorists away from pre- enlightenment truth, revealed in religious manuscripts and church doctrine, toward a naturalist view of a detached truth, detached from divinity or the viewer. Observation of the natural world replaced the authority of the scriptures. For example, the heliocentric solar system became gospel, regardless of any interpretation of the bible. Observation replaced dogmatism. Truth was to be found through experience. An objective truth, available to all and supported by the evidence of the senses, became the standard for secular scholars. Empiricism was in ascendance and rationalism was in decline.” pg. 399