Formal Attributes of Mesopotamian Scholarly Divination

A large portion of cuneiform scholarship belongs to the extensive tablet series for divination of various kinds. Detailed lists of signs (ittātu/GISKIM.MEŠ) with their correlated events of a public or private nature make up the corpus of cuneiform scholarly divination. The body of celestial signs corresponds by and large but not exclusively to visible phenomena (physical or optical, i.e., involving or related to light). It may be worth noting that the Sumerian writing of the word GISKIM (Akkadian ittu) “sign,” is a compound logogram that includes the graphic element IGI “eye,” or “to see.” But in addition to certain kinds of visible phenomena, signs could be identified in possible, imaginable, or conceivable phenomena as well, i.e., in things not limited to what we consider physical phenomena, though they are clearly grounded in consideration of physical realia. The purpose of the omen compilations appears to be to identify and systematize what, evidently, to the ancients seemed to be the interdependence of elements of their experience, that is, observable events in the environment, with events in social life. The written lists of omen statements, arranged into elaborate paradigms, in the structuralist sense of that term, preserve a Babylonian semiotics whose pre-history is entirely irretrievable. Once formalized in lists, however, the paradigms became traditional and were perpetuated by the faithful copying of the omen lists over the course of many centuries.

Divination series were written, therefore, to preserve a system (of indeterminable antiquity) of associations between signs and their consequences. The signs were compiled according to a variety of subjects, e.g., celestial signs, signs in the exta of sacrificed animals, physiognomic or medical diagnostic signs. The series vary widely in their content but are unified in form. Regardless of their content the lists of signs are formulated as “if . . . then” conditional statements. As D. Sanford says in the introduction to his study of the foundations of reasoning, “we use conditionals to decide what to do. We also use conditionals to decide what to believe, whether or not the belief is immediately relevant to any prospective alternative for action. Much of our inference from evidence is naturally cast in conditional form” (Sanford Reference Sanford1989, 4). “If . . . then” formulations belong to a category of sentences known as indicative conditionals, which express the expectation of something (the consequent or apodosis) on the condition of something else (the antecedent or protasis). Such conditionals seem to have built into them a future state of affairs: “On the condition that (or supposing) P, Q happens, or will happen.” P and Q are then related events, P being that which signifies and Q being that which is signified, that is, Q is expected to occur after P.

The question is not whether Mesopotamian omens reflect a conscious interest in the nature of conditionals or in the logic of conditional statements. They do not. The Assyro-Babylonian scribes did not comment on the form of the omens as such, but the fact remains that observational and theoretical interest in physical phenomena resulted in the creation of systematic and highly schematized lists of conditional statements. The question is: what is the real function of the conditional phraseology in this context? In modern scholarship it has been regarded as a function of the use of omens in prognostication, the “if . . . then” being the way a diviner “divined” the future. In this sense the omens served the same purpose Sanford attributes to “our” use of conditionals, i.e., to help human beings decide whether or what action to take in the immediate future. This is indeed confirmed by evidence of scribal activity at the Neo-Assyrian court (seventh century B.C.), in which learned scribes advised the Sargonid kings on their official business inside and outside the palace on the basis of celestial omens, as in the following passage:

Apart from the omen lists, other written evidence for the practice of divination is available from letters referring to the observation of omens, reports of the observation of ominous signs, and rituals for averting the evil signaled by some. Such action could include prescriptions for ritual magic, as the scribe in the following example recommends: “Let them find out where the evil (portended by) the eclipse has materialized, and eradicate it. Somebody should go and perform (the rituals) in Nineveh” (Parpola Reference Parpola1993, 40 rev. 2–7; broken passages are not represented in the translation here). As implied in the last passage, the reading of a sign and its interpretation prompted action to be taken to respond in the event the sign was considered dangerous. However, this use of omens does not necessarily mean that the omens themselves offer what we would call “predictions.”

The formulation of individual omen statements, “if P, (then) Q,” was already employed in the Old Babylonian period (ca. 1800 B.C.), sharing its form with so-called law codes, the casuistic statements of acts and their punitive consequences, “if a man does thus and such, he shall pay” to varying degrees (including, in capital offenses, with his life). The intellectual affinity between Mesopotamian law and divination is as yet under-explored. Raymond Westbrook has commented that the verb barû, whose basic meaning is “to see,” is also used in the sense of “to establish facts of a case,” noting the relation to its use in the context of divination in which the diviner “establishes the true meaning of ominous phenomena” and taking this to mean that the diviner “does justice, since a judgment has two aspects: the verdict or the facts and the orders that may flow from it for punishment, compensation, restitution, etc.” (Westbrook Reference Westbrook, Skaist and Levinson2005, 35, and n. 25). Ann Kessler Guinan has also made mention of the similarity between the conditional formulation of law cases and omens, but judges the similarity “deceptive,” because “when we read an individual law, we can understand the connection between the protasis and the apodosis,” and “deduce the underlying principles that govern the structure of the text” (Guinan Reference Guinan, Ciraolo and Seidel2002, 19). The relation between protasis and apodosis, or antecedent and consequent, is the working dynamic of Mesopotamian divination, and although to us that connection, at least semantically, is not readily understood, it is subject to certain relational (propositional logical) rules in the same way as are the casuistic statements of the cuneiform laws. I contend that the relation of antecedent and consequent in the omens can be understood as a matter of conditional logic, which applies independently of any semantic, causal, or empirical connection there may be (or not be) between the statements P and Q so related.

Some omens were not introduced with the word šumma “if,” but merely stated as two conjoined statements “P:Q,” with the implication that P, the antecedent clause was associated with or indicated Q, the consequent. The practice of writing šumma in Old Babylonian omens is by and large effected by writing BE-ma [to be read šum ₄-ma] “if,” but later, in the Neo-Assyrian period, by writing DIŠ, meaning “entry” after the fashion of many (not all) third millennium Sumerian lexical lists and a few later such lists wherein the entries in these lists are preceded by a single vertical wedge, meaning “item” or “entry.” The translation of omens written with DIŠ can in fact be “P:Q,” without “if.” The Chicago Assyrian Dictionary (1992, 276) s.v. šumma explains that the logogram DIŠ, when introducing omens written with DIŠ alone, is “unlikely to have the reading šumma,” since it sometimes happens that omens which are introduced by DIŠ can also be preceded by the word “if,” written either šum-ma or BE-ma. With or without DIŠ the logical relationship between P and Q remains the same. P functions as the antecedent clause in which an ominous sign is posited, supposed, or given. We can therefore translate “if P,” “on the condition that P,” or “given that P.”

The grammar of conditionals in Akkadian does not dictate that the posited event P should be expressed with the verb in the preterite, but in omen texts it normally is. The preterite verbs of the protases are in many editions of omen texts translated into English with the simple present, “if P happens.” This is a matter of interpretation, that is of our interpretation of the way the ancients understood the relation between antecedent and consequent (protasis and apodosis) and how they used the omens. The idea is that whenever a sign should occur, meaning sometime in the future, Q is what one expects. Hence our translation of these verbs in the present tense with present-future aspect: “If, or on the condition that, P should ever occur . . .” The consequent is translated as following upon the event in the antecedent in the manner of a prediction. It is expressed as a subsequent occurrence with its verb in the present-future aspect: DIŠ MUL SAG.ME.GAR ana UL Á.MUŠEN itehhi “If (or, “given,” or, “on the condition that”) Jupiter approaches the Eagle Constellation (Aquila)” miqittim būlim išakkan murṣānu ina mati ibašši zunnu arhi 1.KAM ul izannun “there will be (meaning ‘there is as a result’) disease of the cattle herds, sickness in the land (and) no rain for one month.”

What strikes us as peculiar in relating P and Q in this way is that the relationship between the events P and Q bear (to us) no physical or causal connection. Whether the ancients thought that Q occurred because P occurred is never addressed in cuneiform sources, neither indicated in the evidence of the omens themselves nor in ancillary texts such as reports and letters to the king about ominous signs. To us the idea that this kind of (false) causality would apply to the omen texts is extremely discomfiting as it lays the entire system open to the charge of post hoc ergo propter hoc fallacious reasoning. But one would like to have a surer grasp of a Babylonian theory of causality, be it somehow physical or divine, for such a charge to make sense within the ancient context. While no appeal is made to physical reasons or forces to explain the connection between P and Q, a generalized acceptance of a divine causality in the world of phenomena does appear to be the case, though we have no conception of how that causality was understood to work. What can be established from the internal evidence of the omen texts is a strong paranomastic relation between antecedent and consequent clauses, suggesting that the relation between P and Q need not be physical, causal, or even divinely produced for P to indicate Q.Footnote ² The point is, conditional statements need not be causal statements, though they certainly can be when P precedes Q. Moreover, the fact that “if . . . then” statements are commonly used for making causal statements does not mean that all conditionals make causal statements. What the omens do make are implications, in the logical sense, that is, “if P then Q” can be taken to mean “P implies Q,” and this relation does not have to do either with causality or prediction.

The last formal attribute relevant to the discussion of the conditional statements in omen tablets is the organizational character, which can be described in terms of the structures of paradigm and syntagm, two basic dimensions of the analysis of textual form going back to Jakobson and Saussure (de Saussure Reference Saussure, Charles, Sechehaye, Reidlinger and Baskin1974 and Jakobson Reference Jakobson, Jakobson and Halle1971).Footnote ³ On the syntagmatic level, the horizontal axis so to speak, are the elements that come together to constitute the sign, such as “If [Jupiter] in the middle watch has a ṣirhu toward the North” (Reiner-Pingree Reference Reiner and Pingree2005, 124–125 r.1'). The syntagmatic relation of the elements of a given antecedent is constructed by combination. But the antecedents are also structured on the vertical axis such that elements of the syntagm can be replaced forming a new combination of elements, as the lines following the one just quoted demonstrate (only the antecedents are given here, and breaks in the tablet are not indicated):

On the plane of the paradigm, new elements are introduced by substitution. A given paradigm will be expanded until it reaches a stopping point when the elements of that paradigm are exhausted. In the example given, nothing further can be added to the pattern of middle, morning, evening watch combined with the four directions.Footnote ⁴ The consequence of this structural method is that some “phenomena” will emerge within the paradigm that are purely imaginative constructions not possible in the actual world.

Conditionals and Inference Making in Cuneiform Omen Texts

Dorothy Edgington introduces her article “On Conditionals” with the following statement:

This is an encouraging assessment if we are interested in defending a claim against the idea of a difference in cognition between the ancients and ourselves. But there is serious comparative work to do in this regard, and while, as Edgington believes, conditional thought is “basic,” the theory of the conditional statement is not. Furthermore, her own question “are there irreducibly different kinds of ‘ifs’?” seems to me to require some careful analysis on our part with respect to Mesopotamian “ifs” before we issue any general statements about the cognitive in Mesopotamian omen texts.

We are not accustomed to approaching Babylonian omen texts from the point of view of what their form might suggest about their meaning and purpose because we tend to (or want to) view the omens as having, or being based on, an empirical connection. The following example will suffice: If/on the condition that Jupiter leaps in the middle of the (constellation) Fish and stands: no rain for one month (Reiner-Pingree Reference Reiner and Pingree2005, 43 r.1', without marking break). On the standard view, this statement means that whenever the phenomenon is observed (the leaping and standing of Jupiter in the middle of the Fish), a conclusion (or prediction) is drawn (no rain for a month) on the basis of that observation. This interpretation presupposes an empirical foundation for the association of P and Q, namely, that at some time in the past it was observed that following the leaping and standing of Jupiter in the middle of the Fish constellation there was no rain for a month. Whether or not this was the case is not ascertainable from the omen text itself. Neither is there direct evidence outside the omen lists that this was ever the method by which some omens might have been generated, tempting as it is to presume so. The idea of an original empirical connection between sign and signified remains entirely speculative and is also occasionally shattered by the “impossible” phenomena which cannot have been observed at any time, as well as by the paranomastic relations clearly attested in the texts (see note 2).

Perhaps a better approach would be to bracket altogether the problem of supposed empirical underpinnings of omens. If some signs were related to events without an empirical connection, which is certainly the case for the “impossible” phenomena, then perhaps whatever related the antecedent to the consequent in those instances held in other cases as well. Our presumption of an original empirical connection may be motivated by our difficulty in seeing as in any way logical conditional statements where there is no causal or empirical connection between antecedent and consequent. But the logic and the truth-functionality of conditionals (for details, see below) is not dependent upon the meaning of its component statements. R. J. Farrell commented,

Even if the antecedent is not patent nonsense, as in the moon being a green cheese, the relation of antecedent to consequent, if unconnected by physical, causal, or experiential association (such as “If the moon is a satellite of Earth, John F. Kennedy was the 35th President of the United States”), still seems bizarre to us. Just as in these two deliberately bizarre conditionals, it is difficult to assess the nature of a Babylonian omen as a conditional statement when taken in isolation. Although the ancient omens were not constructed for the purpose of illustrating material implication in a conscious exploration of the logic of conditional statements, from a formal point of view they may functionally be viewed as a series of implications (P implies Q).

Seen in the context of the written list it is easier to see the difficulty of the question about a physical connection between antecedent and consequent particularly given the schematic (or paradigmatic) nature of the development of the list. The following is a section from omens for the planet Jupiter from the series Enūma Anu Enlil (Reiner-Pingree Reference Reiner and Pingree2005, BPO 4 Group G K.8097:4'-19'; tablet number is unknown). Square brackets indicate breaks in the clay tablet:

The purpose of the omen list seems to be to provide a series of cases that serve as a basis for knowing what happens if P, or, put another way, what is indicated or implied by P. Although the omen lists provide only the series of “If P then Q” statements, the use of the omen texts as reference works seems to be well indicated by other sources for the practice of divination (the letters and reports from the scholars in Hunger Reference Hunger1992 and Parpola Reference Parpola1993). If ever P is observed, we presume, the omen statement in which P is mentioned permits the association to Q.

In effect, Q can be inferred from P in a manner that, at least from a formal standpoint, follows the logic of indicative conditionals as follows: “If P then Q. P: Therefore Q.” This is the most common rule of inference, known as modus ponens (“the mode that affirms”). The modus ponens formulation will appear completely familiar to anyone with an acquaintance with Babylonian omen and other divinatory cuneiform texts. Logically speaking, two premises are brought into relation. The first is simply the conditional statement “if P then Q,” where the logical relation is one of implication, that is, P → Q (“P implies Q”). The meaning of the conditional is then “if P implies Q.” The second is the truth of P (when it is observed), from which, by the inferential rule of conditional logic, it is concluded that Q.Footnote ⁵ From a formal point of view, therefore, the written body of omens can be construed as a list of conditional statements that offer inferences from established premises.Footnote ⁶

Apart from any empirical considerations of omen taking, or questions about the physical reality of the signs, the logical relationships between the signs and what they signify stem from the syntax of their conditional formulation. As Edgington pointed out, conditional thinking is a basic cognitive function and the logic of conditionals is tied to conditional statements. On this formal level of analysis, the cognitive nature of the Babylonian divinatory science can be said to be characterized by inferential reasoning. Although the omen lists provide only a series of “If P then Q” statements, the use of the omen texts as reference works seems to be implied by other sources for the practice of divination (the letters and reports from the scholars). From these texts it follows that when P is observed, the omen list is consulted. On the basis of the entry in the list in which P is found, a correlation to Q, i.e., the meaning of P, can be inferred. This reading of the omens, as just suggested, can also be expressed as P → Q (“P implies Q”), removing temporal, causal, empirical, or otherwise physical elements from their relation.Footnote ⁷ On this view, the omens are not what we would understand as predictions.

The relation established between P and Q is based on or determined by a paradigmatic structure, which becomes ossified by tradition and is subsequently taken as authoritative. And though the relation between the signs and physical existence, much less observational reality, is not a requirement for a phenomenon to function as a sign, at least not to be included in the written list of ominous signs, we must allow that on the formal level, those antecedents which are obvious constructions of the imagination did function as signs. The consequents associated with them are still inferences to Q given P. This feature of the omen texts challenges our understanding of the connection between antecedent and consequent, particularly if we are looking for some kind of physical dependence (such as an empirical connection) of the consequent upon the antecedent; for how can we understand the establishment of a meaningful dependence on something that does not exist?

Possibility and Impossibility

As Gendler and Hawthorne explained in the context of the conceivable and the possible,

In reference to the omen texts, as pointed out above, ominous phenomena as entries in the lists do not carry observational weight, i.e., do not represent actual events. Even in the cases where some potential relation to physical reality exists, the omens in the lists are not observations. They are hypothetical statements representing a conditional belief that Q if P. Gendler and Hawthorne's indication that we are not on firm, or at least established, ground when it comes to accounting for the relation between the conceivable and the possible raises interesting questions that pertain to the ominous signs included in the cuneiform lists. Some ominous phenomena seem to have no actual properties in the world, yet in terms of their function as signs, and the fact that all ominous signs are correlated with consequents, it would seem that such actuality was at stake.

How certain an Assyro-Babylonian diviner would have been that Q would occur on the condition that P is a judgment we might make on the basis of our knowledge of the practice of scholarly divination. Rituals to ward off the consequences of observed signs were ordered with enough regularity in the correspondence to the Neo-Assyrian kings that we can surmise a high degree of belief in Q given P. But provided we refer only to the omen statements in the lists, any consideration of the empirical is irrelevant for an analysis of how P and Q are related. The modality of the statements P and Q that make up each omen allows us, for the sake of an analysis of the internal logic of the omen statements, to treat the antecedent and consequent of an omen statement as the conjunction of two propositions. The statements P and Q can be said to function like propositions in the sense that they do not represent actual empirically established events, but rather something more like beliefs or some other “propositional attitude.”

The epistemic character, particularly of the signs themselves, is further complicated for us because some of them are imaginative constructions. On the criterion of empirical veridicality, therefore, such constructed or imagined phenomena are “impossible.” If the omen lists constitute a body of knowledge, we ask ourselves, what would it mean to “know” such phenomena? Despite the fact that the omens as listed in the texts are not tied to observations, the signs by and large refer to phenomena with real properties. Occasionally, however, due to the completion of paradigmatic substitutions, such as the three watches, the four directions, or the five colors, some signs do not refer, but stand in the text as “mere” constructions. Examples of such “impossible” phenomena are the appearance of the sun at midnight or the lunar eclipse shadow that travels from west to east across the lunar disk. From our point of view, the criterion of empirical veridicality would have ruled out the inclusion of these phenomena. But they are included because they fulfill paradigmatic schemes and belong to the structure and logic of the omen lists. This presents a puzzle to our way of thinking because if we know that P cannot occur we wonder what purpose statements beginning “If P . . .” serve. If we know, for example, that Venus can never be seen at the zenith, a statement beginning “If Venus is seen at the zenith” seems pointless and wrong.

It may seem facile, but for purposes of analysis it might be more useful to speak of possibility rather than impossibility. To say certain phenomena in the omen lists are “impossible” or “absurd” because they do not occur and cannot be observed is our judgment and occurs nowhere in the ancient sources. That is to say, our definition of impossible (not in accordance with real properties) is not expressed in the texts. It seems more consistent with the overall makeup of the omen lists that recording a phenomenon as an entry in a codified omen list is evidence that it was regarded as epistemically possible. That is, the list of statements (P) constitute data, or knowledge, on the basis of which the diviner makes judgments and draws conclusions about what will happen. The use of the terms possible and impossible are, among other things, relative to one's accepted knowledge of how and what things are. Gendler and Hawthorne put it this way: “One might offer a permissive account of epistemic possibility, according to which P is epistemically possible for S just in case S does not know that not-P, or in a strict account, according to which P is epistemically possible for S just in case P is consistent (metaphysically compossible) with all that S knows” (Gendler and Hawthorne Reference Gendler and Hawthorne2004, 3). There are as well intermediate definitions between the permissive and the strict accounts, where, for example, “P is epistemically possible for S just in case S's evidence does not warrant S's believing not-P; or P is epistemically possible for S just in case S could not reasonably be expected to ascertain not-P on the basis of what S knows” (ibid., 3 n. 4). This approach opens up the field for discussion of the epistemic character of the non-occurring phenomena that appear in the omen lists.

Taking the permissive account first, we might conclude that phenomena such as Venus appearing in the zenith or the sun appearing at midnight are conceived of within the omen list as possibilities because the scribes did not know that such phenomena cannot occur. The elaboration of the antecedents in the omen lists by means of paradigmatic substitutions, such as the three watches, the four directions, or the regions of the sky, produces such possibilities, extending known phenomena to possible phenomena. The paradigm then serves as a guide for the conception of possibilities. An Old Babylonian text (BM 97210) has the following lines:

Another example of possibilities conceived in omen texts that have no physical properties are the eclipses that occur on days of the month when eclipses are not possible. The pressure of the paradigm produces lists of eclipse omens on days when they will never occur. The Babylonians' perspicacity in matters of periodicity is attested in the early ability to predict eclipses (Steele Reference Steele2000) and so we hesitate to say that the scribes were unaware of the impossibility of a solar eclipse, say, on the tenth day of the month, or a lunar eclipse on the twentieth. In fact, the high degree of the scribes' understanding of the behavior of phenomena suggests that such phenomena as had never been observed were included not because they were thought to be usual or likely occurrences, but because they stood at the extreme negative end of possibility, that is to say the extremely unlikely. How such phenomena were thought to “fit into” a (metaphysical) conception of the world is interesting to contemplate. Perhaps, as Stephen Yablo pointed out, there is a meaningful difference between conceptual and metaphysical possibility.Footnote ⁸

On the strict account, P is epistemically possible for someone if it is consistent with everything that person knows. In such cases, epistemic possibility then corresponds to metaphysical compossibility. If there were such a metaphysics in ancient Mesopotamia that permitted the compossibility of all sorts of non-occurring phenomena, the divination corpus in effect constitutes one. There are in fact other texts to support the idea that the Babylonian scribes held a metaphysics allowing for the possibility of all sorts of freak occurrences. These are the texts that deal in obvious prodigies, phenomena that transgress rules of order either in “nature” or society (Guinan Reference Guinan, Ciraolo and Seidel2002). But perhaps this is where we step into the realm of the conceivable, or the conceptually possible, as differentiated from the possible, or at least the metaphysically possible. However, it is clear from the texts that refer to prodigious events such as a bearded woman being seen in the city or stars falling from the sky, that the same logic applies to prodigies as to omens constructed from regularly occurring events. The ominous nature of an event did not seem to correlate with its degree of regularity, conceptual or metaphysical possibility, though the severity of their consequents perhaps did. The prodigies discussed by Guinan all presaged the extremely grievous condition of the fall of the state.

The conception of possibility and impossibility, in addition to being relative to the things one knows through observation and experience, is also relative to one's understanding of the reasons for the variation in the things observed, e.g., why it is that certain celestial bodies appear at the horizon but not on the zenith, or why a lunar eclipse occurs at the middle not the beginning of a month. Only when one has such understanding of the reasons for a particular range in variation of certain phenomena can one begin to speak of possible versus impossible phenomena. On the face of it, however, the omen texts can be read in terms of a position that does not rule out certain variations whose particular character is grounded in the paradigms. What is taken into account, therefore, is not actual properties of the phenomenon, but rather paradigmatic “possibilities” (conceptual possibilities). The paradigms do not permit just any phenomenon, but only those whose variations belong within the fairly tightly reasoned parameters of each paradigm (right-left, four directions, three watches, etc.). The “possibilities” are not limitless. They are only possible on the basis of the assumptions given in the paradigmatic structure of the list. All phenomena given as antecedents in omen texts are epistemically possible by virtue of being consistent with the structural rules of the list. By this reasoning, we err in classifying as “impossible” phenomena in the omen texts that do not conflict with but rather satisfy and effect paradigmatic structure and for which some causality or justification must apply at some level.

In describing the convention for introducing omens with the sign DIŠ, a comparison was previously made to the Sumerian lexical lists. But there is further relation to lexical lists that should be made explicit here. Niek Veldhuis explained in reference to the archaic lexical lists from Uruk, that “it has often been observed that these archaic lists contain much that seems utterly irrelevant and that may not be explained by the purely utilitarian reason of teaching a new generation of scribes how to compose an administrative record” (Veldhuis <http://cuneiform.ucla.edu/dcclt/intro/lexical_intro.html>). He notes that very few of the professions in the list Lu A ever appear in contemporary administrative texts. He has challenged the notion that the lexical lists reflect some ordering cosmological sensibility, the old idea that somehow the Sumerians were cognitively disposed to order the world through list-making. The lists clearly provide more than what is needed if we are to use actual administrative records as a guide. In response Veldhuis says, “the direct relevance of the lists for the practice of writing is, indeed, low because these are manuals that cover every possibility, including the unlikely and the very unlikely ones. The archaic lists betray the problem of creating a new bureaucratic system that is capable of recording every transaction that is possible or even imaginable within the bureaucratic context. Therefore, the scribes who created these lists went out of their way to invent signs for birds and fish and professional titles that some future scribe once upon a time might need to write down” (ibid.). The idea of inventing items for a list because at some time there would be a need for such an item suggests the very opposite of a conception of “impossible” phenomena. Indeed, the phenomena or items in the list seem to have been thought of not only as conceivable but possible. They are epistemically possible not because they are consistent with actual physical properties in the world (our epistemological category) but because they are consistent with the conceptual rules of the list (their epistemological category).

In the context of physical science, in which physical laws allow or disallow certain phenomena to occur, to posit a non-occurring or “impossible” phenomenon seems to indicate a lack of knowledge of the laws involved. The eclipse omen in which the shadow makes its transit from right to left (or west to east) could be taken to demonstrate such a lack of understanding. That is, a failure to know that such a thing cannot occur. The character of omen lists, however, shows the importance of a different kind of knowledge. The paradigmatic treatment of the ominous phenomena creates room for expansions into the realm not of the empirical but the conceivable. The conceivable (or conceptually possible) does not always map neatly onto the actual, and the meaning of “possible” does not necessarily refer solely to physical actuality.

Earlier the question was raised what purpose statements beginning “If P . . .” serve if we know that P cannot occur. It may seem as though the impossibility of P renders the entire omen statement senseless, but a closer consideration of the logical structure of indicative conditionals puts the ancient omen statements containing conceptually, if not metaphysically, possible phenomena in a different light.

Truth-functionality of Conditionals in Babylonian Omens

As discussed in a previous section, the validity of inferences such as are allowed by conditional statements is syntactic not semantic: That the antecedent P proves not to occur (= is false), as in the sun appearing at midnight, is not damaging to the validity of the statement “if P, Q” to which it belongs. Inferential reasoning is one of the fundamental ways in which we describe a method for knowledge. But an inference makes no promise as to truth or falsity, correctness or incorrectness. It must only follow from a pre-existing statement or premise, but true premises are a necessary element in valid inferential reasoning. Other ingredients are sometimes thought to be necessary for valid inferences to be made, for example, a causal relationship between the evidence and the conclusion or hypothesis drawn from it, such as my conclusion from the evidence of the darkened face of the moon that the earth's shadow has crossed it, or that the moon has approached very near to the ecliptic and is at opposition to the sun which is also very near a node. I could also conclude or hypothesize on seeing the darkened moon that the evil Sibitti (seven demons) were whirling ‘round him in heaven. Any of these relationships could be defined as causal. Alternatively, I could see the darkened face of the moon and decide that the king was in danger because I believed a temporal connection applied between lunar eclipses and bad luck for kings. Or thirdly, I could determine that lunar eclipses signified a range of events because a traditional code existed for making such interpretations of the sign “lunar eclipse,” and any such interpretation or conclusion had an inferential relationship to the evidence, that is, the sign.

From a logical standpoint, the truth-functionality of such conditionals entails that the statement “If P then Q” is independent of all such relations just mentioned, i.e., temporal, causal, empirical, or traditional. As Michael Woods has said, “One thing that gives rise to doubts about the truth-functionality of conditional statements is that it seems so easy to construct sentences which have no natural use but which would have to be counted as expressing truths if conditionals are understood truth-functionally” (Woods Reference Woods, Wiggins and Edgington1997, 3). We (mistakenly) see the omens as presenting nonsensical relationships between antecedent and consequent because of their counter-intuitive yet truth-functionally legitimate nature as conditionals. Woods cited as an example of a bizarre conditional “If Rome is the capital of Greece, there are no snakes in Ireland” (ibid.). Yet, from a truth-functional point of view, a Babylonian example, such as “If Jupiter leaps in the (constellation) Fish, there is no rain for a month” can serve just as well. Each example exhibits a bizarre juxtaposition, but, in terms of the truth-functionality of conditionals, such juxtapositions are as true as other statements that seem more intuitively “reasonable.”

A conditional statement of the kind “If P then Q” (as material implication P → Q) is simply true in every case but when P is true and Q is false.Footnote ⁹ From this it is clear that no matter the truth or falsity of the individual statements, antecedent or consequent, it is their relation that determines the truth or falsity of the conditional. If we are to consider as a criterion for truth whether a phenomenon can actually occur or not, it is clear that even such “false” phenomena can be enjoined in true conditionals, provided the consequent's truth-functional value is true. P can be “false” in some sense, such as in the guise of a non-occurring phenomenon, and the statement “If P then Q” can still be true by virtue of conditional logic.

The seeming incompatibility of the possible and impossible phenomena can be reconciled by further formal analysis of the genre. As already briefly indicated, the organization of the omen tablets can be described in terms of the structures of paradigm and syntagm. On the syntagmatic level are the elements that come together to constitute the sign, such as [Jupiter] leaps in the middle of the Fish to the right and stands (Reiner-Pingree Reference Reiner and Pingree2005, 43: rev. 2’). The syntagmatic relation of the elements of a given protasis is constructed by combination. But both antecedents (and consequents) are also structured on the vertical axis such that elements of the syntagm can be replaced forming a new combination of elements. On the vertical plane of the paradigm, new elements are introduced by substitution, as illustrated by the series of Jupiter omens cited above. The mechanisms by which paradigmatic structure is created in omen texts are not unique to the genre of omen texts, but can be seen in lexical texts, as in the following extract:

What the omen lists share in common with the lexical lists is an internal constructed nature and a certain resultant detachment of some of their content from external realia. These scholastic texts share a systematic and logical treatment of words and phenomena, and, seemingly, a point of view on what constitutes knowledge.