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Logic and Language

Daniel J. Castellano

(2009)

Part I: Logical Functions of Linguistic Elements
Part II: Propositions
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

Part III: Non-Indicative Moods

17. Possibility and Impossibility

Thus far we have spoken of affirmative and negative propositions, which declare the presence or absence of ontological relationships, corresponding to evaluations of truth and falsity. Not all statements reflect this simple dichotomy; in actual conversation, we often declare that we regard a certain affirmation as more or less probable or improbable, even impossible. We are qualifying our position with respect to the proposition’s content as something other than unequivocal affirmation or denial. Our full statement may be considered to be composed of an affirmative or negative proposition and the probabilistic modality imposed upon it. Medieval philosophers identified these components of a probabilistic modal statement as the dictum and the modus. As an example:

It is possible that Socrates is a white man.

Here the modus is represented as ‘It is possible’ and the dictum is written ‘Socrates is a white man.’ The dictum is always some affirmation or negation, but the statement as a whole has the modus as its principal declaration, modifying the dictum. The simplest probabilistic modes are “it is possible” and “it is impossible.” Applying these modes to affirmative or negative propositions, we come up with the four modal statements labeled by medieval philosophers as A, E, I, and U.

ModusDictumExample
AAffirmativeAffirmativeIt is possible that Socrates is a white man.
EAffirmativeNegativeIt is possible that Socrates is not a white man.
INegativeAffirmativeIt is impossible that Socrates is a white man.
UNegativeNegativeIt is impossible that Socrates is not a white man.

In all these statements, the dictum is subordinate to the modus. In many languages, this is signified by the use of the subjunctive for the dictum, especially when it or the modus is negative, thereby signifying doubt. The effect of each statement on the modus and the dictum is expressed by this saying of St. Thomas Aquinas:

Destruit U totum, sed A confirmat utrumque,
Destruit E dictum, destruit Ique modum.

That is, U destroys everything, but A confirms both; E destroys the dictum, and I destroys the modus. The Jesuit philosopher Pedro da Fonseca (1528-99) put it even more pithily:

E dictum negat Ique modum,
Nihil A, sed U totum.

In these sayings, both the modus and the dictum are considered in the affirmative sense, which may be confirmed or denied by a statement. Thus the modus that is denied by U is, “It is possible,” and the dictum that is denied by U is, “Socrates is a white man.”

In all modal statements, the dictum is subordinate to the modus, which has the last word, so to speak, about the overall meaning of the sentence. In other words, we first take the sense of the dictum (affirmative or negative), and then apply the modus to it. When the dictum is in the same sense in two statements with opposite modes, the statements are contradictory. Statement I is the negation of A, and U is the negation of E, since the modus of one negates the other, and the modus contains the primary rhema of the statement.

The modal statements have implicative relationships with the simple indicative statements corresponding to the dicta. In our example above, the indicative statements would be “Socrates is a white man” (P), and its negation “Socrates is not a white man” (~P). We can easily see that P implies A, ~P implies E, I implies ~P, and U implies P. By inference, U implies A and I implies E.

The statements A and E do not imply the truth or falsity of P, but they do declare something about the truth value of P. A affirms that P could be true in some circumstances, perhaps even in all circumstances. E asserts that P could be false in some circumstances, perhaps even in all circumstances. When both A and E are declared, we can no longer allow that P is true in all circumstances, nor that P is false in all circumstances. This pair of statements declares that P is contingently true (or false).

The statements I and U imply something stronger than merely ~P and P respectively. They declare that ~P (or P) must be true in any circumstances whatsoever. In other words, statement I declares that P is necessarily false, and U declares that P is necessarily true.

These statements have allowed us to define necessary and contingent dicta or propositions. “A AND E” declares a dictum to be contingently true; “I” declares it to be necessarily false; and “U” declares it to be necessarily true. Our understanding of ‘necessary’ and ‘contingent’ depends on our understanding of ‘possible’ and ‘impossible’, which can have several meanings.

The broadest sense of ‘possible” is “logically possible,” meaning that the truth of the dictum does not entail any intrinsic logical incoherence or imply a contradiction. I often refer to this as ‘conceivable’, though this term may admit of a narrower sense, signifying that which is imaginable to the human mind as possible. ‘Possible’ may also refer to “metaphysically possible,” that which does not contradict any established principle of metaphysics, or “physically possible,” that which does not contradict any principle of nature. Physical possibility may more specifically mean possible for some agent, i.e., some agent has the power to perform the prescribed act. It is the Latin term for “power” or “ability” that is the root of our term ‘possible’. Since we are discussing a priori logic, we are principally concerned with logical possibility. In this sense, as with all senses, ‘possible’ means that which we can admit as true within some scope. We can give a formal definition of “possible” that could be applied to all of the senses described.

A dictum D is possible in some theory X if and only if the truth of D is consistent with X.

For logical possibility, X is null, or simply the axioms of logic. For metaphysical or physical possibility, X is the relevant metaphysical or physical theory. ‘Impossible’ simply means “not possible,” so, “It is impossible that D” denies, “It is possible that D.” The negative mode negates the affirmative mode, so when the dictum is the same, the statements negate one another. Thus we have seen that A contradicts E and I contradicts U. For every dictum D, we can conceivably say that it is necessary, contingent or impossible in some theory X.

Properly speaking, it is not the dictum that is necessary, contingent, or impossible, but the reality it signifies. The dictum is always a proposition, so it is the ontological relationship signified by the proposition that is to be regarded as necessary, contingent or impossible. Nonetheless, we may speak of propositions as having these three attributes by correspondence with the realities they signify.

A proposition is logically necessary when it is implied by the logical axioms, or its negation implies a contradiction. In this case, it is necessary that the proposition should be true, and the force of this necessity is grounded in the veracity of the logical axioms. A proposition is metaphysically necessary when it is implied by the principles of some metaphysical theory, or its negation contradicts those principles. If the principles are true, then the proposition must be true, and its necessity is derived from whatever causes the metaphysical principles to be true. Once we descend from logical to metaphysical necessity, the concept of necessity entails some sort of causality, insofar as the reality of one metaphysical structure (represented by a theory) rather than another requires some cause. The same is true of physical necessity, for the principles of physics are not tautologies, so that which is physically necessary must appeal to the same metaphysical agency that caused the natural order to be this way rather than some other way.

That which is possible, yet not necessary, is said to be contingent. A logically contingent proposition does not contradict the logical axioms, but it may be true in some circumstances. If we make a particular assumption, the proposition may be regarded as true, so the truth of the proposition is contingent upon some assumption. A metaphysically contingent proposition is not necessarily implied by the principles of metaphysics, so some contingency beyond these principles needs to be assumed in order for the proposition to be true. Since metaphysics deals with reality, the contingency must be some real set of circumstances not specified by our metaphysical theory alone. Thus the truth of the proposition depends on such circumstances, which we may call a necessary condition of the proposition P. Similarly, a physically contingent proposition requires some particular physical state (or range of states) to occur in order the proposition to be true. This state would be the necessary condition of the proposition.

The concepts of possible, impossible, necessary and contingent may be applied to statements where the dictum is a simple ontological affirmation of the form ‘X is’ or ‘X exists’, or its negation, ‘X is not’ or ‘X does not exist.’ ‘Possible’ and ‘impossible’ are simple enough to understand for these dicta; we are asking whether the being of some entity entails a logical contradiction. As long as an entity is coherently defined, it is logically possible or conceivable. Metaphysical or physical possibility, by contrast, depends additionally on consistency with the principles of some metaphysical or physical order. Just because something is conceivable, that does not mean it is possible in reality.

It is highly doubtful that there is any entity that is logically necessary. The logical axioms do not represent entities, nor do they seem to imply the being of any entity in one of the four ontological classes. Logic only considers what is hypothetical or conceivable, not what truly exists. The distinction between necessary and contingent breaks down for ontological assertions with respect to logic, since there is no distinction between “necessarily conceivable” and “contingently conceivable.”

This is not the case with respect to metaphysics and physics, which do deal with entities that actually exist or might not exist. Here a necessary being is one that absolutely must exist, according to the principles of metaphysics or physics. In other words, there is no metaphysically or physically possible scenario where that being would not exist. Both A and U hold where the dictum is ‘X is’. God has been posited by many philosophers as a metaphysically necessary being, indeed the only necessary being. The arguments for this position need not concern us here, but we should note that this necessity is not logical necessity, so any counter-argument that would show it is logically possible for God not to exist misses the point.

It is tempting to express “necessary,” “contingent,” and “impossible” as numerical probabilities. “Necessary” would correspond to probability 1, “impossible” to probability 0, and “contingent” to any fractional probability between 0 and 1. While that which is regarded as impossible must certainly be assigned a probability of 0, there are problems with the other characterizations. “X is necessary” entails U: “It is impossible that ~X.” Even an infinitesimal possibility of ~X would contradict U, as is especially evident in the case of logical possibility. There are many mathematical propositions that would have a measure-theoretic probability of 1 yet are not logically necessary. For example, the probability that a real number is irrational is 1, yet it is clearly conceivable for a real number to be rational. Similarly, the probability that a real number is rational is 0, though it is possible for a real number to be rational.

Probability theory introduces concepts of frequentism, potentiality, and random sampling that may or may not be valid. At any rate, they pertain to studies such as mathematics, physics, metaphysics, even psychology, but not pure logic. From a logical standpoint, we can only clearly define possible and impossible, necessary and contingent. Human language does allow for such modes as “probable,” “improbable,” “likely” or “unlikely” to express our own subjective quantification of the probability. These assessments can be based on our past experience, our understanding of how the world works, or our estimate of the number of contingencies necessary for an event to occur. Since these assessments can mix and match many theoretical factors, we cannot give a simple logical account of them, and reserve such discussion for work on probability theory.

Lastly, we may consider the distinction between a declaration of impossibility and a declaration of falsity. When we say, “It is impossible that D” (statement ‘I’), we do more than simply declare D to be false. We are saying that, not only is it actually the case that D is false, but D could not be true in any circumstances within the theory we are considering. A declaration of impossibility (necessarily false) is the contrary of a declaration of necessity (of truth). Thus U and I are contrary statements.

Declarations of necessity or impossibility, i.e., of what “must be” or “must not be,” correspond to what Kant called apodictic judgments. Statements of possibility that do not determine the truth value of a proposition (A and E) are called problematic judgments by Kant, while affirmations and denials are called assertoric judgments. In every case, the modality relates to the determination of logical truth and falsity, so Kant is not guilty of confusing epistemology and logic here. More importantly, he recognizes that the modality of a statement is something extrinsic to the syntax of the dictum. This is why the modus of a judgment ought not to be represented by an operator (as is done in symbolic logic), as if to say the modus itself could be part of some dictum. There is no added meaning in, ‘It is possible that it is possible…,’ any more than in, ‘I affirm that I affirm….’ If we keep in mind that mood is extrinsic to the syntax of a dictum, we will avoid many of the self-referential pseudo-paradoxes of modern logic.

In the foregoing discussion, I have assumed that “possible” does not exclude “necessary.” This is a departure from the convention of Aristotelians, who held that “X is possible” logically implies “X is not necessary.” This unfortunate convention leads to inconsistencies with the notion (also admitted by Aristotle) that “possible” is logically equivalent with “admissible.” We clearly can admit the truth of a necessary proposition, so it is admissible and therefore possible.

We could have validly defined “possible” as excluding “necessary,” but this convention would lead to some counterintuitive consequences. First, the A-E-I-U model would lose much of its value as defining independent modal statements. A would imply E, and E would imply A. Further, modal statement ‘I’ would imply that the negation of the dictum is necessary, which implies the negation of E. U would imply that the affirmation of the dictum is necessary, which implies the negation of A. Strangest of all, we would have to admit a distinction between “not possible” and “impossible,” since “necessary” is now classified as “not possible,” though it is clearly not impossible. This confusing syntax would be in sharp disagreement with ordinary usage, and could easily lead us astray without adding any real logical content. Instead, we have chosen to use the term ‘contingent’ to define that class of “possible” that excludes necessity.

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18. Conditional Mood

The notion of contingency introduced by modal logic makes possible another type of mood, which we call the conditional. In English, this is typically expressed in the form, ‘If P, then Q’, where P and Q are propositions. The copula ‘to be’ receives a special conjugation in each clause. The subjunctive is used in P, and the conditional in Q. For example: ‘If I were rich, then I would not work.’ The clause ‘If I were rich,rsquo; represents the condition upon which ‘I would not work’ would be true. When we defined contingent propositions, we said that these are true only in some circumstances, but not all. A conditional statement provides a means of identifying some of those circumstances where a contingent proposition is true.

A conditional statement of the form ‘If P, then Q’ does not declare Q to be true. Rather, it proposes P as a supposition (which is not declared to be true or false, hence the use of the subjunctive), and declares that if P were true, then Q would be true. The auxiliary ‘would’ modifies ‘to be’, so that the declaration of being is made contingent upon the supposition, which itself is uncertain. The uncertainty of P’s truth implies a similar uncertainty regarding Q, yet we do know that if P were true, then Q would certainly be true.

In modern symbolic logic, conditional statements are represented as the so-called “material implication,” or ‘P→Q’. The connective ‘→’ is defined by the following truth table:

PQP→Q
TTT
TFF
FTT
FFT

It should be evident from this table that “material implication” is a considerably broader relationship than that expressed by conditional statements. This truth table would correspond to a consistency table for conditional statements. For example, P being false and Q being true does not contradict “if P, then Q,” but neither does it confirm it. The same is the case when both P and Q are false. A more accurate truth table for conditional statements would be:

PQIf P then Q
TTT
TFF
FT ?
FF ?

It is a mistaken endeavor to try to define conditional statements with the same binary truth tables used for the connectives ‘AND’, ‘OR’, and ‘NOT’, since we can only assume well-defined truth and falsity for indicative statements. Conditional statements are of a different mood, and do not have well-defined truth or falsity in their component propositions. Even in the case that confirms the conditional statement, where both P and Q are true, we are not really defining a conditional statement, since a conditional statement does not involve an assertion that P and Q are true, but only considers P (and hence Q) as a supposition, whose actual truth value is regarded as uncertain. This modal distinction is lost in binary truth tables. Material implication may be a useful concept in mathematics, computer science, and even logic, but it should not be confused with conditional statements (nor with logical implication or inference).

Conditional statements are semantically distinct from logical implication or inference, a truth that is obscured by the fact that we use similar grammatical forms for these. ‘If P, then Q,’ considered purely as a conditional statement, does not state that Q is a logical consequence of P, much less a metaphysical or physical effect, though we often use the same ‘if…then…’ syntax to express these types of relationships as well. As a conditional statement, ‘If P, then Q’ simply means that Q would be true in every scenario where P is true, but we are not saying why this is so. Logical implication carries the additional claim that Q is necessarily true by virtue of P being true; that is to say, the truth of Q follows by logical necessity from the logical content of P. “P implies Q” does have the same truth table as “If P then Q,” but there is more to logical relationships than truth values. With logical implication, the meaning of Q is analytically “built into” P, so to speak. With conditional statements, on the other hand, we are declaring nothing about the intrinsic logical structure of P or Q and how these relate to one another. Rather we are simply saying that Q is true in all circumstances when P is true. Consider the following example:

‘If I were a dog, I would be an animal.’

Considered as a purely conditional statement, this sentence means that in any scenario where I am a dog, I would also be an animal, yet the sentence does not say why this is so, only that it is so. What do we mean by “any scenario”? The range of “any” depends on whether we are speaking of logical, metaphysical, or physical possibility. In ordinary language, this may be understood from context or immaterial to the discussion, but in a formal logic, we will want to explicitly indicate this range. Here the sentence will hold even if we mean all logically conceivable possibilities, which means this conditional statement is logically equivalent to “I am a dog → I am an animal.” The logical implication is distinct from the conditional statement in that the former explicitly declares that “I am an animal” is a logical consequence of “I am a dog,” and further, the mood is different, since we do not consider “I am a dog” with subjunctive uncertainty, but as a working assumption declared indicatively. Since we are dealing in the realm of pure logic, there is no distinction between the hypothetical and the actual.

The distinction between conditional statements and logical implication may seem overly subtle when dealing with a priori logical possibility, but the necessity of this distinction is more clearly brought out with metaphysical and physical conditional statements.

If God were to have attributes, He would be composite.

If a solid object could float in water, its substance would be less dense than water.

The first statement is not a matter of logical necessity, for we must assume that there is always a real metaphysical distinction between an essence and an attribute. This conditional statement is equivalent to logical implication only if we further introduce a particular metaphysical thesis into our assumptions. (Actually, this would be an inference, but we are not presently concerned with the distinction between logical implication and inference.)

The second statement, similarly, requires the additional assumption of a physical thesis in order for it to have the strength of logical implication (or rather, inference).

Conditional statements are further distinguished from logical implication in that the former can be erroneous, or even subjective. A purported logical implication that is false is no true implication at all, yet a false conditional statement still is truly a conditional statement. It may be erroneous because the condition is only something uncertain, and there need not be any link of necessity between clauses. For example:

‘If I were rich, then I would not work.’

There is no logical, metaphysical, or physical necessity that a rich person should not work; I am simply declaring my intent as to what I would do in that condition. This statement can be verified or falsified only if the condition becomes actual. If I should become rich, then we could see whether or not I indeed stopped working. I might change my mind, or I might have misjudged social circumstances (perhaps I would still be required to work by law). Such misjudgment did not involve any logical error in the above statement, since it does not affirm any logical necessity, but only makes a subjective judgment as to what I would do in a hypothetical circumstance.

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19. Interrogative Mood

The interrogative mood does not express a judgment, but rather solicits a judgment from the person addressed. It is tempting, therefore, to follow Aristotle in relegating this mood to the domain of rhetoric, yet even questions must have logical constraints.

The simplest way to form an interrogative is to take a proposition (“x is P”) and impose a querying tone (“x is P?”). With an interrogative mood, we at once seem to declare doubt about the proposition’s truth status and solicit a judgment from whoever hears. Doubt is not essential, since we may ask a question simply to determine what someone else thinks, even if we are already convinced of the correct answer. The interrogative is distinguished from other statements in that it is directed to the judgment of the hearer rather than the declarer. We may ask questions to ourselves, of course, but they are directed to our judgment qua hearer, not qua declarer. The interrogative looks for judgment beyond itself, so it supposes the possibility of communication. This is why it necessarily has a rhetorical dimension, yet there are logical limits to how we may solicit a judgment.

The simple interrogative proposition (“x is P?” or “Is x P?”) seems to demand an affirmative or negative judgment (“yes” or “no”) regarding the proposition, yet other responses are possible. We may reply “It is possible that x is P,” or “It is not possible…,” or with the other modalities discussed, including subjective assessments such as “likely” or “unlikely.” We may even impose a condition to our assent or denial: “If Q, then x is P.” Lastly, we may disclaim any insight to the matter, giving a null response such as “I don’t know.”

Another class of questions is more open-ended, soliciting not a judgment about an already formed proposition, but to complete a statement whose subject or predicate is unknown. These questions use interrogative words, such as ‘who’, ‘what’, ‘when,’ and ‘where’. We will examine each of these below.

Questions asking “What?” solicit an answer that represents a substance or quality meeting some specified criteria. The question “What is the color of my tie?” asks us to supply the quality X where “X is the color of my tie.” Similarly, “What is the tallest mountain in the world?” asks us to identify a substance Y such that “Y is the tallest mountain in the world.” The interrogative term ‘what’ syntactically resembles a variable (X or Y), and the interrogative mood solicits a determinate entity in place of that variable. (This is less evident in other phrasings of questions. For example, we may say, “What color is my tie?”, but the sentence ‘X color is my tie,’ is grammatically incorrect in English.)

The interrogative term ‘who’ is used when the answer solicited is a person. Logically, we might as well use the term ‘what’ for such questions, since a person is a substance, but most human language emphasizes the distinction between personal and impersonal subjects, probably owing in part to a sense that these involve fundamentally different kinds of agency.

The term ‘which’ in a question prompts us to a select an entity from some group or class. The question “Which Y is Z?” asks us to identify an entity X (substance or quality) that belongs to Y (as an instance of a universal, as a member of a group, or as a subgenus) and “is Z” (in one of the various senses discussed in Part II).

Questions about quantity, in most Western languages, have a particular interrogative term (e.g., Cuánto in Spanish, Combien in French). English uses the compound terms ‘how much’ and ‘how many’, for continuous and discrete quantity, respectively. The subject of a quantitative interrogative can be understood as a mathematical variable, the X in ‘How many X are there?’ This is one place in philosophical logic where the use of mathematical symbolism involves no loss of meaning.

‘Where’ solicits an account of the spatial aspects of some subject or state of affairs. If we cannot give an absolute position, we may at least give a position relative to some reference point. We may solicit “place” in any of the three Scholastic senses: locus, situs, spatium. Locus refers to some chunk of space (or a point), while situs refers to the spatial disposition of some substance within its locus. Spatium refers to the extension or distance between loci. ‘Where’ questions are ordinarily understood as soliciting the locus: ‘Where is Kenya?’, ‘Where are we?’ To solicit the situs, we may ask ‘Which way is it facing?’ or some other question to solicit spatial orientation, usually with reference to some external point. To solicit the spatium, we may ask ‘How far is it?’, though we may also give the spatium in answer to a ‘where’ question.

We may also solicit answers about place in terms of the direction of motion. ‘Whither?’ means “Toward where?”, and ‘Whence?’ means “From where?” Such questions presume a subject that is in motion. ‘Whither goest thou, Peter?’ asks for the destination of the subject’s movement. As the future is uncertain, any answer to this question cannot be a judgment of fact, but can at best state a subjective intention or a conditional or probabilistic judgment. The answer to ‘Whence?’, by contrast, can be a simple affirmative or negative judgment.

‘Whither’ and ‘Whence’ can also be used analogously for sources and destinations not related to place. They can be used to solicit the cause or effect of a subject, its source or its end. Some examples follow:

[Cause] From where (whence) does heart disease come?
[Effect] To where (whither) will the President’s policies lead?
[Source] From where (whence) did the universe originate?
[End] To where (whither) is my life headed?

None of these questions are really asking for a place, but they use place as a metaphor for cause and effect, origin and destiny. The proper form for these questions is ‘Why?’, which will be discussed further below.

‘When’ solicits an account of time. It is generally problematic to identify time absolutely, so we must establish some reference point. We may make the present our reference point, and say “two years ago,” where “year” is a measure of time based on some motion presumed to be uniform. Some past event or a potential future event might also serve as our reference point. “Eight years before the French Revolution…” and “Two months after the next presidential election…” are examples of such reference points.

We may also use the interrogative to solicit information about the derivatives of space and time, such as speed and acceleration. For this we ask “How fast?”, “How slow?” or other questions that solicit the magnitude of some intensity or a numeric quantity.

The question “Why?” is of a different character from all those preceding, since it is not necessarily asking for us to identify a subject or predicate, but to give a reason or cause for some fact, and this might not always be expressible as a simple subject or predicate. The sense of soliciting a reason is more fundamental, as our notion of causality derives from our conviction in the basic rationality of reality. The one who demands an answer to “Why?” seeks to understand this rationality, and indeed all philosophical inquiry is at its base a search for the answer to the question “Why?”, without which our knowledge would be nothing more than a collection of facts and judgments without logical connection. In a priori logic, the answer to “Why is Q?” would be P in the statement “P implies Q.” Asking “Why?” causes to follow a chain of implication (or inference) in reverse, proceeding to ever more fundamental theses.

In metaphysics and physics, the question “Why is Q?” could be understood as a search for more fundamental theses in a particular metaphysical or physical theory, or it could be searching for a determinate entity or state of affairs that results in Q being true. This entity or state of affairs is the cause of Q. The Greek term for “cause,” aition, means “blame,” signifying that the cause is responsible for the effect in question.

The question ‘How?’ has many uses, one of the most common of which is to solicit the means by which something is effected. ‘How does P effect Q?’ solicits an intermediate cause between P and Q, or a necessary condition (such as a material basis) for P to cause its effect. Another use of ‘how’ is to solicit some modality of an action, usually represented by an adverb. It may even ask for clarification of the mood of a statement: ‘How do you mean?’ The question ‘How?’, next to ‘Why?’, is arguably the most important in philosophy, and this is not counting its various rhetorical and grammatical uses, such as, ‘How much?’, ‘How come?’, ‘How do you do?’ ‘How come?’ originally meant “How did this come to be?”, but now it effectively means “Why?” This change in usage reflects some overlap between “how” and “why,” in that both may ask for causes.

Questions may explicitly solicit modal judgments, as in ‘Is it possible that X?’, or conditional judgments, as in ‘Would Q if P?’ The primary mood of such questions is still interrogative, but now we solicit a different kind of judgment regarding the proposition in question. In other words, we first take a modal or conditional judgment, and then declare it interrogatively. Let us label as M the modal judgment “It is possible that X.” Then ‘Is it possible that X?’ means “Is M?” Similarly, if we label as N the conditional judgment “If P, then Q,” then ‘Would Q if P?’ means “Is N?” The interrogative mood is superimposed over the mood of the modal or conditional judgment, so it remains the primary mood of the question.

Questions may solicit judgments about what one ought to do, as in, ‘Should I wear this dress?’ Normative judgments (“X should Y”) are really a distinct mood, commonly used in ethical evaluations, but they may also express aesthetic tastes or metaphysical convictions. Most languages do not have a distinct grammatical mood for normative judgments, using the subjunctive or conditional moods to express these. As a result, the distinction between normative judgments and other kinds of statements is not always clearly perceived. We will examine normative judgments in more depth in works on ethics and metaphysics.

The interrogative form is also used for requests: ‘Would you open the door for me?’ or ‘Could you open the door for me?’ This usage of the interrogative is partly rhetorical, for we are not really asking if the person would open the door, or if they are capable of opening the door, but are politely requesting that they do so. Such requests differ from the imperative (discussed below) in that there is no expectation of obedience, as we respect the right of the hearer to refuse. This uncertainty is expressed by using interrogative syntax and tone, which softens the austere directness of an imperative. Sometimes requests are nothing more than politely stated imperatives, but taken literally, they are true interrogatives, as they solicit the hearer’s judgment. The hearer is not necessarily asked to express this judgment in words, but in deeds, by acting or refusing to act. A request therefore presumes agency in the hearer.

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20. Imperative Mood

When a proposition is declared imperatively, the speaker intends that the hearer should make the content of the proposition a reality. An imperative statement, like an interrogative, is directed toward the hearer, but it solicits an action rather than a judgment. Imperatives are necessarily immersed in concrete reality. Although their propositional content is conceptual, the mood demands that the conceptual be made actual. The hearer is assumed to be more than a mere intellect, but also an agent who can affect reality. The imperative is not a judgment, though it may imply a judgment that the state to be realized is desirable.

Logically, the command form of a proposition P would mean, “Make it so that P.” For example, the command ‘Clean this room!’ means “Make it so that this room is clean.” We convey the imperative in English by reordering the sentence and giving it a different tone; other languages give a distinct conjugation to the imperative. In an imperative, the implied subject is “you,” the hearer. (E.g., You clean this room; You make it so…) “Make it so” represents the imperative separate from the proposition, which becomes a dependent (subjunctive) clause. It refers to the act of making reality (“it”) similar to (“so”) the conceptual content of the proposition. We have not thereby defined the imperative, since “make” is in the imperative mood, but this formulation could reduce all other imperative verbs to this verb (“make” or “do”). The specific form of action is not what is essential to the imperative mood, but rather the act of bring a state of affairs into being.

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21. Optative and Cohortative Moods

Ancient Greek had a grammatical mood known as the optative, expressing wish or desire. It had generally fallen in to disuse already by Plato’s time, though we may still find it in the epic poetry of Homer. In English, we may express the optative and other moods expressing desire using auxiliary phrases. For example, ‘Would that you would live long’ is an archaic way of saying “I wish that you would live long.” Here we are describing a state of affairs that we desire, but there is no imperative dimension to this mood, since we are not instructing anyone to perform a particular act. It is not even a petition, for we are not asking the hearer if he would do us the favor of living long, but we are simply describing a state of affairs that we find desirable. The optative lacks any practical dimension, so it does not presume agency in the speaker or the hearer. We are not soliciting an action or even a judgment, but we are simply expressing our preference.

A wish can be indicated in a deprecatory prayer, as in ‘May God have mercy on you.’ This sentence could be interpreted in a purely optative sense, as merely expressing what one desires, or it may be positively petitioning God to realize this desired state. Deprecatory prayers for blessings (‘May his faults be forgiven’) have counterparts in imprecatory curses (‘May his daughters be barren’). In both deprecatory and imprecatory utterances, there is a practical dimension to the statement, as the speaker does more than express his desire, but hopes to effect its realization somehow by giving voice to it.

The cohortative mood has some similarity to the optative, in that it expresses a desire. It may be used in lieu of the optative, yet it contains something more than the expression of a preference; we are exhorting the hearer to make our preferred state of affairs become reality. The cohortative can be represented with a deprecatory sentence ‘May X be Y’, where the subject X is the hearer (“you”). Let us take the sentence:

‘May you always exercise discretion.’

This sentence could be understood in a purely optative sense, meaning I (the speaker) find it preferable that you always exercise discretion. It might have a deprecatory dimension, where I am praying that this becomes reality. Lastly, we may consider this in a cohortative sense, where I am positively encouraging you, the hearer, to always exercise discretion. We may express the cohortative less equivocally if we say ‘I exhort you to Y.’

Another example of the cohortative is ‘Live well,’ which is grammatically structured as a command, but the intent is not to say, “You must live well,” or, “I demand that you live well,” but rather, “I desire that you should voluntarily choose to live well.” The cohortative is perhaps the noblest mood of all, in that it presumes an independent and free will on the part of the hearer. It attempts to persuade, rather than compel, so it is a more nuanced mood than the imperative.

In many languages, the grammatical subjunctive is used to express wish or desire. The subjunctive varies in usage from language to language, expressing doubt, uncertainty, supposition, or desire in dependent clauses. It does not represent a single logical mood, but is employed in the representation of various moods, as we have mentioned above. There are many other moods that express hope and desire, but these differ from those we have discussed only in subtle nuances of intention, and are best reserved for a discussion of rhetoric.

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22. Concluding Remarks

This is not an exhaustive list of grammatical moods, but most of the others can be understood from what has been discussed above. More generally, we have established many of the basic tools of analysis that will enable us to assess the logical value of other grammatical features of language.

It may seem strange, even circular, that I should use rather complex language to explain the logic of the most basic elements of language. The validity of this approach can be admitted if we accept that we have already been using language to do logic for most of our lives. Only now, our linguistic thought is sufficiently sophisticated that we are able to review our use of language and conform it to logical norms, correcting any deficiencies as needed. We owe it to the basic logical soundness of language and grammar that we are able to identify, analyze and correct such deficiencies. Admittedly, there remains a question as to whether there could not be other logical deficiencies of ordinary language to which we are blind. This is an epistemological inquiry we will reserve for another work.

Throughout this work, I have distinguished linguistic expressions from their meanings by use of single and double quotation marks, respectively. When we talk about words as words, we refer to their mention, and when we talk about the words as surrogates for what they signify, we refer to their use. Ordinarily, we intend the use of linguistic objects as surrogates for concepts. However, it remains to be seen what is the relationship between these concepts and the reality they intend. This is a question for epistemology, metaphysics and philosophical psychology.

The next inquiry of immediate concern involves learning how to use our insights about the logic of language to construct a formal logical system that loses none of the logic in which we have been conversant for much of our lives. Too often, modern formal logic has stumbled into paradoxes resulting from inadequate representation of the logical structure of ordinary language. Foolishly, these paradoxes are not seen as evidence of the shortcomings of the mathematical formalism, but rather of our common sense intuitions. To correct this erroneous view, I have started with ordinary language and explored the logic that is implicit in it. With this basis, we can pass judgment on the shortcomings of modern formalistic logic, and make the necessary corrections so it has the robustness of the logic of language, yet retains the advantages of precision and unambiguousness enjoyed by a symbolic formalism.

See also: Ontological Categories | Formal Logic


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