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Logic and Language

Daniel J. Castellano

(2009)

Introduction
Part I: Logical Functions of Linguistic Elements
1. Language, Thought and Reality
2. Names as Natural or Conventional
3. The Interface of Concepts and Language
4. Overview of Affirmations and Truth in Language
5. Nouns or Substantives
6. Verbs and Predicates in General
7. ‘To Be’ and the Ens Copulae
Part II: Propositions
8. Sentences and Statements
9. Affirmations and Negations
10. Truth, Falsity, and the Principle of Contradiction
11. Simple Predicate Propositions
12. Universal and Particular Quantifiers
13. Contradictory and Contrary Opposition
14. The Excluded Middle
15. Propositions with Negative Terms
16. Composite Subjects and Predicates
Part III: Non-Indicative Moods
17. Possibility and Impossibility
18. Conditional Mood
19. Interrogative Mood
20. Imperative Mood
21. Optative and Cohortative Moods
22. Concluding Remarks

Introduction

One of the greatest challenges facing any philosophical system is the construction of a language that can reliably analyze reality according to logical criteria. If philosophy is to teach us any truth, it must speak in a language that we can understand, or it will remain a meaningless string of symbols. The practical need to express logical arguments in human language, however, exposes us to the danger of conflating grammatical and logical relationships. Even individual terms may distort our analysis, since many of our words were coined from casual intuition, without concern for logical or philosophical rigor. If we are to use language for logical argument, we cannot accept it as is, but must bring it into conformity with clearly intelligible logical principles.

This endeavor faces two potential modes of failure: (1) it might be impossible to bring human language fully into conformity with known logical principles, and (2) there might be fundamental aspects of logical analysis to which existing human language is blind. These linguistic problems, if intractable, could foil any attempt to construct a philosophical system that yields positive knowledge.

Taking the linguistic problems of philosophy seriously, we must avoid those common yet false solutions that would simply slice the Gordian knot. First, we cannot reduce logic to mere formalism, such as the symbolic logic of mathematics, because in order for a formalism to be intelligible, we must be able to translate its symbols into the concepts of human language. Second, we must not lapse into the fallacy of origins and try to reduce the question to pseudo-evolutionary speculation about the origin of human language. The entire point of constructing a logical language is that we are not slaves of the languages we have inherited, but can conform them to our thought and ascribe new meanings to old symbols. The history of the last two thousand years of philosophy amply demonstrates how Greek and Latin vocabulary and grammar were modified to convey ideas more precisely. Nonetheless, we must respect the possibility that there might be limits to how much we can modify language to mirror logical analysis.

If the ancient Greek philosophers did not neatly distinguish between grammatical and logical analysis, it is because they believed they were constructing a genuinely logical language. Non-dialectical language was relegated to the domain of rhetoricians and grammarians, but logic could be seen as a linguistic domain pertaining to philosophical analysis. Thus, it is unsurprising that the Greeks should find linguistic objects to be the locus of truth and falsehood. They did not regard dialectical language as a barrier to reality, but rather as the very image of reality. As naïve as this may seem, it would be self-stultifying to tend to the other extreme and deny that language can be linked to objective reality. For one thing, it is circular reasoning to use language to generate the knowledge that language cannot generate knowledge. Secondly, ordinary men have in fact been able to teach each other many verifiable truths through colloquial common speech, so we should expect at least as good results from a more rigorously developed logical language, however imperfect it may be.

Above all, we should not suppose that the fundamentals of logic, such as the principle of contradiction, are merely accidental products of human grammar. Regardless of the anthropological origins of our grammar, those who live now may freely invent new rationales for linguistic usages, including the rationale of developing logical systems. With an understanding of the breadth of languages from the Americas to east Asia, we are much less linguistically naïve and can clearly distinguish, for example, a belief in substance and accidents from a grammatical construction of subject and predicate. Still, it would be foolhardy to suppose that we can think in “pure ideas” without language, so we must use language, yet at the same time subject it to the test of logical principles, to guarantee its coherence and to resolve ambiguities of meaning.

In the classical Western tradition, the starting point for study of the intersection of language and logic has been Aristotle’s Peri Hermaneias or De Interpretatione. As mentioned, the ancient Greeks did not neatly distinguish grammar from logic, but rather we might say the latter was a special case of the former, as applicable to dialectical argument. We will rectify this confusion in our own discussion, and construct a clearer account of the basic principles of classical logic. At the same time, we will also attempt to develop a better understanding of the relationship of language to logical analysis, and show how language is often informed by our philosophical intuitions, rather than the other way around. The use of Greek and Latin in classical philosophy is less a cultural accident to be lamented than a fortuitous development, for these languages more clearly and precisely express true philosophical intuitions, and lend themselves more readily to the construction of a logical language. We will also address the question of whether modern philosophy draws too sharp a distinction between logic and grammar, so that we might regard logic as a genuinely linguistic phenomenon after all, which is not necessarily a liability.

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Part I: Logical Functions of Linguistic Elements

1. Language, Thought and Reality

For Aristotle, language is primarily the spoken word, and only secondarily the written word. Spoken sounds are “symbols of affections in the soul,” while written words are symbols of spoken sounds, a level of abstraction further removed from the “affections of the soul.” [De Interpretatione, 1] This viewpoint agrees with what we commonly observe, as young children can learn complex spoken language by imitation without formal training, while learning to read and write even simple phrases is a cumbersome, laborious process for older children and even adults. Thus it would seem that speech is the more natural, immediate expression of human thought. Even when we are experienced writers, we still articulate the words phonetically in our minds (which is why homonymous typographical errors are common). I would contend that surrogate languages for the disabled, such as sign language and braille, are more similar to written language than spoken language, as they are learned only with great effort, and are in many aspects derivative of phonetic language. Sign language, once learned, however, can become a mode of expression as familiar and direct as spoken language, though the partially deaf tend to think phonetically. Although it is by no means a metaphysical necessity that spoken language should be primary, this seems to be a genuine feature of human nature.

While it is uncontroversial that words are symbols of our thoughts or other “affections of the soul,” it is far less obvious that these affections are necessarily likenesses or images of extramental things. We do not need to develop a full psychological theory of meaning in order to explore the relationship between language and logic, but we do need to clarify how language expresses thought, since logic is concerned primarily with concepts (the objects of thought), and only incidentally with language, as a means to an end. In particular, we need insight into whether and when language expresses the mind’s images of reality, or if it is merely an arbitrary artifice having no necessary connection to the structure of reality.

The relationship of language to logic concerns us because we wish to know whether and how language can relate truth, which is properly the domain of logic. Logical propositions can be true or false, so the linguistic representations of these propositions, which we also call “propositions,” though in an equivocal sense, have an expressive relationship to truth and falsity. For most of history, in fact, philosophers have spoken of linguistic propositions as being true or false, without making a clear distinction between the grammatical and the logical. We can see the need for such a distinction by considering the sentence, ‘Socrates is alive.’ This grammatical expression can correspond to different affirmations, depending on when it is uttered. If it is uttered now, it would correspond to an affirmation that is false, but if the same sentence were uttered 2400 years ago, it would correspond to a distinct affirmation that happened to be true.

Realizing that identical linguistic expressions can correspond to distinct statements, we do well to distinguish linguistic objects such as sentences from logical objects, called ‘statements’ in modern jargon. In classical philosophy, ‘statements’ were simply types of sentences that corresponded to affirmations and negations. In modern philosophy, statements are not grammatical objects at all, but concepts that can be represented by sentences, if only equivocally. To clearly distinguish between the linguistic and the logical, I will use single quotation marks to signify a linguistic expression and double quotation marks to signify the logical concept behind an expression.

Notwithstanding this subtle distinction, it would be rash to divorce truth and falsity altogether from linguistic objects. The facts of common experience clearly demonstrate our practical ability to relate truths and generate knowledge through language, so our sentences must correspond to logical objects in some way, and, provided the appropriate context (such as who is speaking, how the speaker uses words, and when he is speaking) they can convey logical meaning unequivocally, enabling understanding on the part of the hearer. Grammatical propositions, when understood according to the sense of the speaker, can relate truth and falsity, even if we still hesitate to ascribe truth and falsity directly to the grammatical expression. Still, we may equivocally refer to a grammatical proposition as ‘true’ or ‘false,’ provided that we do not consider the proposition abstracted from the context in which it is spoken in a given instance.

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2. Names as Natural or Conventional

Among ancient texts, Plato’s Cratylus dialogue is perhaps the most insightful discussion of the nature of language, and it provides a potent counterbalance to modern tendencies (following Aristotle in De Interpretatione) to regard language as purely a matter of convention. The dialogue focuses on a basic linguistic object, the name, and explores whether names are merely conventional or reflect the nature of the thing they name. While it seems axiomatic that we can affix any arbitrary phonetic label to any object, Plato makes a compelling case that in fact some names are better than others, suggesting there is an aspect of naming that comes from nature, not convention.

Plato deduces from the truth or falsity of propositions that individual words can also be true or false. Like other ancient thinkers, he understands a proposition to be a linguistic object, a sentence conveying an affirmation or denial. He presupposes a context in which the sentence can be understood univocally, so that it is effectively what we call a statement. As noted, we might correct classical discussions of propositions by making reference only to logical objects (statements) rather than linguistic or grammatical objects (sentences), but here we will keep to the philosopher’s original meaning of a linguistic object, since we are concerned with language as such and how it relates truth.

A true linguistic proposition (univocally interpreted) relates that which is, while a false linguistic proposition relates that which is not. If a linguistic proposition as a whole is true, it corresponds to that which is, so its grammatical components must correspond to things that are, insofar as these components correspond to logical components of the logical proposition (i.e., the statement expressed by the lingustic proposition). Thus Plato infers that words can be true or false, depending on whether or not they correspond to some reality. This notion of truth (and falsity), sometimes called ontological truth, deals with simple declarations of existence, as contrasted with the familiar Aristotelian and modern notion of logical truth, which evaluates only composite expressions or judgments.

A principal difficulty in constructing a logical analysis of language is determining which words correspond to logical components of a statement. Some languages incorporate prepositions by inflection of nouns, while others have these as separate words. We would hesitate to ascribe even ontological truth or falsity to such terms as ‘in’ or ‘on,’ so we must recognize that only some words can have truth or falsity, while others must be coupled in order to make a logical affirmation or an ontological expression. Plato is concerned only with those words that correspond to entities, which we have discussed elsewhere as being universal or particular substances or accidents (corresponding roughly to the modern categories of property, kind, object and trope). These entities can be described by individual nouns, verbs, adjectives or adverbs, or by prepositional phrases and other composite expressions.

In Cratylus, Plato restricts his discussion to names, which may be taken as substantives or nouns, though much of his discussion can be applied more broadly. He regards a name as the smallest part of a proposition, representing an entity that is the object of logical analysis. A name in this sense need not be confined to substantives, but may include verbs, adjectives, adverbs, and the various predicate expressions used to denote accidents. The basic question with which Cratylus is concerned is whether the linguistic objects we choose to represent ontological entities are a matter of mere convention, or are constrained by the nature of the entity described.

The initial reaction of most modern readers of Plato would be similar to that of Aristotle, who regarded words as completely arbitrary conventions, a set of sounds or scripts that can be chosen as whimsically as we please, so long as we agree by common consent that they should be ascribed a certain meaning. “A rose by any other name would smell as sweet,” as the Bard says, succinctly expressing how the essence of a thing is not contained in its linguistic representation. This is an ironic claim by a master of poetry, where the sound and form of words are essential to the relation of meaning. Regarding the relationship between reality and language, most realists are no different from Protagoras in declaring man to be the measure of things.

Plato tries to bring us to an understanding of how language is to some extent natural, and not merely conventional, beginning with a refutation of the sophistical relativism we rightly reject in many others aspects of philosophy. He opens his inquiry with a criticism of Protagoras’ principle, “Man is the measure of all things.” This principle, construed in its most radically subjectivist form, would deny the existence of noumena, things-in-themselves, and affirm that only phenomena, things-as-they-appear, have existence. A softer interpretation would be that only phenomena are knowable, while things-in-themselves are unknowable. An even milder interpretation would be that things-in-themselves, though knowable, are not expressible in human language. The entire range of modern nihilism was already succinctly expressed in Gorgias’ dictum that there is no truth, and if there were, man could not know it, and if he could, he would not be able to relate it. The Socratic philosophers were not naïve regarding relativism, as in fact they were exposed to modern skepticism in its fullness, and they disdained it as sophism or mere wordplay.

When criticizing Protagoras’ principle, Plato interprets it in the strongest sense, as denying the existence of objective entities, though some of his argument applies also to the softer interpretations. If things are simply as they appear to a person, then there would be no such thing as a bad man, since no one regards himself as evil. Similarly, there is no basis for regarding some men as wise and others as foolish, so the sophists hold a self-stultifying position, undermining all ethical and intellectual activity, including their own. The sophists and their modern counterparts avoid this conclusion only because they are inconsistent, and do in fact believe in many objective truths.

Although this critique of relativism could apply to many kinds of truth, Plato is concerned in particular with truths about the simple reality of entities. If Protagoras is truly wise, or truly a man, he must have his own proper essence that is independent of what anyone else thinks. The same holds for all other substantive entities, as well as their actions.

As proof of the objective reality of action, Plato observes that if we wish to cut something, we must use the appropriate instrument, or we will not be able to do so, no matter how strongly we opine that some blunt object might be used for cutting. Those instruments that are capable of cutting are so by their objective nature, not by mere convention. Note that ‘nature’ here simply means a thing as it really is, and does not imply a distinction between man-made objects and so-called works of nature.

Understanding ‘nature’ in the above sense, as referring to the objective capability of an instrument and not whether the instrument is man-made, we may regard human speech as a kind of action and ask whether our instruments of speech act according to nature or mere convention. Just as some instruments are better suited to cutting then others, so perhaps some instruments are better suited for speech than others. Plato confines his analysis to a particular aspect of speech: that of naming entities. A “name” or onoma (not limited to substantives, but including words symbolizing accidents) is an instrument of naming (a type of speech), and what is more, it is a natural instrument of naming.

This last claim seems bold, even if we accept that it is not inconsistent for a man-made instrument to have a “natural” capacity. In the act of naming an entity, we give information to one another, and distinguish things according to their natures. If a name is an instrument of naming, as seems trivially obvious, then it is an instrument of teaching and distinguishing natures. The assertion that names can be natural instruments of naming entails that they should be intrinsically well-suited to the relation of the real nature of the things they signify. In other words, the name we choose for an entity is not a matter of indifference; some names are better than others.

When choosing an appropriate name for a thing, we must take care that the ideal or conceptual form of the name resembles the idea or concept of the named entity. The material aspect of the name, its sounds and syllables, may vary greatly, but its conceptual or ideal form ought to resemble what the name signifies. Similarly, an artisan may have wide discretion in selecting the material to build a cutting tool, but if it is going to cut well, it can only have relatively limited forms.

The user of a tool determines if the artisan has done his job well. In the case of names, the user is the questioner or dialectician employing a name. A name may identify a kind of entity, as when we give animals of a species a common name. It is logical to name the offspring of a horse also a horse, if we see they are similar in nature. If, contrary to nature, a horse should give birth to a creature altogether different in species, we would give it a different name. Names of kinds are not purely arbitrary labels, but their application to various objects assumes a logical content. Our application of names signifies the presence or absence of certain similarities of essence.

Even the names of individuals need not be completely arbitrary. Plato, like most of the ancients, thought it important that the meaning of a personal name should reflect the individual’s character. He regarded Agamemnon (“admirable for remaining”) as well-named, since this king demonstrated perseverance in the Trojan War. The name Tantalus, he speculates, was derived from the stone suspended (talanteia) over his head, or from talantatos (“most weighted down by misfortune”). Even the gods are often aptly named, as ‘Zeus’ is composed of his names ‘Zena’ and ‘Dia,’ which mean “life” and “lord,” signifying that all creatures have life through him. Similarly, the name of the sky-god Uranus comes from apo tou oran to ano, or “looking upwards.” It is not necessary for Plato’s etymologies to be historically correct in order to establish the point that these men and gods are well named. Even if a name’s meaning is defined post hoc, that meaning no less effectively conveys the character of the person. In some instances, a famous person may give meaning to his name, as Tantalus has become a byword for his condition, giving us the English word ‘tantalize.’

In modern practice, Westerners rarely give much thought to the meaning of personal names, as practically all of our names are derived from Greek, Latin, Hebrew, or some other language largely in disuse. We customarily choose for children names that are pleasant-sounding or fit harmoniously with the family name, or we name them after some admired figure, such as a relative or a saint. When we name a child after someone else, it is either to express a wish that the child should have some of the character of his namesake, or to dedicate that child in honor of the namesake. The long-forgotten literal meaning of the name becomes irrelevant, if we care only about the emotions conveyed by the sound of the name. If a child is named after someone else, the name represents to us not its literal meaning, but the character of a previous bearer. Even by these modern criteria, some names are better than others, and the name is not utterly meaningless. We would think an ugly-sounding name ill-chosen if it had no other merit, since it appears to insult the child, nor would we name a child after someone we found contemptible.

Plato proceeds to apply his principle of naming to classes of persons, beginning with the gods. He suspects that the ancient Hellenes knew only the celestial bodies as gods. Since these bodies are seen running across the sky, they were called runners (theontas), from which the word for “gods” (theous) is derived, and this term was later applied to other kinds of gods. Once again, Plato’s etymology should not be taken as an anthropological fact, but as an illustration of how words might come to have meanings different from their literal sense. In this hypothetical scenario, the Greek word for “gods” would no longer be apt, since its literal sense describes the nature of only some gods, namely the celestial bodies. The naming of the gods as “runners” would be an historical accident based on an imperfect understanding of the divine nature, yet the name remains even when the nature is more perfectly understood. The usage of a word can develop over time, as its object becomes more clearly understood, so it acquires a meaning that is distinct from its etymological origin, yet more precisely relates the essence of its object.

The dialogue continues with Socrates postulating sometimes fanciful origins of the Greek terms for daemons, heroes and men. Daemons are so called because they are knowing or wise (daemones), and heroes are so named because they sprang from Eros. Man is called anthropos in Greek because he is the only animal who “considers and looks up what he sees” (anathron a opopen). These imaginative etymologies are highly dubious, and Plato perhaps uses them to illustrate how uncertain is our knowledge of the original meaning of most names. Instead, we judge that something has been named well if the nature of the object corresponds to the presently constructed meaning of the word.

Plato recognized that etymology can only carry us so far, and ultimately we must find ourselves with primary linguistic elements that cannot be explained in terms of derivation from other words, or at any rate, we are so ignorant of their original meaning that they might as well be arbitrary labels. To account for such primary elements, Plato considers what we would do if we did not have the power of speech. Surely, he says, we would convey our meaning through gestures. In this primitive form of communication, we would imitate with our hands or bodies the action we wished to describe, or create the shape or form of the object we sought to represent. Plato supposes that spoken language, in its most primitive form, would have this same function of imitation. Thus he postulates that a name is a vocal imitation of that which is named.

If a primitive name, one that is not derived from any other word, truly is a vocal imitation of its object, then the essence of its object should be imitated in its own essence. More generally, if X resembles Y, the essence of X should resemble the essence of Y. An essence, we recall, is simply that which makes a thing what it is. The essence of a vocalized word is in its phonetic components that correspond to the syllables and letters that uniquely distinguish a word from others. These phonics must somehow imitate the thing represented. Plato speculates that rho corresponds to kinesis, since the tongue is in motion, while lambda conveys softness or smoothness. This onomatopoeic view of language does not mean that we should describe a sheep by baa-ing, for we are not imitating the sounds of the object, but its essence. It would be unseemly to use a harsh-sounding word for something beautiful or elegant, and indeed our terms ‘beautiful’ and ‘elegant’ are consonant with their meaning, both in terms of how they sound and how they appear when written.

Although Plato conceives of language as primarily spoken, he speculates that even the shapes of letters might convey meaning. We might attribute meaning to the shapes of letters simply from long association with them, so that we instantly identify the shape of the letter with its sound, which in turn may have some onomatopoeic meaning. When we read or write, we simultaneously think of the words phonetically, but when we speak to each other, we do not customarily visualize in our minds what our words would look like written. This further suggests that language is fundamentally vocal for most people, and that phonetics permeates our interpretation of even the written word. Yet the sound of our speech cannot be an end in itself, for it must direct our thoughts to some idea if it is to be truly linguistic.

The crux of the argument as to whether or not language is arbitrary is expressed by Plato in an exchange between Socrates and Hermogenes where they consider if it is possible for words to be false. For Hermogenes, all language is arbitrary, so any utterance whatsoever is valid as a name for something. Since every utterance says something, there can be no such thing as a false name or word, for falsehood would be to speak that which is not. Socrates counters this sophistry with the evident fact that lies and falsehoods are spoken regularly. Hermogenes replies that an expression that does not correspond to reality is not a falsehood, but a meaningless sound “like the hammering of a brass pot.”

Here we touch the intersection of language and logic. The problem is how to determine the truth value of an expression that has no referent. Should we regard it as a meaningless collection of sounds? This would be dishonest in many cases, for we certainly understand what an expression such as ‘the king of the United States’ means, though it has no referent. If we called a particular person ‘the king of the United States,’ we would be speaking a coherent falsehood, not making an ill-defined grunt. We should resist, therefore, the tendency of modern sophists to declare meaningless anything that leads to paradox, if we are to be honest with ourselves.

Socrates and Hermogenes agree that pictures can rightly or wrongly represent an object. A crude drawing might fail to represent essential qualities, and a detailed drawing might include properties the actual object lacks. Hermogenes denies, however, that words can falsely represent an object, since they are arbitrary signs anyway. This argument is on stronger ground when dealing with primitive terms, which indeed seem arbitrary, but expressions composed of established terms could falsely represent an object, as when we say ‘the black sun.’ This is not a nonsensical expression, but an ontologically false one. An expression such as ‘Green dreams sleep loudly,’ by contrast, is genuinely nonsensical, as there is no coherent concept asserted, but only the syntactic form of an assertion. Even here, we have something more than a clanging pot, for the individual terms have meaning, and it is precisely from our understanding of their meanings that we are able to determine that the expression is incoherent. The expression considered as a whole may be incoherent, but not its parts.

The sophist’s position is further undermined when we consider language as belonging to a society and not to an individual. Words then cannot mean whatever we choose them to mean, but we must accept established meanings for basic terms. Unless we formally define a different meaning for some technical usage of a term, we are guilty of falsehood when our common language expressions have no referent. If I say that George Washington was king of the United States, I am not excused of speaking falsehood by the supposition that the term ‘king’ could have been used to mean “president.” Such is not the actual usage of the term ‘king,’ a word that belongs to all English speakers, and is not mine to redefine in secret.

Convention or custom is necessary to establish that the same meaning is assigned to a word by both the speaker or the hearer. Even if we do not believe language is completely arbitrary, there is no way to determine a word's meaning unequivocally from its sound, or else we should be able to understand the words of foreign languages just by hearing them. Plato does not pretend that the sound of a term can uniquely determine its meaning, and he freely acknowledges that convention plays a necessary role in establishing the meaning of words.

There may be cases, however, when conventional language is poorly constructed with respect to some point of logic or the actual nature of a referent object, so that we would be better off departing from common usage, perhaps introducing a more proper technical term. Such has long been the practice in philosophy and other sciences. Plato himself was one of the earliest practitioners of the art, famously giving a new meaning to the Greek term idea, which formerly meant the appearance or form of a concrete object, and now is understood to mean an abstract concept.

A well-crafted name, combined with established conventions of usage, may give knowledge of the thing it signifies. When we are fluent in a language, we effectively identify the word and the thing without thinking of them as distinct. We know what is meant when we hear the word ‘justice,’ even though we might fumble if we were asked to express this in words. In our mental life, the words act as surrogates for the things they signify, so we seldom perceive a need to explain basic words in terms of something else, which is why we are not ready to do so when asked. Without words, we could have no knowledge of most things except by direct apprehension.

Plato’s Cratylus dialogue is concerned primarily with whether the most primitive aspect of language, names, are arbitrary correlations between sounds and objects, or if they somehow convey the essence of what they represent. On one level, it is obvious that words must convey essences, since we are able to understand concepts via their names; this is in fact our ordinary mode of thought. However, it is not clear that our knowledge of the essence comes from the vocal qualities of the name itself, thereby conveying meaning in an onomatopoeic way, as Plato suggests. It is possible that, in the process of learning language, we have come to associate an arbitrary name with its conventional meaning so closely that we have learned to summon our ineffable knowledge of the essence whenever we think or hear the name. Yet we must admit at least that complex terms and expressions certainly help us construct knowledge of an essence by appeal to their linguistic form.

The fanciful etymologies proffered by Socrates in Cratylus need not be taken seriously; indeed, it is likely that many of these were humorous literary devices. Still, the basic point remains that all but the most primitive terms are constructed or derived from other terms, in an imperfect attempt to include the essence of an object in the composition of the word that represents it. If the ancients did not always do this job well, or if we now have a broader or deeper understanding of a concept than when its word was coined, it may be profitable to assign a new name or impose a new technical meaning on an existing term.

Lastly, language is to be conceived as belonging to society, not individuals, for it is essential to language, whose purpose is communication, that both hearer and speaker apprehend the same meaning in a term. Such agreement cannot be assumed unless there are well established conventions for the use of words. These conventions are not immutable, but they must have a basic stability in order for communication to be effective. Since words belong to society and not to individuals, there is a social expectation that a spoken word is intended to convey a certain meaning, so speech may be judged as true or false depending on whether its conventional meaning corresponds to reality.

This dialogue touches basic questions of philology and logic, and serves as an important background to a discussion of Aristotle’s De Interpretatione. Aristotle, we have mentioned, assumed the position that names are completely arbitrary, so Plato provides an important counterbalance to this view, enabling us to construct a more complete picture of the capacity of language to convey meaning.

Plato did not attempt to construct an ideal language, though he seems to have hinted that such a language might be known to the gods. He says we do not know the names that the gods called themselves, which are names that conveyed their divine essence. He seemed to believe that it was at least conceivable for such a language to exist, though he comically pointed out the practical limitations of such an endeavor for human language.

A language whose sound is its very meaning has been attributed to the angelic choir in certain Christian revelations, such as the mariophany of St. Juan Diego, and can be found in the fantasy literature of J.R.R. Tolkien and C.S. Lewis. Music, often called the universal language, seems a likely basis for such a “pure” language, if it exists, since harmonies seem to be a feature of nature itself. Indeed, that substudy of physics called string theory presumes to express all natural phenomena as harmonic vibrations at the most fundamental level.

3. The Interface of Concepts and Language

We are concerned with philology only incidentally, insofar as it might help us understand the relationship between language and logic. From our review of the Cratylus dialogue, it appears that inquiry into the historical development of language yields little insight into this question. This is because often the original meaning or use of a term or expression varies wildly from its current meaning or use, and in any event, most people use language in near-total ignorance of etymology. Whatever means we use to relate logic to language, it is a process that is not strongly dependent on philology. This does not mean that the specific form a word takes is irrelevant. Some names may indeed be better than others, but this judgment can be made post hoc, without recourse to the historical development of language.

Further, we find that the mode of analysis favored in the physical sciences, whereby a composite entity is explained in terms of its parts, is of limited utility when applied to the logic of language. In the Cratylus dialogue, Socrates humorously illustrates the futility of searching for the meaning of language in its phonetic or literary components. He breaks down meaning to the level of words, syllables, letters, and parts of letters, with increasingly fanciful results. With complex expressions and grammar, we do see an imperfect attempt to define terms and rules in a way that mimics logical or ontological relationships. With simpler terms, however, there is no effective imitation of an essence except in cases of onomatopoeia. We must, then, search for meaning elsewhere than in sounds or letters.

The study of natural history might be helpful incidentally, insofar as it helps us understand human psychology. Nonetheless, any attempt to explain the development of articulate speech out of the inarticulate “speech” of animals should avoid two classes of error. First, there is the error of Descartes, who famously denigrated the psyche of animals to the point of being mere automata. This is utterly contrary to the experience of those who live or work closely with animals, many of which exhibit at least rudiments of genuine cognition and volition. Modern experiments on animal behavior have amply borne out this thesis, but it is possible that current scholarship has leaned toward the opposite error of crediting too much to animals. The ability to convey signals representing concrete objects or actions need not entail ideation of an essence.

Modern experimental scientists often have a poor philosophical conception of human intelligence, reducing this to things they can analyze, such as signal processing or behavior outcomes. These empirical data do not give us ideas or essences, but their neural or behavioral correlates. If we are concerned primarily with logic and its relationship to language, we need to deal with ideas themselves and not just their physical representations. A failure to distinguish ideas from their representations permeates the literature of neuropsychology and so-called artificial intelligence, and not a few philosophers have been infected with this malady. Since the very object of our study is the interface between ideas and their representations, we obviously cannot enjoy the luxury of ignoring this distinction.

We know from experience that ordinary human speech can convey knowledge of the essences of things-that-might-be. Language for us is more than simply assigning arbitrary symbols to objects. We must also understand the symbols as signifying some idea, and be able to manipulate the symbols in ways that correspond to perceived logical or ontological relationships among ideas or the objects to which ideas point. We take for granted this linguistically-induced immersion in ideas (which, being universals, define essences), so much so that we would be hard-pressed to translate even an ordinary sentence into a series of concrete objects or sensations. Essences, which many philosophers have found fashionable to deny, are constantly before us in a stream of mental experience, so that it is impossible for any consistent thinker to deny at least the psychological reality of ideal essences, and thus we must admit their a priori conceivability.

Although ideal essences are psychologically real, the object of our study is not properly psychological, for ideas or concepts are distinct from language, which is the expression of thought. Language is a psychological phenomenon, consisting primarily of vocalizations intended to represent our thoughts. Language does more than provide a means of communicating our thoughts to others, for it may form the substance of our own inner thoughts, which we express as vocalizations in our mind’s ear. Although language is an expression of thought, we should not say that language consists of ideas or concepts, for these are the objects of thought, not thought itself. It is true, nonetheless, that language attempts indirectly to express concepts or ideas (or rather, the essences they define), since it expresses thoughts that are directed toward ideal concepts.

We must take care to distinguish the conceptual (governed by logic) from the psychological (expressed by language), since the interaction between the conceptual and the psycho-linguistic is precisely the object of our study. We wish to know to what extent and in what manner language may truly relate concepts and give understanding of their logical relationships. We are not at the moment directly concerned with our ability to truly know external reality, but only our ability to construct a language that truly captures a logic of concepts, of things-that-might-be, not necessarily things-that-are.

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4. Overview of Affirmations and Truth in Language

From our Introduction to Ontological Categories, we know that an entity P may be ontologically “predicated” of another entity S when the essence of P pertains to the being of S. For example, “man” is predicated of “Socrates” because that which is essential to “man”—being a rational animal—does in fact pertain to the being of Socrates. Here we are considering the ontological relationships among real entities, not mere linguistic relationships among terms. Nonetheless, most languages have adopted a syntax that explicitly mimics this logical structure, so there is always a grammatical subject and predicate corresponding to S and P. Grammatical predication intends to illustrate ontological predication between the entities corresponding to the words used for S and P.

Most Western languages explicitly include a verb in every predicate, in order to show how the being of the subject is related to its predicate. At a bare minimum, we see a need for an ens copulae: the ‘is’ in ‘The sky is blue.’ Ancient Greek admitted of a shorthand whereby subject and predicate were juxtaposed, and the “is” was implied. For example, anthropos politikon zoion means, “Man is a political animal,” even though no verb is written. Notwithstanding this shorthand, of which he himself often made use, Aristotle recognized the logical necessity of having a verb in an affirmative sentence. (The same holds for negative sentences, but I will avoid mentioning this where it is obvious, to avoid tedious repetition.) This is because all ontological predications of entities are relationships of being, so if a grammatical sentence is to mimic such a relationship, it must have at least an implied verb that represents the mode of being that is affirmed. For example, ‘sky blue’ cannot represent any assertion unless we specify if this means “the sky is blue” or “the sky was blue” or “the sky is becoming blue” or “the sky may be blue” or “the sky ought to be blue,” et cetera.

Ordinary action verbs also fulfill this role, since they are understood to contain the existential relation. We understand ‘Socrates walks’ to be more than a mere juxtaposition of terms, and take it to mean that Socrates is walking (or at least that he is capable of walking). If we denied that there is any existential relation intended, then ‘Socrates walks’ would just represent a succession of ideas: think of Socrates, then think of walking, but do not necessarily combine the two in any definite relationship.

A verb (or at least an implied verb) that represents a mode of being is necessary for a sentence to represent an affirmative statement. When we affirm something, we are not simply describing a concept, but intend a declaration regarding an entity’s mode of being. The explicit or implied verb ‘to be,’ or one of its modes, is necessary to specify the mode of being that is affirmed. This does not require us to admit that “to be” is an action or that the copula ‘is’ corresponds to a distinct predication. It suffices for the ‘is’ to represent a modification of the predicate, specifying what mode of ontological predication we affirm: e.g., it is; it may be; et cetera.

Since logic concerns the relationships among conceptual entities, a properly logical assertion should represent at least two entities, a subject and a predicate. Our grammatical structure for sentences mimics this ontology, with a noun or noun phrase used as a subject, and some modifying phrase, including an explicit or implicit verb, as the predicate. As discussed in Part VI of the Introduction to Ontological Categories, it is necessary that the entities represented in an affirmation belong to two distinct ontological categories.

When we have an ontologically simple subject, with no predicate, there can no longer be a properly logical assertion. We do not understand ‘Socrates’ to represent an assertion, because in our language declaring a noun does not imply asserting anything about its being. However, we can add a verb without a predicate, to say “Socrates is,” or “Socrates exists,” which we generally recognize as affirmations. We call these affirmations ontological, as distinct from logical affirmations, which must have predicates.

In the Categoriae, Aristotle identifies statements declaring truth or falsity—affirmations and negations—as combining entities in two or more ontological categories. This corresponds to what we have said about logical affirmations. In De Interpretatione, 1, however, he invokes a different standard, declaring that truth or falsity is to be found in an expression only when ‘is’ or ‘is not’ is coupled to a subject. Here the existential verb, not a predicate, is essential, as was the case for our ontological affirmations. We have noted that the existential verb is at least implied in the predicates of logical affirmations as well.

Like other Greek philosophers, Aristotle makes no distinction between a sentence, which is a linguistic object, and the conceptual object or statement that the sentence represents. He does, however, recognize a distinction between thoughts and words, and contends that just as certain thoughts are subject to the distinction of truth and falsity, while others are not, so it is with the words that correspond to these thoughts. Thus he makes language a locus of truth and falsity. This has a fair degree of plausibility, since in our mental life, we regularly treat linguistic objects as though they were logical objects. In fact, the power of language lies precisely in its ability to stand as a surrogate for logical statements and ontological essences.

To affirm something is to assert it as true in some sense that is specified by the mode of being. We may say “Socrates is,” or “Socrates was,” or “Socrates may be,” either simply or in relation to some predicate. The form of the verb ‘to be’ indicates the mode of being, and thus the sense in which we take the statement to be true. The context of our speech may provide further modification, for it may turn out that we are speaking of Socrates as a literary character in a dialogue, or as a hypothetical person. In any case, the specification of being is essential, for without it, we could hardly claim to be declaring anything as true. ‘Socrates’ represents no declaration of truth, unless it is understood to mean “Socrates is,” or to declare some other mode of being.

We say that an affirmation is true if we judge that the existential mode that is affirmed indeed describes reality. Judging an affirmation as true or false is a psychological event, dependent on our notion of what is real, whether we are considering reality a priori or a posteriori. Nonetheless, truth and falsity seem to be governed also by logical rules, which are independent of our psychological judgment. The most basic rule is that of non-contradiction. If we judge that the affirmation “X is P” is true, logic requires us to admit that “X is not P” is false. With tautologies, such as, “Given X, X is P or X is not P,” we are logically bound to admit that the statement is true, regardless of circumstances. So there seems to be an aspect of judging an affirmation as true or false that is independent of psychology.

Further, the affirmation itself, considered as a concept, is independent of any particular mind, though it is only intelligible as the declaration of an indeterminate mind. For example, the logical affirmation, “The sky is blue,” declares the same thing regardless of who thinks it, so it is not the mere thought process of an individual mind, since it has a meaning that transcends individual psychology. Were this not so, intellectual communication would be utterly impossible, and we could never convey conceptual statements to one another. Nonetheless, in order to understand the affirmation, “The sky is blue,” we must conceive of a mind, whether our own or that of a hypothetical other, as proposing this logical relationship. Though the meaning of “The sky is blue” does not depend on the psychology of any particular individual, its declarative aspect implicitly assumes an indeterminate mind that declares it.

The concepts “dog” and “walking dog” can be understood as describing potential ontological entities, without considering them as the thoughts of some mind, but, “The dog walks,” is a proposition or declaration, requiring us to conceive of at least an implicit proposer or declarer. In ordinary practice, we make the speaker or author of a sentence its proposer or declarer in the first instance, and ourselves its declarer in the second instance, insofar as we accept what the sentence expresses. Assertions, or propositions more generally, are not static concepts, but intellectual acts of asserting or proposing, so they can only be conceived as the products of some intellect. They are intrinsically intellectual, but only in a generic sense, for a statement’s meaning is not confined to the thought process of any particular individual.

More succinctly, concepts such as “Socrates the philosopher,” “Socrates in Athens,” and “Socrates walking” are not intrinsically dependent on being the object of some thought, since they can simply denote extra-intellectual objects. Still, a proposition such as “Socrates is walking” necessarily entails an intellectual act of proposing a potential reality, so its meaning cannot be considered apart from at least a hypothetical mind who thinks it.

Given that language can represent logical statements, it would seem that it can also express judgments of truth and falsity. When we simply declare an assertion without qualification, we are understood to affirm it as true. If we wish to declare that an assertion is false, we instead declare its negation, invoking some linguistic construction such as ‘not’ or ‘I deny that…,’ which are understood to represent denial of the linked predicate or proposition. Truth and falsehood pertain primarily to (conceptual) statements, but we often equivocally speak of them inhering in (linguistic) sentences. We may even punish a person for speaking “false words,” thereby committing perjury or slander. This is not necessarily because the words themselves are false, but because the assertions they represent, when interpreted according to general usage, certainly are false, from which we infer that the speaker intended to deceive the hearers. Insofar as words are the likenesses of concepts that they represent, we may say they contain the likeness of truth or falsehood as the statements they express are true or false.

Plato suggested in the Cratylus that even words or phrases may be false, if they do not correspond to any real object. This view is coherent if we understand the utterance of a name to entail an assertion of its object’s existence, in which case there is ontological truth or falsity in a name. “The king of the United States” is ontologically false, since no such being actually exists, and thus the utterance ‘king of the United States’ may be considered false to the extent that it asserts the existence of such a being. In actual experience, we often make this assumption, for if someone should ask, “How old is the king of the United States?”, we would take this to imply that the questioner supposes there may in fact be a king of the United States. To conceive of something is to contemplate it as at least potentially existing. Nonetheless, strictly speaking, simple ontological concepts are not true or false unless we explicitly add a verb specifying the mode of being we intend to affirm or deny. Thus most modern logicians follow Aristotle in his view that a name that has no referent (e.g., ‘king of the United States’ or ‘goat-stag’) is not false, since it asserts nothing.

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5. Nouns or Substantives

Proceeding more methodically, let us examine the logical structure of language beginning with its more basic components. Perhaps the simplest linguistic entity is a name, or onoma in Greek and nomen in Latin, from which we derive our grammatical term ‘noun’. A noun in the modern sense is not a name for just any kind of entity, but only that which is capable of being an ontological subject. For this reason, it is called a sustantivo (“substantive”) in Spanish, since it can function grammatically as a substance does ontologically. In De Interpretatione, Aristotle proposes the following definition for a noun (onoma):

A noun is a spoken sound that is (1) significant by convention; (2) without time; (3) has no part that is significant in separation.

Evidently a noun is a purely linguistic object, being a spoken sound. It is “significant by convention,” as opposed to being “significant by nature,” like animal calls and cries. It is “without time,” distinguishing it from verbs, which specify action and therefore time, since action is a time-dependent relation. It also has no part that is significant by itself, so it is a single word and not a phrase. Aristotle holds that a word expresses the smallest unit of meaning in language. There is no conceptual content in letters and syllables. These form the phonetic structure of a word, but they do not express parts of its meaning.

According to Aristotle and most modern thinkers, all names hold their significance only by convention and not by nature. Yet, as we saw in our discussion of Cratylus, this is not entirely true, for complex and derivative words may be considered better or worse names if their roots denote the nature of their object. Still, when we get to more basic terms, we must admit that most if not all names are arbitrarily assigned to objects, save perhaps for some onomatopoeic rendering of meaning. Further, even if we chose an unnatural meaning for complex terms, our language could still function quite well if the conventional meaning is well established. For example, we could define ‘rainbow’ to signify “dog,” and our language would be fully functional, as long as this convention was widely known.

In actual practice, of course, most complex terms do follow an internal logic based on the meaning of their linguistic components. Sometimes, this logic is not immediately apparent, as in the case of ‘inflammable,’ which we might think should mean “not flammable.” In fact, the prefix ‘in-’ here refers to the Latin for “into,” rather than “not,” which is another meaning of the same Latin prefix. Here the term was constructed logically, but the original meaning is now unknown to most people, who know the meaning of ‘inflammable’ only by convention, despite its apparent illogic.

It is not immediately clear why we should regard all animal noises or cries as natural rather than conventional. We may regard as natural those inarticulate utterances that have no meaning apart from their sound, but it is less obvious that the same should be said of sounds that signify some object or action, as do the calls of birds, cetaceans, and primates. These sounds do not convey meaning in an onomatopoeic way, yet neither can we say that animals have consciously adopted some convention whereby they interpret these sounds. Rather, they respond to these sounds instinctively, that is, by their innate nature, or through social conditioning by members of their kind. Animals can learn from instinct or experience to associate sounds with objects or actions, but they exhibit no ability to arbitrarily define new terms or construct new meanings with existing terms, so we cannot say that their system of vocal signals is the product of a consciously adopted convention. This does not mean that animal systems of communication never change, but only that change is effected through conditioning or instinct, not a conscious decision to adopt a new convention.

It was once supposed that aquatic mammals possessed a true language, yet it now seems to be the case that their utterances are not indicative of an ability to assign arbitrary symbols to concepts. No animal “language” appears to reflect such an ability, but experiments have shown that some chimpanzees and gorillas can at least be taught a language of arbitrary symbols constructed by humans. It remains unclear, however, to what extent these primates can truly conceptualize the meanings signified by our symbols. On the whole, then, animal utterances are natural, not conventional, though it is possible that they might be taught conventional language.

The importance of convention rather than nature as a defining characteristic of a name is that the arbitrary aspect of a word is what makes it truly a representation of a concept, and not just a sound. A purely onomatopoeic word has no meaning beyond its sound, so it cannot point to a non-phonetic concept. An animal utterance that evokes an instinctive or conditioned response is also not truly language, since no understanding of a concept is necessarily conveyed. A term that is defined principally or entirely by convention, on the other hand, must certainly convey a conceptual meaning, since its meaning is not defined by its sound, nor by instinct, nor by behavioral imitation. A creatively defined word is defined with respect to some concept apprehended by the intellect. Only when there is an element of convention in the definition of terms can there be a truly conceptual language. It is impossible for there to be a complete language whose meaning is expressed in its sound, since there is more to meaning than mere sound. If there truly were an angelic or divine language whose words give any hearer knowledge of their meaning, this language could not be mere sound in the ordinary physical sense.

We pass over the second condition to the third, namely that no part of a noun is significant in separation. This condition may be taken to apply to words in general. Aristotle regarded the word as the smallest linguistic unit with meaning, notwithstanding Plato’s speculation about the possible meanings of syllables and letters. Even if the phonetic components of our words really did have meanings at one point, it is certainly the case with most speakers today that we do not intend any meaning in our letters or syllables, but only in our words. If we pronounce a word differently, we do not necessarily intend it to have a different meaning, and inversely, there are words in a language that sound identical yet have different meanings (homonyms). Thus it would seem that words truly are the fundamental units of expressed meaning in a language.

Nonetheless, there can be parts of words, including nouns, that have meaning. Prefixes, suffixes, or inflections of declination (called ‘affixes’ in general) can convey the same meaning as parts of different words. We understand ‘ex-’ to mean “out of” in many different words, for example. Some words may be compounds, such as ‘rainbow,’ ‘bookcase,’ or ‘thunderbolt,’ where each part conveys a meaning that tells us an aspect of the whole. Arguably, words composed of several meaningful elements do not denote simple subjects, so they should not be considered pure nouns. By this standard, however, virtually nothing is a noun, since all but the simplest entities have accidents, so their names at least implicitly include that which is not substance. If we admit that a substantial essence can include accidents (as differentiae), we cannot deny the status of nouns to words simply because they include accidental specifications, since these too can truly name essences. Whether a term declares a substance’s accidents explicitly (e.g., ‘quadruped’) or implicitly (e.g., ‘horse’), in both cases it names an essence and is truly a noun. If we admit that ‘horse’ is a noun, we can hardly deny that the term for its genus, ‘quadruped’, is also a noun.

A composite term such as ‘quadruped’ can function as the name of a single concept, without reference to the meaning of its linguistic components. We could substitute the simple term ‘blort’ for ‘quadruped’, and the same logical function of naming an essence would be performed. Similarly, when we hear ‘rainbow’, we may think immediately of a rainbow, without necessarily thinking of rain or a bow. In this view, the internal composition of a word is incidental, since it functions as a simple term and could be substituted by any arbitrary sound. Here we see how Aristotle’s view that all names are arbitrary leads to the thesis that parts of words have no signification in separation, at least not as long as they are truly acting as parts of a word. Thus the word remains the fundamental unit of expressed meaning.

We may come to a synthesis by declaring that the parts of words can indeed have meanings, yet not insofar as they act as parts of words. ‘Quad’ means “four” only when it is considered separately as a word, not when it is part of ‘quadruped’. There is no necessity that the meaning of the whole word will follow the logic of its composition. Even when such logic is followed, as is the case here, the part does not have the meaning it would have as an independent word. ‘Quad-’ in ‘quadruped’ does not declare the concept “four,” an abstract number, but is inextricably bound to the rest of the word, so that “four” is declared only in the very limited sense of “four-footed.” It is conceivable for a person to fully understand what a quadruped is without understanding the abstract number “four” in its full range. This would be a person who, for example, knows how to count concrete objects, but does not understand “four” as a multiple or as a continuous measure. Similarly, one can understand what ‘rainbow’ signifies without necessarily knowing what a bow is.

The distinction between words and phrases hinges upon whether concepts are declared independently or not. In the sentence, ‘It is a white camel,’ the concepts “white” and “camel” are declared independently, so the hearer is expected to understand both concepts and combine them. However, if there were a term ‘white-camel’ that signified a species of camel that happened to be white, it would be conceivable for a hearer to know what a “white-camel” is (e.g., recognizing it by smell or sight) without knowing what ‘white’ means (e.g., the hearer is blind or a non-native speaker).

It is not necessary for a word to be denoted by an unbroken string of characters. For example, ‘great white shark’ is a single word referring to a species of animal. The first two parts, ‘great’ and ‘white,’ do not declare in this context what they would mean as independent words. As a phrase, ‘great white shark’ would mean any shark we consider to be “great” and “white.” As a single term, ‘great white shark’ refers to Carcharodon carcharias, regardless of size or color. Even ‘shark’ does not retain its independent meaning when it is part of the term ‘great white shark,’ since we could understand what a great white shark is without necessarily knowing what distinguishes a shark from other kinds of fish. This ignorance would not be possible if we understood the independent meaning of ‘shark.’

Although the parts of words have no independent meaning when acting as parts of words, their phonetic identity with independent words can serve as mnemonic devices to help us keep track of the meanings of complex terms. If we assigned arbitrary, phonetically dissimilar terms such as ‘blort’ and ‘garf’ to each and every object in the world, it would be incredibly tedious to learn and use language. Internal structure in a word helps us remember its genus and differentia, so that our concepts are not just a list of things, but a structured body of interrelated knowledge. The parts of a word do not have independent meaning, but neither are they devoid of information about the concept the word denotes. Thus Plato was correct in his insight that the components of a word can be meaningful, and therefore some words are better names than others, since some give better insight into the essence the word denotes.

In modern linguistics, meaningful parts of words are called morphemes, of which there are several types. A root is a single morpheme (e.g., ‘rain’), which may be compounded with other roots to form a complex stem (e.g., ‘rainbow’). Other morphemes called affixes (which include prefixes and suffixes), may be added to a stem or root. Many linguists also classify the clitic (e.g., the ‘’s’ in ‘what’s’ or the ‘’ve’ in ‘should’ve’) as a morpheme, but this is really a phonetically contracted word, since it functions as a unit of independent meaning.

Languages that have only one morpheme per word (e.g., Mandarin Chinese) are called “isolating” languages since they isolate units of meaning from one another, rather than synthesizing them into contiguous phonetic or written units. Words in such languages have no internal structure; they are all roots. These languages are also called analytic, in contrast with synthetic languages, which can have more than one morpheme per word, as is the case in all European languages.

Returning to the proposed second criterion of nouns, we examine why time specification might be excluded from nouns. We recall from our discussion of ontological categories that time is an accident that cannot be the subject of any other accident, nor can there be “time of a time.” Since time cannot be an ontological subject, it would seem that we should not include it in a term that is intended to represent only an ontological subject, i.e., a noun or substantive. However, it is easy to produce counter-examples: ‘bride-to-be,’ ‘ex-husband,’ ‘president-elect,’ to name a few. It is not illogical to specify time in the term for a subject, any more than to have an accident be part of the definition of a substance. Aristotle intended to exclude from nouns any assertions of action or existence by excluding time, the medium of action, yet we can accomplish this aim without excluding references to time or action in a noun. Declaring the term ‘ex-husband’ does not assert the existence of the ex-husband or any action on his part. Further, we can modify nouns to create temporal expressions that do not involve assertions of action or existence. To take a literary example, consider ‘Christmas Past,’ ‘Christmas Present’ and ‘Christmas Future.’ These expressions specify time without introducing a verb or existential copula.

The possibility of including multiple functions in a single term should make it clear that when we define nouns and other types of words, we are not necessarily identifying distinct, non-overlapping groups of words. Rather, we are identifying the various functions of words, and in the case of nouns, the function defined is that of naming an ontological subject. A subject need not be a substance, for even accidents can be subjects of other accidents, so a noun may signify an accident. The same entity may be the subject of some accident and predicated of another entity. To reflect this identity, in English the same noun may be used as a grammatical subject or object. In highly inflected languages such as Greek and Latin, the noun takes a special suffix to signify when it functions as an object. Aristotle restricted nouns to the nominative case, which signifies subjects, while he regarded inflected cases such as the accusative (used for grammatical objects) as “not nouns, but cases of a noun.”

Specification of time is not essential to the function of a noun, but neither is it necessarily in contradiction with that function. Many essences, such as “horse” or “man,” are essentially atemporal, so any term that names these must also omit any indication of time, yet it is at least conceivable for time to be used as a differentia to define substances temporally, as in the examples considered previously. The only thing that is essential to a noun is that it names a subject, so even nouns with time dependence may not simply denote time, since time cannot be the subject of anything.

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6. Verbs and Predicates in General

In order to complete an affirmative sentence, it is not enough to simply declare a subject, but we must also give some existential modifier or predication of being. We must not simply give a name to some entity X, but we must also indicate in what sense we consider X to be or not to be, either simply or as the subject of some predicate. Grammatically, we perform this function with verbs and predicates. In Greek, this breadth of linguistic function was represented by the term rhema, which means “word, saying, phrase” and is translated as “verb” in some contexts. The Latin verbum has a similar range of meaning.

Rhema has the same root as rhetor (“orator, speaker”) from which we derive the term ‘rhetoric’. A rhema is a constituent of rhetoric, for it does not merely label an entity, but it actually says something. As Aristotle puts it, the use of a rhema “arrests the hearer’s mind, and fixes his attention,” though it does not constitute a full affirmative sentence. It is no accident that our term ‘verb’, which means a word signifying action, should overlap in meaning with the Latin verbum and the Greek rhetor, for in these languages, an inflected verb functions as a full phrase. The Latin ambulaverat does not merely label the action “walk,” nor does it mean “had walked,” but it carries the full meaning “they had walked,” where “they” is indefinite.

A verb is but one example of a rhema. Aristotle also identifies the predicate expression ‘is healthy’ as a rhema. What verb and predicate expressions have in common is that they declare something about a state of being, either simply or in relation to some declared predicate. The one thing a rhema lacks as a sentence is a subject, which in some cases is implied by inflection. Indeed, we might dare to say that a rhema is an indefinite affirmation, that is, an affirmation whose subject is unspecified.

Aristotle gives the following conditions for his definition of a rhema (paraphrased from De Interp., 3):

(1) it is a sign of something that is said of something else;
(2) no part of it has any independent meaning;
(3) in addition to its proper meaning, it carries the notion of time.

Condition (1) stipulates that a rhema is a sign for an accident that is ontologically predicated of some other entity. We discussed the concept of ontological predication in our previous work. Aristotle’s choice of wording here is unfortunate, for “said of” in the Categoriae refers to the relationship between individuals and universals, not accidents and their subjects. We should rewrite the first condition to read: “it is a sign of something that is ‘in a subject’,” where ‘in a subject’ was formally defined in the Categoriae. A rhema is more akin to what we would call a grammatical predicate rather than a verb, though it can include verbs, since actions are predicated of subjects. We further note that since a rhema is a sign for an entity, it shares the ability of a noun to name things, though the entity named need not be a subject.

Condition (2) implies that a rhema must be a single word of indivisible meaning. This is problematic when applied to languages other than Greek, as we can see from our English translation of Aristotle's example of a rhema, ‘is healthy,’ which is a simple predicate expression consisting of two units of independent meaning. Aristotle apparently wanted to eliminate complex expressions from his notion of rhema, yet we can accomplish this without insisting that a rhema must consist of a single word.

Simple existential modifiers and predicate expressions can be distinguished from more complex expressions by demanding that there be at most one predicate. The predicate names an entity ontologically predicated of some (unspecified) subject. The only way to indicate that an entity is a predicate is to include some explicit or implicit existential modifier (e.g., ‘is’, ‘is not’, ‘may be,’ ‘was’). These two necessary components of a predicate expression—the name of the predicable entity and the existential mode—constitute a simple expression or rhema when the predicate name is a single word, though the existential mode may be indicated by auxiliary words. In simple ontological affirmations, the rhema would consist of nothing more than the existential modifier.

The necessity of at least an implicit existential modifier in a predicate expression is often overlooked in modern symbolic logic, which represents ‘x is P’ as ‘P(x),’ as though the meaning of the copula ‘is’ could be discarded. In fact, our understanding of expressions such as ‘P(x)’ as propositions necessarily require an assertion of being, or else nothing would be proposed, and we would simply have two juxtaposed concepts, “P” and “x,” with no sense of what their relationship to one another would be. The logic of P(x) is different, for example, if we consider it to mean “x is potentially P” rather than “x is actually P.” In the first case, it is no contradiction to say P(x) and Q(x) are both true when Q is the complement of P, but it would be a contradiction in the second case.

Condition (3), the claim that a rhema must indicate time, does not appear to hold up well in non-European languages. In Mandarin Chinese, there is no past, present or future tense. Time may be indicated by an adverbial term, but this is optional. It would seem then, that time specification is not essential to a verb, nor to predicate expressions in general. Curiously, Aristotle regards only the present tense as a rhema, while the past and future are merely tenses of a rhema, just as non-nominative cases of nouns are not nouns. However, the non-nominative cases are not nouns because they fail to name a subject, which is the essential function of a noun. It is far less clear that the essential function of a rhema should be to declare the present.

While Chinese verbs do not have tense, they do have three aspects (sometimes improperly called moods): ongoing, completed, and experiential. In many Western languages, the ongoing and experiential aspects are combined in a single “imperfect” aspect, while completed actions are signified by the “perfect” aspect (e.g., the Spanish pretérito and the French passé complête). These aspects may also characterize the action as progressive, habitual or punctual. In highly inflected languages, each aspect of a verb may have a past, present, and future tense, greatly complicating conjugation. In grammatically simpler languages such as Russian, verb forms signify both tense and aspect simultaneously. This may also have been the case with ancient Hebrew verbs, which have only two forms, yiqtol and qatal. These are commonly referred to as ‘imperfect’ and ‘perfect,’ as though they were purely aspective in significance, denoting incomplete and completed action regardless of time. A more careful study of Biblical Hebrew usage suggests that verb forms also carried a significance of tense, though perhaps not distinguishing present and future. A foray into historical linguistics is outside the scope of our inquiry, so it suffices to observe that there is no linguistic or logical obstacle to having a verb signify both aspect and tense.

Mood in the formal linguistic sense is a kind of modality, where modality is any expression concerned with possibility and necessity. Mood specifically treats the modality of verbs insofar as they affect the character of the statement. Perhaps the simplest mood is that of a statement declaring what one proposes as true (at least hypothetically). This is the indicative mood, which characterizes simple affirmations and negations of what “is” and “is not.” The subjunctive mood is more subtle, existing only in complex sentences, and signifying the modal relationship between what is represented by a dependent clause and by the main verb. For example, in the sentence, ‘If I were rich, I would not work,’ the subjunctive ‘were’ signifies that we are not asserting that I am rich nor that I am even likely to become rich, but only making a supposition for the purpose of articulating what I would do or not do in that scenario. The subjunctive in many languages also encompasses expressions of desire and exhortation, which may be distinguished as the optative and cohortative moods. Another common mood is the conditional, which in English uses the auxiliary ‘would,’ showing that the verb does not assert the existence of an action, save on some condition to be specified in a dependent clause. Yet another mood is the imperative, expressing a command. The moods basically signify how the sentence or verb clause as a whole is to be understood, as a statement of fact, a plea, a suggestion, et cetera, or in a word, its modality.

Verbs may also have active or passive voice, denoting the relation between the action and the subject. Active voice signifies that the subject performs the action (e.g., ‘The dog ran’), while passive voice means that the subject receives the action (e.g., ‘John was expelled’). A passive verb simply signifies the inverse of an action, which is also an action. When the verb is transitive, representing an action between two entities, with one acting and the other acted upon, the active voice sentence ‘X expelled Y’ represents a statement logically equivalent to that signified by ‘Y was expelled by X.’ Passive voice is discouraged by grammarians for a sound logical reason: ‘John was expelled,’ is indeterminate. It is of the form ‘Y was expelled,’ being equivalent to ‘expelled Y’, which is logically incomplete. An action can only have an inverse if it has both a subject and an object, so the passive voice is properly expressed only when we give both. ‘John was expelled by the headmaster,’ should satisfy both the logician and the grammarian.

Which of these qualities—tense, aspect, mood, voice—are essential to a rhema? Aristotle proposes that tense is essential, and that only the present tense is proper to a rhema. We have noted that Chinese does not declare tense explicitly in the structure of a verb, nor even necessarily with an adverbial helper, yet tense may be understood from context. Is it even intelligible to have a statement or a rhema where no tense is at least implied? Consider a tenseless expression with no context to indicate time: ‘Confucius speak,’ where ‘speak’ is an atemporal verb form. If we do not know the tense, we cannot know if we are asserting “Confucius spoke,” or “Confucius speaks.” “Confucius spoke” is consistent with the negation of “Confucius speaks,” i.e., “Confucius does not speak,” so without tense we cannot distinguish whether ‘Confucius speak’ affirms “Confucius speaks,” or its negation. The atemporal expression ‘Confucius speak’ could mean “Confucius speaks or Confucius spoke or Confucius will speak” (assuming indicative mood), which leaves aspect and mode indeterminate, since without tense we have no way of knowing if the action is complete or incomplete, potential or actual. How, then, can this expression be said to affirm anything? It would appear to be nothing more than a juxtaposition of concepts: “Confucius” and the action “speak.” Without at least an implied tense, we cannot constitute an affirmative (or negative) statement of action. This is unsurprising, since time is the medium of action. By extension, if we remove the subject noun ‘Confucius,’ what remains (‘speak’) cannot be a full rhema (a sentence with indeterminate subject). Therefore a rhema does require at least an implicit tense. This can be provided by context, or by assumption (e.g., if time is unspecified, assume the present tense). When tense is explicitly indicated, it need not be as part of the verb, but could come in the form of an adverb, or, as in Japanese, adjectives can be inflected to show time.

Aspect is not essential to a rhema, for we can still have an intelligible assertion without knowing if the action is complete or incomplete. English often fails to distinguish the imperfect and perfect past, but this does not render statements unintelligible. In fact, it would seem that a declared or implied aspect is necessary only insofar as it helps to specify tense. If we said, ‘George cut the tree,’ without indicating in any way if this complete action takes place in the past or the future, we have no way of knowing the modality of the action (potential or actual) and encounter the same problems mentioned above. When the declaration of aspect is also understood to entail some specification of tense, as in Russian, then we can resolve modality and the statement becomes well-defined.

Mood and voice are essential to a rhema. At least an implied mood is necessary for a sentence to represent a well-defined statement. If we do not know whether ‘Socrates walk’ means “Socrates walks” (indicative mood) or “Socrates, walk!” (imperative mood), we cannot regard the expression as an intelligible sentence. Thus ‘walk’ cannot be a rhema unless the mood is specified. Voice is necessary only for statements whose (transitive) verb denotes an action that has an inverse. We generally assume active voice by default, and use a special construction for passive voice, since the latter is defined by inversion of the former.

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7. ‘To Be’ and the Ens Copulae

Thus far there would seem to be two essential components to a sentence representing a well-defined statement: a noun representing a subject, and a predicate or verb phrase specifying some modification of the subject’s being that is affirmed. When this phrase includes an explicit action verb, it needs to indicate time through a formally declared tense or by implication, as well as mood and voice when applicable. How then, do we treat those predicates that do not have action verbs?

In English, as in many Western languages, simple predicates use the ens copulae, exemplified by the ‘is’ in ‘The sky is blue.’ ‘To be’ is grammatically a verb, with grammatical tense, aspect, and mood, so it supplies the necessary linguistic qualities that an action verb would provide for the expression of a statement. However, “being” is not an action, so we should not assume that the logic behind ‘to be’ is the same as that for action verbs, notwithstanding their grammatical similarity.

Modern symbolic logic discards the ens copulae, typically representing ‘x is P’ as ‘P(x)’. As we have noted previously, this does not eliminate the ‘is’, for it is incorporated in our understanding of what ‘P(x)’ means, if it is to truly represent a statement and not just juxtaposed concepts. The logic behind ‘x is P’ may vary depending on what kind of predicate P is. We recognize this to some extent in our grammar, by distinguishing predicative nominatives from predicate adjectives. In Mandarin Chinese, the copula shi (“to be”) is used only if P is a noun, but not when it is an adjective. In Latin and Greek, predicate nominatives use the nominative case, rather than the accusative, which is used for the object of an action. Thus the ancient languages recognize that “being” is not an action that one entity “does” to another.

What, then, is the logical function of the ens copulae? Without it, we could construct expressions where the grammatical and logical structure is understood from the order of declaration, just as in symbolic logic ‘P(x)’ is not the same as ‘x(P)’. We could say, for example, ‘Me Tarzan,’ and, ‘You Jane,’ where these expressions are understood to first declare a noun (or pronoun in these cases) and then to propose a second name that is applicable to the subject of the first name: e.g., the name ‘Jane’ applies to “you.” Such a statement does not necessarily require us to think of an existential relation (e.g., “you are Jane”), so the ancient Greek, Latin, and Chinese custom of omitting the copula for predicate nominatives seems appropriate.

Some predicate nominatives, however, do more than simply apply another a label to the same object. For example, ‘Socrates man’ (Socrates anthropos) does not merely give another name for Socrates, but implies an ontological relationship between the conceptual essence “man” and the individual “Socrates.” We are declaring that the conceptual essence “man” somehow pertains to Socrates or is manifest in him. In other words, not merely the name, but the concepts that define “man” are to be found in Socrates (though there may be more to Socrates than simply being a man). A copula of some sort would seem appropriate here, to signify a distinction between these kinds of statements and simple re-labeling statements represented by ‘Me Tarzan,’ and the like. Unfortunately, most languages that do use a copula here employ the same verb ‘to be’ that acts as the copula for logically dissimilar predications, such as the predicate adjective.

Predicate adjective sentences might be constructed without a copula, as ‘Sky blue’ instead of ‘The sky is blue,’ for example. This sentence means that “sky” is the subject of the quality “blue,” so “blue” is “in” the sky as in a subject; that is, blue is ontologically predicated of the sky, or “blue” is an accident of “sky.” All statements with predicate adjectives signify an ontological predication rather than an identity, since an adjective cannot represent the same object as a noun. This makes the need for an existential copula more obvious, which is perhaps why even Chinese uses a copula for predicate adjectives.

We should take care, however, to distinguish the predicate adjective copula from that of the predicate nominative. In the sentence, ‘I am Tarzan,’ the copula ‘am’ signifies identity, meaning the same object is named by both nouns. In the sentence, ‘George is [a] man,’ the word ‘is’ does not signify identity, but an ontological relationship whereby the conceptual essence “man” pertains to George. When we say, ‘George is tall,’ the word ‘is’ signifies a different kind of ontological relationship, whereby ‘tall’ is ontologically predicated of George as a subject. We explored the difference between the universal-individual and substance-accident axes of the ontological square at length in our previous work. It is unfortunate that most languages use the same copula for both kinds of logical relationships, which can easily lead to confusion. It is hardly less equivocal, however, to abolish the copula altogether, since that would leave us without any distinction among these kinds of predications.

In English, unlike Greek or Latin, we distinguish predicate nominatives from identities by introducing the indefinite article, saying, e.g., ‘George is a man.’ The indefinite article signifies that we are dealing with an individual-universal or species-genus relationship, not declaring an equivalence between two names. The use of an article, nonetheless, has the unfortunate effect of conflating instantiation of an essence with being a member of a collection of objects; an error that has plagued modern logic in the English-speaking world.

Creating further ambiguity, the word ‘to be’ can also be used in simple ontological affirmations. In classical Greek, the same word is used both as the ens copulae and to signify “exist.” Thus the same verb is used in ‘Man is good’ (Anthropos esti agathos) and ‘Man exists’ (Anthropos esti). In English, it sounds awkward to say ‘Man is,’ as we use ‘to be’ only in a copulative way with some predicate, if only an implied predicate. For example, in reply to, ‘Were you sick yesterday?’, one may reply, ‘Yes I was [sick]’, where the unspoken predicate ‘sick’ is only implied.

Expressions of the form ‘X is’ do not represent affirmations if X is an inflected noun. This is because inflections other than the nominative case do not represent subjects. Thus ‘is of Socrates’ (genitive case) and ‘is to Callias’ (accusative case) are not affirmations.

Many languages omit the copulative ‘is’ in predicate statements, possibly leading one to think that ‘is’ is logically superfluous, and that ‘X is’ says no more than ‘X’. However, if logic is to deal with potential realities, we must distinguish between what “is” and “is not.” Existence or being is the very object of logic, though it is not a category or entity, i.e., a thing that exists. Existence or being is pre-categorical, which is why any term by which we represent it seems inadequate, for a name reifies an idea as an entity, but existence is not an entity. It is not a substance, though ‘existence’ is a noun; it is not an action, though ‘to be’ is a verb. Yet though existence is no thing, it is not nothing. When we say ‘X is,’ we should not understand ‘is’ as some substance or accident superadded to X, nor is it an action that X does, since action is an accident. Nonetheless, “being,” far from being superfluous to an affirmation, is essential, for without it we affirm nothing.

If I declare the name ‘John’ without providing any context whatsoever, I have not made any intelligible affirmation. The hearer may recognize that ‘John’ is often used as a name for various people, but will have no idea whom I intend. When I gesture toward a person and declare ‘John,’ it may be understood that I am affirming that this person is named ‘John.’ I am declaring a relationship between an ontological object and a linguistic object, yet such a relationship is unintelligible if we do not consider both objects as truly being. A man could hardly be named ‘John’ if either he or the name is not regarded as existing in any sense. When we affirm statements about objects, we declare their reality on some level, if only hypothetical. Without a verb representing “to be,” it must be understood from context if we declare being indicatively, conditionally, et cetera. Otherwise, one could not know if I am declaring that someone is named ‘John’ or giving John an order or expressing a wish that this were John. The necessity of intending being is even more evident when I point at someone and declare ‘man’, for this requires one who understands what “man” means to apply that meaning to an object distinct from the concept. Here we are relating two non-linguistic objects, so we are not declaring a linguistic relationship, but a relationship of being, making it eminently necessary that both objects be considered as being (or not-being, if there is a negation) on some level.

That which seems linguistically most superfluous, being, is logically most essential. We can omit to have a distinct word signifying being, but we cannot omit to intend its meaning, or we will not have a statement. Every statement must indicate being, and to be well-defined, it must indicate the modality of being that is asserted. It is not always necessary to have a distinct term like a copula to indicate being, but the meaning must at least be implied. In sentences with action verbs, the verb specifies the modality of being through its mood, as well as through tense and aspect. If there is no action verb to specify the modality of being, as in predicate nominative, predicate adjective, and simple ontological assertions, we need to do so by some other means.

It is only natural that we should represent modalities of being as a verb (‘to be’), since we are accustomed to representing modalities of being through action verbs. As long as we avoid the error of supposing that being is an action, it seems perfectly safe to use ‘to be’ to perform this function, though we must take care to note that ‘to be’ means different things in ‘Socrates is a man,’ ‘Man is an animal,’ ‘Socrates is Athenian,’ and ‘Socrates is.’ I have already examined these differences at length in my Introduction to Ontological Categories (Part I).

A predicate nominative or adjective, to be well-defined, requires tense and mood, just like any other rhema, at least when the subject is a time-contingent being. If it is not time-contingent, only mood is required. When dealing with action verbs, we always needed tense in our rhema because action is by definition time-contingent. By time-contingent, I only mean capable of change with respect to the predicate described. ‘A triangle is a polygon’ is not time-contingent, so it may be said in an atemporal sense, as is the case with ‘Man is an animal,’ if we regard “man” and “animal” as conceptual universals (rather than collections of objects). Voice is not applicable to predicate nominatives or adjectives.

Some aspects of action verbs use ‘to be’ as an auxiliary; this is not without logical justification. In the progressive aspect of most European languages, we say someone ‘is walking,’ using ‘to be’ as an auxiliary verb. We regard “being” as most eminently actual in the present, which explains why Aristotle thought a rhema should be in the present tense. When we say that something truly “was,” we mean that at some point in the past, it could have been said that it truly “is.” We can emphasize this point by using ‘to be’ in the past progressive tense-aspect, e.g., ‘was walking.’ To regard a past action as if it were ongoing is to regard the past as though it were the present. The same is true of ‘will be walking’; we are considering the future as though it were the present.

‘To be’ is implicit in all action verbs. Specification of tense, aspect, mood, and voice, are all modifications of being. Such specification is essential to affirming, as opposed to merely naming, an action, so ‘to be’ is essential to the affirmative function of action verbs. When we discussed the features of action verbs, we were really discussing ‘to be’ all along. Aristotle is therefore correct to say that intending “is” or “is not” is essential to a rhema, since these meanings are contained even in action verbs or predicate statements where ‘to be’ is not given a separate word.

Tense, aspect, mood, and voice can be signified in an action verb not only by inflections and adverbs, but also by the use of ‘to be’ as an auxiliary verb. We have just seen this usage with the progressive aspect above, and it could also be used for other aspects. In the past participle form of the perfect aspect, many European languages use ‘to have’ as an auxiliary, but there are exceptions. In French, the passé composé of aller uses ‘to be’ as an auxiliary, so “I have gone” in French is je suis allé, literally, “I am gone.” The same is true for the verbs mourir (“to die”) and naître (“to be born”). The irregular construction of these verbs perhaps owes to the fact that these verbs suggest a stronger identity between subject and action, so that the action is not separable from the subject’s being. For this reason, the auxiliary ‘to be’ seems more appropriate than ‘to have’. Nonetheless, ‘to be’ in this auxiliary sense has a distinct function from the verb in the simple assertion ‘I am,’ or ‘I exist.’

Syntactically, use of ‘to be’ as an auxiliary verb treats the main verb as though it were a predicate adjective. ‘I am walking,’ treats the verb ‘walking’ as an adjective predicated of ‘I’. The difference between ‘I walk’ and ‘I am walking,’ aside from the progressive aspect contained in the latter, is that in the latter sentence the existential relation is brought out more explicitly, so we see that walking is an accident of the person represented as ‘I’, and modifies the being of that person. In the sentence, ‘I walk,’ the existential modification is built into the verb ‘walk,’ so there is no need to state it explicitly. Either construction is logically cogent. An action is a kind of accident, so it may be represented as a predicate adjective, yet it also has different modes of being, which we can represent by tense, aspect, mood, and voice without resorting to a copula.

‘To be’ is also used in English and other languages as an auxiliary for the passive voice. We say, for example, ‘Caesar worships,’ in the active voice, and ‘Caesar is worshipped,’ in the passive voice. The use of the auxiliary ‘to be’ to signify the passive is not necessary. In Latin, the passive is denoted by a special inflected form, adoratur in the present example. When an auxiliary is used, as in English, the main verb becomes a predicate adjective, with the same form as the simple past tense. The use of the past tense perhaps serves to indicate that the subject is temporally posterior to the action, since it is the recipient of the action. Thus, in ‘Caesar is worshipped,’ though the auxiliary ‘to be’ is conjugated in the present tense, since we are speaking of Caesar’s present state, we nonetheless put ‘worshipped’ in the past tense, to show that Caesar is the recipient of the action, and therefore posterior to it. Such use of the past tense is of course imprecise, since the act of worship is also taking place in the present. The term ‘worshipped’ in the passive construction therefore should not be understood to mean the same thing as ‘worshipped’ in the active voice (e.g. ‘Caesar worshipped’). For past passive and future passive, we retain the use of the past tense for the main verb: ‘Caesar was worshipped,’ ‘Caesar will be worshipped.’ The term ‘worshipped’ does not denote tense, but functions as a predicate adjective, hence it has a distinct grammatical name: ‘past participle.’

Continue to Part II


© 2007-2009, 2012 Daniel J. Castellano. All rights reserved.
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