Nonexistent Objects: The Avicenna Transform

Allan Bäck

doi:10.1515/opphil-2025-0073

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Nonexistent Objects: The Avicenna Transform

Allan Bäck

Published/Copyright: May 16, 2025

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From the journal Open Philosophy Volume 8 Issue 1

Abstract

My general concern is how to translate modern formal semantics into medieval metaphysics, itself a theory about objects. I shall use the formal model in Nonexistent Objects by Terence Parsons as a test case for the modern formal system, and the philosophy of Avicenna as one for medieval metaphysics. My investigation has four parts: 1) a summary of Avicenna’s general metaphysical scheme, the threefold distinction of quiddity; 2) translating Parsons’s theory into medieval terms; 3) the location of nonexistent objects of various sorts in Avicenna’s theory; and 4) comparing the theories of Parsons, and concluding that the theories of Parsons and Avicenna are not incommensurate paradigms as Parsons suggests. Rather, they are different theories but under the same research tradition.

Keywords: Terence Parsons; nonexistent objects; Avicenna; modality

During certain periods of history (e.g., the Middle Ages) the view that everything exists would have been regarded as absolutely outrageous.^[1]

Terence Parsons has a theory of nonexistent objects that is far more detailed in syntax than any medieval one that I have seen. On the other hand, I find some medieval theories more detailed in their semantics than modern theories like Parsons’s.

Parsons talks in terms of the paradigms of Kuhn.^[2] The theories of the orthodox analytic fall under the Russellian paradigm, rejecting the existence of impossible objects, like round squares, and even of possible beings not actually existing. He proposes to construct a formal system for the Meinongian paradigm, allowing for the existence of such nonexistent objects. He also contrasts the Russellian paradigm with the medieval paradigm, which holds, like Meinong, that there are things that do not exist – although perhaps not that there are impossible objects – I shall consider that case below.

I propose to compare Parsons’s theory to a theory under a medieval paradigm. I shall focus on the theory of Avicenna, the main figure in Islamic philosophy but also a fundamental one for the Latin medievals: not only did he write the first Summa but also he bequeathed doctrines to the Latin medievals, which were received and adapted by those like Albert the Great, Aquinas, Scotus, and, yes, the modists.

Parsons says that the Russellian Rut has the dogma that there cannot “be” things that do not exist. Avicenna would serve well as a prime target for Russell’s attacks. Not only does he admit that there are possible objects, both universal and singular, that do not exist in re but only in intellectu, but also he talks about there being quiddities in themselves, which do not exist at all but “subsist.”

How much do the theories of Parsons and Avicenna differ? Do they fall under different paradigms? Speaking of paradigms in Kuhn’s sense suggests that the theories are incommensurate. Yet not all differences in theory make different, incommensurate paradigms. Various versions of Newtonian physics are inconsistent with each other but lie under the same paradigm. I shall claim that the two theories, while different, do not fall under different paradigms. At the least, they fall under the same research tradition, in the sense of Larry Laudan.^[3] Their similarities seem strong enough for that.

In the Chinese style of matching concepts, I shall consider how to state Parsons’s formal theory in Avicenna’s terms. I then focus on Parsons’s central case of nonexistent objects, and how they appear in Avicenna’s theory.

For background, I give a short summary of Avicenna’s metaphysics.^[4]

1 The Threefold Distinction of Quiddity

Avicenna has a theory of the threefold distinction of quiddity (triplex status naturae), where essences have three respects: in themselves, without regard to existence or material conditions; in re, in regard to the individuals actually existing in the world; and in intellectu, in regard to concepts abstracted from individuals. Quiddities in themselves (in se) have no accidents, whereas quiddities in individuals (in re) and those in the mind each have accidents proper to them. Quiddities in individuals and quiddities in the mind “exist,” in different ways, while quiddities in themselves do not exist, yet have “reality” (ḥaqῑqa) and “being” (kaun). ^[5] An object may have being as a quiddity “subsisting” in itself, a quiddity “existing” in individuals, in re, or as a quiddity “existing” in the mind, in intellectu. Avicenna views himself as following Aristotle, the First Teacher. He rejects Plato’s Forms, although many quiddities in themselves seem to amount to them.^[6]

2 Parsons and Avicenna: Matching Concepts

In contrast to the Russellian Rut, the model of Parsons has all objects, existent and nonexistent, be of the same type, as constants in a single domain: the same mode of being, if you will. Some of them have the extranuclear property of existing in reality; others that of possibly existent in reality, and others that of being impossible to exist in reality. Yet they all “are” individual constants.

How well does the threefold distinction of quiddity align with this approach? In contrast to Parsons’s objects, quiddities seem to have different modes of being. But looking at the details suggests more congruence between the two theories.

2.1 Theories, Uninterpreted and Interpreted; Formal and Material

Parsons describes his theory as “a formal system.”^[7] It is uninterpreted, but may have various interpretations. Some confusion perhaps arises here. Parsons means by an interpretation a formal semantics for the language.^[8] He then allows it to have various applications, say to fictional or to impossible objects. However, I shall mean by “interpretation” such an application.

I suggest pairing the distinction of uninterpreted and interpreted formal systems with the medieval distinction of the form and the matter of propositions. For a theory consists of a body of propositions. From Aristotle on, people talk about having the same form in different matters in the same proposition.

Avicenna contrasts the mode, or form, of a proposition with its matter.^[9] The matter of a proposition, he says, concerns the necessity of the expressions in terms of the objects signified by them. In the Aristotelian tradition, the logical matter is determined by the predication relation: if the predicate belongs to the subject necessarily, the proposition has necessary matter; if contingently, contingent matter; if impossibly, impossible matter. So a proposition connecting, say, “goat” with “animal” will have necessary matter; “goat” with “standing,” contingent matter; “goat” with “rock” impossible matter. The difference between the mode and the matter is that the mode comes from the predication relation actually used. For instance, the (false) proposition, “every goat is necessarily a rock,” has a necessary form or mode, while its matter is impossible. The mode (“respect”) of a proposition that is actually stated constitutes part of its form. And so Avicenna says:

The difference between the respect [mode] and the matter is that the respect is an expression added onto the predicate and the subject and the copula, when it is explicit, by which that signifies the strength of the copulation or its weakness (in) a signification by the utterance that might be false. As for the matter, as it may also be called an element, it is the state of the predicate in itself, in an affirmative relation to the subject in quality, whose existence is what would be signified by the respect, if an utterance signified it. A proposition may possess a respect different from its matter. So when you say (that) it is necessary that every man is a scribe, the respect is of the necessary (wājib), while the matter is of the possible.^[10]

A proposition may then have a certain logical form, such as being a simple universal affirmative statement, of form “every A is B.” However, its matter and hence its modality are determined by comparing relationships of the quiddities of A and of B. The existence of A or B does not matter.

The material content of the terms actually used determines which modality obtains, so as to make the modalized proposition true. De re statements, like “every goat is necessarily an animal,” generally make an appeal to the matter; de dicto ones, like “it is necessary that every goat is an animal” to the form.

Thus, the logical form is determined by the syntax, while the matter of the proposition is determined semantically, with respect not to a formal semantics but to an interpretation of it – what Parsons calls an application.

2.2 Objects and Intentions

Parsons has an uninterpreted formal system. There all objects are represented by individual constants.^[11] He offers various interpretations, his “applications,” of this system, to objects of fiction, myth, fantasies, and dreams, and, in particular, to impossible objects like round squares. In this system, for something to exist, in the sense of being the value of an existential quantifier, is for it, that constant, to be in the domain.

Parsons pairs each object with a set of nuclear properties, which are fixed.^[12] These sets picture or represent the correlated objects.^[13] In the formal model, Parsons has a function to do this. However, he does not want the objects to be paraphrased away in a semantic ascent.^[14]

By the Axiom of the Identity of Nuclear Indiscernibles, if two objects have exactly the same nuclear properties, they are identical.^[15] So any change of property in the set of properties results in a correlation to a new object.^[16] Parsons admits that his objects are like the monads of Leibniz. Also, like Leibniz, relations are reduced to one-place predicates.^[17]

In contrast, Avicenna allows for it to be possible for an object to change accidental, nuclear attributes of an object and remain the same object. In fact, he considers the theory that an object is just or can be represented completely by, a set of predicates, and then denies it:

So if you say: Zayd is the handsome, tall, literate so-and-so [man]—as many attributes as you like—still the individuality of Zayd has not been determined for you in the intellect. Rather it is possible for the concept consisting of the totality of all that to belong to more than one.^[18]

So then even a full set of predicates does not determine Zayd completely, as it is possible for him not to have them all and for some other object to have them. Moreover, Avicenna takes a bundle of predicates to be a universal, which can have more than one instance, at least in the sense that some other individual could have them all. The partial bundles of predicates, rather like Parsons’s incomplete objects, discussed later, also could apply to more than one individual, even at the same time. The difference is that for Avicenna even a complete bundle of predicates possibly has instances other than the one that it actually has – but not for Parsons.

Having this correlation with sets of properties allows Parsons to avoid a problem with many modern modal systems, which identify objects with sets of possible worlds. Possible, contingent objects exist in only some possible world: fine. However, necessary objects exist in all possible worlds, and impossible objects exist in no possible worlds. All impossible objects have the same extension, the nullset; likewise, all necessary objects have the same extension of the universal set. If meanings or intensions are reduced to these extensions of possible worlds, it seems that all impossible objects are identical; likewise for all necessary ones. But the correlated sets allow for impossible objects to be distinguished, likewise for the necessary objects.^[19]

Parsons does not want a semantic ascent focusing on propositions having terms for nonexistent objects. He wants an ontology and offers a theory of objects. Thus he opts for de re and not for de dicto necessity.^[20] Still, the model gives a formal semantics. For Avicenna, such a theory would concern quiddities in the mind. With a model, it remains an open question how to interpret the model for real cases.

What in Avicenna’s theory corresponds to such objects? I suggest: items existing in the mind. General theory, like propositions in general, concerns quiddities in intellectu.

Parsons does say that he is concerned only with concrete objects, like goats, and not with abstract objects, like properties and relations, which Meinong took to subsist although not to exist.^[21] Meinong seems close to Avicenna here with quiddities in themselves. Parsons does use relations and properties, the analog of quiddities in themselves, in his theory; he just does not make them into objects, namely, individual constants. We shall see him, though, allowing for incomplete objects, which seem a lot like the universal species and genera of Avicenna. Then species and genera would be objects, some existing in re, while the quiddities in themselves may have only subsistence – for Parsons, they are in the domain too, but not there as individual constants.

Would Parsons object to his objects becoming concepts, quiddities in the mind? Such quiddities do take the existential quantifier; they can be said to have the E! robust existence only so far as they signify quiddities in re. Such is the case too, when quiddities in the mind are taken to signify items in re.

Some differences arise on account of the particular theory that Parsons chooses to develop, among many alternatives he recognizes, like not having a distinction between the essential and the accidental. Others seem more fundamental: Parsons has unified all objects into a single category in his formal semantics.

Avicenna might be thought to do so too, as he locates all propositions and all general theories on the level of quiddities in the mind. But then take his metaphysics as an interpretation of the theory. There Avicenna puts truthmakers for the propositions including those about nonexistent objects in different nodes of his metaphysical system, as we shall see below.

Such a difference may come from Avicenna having an interpreted theory while Parson has an uninterpreted model. But, in general, they have the same approach. It is just that Parsons has a far more detailed syntactic account of such quiddities and their relationships and compounds, while leaving the interpretations open.

2.2.1 Properties: Nuclear and Extranuclear; First and Second Intentions

Parsons distinguishes nuclear from extranuclear properties. Nuclear properties amount to first-order ones; in medieval terms, these are the categorematic ones, items belonging to the categories, like being a goat and being blue, as opposed to syncategorematic ones like being a predicate or being a form. As discussed earlier, Avicenna marks this distinction by speaking of the first and second senses (intentions).

In the uninterpreted system, the nuclear and extranuclear properties just have a certain type of notation, Pⁿ with different subscripts.^[22] In the intended interpretation, examples would be for the nonexistent object Sherlock Holmes, being a detective, living in London, being human, etc.^[23] In contrast, extranuclear properties include the following: exists, is possible; is fictional; and is thought about by Meinong.^[24]

2.2.2 Existence and Being Existent: In Re versus In Intellectu

Parsons has the existential quantifier apply to all objects, that is, range over all individual constants. He then constructs an existence predicate E! on a par with other first-order properties via applying a watering-down function to that quantifier.^[25] In the interpretation, the predicate E! signifies robust existence, like existence in re:^[26] Parsons says that his model allows that “there are objects that don’t exist: (ⱻx) ∽ E!x.”

Avicenna in contrast has an existence predicate built into predication: “Every S is P” is to be understood as “every S exists as a P.” But he has two types of existence: in re and in intellectu Existence in re is robust E!; existence in intellectu corresponds to the logical ⱻ quantifier.

For Parsons, an object is represented only by its nuclear properties. His Axiom of the Identity of nuclear indiscernibles rules out certain objects. Consider the actual Donald Trump with all his nuclear properties and the merely possible, nonactual Trump with all the same nuclear properties, without being actually existent. The corresponding sets differ in the extranuclear properties only. Still, by this Axiom, these two Trumps are the same, identical object.^[27] If a fictional description agrees completely, fully determinately, with the description of a real person, the two objects are identical. Parsons admits that one might require the object to be represented by all of its properties, extranuclear ones too, but chooses not to opt for this.^[28]

Avicenna recognizes two types of accidents for quiddities in the mind, which I call 1) material, accidents grounded in the attributes of quiddities in re, and 2) formal, accidents grounded in quiddities in the mind, like being a predicate or being essential.

And the quiddities of things may be in individual things, and may be in thought, and so they have three considerations [aspects]: the consideration of the quiddity insofar as it is that quiddity without a relation to one of the two [types of] existence and what is attached to it, insofar as it is like that. And it has a consideration insofar as it is in individuals. Then there it has attached to it accidents that particularize its existence (in) that. And it has a consideration insofar as it is in thought, and then there it has attached to it accidents that particularize its existence (in) that, like being a subject and being a predicate, and like universality and particularity in predication, and essentiality and accidentality in predication etc. as you shall learn. So in external existents there is neither essentiality nor accidentality (in) predication, nor something being a nominal subject [mubtada’], nor its being a nominal predicate [kabar], nor a proposition nor a syllogism etc.^[29]

These two types of accidents came to be called first versus second intentions (senses or meanings). Although Avicenna says that material accidents belong to quiddities in individuals, they also appear attached to concepts in the mind, since all propositions and theory have existence there. It is just that the truthmakers for statements about such accidents lie in the quiddities in re.

Theoretical terms, like higher-order predicates and those in the metalanguage, amount to Avicenna’s second intentions. Avicenna’s first intentions, like “goat” or “walking,” have a dual status: as existing in the mind but pointing to things outside the mind, normally in re.^[30]

2.2.3 Objects: Particular and General; Complete and Incomplete with the E!

Parsons stipulates that an object is complete if for any nuclear property, an object either has it or does not. He does not require logical closure for such completeness.^[31] To take his example, an object may have the property of being blue and the property of being square without having the property of being blue and square.^[32]

He says that most nonexistent objects are incomplete, as often some of their features are left undetermined.^[33] Parsons sees this happening frequently with fictional objects. For instance, in the Doyle mysteries, the grandparents of Sherlock Holmes are not identified, although it is physically necessary that he has grandparents.

Such incomplete objects may be completed in various ways, by determining all their nuclear predicates. I may specify that John Stuart Mill was the grandfather, and William de Baskervilles the ancestor of Sherlock Holmes.

Parsons speaks about the nonexistent incomplete object, the golden mountain, as not having a location.^[34] But once a location and all else are specified, there arises an individual gold mountain. The incomplete gold mountain will be an unsaturated, incomplete individual. Species and genera in an Aristotelian theory are incomplete objects in this way. When the species goat gets a full set of accidents, it then turns into an individual goat. Note that in Parsons’s notation, it cannot be determined whether an object is complete: all objects are signified by individual constants, although their representations would determine their completeness. In contrast, the Aristotelian system makes the difference self-evident in the very names.

In the threefold distinction of quiddity, Avicenna has universals existing only in the mind, although the Aristotelian tradition speaks of universal, secondary substances like the species goat and the genus animal existing in re. How can Avicenna’s view be consistent with this doctrine?

Perhaps here we should look to Parsons’s theory for a solution. Species and genera exist in re not as independent things but only as constituents of individuals. They have only the essential properties being determined. Take them as incomplete objects. Predicating the species goat of individual goats occurs only in intellectu. Predicating is conceptual; being a constituent, in a mereological relationship, occurs in re.

Parsons even offers a way to understand species and genera as such. He allows for radical incompleteness for an object neither having some property p nor having not p, where that determination cannot be made.^[35] Such would represent Plato’s universal Forms.

Whatever objects there be in re, individuals and species, incomplete and complete, they all have the robust existence of the E!; Merely mental objects do not.

2.2.4 Possible and Incomplete Objects Without the E!

At times, Parsons talks of the same object in different possible worlds.^[36] To be consistent with the formal model that he has proposed, such objects would seem to have to be incomplete ones or surrogates.^[37] For Parsons says that a monad, corresponding to a fully determinate set of nuclear properties, exists in exactly one world.

Parsons does not allow an object to have properties other than the ones in the corresponding set. How to get the same object in different possible worlds then? Use incomplete objects. They can be made more determinate in different ways in different possible worlds.

How then to talk about a complete object existing in different possible worlds? Parsons admits that one could have a model with objects having all the same nuclear properties, while different in extranuclear ones, like existing in W₃.^[38] But he does not do this.

As discussed extensively below, Avicenna seems to allow for possible and perhaps even impossible objects of various types. He certainly allows for unactualized potentialities for actually existent individuals, as with Aristotle’s example of the cloak that can be cut up but never is. Parsons, however, does not allow for such potentialities. At best, he would have an incomplete cloak, needing further determination about being cut up, or a surrogate, a counterpart, of the complete individual cloak while still being a different object.

2.2.5 Properties: Essential and Accidental; Native and Immigrant

In line with the Russelian paradigm, Parsons chooses not to have certain nuclear properties be essential and necessary for the object, and others accidental and contingent.^[39] The Sherlock Holmes case makes this clear.^[40] Parsons allows that some properties could be made essential, but instead, like Quine, properties become essential only relative to a certain description and pragmatic interest: a human being qua bicyclist need not be rational, but qua mathematician must be rational. Although admitting that he could have, Parsons does not make a distinction between essential and accidental properties in an Aristotelian way, such that it must have a certain property in any world in which it appears.^[41]

Sets of properties representing objects have no privileged essential subset such that it is necessary for the object to exist and persist with another accidental subset not necessary for the object to exist. Nuclear properties all have the same status in the formal model.

Parsons does though distinguish for nuclear properties the native and the immigrant: those determined by the frame or particular interests and those not so determined. For example, with Sherlock Holmes stories, the detective Holmes is a native object, while London is an immigrant object, as London exists outside of the story. Parsons allows the option that instead of the real London, a surrogate London may be postulated.^[42]

In contrast, Avicenna has the properties constituting the essence of the object along with its propria be essential and necessary, with the rest being contingent and accidental.

3 Avicenna’s Modalities

Having compared the terminology of Parsons’s formal model to that used by Avicenna, I now provide the elements of Avicenna’s theory on sorts of nonexistent objects that he recognizes, both the contingent and the impossible ones. I shall be concluding that the types of nonexistent objects recognized by Avicenna and Parsons have some differences but much greater similarities.

3.1 Logical and Physical Necessity

In the logical works, Avicenna distinguishes two types of modality: the logical and the physical. The logical has its basis on the level of quiddities in themselves and deals with all possible beings. Logical necessity requires no existence in re. Physical necessity requires existence in re. The physical has its basis on the level of existing quiddities, normally in re, and deals only with actual beings, whose operations are restricted by the laws of nature and conditions that actually obtain in addition to the principle of logical necessity. Avicenna gives this doctrine in the logical writings. He does not state it but presupposes it in his metaphysical writings, where he says, more than once: go look at the logic. Unfortunately, current scholarship sometimes does not heed his advice.^[43]

Indeed, Avicenna distinguishes sharply logical necessity (darūra) from natural necessity (wajūb):

Some of them have understood of the necessary (darūrī) the necessary (wājib) in existence. This has been an error. By the necessary (darūrī) in this type of logic is meant a sense more general than the necessity (wajūb) of existence.^[44]

The distinction agrees with the threefold distinction of quiddity. The logically necessary has its basis in the relationships between quiddities in themselves. In this sense not only are logical tautologies like the Law of the Excluded Middle (P or not-P) necessary but also propositions like “a goat is an animal.”

Physical necessity has its basis in quiddities in re. Here, the rules of logical necessity still obtain, but also other conditions actually exist in the world. For instance, Avicenna says that it is necessary, physically, that only one cosmos exists, although that is not necessary logically. The claim becomes necessary only given the fact that all the matter available has been used up for the single cosmos.^[45]

Logical necessity can be taken to be absolute, although, to be sure, it does assume the relationships between quiddities in themselves with their principles and definitions. In contrast, physical necessity can be taken to be hypothetical, given the conditions of the actual world, along with those from quiddities in themselves. Avicenna makes this point explicitly:

[…] there are two ways that something exists necessarily (wājib). One of them is to exist necessarily and through itself, while the other is to exist necessarily conditionally and through another.^[46]

That is, statements of necessity in re may have their basis absolutely, grounded on quiddities in themselves, or hypothetically, grounded on quiddities in re.

3.2 Types of Possibilities

Avicenna does not discuss the logical structure of impossibility directly. Still, since the impossible is the necessary-not and also the not-possible, we can get insights from them. As for being necessary-not, the impossible will have two modes: the logically absolute or the physically hypothetical. We can advance further to understanding Avicenna’s conception of the impossible by looking at his distinctions concerning the possible.

Already Aristotle had various senses of the possible, as well as of the necessary.^[47] In particular, he distinguishes 1) the one-sided possible (“not impossible,” namely, “not necessary not”) from 2) the two-sided contingent (“not necessary and not impossible”).^[48] Aristotle normally uses the contingent in his syllogistic.^[49] However, sometimes he will discuss and use the one-sided possible.^[50]

3) Another sense of possibility as an actual potentiality may be found in Aristotle’s On Interpretation 9 and On the Heavens I.11. Aristotle speaks of an actual cloak that is never cut up but could be cut up.^[51] Call this sense the actual contingent. When Aristotle calls the soul a first actuality, something that has actual abilities, whether they are actually being used, he has the soul being such an actual possible.^[52] Actual contingent has these truth conditions for “it is possible that s is P”: An individual s exists in re, and it is contingent that s is P.

Since contingency is two sided, it follows that it is possible that s is P, and it is possible that s is not P. That is, s has the potential of being P. Take the modality here as hypothetical. That is, in addition to the axioms and definitions grounding quiddities in themselves, and the additional postulates of physical modality, like there being only a single cosmos, there are also the assumptions like a certain individual s exists for a certain stretch of time and has a certain nature. s then will be a possible object, neither necessary nor impossible.

For Avicenna, the general sense is the one sided; the specific sense the two sided or contingent:

So the sense is the common one, namely that it is something whose judgment is not impossible, where I mean by the judgment the judgment being made in an affirmation or a denial. The specific sense is that its judgment is not necessary (dārūrī), and the third sense is that (whose) judgment does not hold at present and is not necessary in the future.^[53]

Avicenna prefers this definition of the contingent: “The possible is not necessary, and, whenever it is postulated to exist, nothing absurd results.”^[54] Following Fārābī and Aristotle on the sea battle, Avicenna here recognizes also the third sense, for things that do not actually exist now but have the possibility of existing or not existing in the future, but need not exist ever.^[55]

These are future contingents, like the sea battle that may or may not happen tomorrow, and the cloak that has the possibility of going to be cut up or not.^[56] Note that one could be a complete determinist and allow that not all things exist at all times: the cause and maybe even logical necessity could bring it about that the thing, or event, exists only at some times, say, as a part in a necessary sequence, like the phases and eclipses of the moon.^[57] But Avicenna is saying that it is radically indeterminate whether the thing exists or not at all, at any time: a radical contingency. Such future contingents still have the logical form of the contingent, the two-sided possible, but with the additional condition that the presently existing subject does not exist now with that attribute – and need not ever have it. Thus, Avicenna says that it is possible that Zayd is sitting, apparently now, while he is standing, because Zayd can be sitting in the future. Still his sitting a week hence is possible now, even if he never sits in the future – and, perhaps, even if Zayd ceases to exist earlier.^[58]

Avicenna defers discussion of this third type to the sciences dealing with potentiality. The most extensive text is in his metaphysics. There he says that certain things, corruptible ones, have potentialities that may never be actualized. Avicenna ties there being a potentiality for coming to be in matter.^[59] He also insists that something that does not exist now but can exist in the future is possible in itself. So he says:

Everything that is originated after not being must necessarily [literally: “no doubt” lā muḥāla] have matter, [This is] because every generated thing requires for its generation—before its generation—that it be possible in itself … For if it were impossible of existence in itself, it would not exist at all. The possibility of its existence does not consist in [the fact] that the agent has the power [to enact] it. Rather the agent has no power to [enact] it if it is not possible in itself.^[60]

There are then possible beings that may never exist. Their possibility is determined in themselves, namely, in virtue of the relations between quiddities in themselves. Whether they actually exist is determined not in themselves but through others, via external causes.

In ordinary contexts, in speaking of “possible beings,” we are often speaking about things that exist in fact but contingently so, depending upon external causes. Avicenna generally uses this sense when speaking of “possible beings” in his metaphysics: beings that do exist but need not exist.^[61] However, we might speak of possible beings that could exist but do not ever in fact. Avicenna has such a “third” sense for future contingents that may never exist in re, but are based on actually existing potentialities. Future eclipses occur necessarily, but it is contingent whether at some time every man is a scribe.^[62]

Now, if Avicenna thinks that all propositions have their truth values necessarily, that is, if he be a logical determinist, it is very strange that he uses the two-sided contingent at all. Rather, anything possible would have to exist necessarily. Like Spinoza, Avicenna should be saying that an assertion of contingency is nothing factual; at best, it just marks our ignorance of the real causes, of all things following necessarily from God’s activity.^[63] But he does not say this. Instead he says that for the contingent, there is no need to pay attention to the existence or nonexistence.^[64] Is he befuddled? Or just following the Aristotelians with blind faith?^[65] Rather, let us try taking Avicenna seriously: he admits real contingency in the world.^[66]

Avicenna tends to use “mumkin” and its cognates for all of these three senses of “possible,” where the first two are logical (one-sided and two-sided) and the third a physical sense dealing with actual potentialities of existent things. So here he has no clear terminological distinction between logical and physical possibility. Thus, he speaks about the necessary (wājib) and the possible (mumkin) in existence.^[67] However at times he seems to use “mumkin” and its cognates for logical possibility, but also uses expressions like “jāza” (“it is possible or permissible”) and “ittifāq” (“chance”; “coincidence”) for it.^[68] Although Avicenna does not use different words for the logically possible and the potentially contingent regularly, perhaps it is worth noting that, when he talks about possible times in hypothetical propositions, he does not use “mumkin.” Rather, he says, “there might be” (rabbamā) and “maybe” (qad yakun).^[69]

3.3 Types of Impossibilities

As for Avicenna on the impossible, consider the contradictory of the possible in each of these senses: 1) the impossible in the sense of “necessary not” and 2) the impossible in the sense of “either necessary not or necessary”: in this case, as the impossible is not possible to be and hence not necessary to be, the second disjunct is ruled out. So the second sense reduces to the first sense. 3) What about the denial of the third sense, the actual contingent: there existing an individual s with a certain potentiality? Its contradictory makes the claim: it is not the case that an individual s exists in re, and it is contingent that s is P. Then either s does not exist in re, or s does not have that contingent ability; that is, it is not contingent that s is P – then it would be either necessary or impossible, necessary not, that s is P. For example, in this third sense, it is impossible that an individual rock s choose between alternatives; it is also impossible that the human being s be a body. That the individual does not exist seems often to be a contingent fact. As Avicenna recognizes absolute and hypothetical modality, take this third sense to express hypothetical impossibility: given what exists in re, it follows, say, that s does not exist, or that s does exist but not with such a potential, like an illiterate human being who has no actual potential to be writing right now.

From this, it follows that Avicenna’s theory allows for the following types of impossibilities:

impossible as necessary not
Impossible as not actually contingent

Each of these may be taken:

logically and absolutely

or
physically and hypothetically

For the impossible, Avicenna generally uses manī’ and its cognates. However, when he is speaking about what is impossible in existence, he tends not to use manī’ but rather muḥāl (“inconceivable”) or mustaḥīl (“absurd”).^[70]

I shall now discuss which types Avicenna actually uses. I leave open the possibility that he might admit other types. As he himself says more than once, mainly in his logical works, he has plans to extend his theory in a Book of Appendages (Lawāḥiq), which seems never to have been written.^[71]

4 Avicenna’s Nonexistent Objects

In accordance with the threefold distinction of quiddity, Avicenna recognizes objects of various types: most clearly individuals existing presently in re and senses existent in the mind, just as Parsons has the robust existence of E! and the logical existence of (ⱻx). Beyond that, he allows for various types of nonexistent objects, as I shall now detail.

As noted already, Avicenna recognizes objects perceived and objects conceived. He has the usual Aristotelian view that thoughts in a mental language signify objects and states of affairs, the spoken language signifies the mental language, and the written language signifies the spoken language. The mental language exists in the mind and has quiddities in intellectu as its constituents. A simple declarative statement, at least those about individuals of sense perception, of the form “s is P” makes the claims that s exists and that P is predicated of s. The simple denial, read as the negation of the affirmation, has the form “it is not the case that s is P.” It has disjunctive truth conditions:

‘Zayd does not exist (as) just’ - is true in all cases but one. So it is true when he is non-existent, and tyrannical, and mixed, both in potency, and not in potency, and it is false when he is just.^[72]

Suppose that denial is true because Zayd is nonexistent. Its truthmaker then becomes a nonexistent object. A Neoplatonist might suppose that falsity does not require a truthmaker, but only an absence or privation of a truthmaker. However, Avicenna does not take that route.

Although all objects, existent or not, exist in the mind as concepts is a theory, they are grounded in different niches of Avicenna’s metaphysical structure, as I now discuss.

Parsons has any object not having the E! property being a nonexistent object. Those whose properties are mutually consistent are possible; those whose properties are not are impossible. So too for Avicenna objects not existing in re are nonexistent, some possible, some impossible. Aristotle, according to Alexander, had already characterized the strictly possible as neither necessary nor actual.^[73] I turn now to the various types of nonexistent objects recognized by Avicenna.

4.1 Contingent Types and Individuals

Avicenna has actually contingent individuals, like this cloak, whole but able to be cut up. This cloak cut up does not actually exist ever but could. So too for such types such as being a sea battle in the Antarctic.

4.1.1 Past and Future

There may be true statements in science about what does not exist now, like eclipses in the past and eclipses in the future. This way of understanding the existence condition has the drawback of ignoring or at best re-describing the present tense of the statement. However, Avicenna seems content, at times, to allow for that, just as Ockham will say that “reprobate” in “Judas is reprobate” changes the reference of “Judas” from Judas now to Judas at a future time. Arabic makes it easier to ignore tense than Greek or Latin does. The verb system focuses on the perfective and imperfective, where the time being signified is determined contextually, especially by the context of the subject and predicate terms.

Such ampliation of the scope of time has some relation to phantasms, constructs of the imagination. For we know about past things via memories of events. But what we remember are not the phantasms as such but rather what the phantasms are about: events like eclipses. The phantasms just enable us to know about the past events; the ampliation in contrast makes the words refer to those events.

Ampliation to the future though cannot use phantasms constructed from memories of the past. Perhaps, it can use imaginary phantasms, to imagine an eclipse next year.

Along these lines, like the rule of Sherwood in Latin supposition theory,^[74] Avicenna allows for the sentential context, mostly the predicate, to fix or modify the signification of the subject. Thus, “the moon is eclipsed” is true since there are times in the existence of the moon when it has eclipses.^[75] Here, the predicate, “eclipsed,” determines the time at which the statement is to hold true.^[76] Even if we construe this claim to mean that the moon has eclipses, still we use contextual information to understand that we are not talking about the moon at all times but only at some times. In contrast, with “the moon has phases,” we intend the statement to hold at all times. Hence, the predicate term can restrict the reference of the subject term or not. Still, sometimes the predicate does not fix the time principally. Demonstrations in the second and third figures require conversions of propositions, where the subject and predicate are reversed. For an obvious case, just convert “the moon is eclipsed” to “some eclipsed thing is the moon.”

Avicenna is willing even to ampliate the reference modally too. For instance, “every baby has been in the womb” is true since there was a time when the baby in potency – not the actual baby but the fetus, the baby in potency – was in the womb.^[77]

In arguing against the existence of an infinite series of motions, Avicenna says that neither past nor future motions exist, since they do not exist now. To be sure, the past ones did exist in the past; the future ones exist now only possibly and will exist in the future.^[78] Ordinarily, an affirmative statement in the present tense requires the subject to exist now. Taken thus, saying that there are eclipses is false when there are now no eclipses. The statement becomes true only if the context changes the statement to one about the past, or, perhaps, if we are talking about eclipses as intelligible individuals. Avicenna perhaps is marking the latter when he allows that past, present, and future motions:

[…] have been collected together in an intellectual depiction of them as existing, but the collection with respect to predication and intellectual depiction is different from the collection in existence.^[79]

From present memories of past individuals and the universals abstracted from them, there can also exist in the mind universal concepts having no present instances. Think of our dinosaurs. These once existed but do no longer. Still there can be a science of the species of dinosaurs.

4.1.2 Present and Nonactual

In line with the actual possible, individuals and types arise that do not exist: this-here cloak having the never actualized potentiality of being cut up. Once the actual contingent concerns the past, it remains logically contingent but now is hypothetically impossible.

4.1.3 Intelligible

Avicenna is willing to drop the existence requirement for intelligible objects. “Rather attention is not paid to their existence but to their quiddity only.”^[80] These concern cases where no singulars of a certain type exist, but are needed for science. Think of numbers having no actual instances but still being used in arithmetic: often more than one singular is needed, as in “a × a = b.” Again in indirect proof, a logically impossible proposition may be assumed. In such cases, the predication relation alone determines the truth of the proposition. These objects too are nonexistent.

Another motivation for dropping the existence requirement may come from the truth conditions for negative propositions. As discussed earlier, Avicenna does say that the particular negative, “some S is not P,” is true either when there are no S’s or when P is not predicated of S. When no S exists, it will follow that the statement is true for any predicate P whatsoever.^[81] Then “some goatstag is not a goatstag” and likewise “no goatstag is not a goatstag” will be true, as no goatstags exist. This result does work, but not if Avicenna wants to have scientific demonstrations with terms having no instances in re.

Avicenna has a complex theory of how the imagination constructs individual instances of universals. These do not, or need not, exist in re; once thought about, they exist in intellectu as phantasms. For Avicenna, the imagination receives content both upward from quiddities in re via sense perception and downward from quiddities in themselves via intellectual intuition. It then may combine, or synthesize, this content into new concepts, including ones that go beyond the information provided.

On the upward way, imaginary individuals can come from senses arising from things existing in re, from perception via abstraction. We may get the concept purple and the concept cow from our sense experience and then put together the concept purple cow via the imagination. In this way, we can have dead poets and purple cows and flying men and griffins, from concepts of eagles and lions, as the individual subjects for universal propositions.

Such concepts then cannot get content beyond what is provided via sense perception. So such an account of existence does not give a way to provide instances for terms having content constructed from concepts that never have had instances in re. If I have never seen a heptagon or chiliagon in re, I cannot abstract the conception of heptagon or chiliagon and then imagine a house shaped thus.

Why could not concepts like heptagonal house and the megagon and the googol be constructed likewise by the imagination from perceptions of things in re? We perceive seven and sides and houses, and, after abstracting these, then construct the concept of heptagonal house; we see sides of polygons and somehow talk of millions and then construct the concept of megagon. So, perhaps even large numbers and chiliagons could be constructed from our sense experience, along the lines of some modern intuitionist theories?

Perhaps so, but Avicenna does not take this route, because, I suggest, it is tinged with the sophistical. How to distinguish reputable imaginary constructs like heptagonal houses from disreputable one, like the griffin or the “anquā”? This imaginary process by itself cannot do that job. Rather, doing that requires the intellect and the quiddities in themselves. Accordingly, Avicenna talks instead about intelligible individuals.

Avicenna begins by discussing intellectual abstraction.^[82] The intellect abstracts and unifies features of particular instances given in sense perception, so as to compose a single universal concept, a quiddity in the mind. The process of abstraction eliminates many features of the sense perceptions of individuals, some accidental, and some essential. Thus, in the conception of a sphere, the intellect ignores the particular location and time and size of an individual bronze sphere as well as its being bronze and being able to move. (All these characteristics are accidental to being a sphere, although the latter group is essential to there being a bronze sphere in re.) The intellect then unifies the various features left, including being three-dimensional, solid, and occupying a certain volume of space, which are essential to being a sphere, from this perception and the perception of other spheres, into a single concept of a sphere.

But how then to abstract the sphere away from the bronze, if, say, all our perceptions of spheres are of bronze spheres? Aristotle himself raises this puzzle.^[83] He says only that it is difficult to make the abstraction in thought. In contrast, Avicenna is trying to work out the details of what is required to make such an abstraction.

In addition to the imagination abstracting universal quiddities from senses perceptions of individuals in re, Avicenna holds that the intellect may think the universal quiddities in themselves, via direct intuition.^[84] This intuition makes it possible to abstract away being bronze and being movable from the concept of sphere. Completing the abstraction process so as to get the concept of sphere, free from matter and from essential accidents like being movable, would depend upon the imagination having some access to the quiddities in themselves. Avicenna insists that our intellects, once activated, have such direct access to quiddities in themselves.^[85]

For the intellect to descend from the radiant realm of these quiddities in themselves to the cave-like world of particulars, it needs the imagination.^[86] For the imagination returns the intellect from intuiting universal quiddities in themselves to dealing with particulars.^[87] The Greek commentators had already found themselves to be able to distinguish in the cryptic passages of Aristotle’s De Anima a complex doctrine of noûs whereby Aristotle distinguishes a transcendent, eternally active noûs from the noûs in us, which acts only in fits and starts and can be blinded and dissuaded by passions and inadequate evidence. Avicenna had sharpened and perhaps added on to the types of noûs being distinguished. Now, in this noetic hierarchy, theoretical noûs deals with universal and unchanging objects – for the neo-Platonic commentators, the Forms of Plato. In contrast, practical noûs deals with particular things and events, which we as finite animals must seek or avoid in order to survive. This latter, practical noûs has to deal with the content of sense perceptions, which present the “phenomena,” which are the things as they appear to us. Avicenna too says that the human soul has both theoretical and practical intellect, which are not “intellect” in the same sense.^[88] Thus the intellect has two sides, one rising upward toward the quiddities in themselves, the other descending toward particular things, the quiddities in re.^[89]

As with the Greek commentators, Avicenna has imagination enabling a transcendent noûs to become practical and become applied to particulars. Furthermore, imagination makes it possible for the potential intellect in us to become actualized and hook up with the active intellect, that is, with the intelligible – or, to use the Greek term, with the noumenal. Once activated, our intellect can construct scientific demonstrations and definitions. But to move from the universals in se, the quiddities in themselves, to their particular instances, the intellect needs imagination so as to generate intelligible individuals, not abstracted from sense perception, as their instances. For demonstrations typically universal propositions are used, of the form, “every S is M,” which deals with such instances. Commenting on Aristotle’s Prior Analytics I.33, Avicenna gives such an instance of generating an individual, imagined Zayd (Aristotle’s thinkable Aristomenes), from the universal type, imagined Zayd, presumably by ekthesis.^[90] In short, imagination makes science possible through making it possible to intellect to operate in the real world of individuals.^[91]

In scientific practice, Avicenna ideally wants both sense perception and intellectual intuition playing a role. I have discussed his theory elsewhere.^[92]

4.2 Impossible Types and Individuals

Given all his distinctions, Avicenna offers many niches for impossible objects. He does not seem to have used them all, perhaps because he does not find them all “realistic,” or perhaps because he has left us a lot of loose ends in his theory.

At the very least, there “are” impossible objects in the sense that they can be talked about in language. I may speak of round squares or, if you like, squares that are not square – Parsons remarks that to say round squares are impossible may be assuming a lot of Euclidean geometry; in that case, their impossibility would be only hypothetical, assuming those geometrical axioms and definitions.^[93] Expressions describing impossible objects appear here in a written language, and I may read them aloud so that they appear in a spoken language. Like Aristotle, Avicenna has it that expressions in the written language signify ones in the spoken language, which in turn signify senses in the mind, items in the mental language of thought.^[94] But, for Avicenna, do spoken impossible expressions signify senses in the mind, or just only those in written or spoken language? Plato had already noted that some sequences of letters or of words signify nothing.^[95] Does then a complex like “round square” signify no sense, nothing in the mental language? The answer might depend on the type of impossibility being entertained.

Avicenna considers statements like “a goatstag is existent” and “a goatstag is non-existent.” The goatstag serves for Aristotle as an example of a not-being.^[96] Aristotle says that what is not is thought about but is not;^[97] the goatstag is [an object of knowledge] qua non-existent.^[98] Aristotle has it then that the goatstag is an object of belief and perhaps of knowledge in some sense. Such views seem to suffice for making “goatstag” a sense in the mental language.

Likewise Avicenna says:

Know that [this happens] when something non-existent in itself is predicated in its existence, where its thought by itself or the enunciation of its expression by itself has not signified truth or falsity, so long as there is not connected to it that it be existent or non-existent (in) a connection in the intellect or in the expression. For instance, it is believed that a goatstag is existent, or it is believed that it is not existent, and it is said that a goatstag is existent, and it is said that a goatstag is not existent, either simply, without a condition of time, or with the condition of time that it is existent at (this time) or it is existent at (that time) or (at) the present time.^[99]

Avicenna first points out that “goatstag” by itself signifies nothing true or false, as it makes no statement. Still a statement that the goatstag is existent makes a predicative statement in the expression, the written or spoken language, or in the intellect, the mental language. Thus “goatstag” seems to exist in the intellect too. Such considerations seem to suffice for making nonexistent objects concepts existing in the mind.^[100]

Is a goatstag impossible logically or physically? It is hard to tell, without knowing the definitions of “goat” and “stag.” If the two have inconsistent constituents, goatstag is a logically impossible object; if they do not, then only a physically impossible object. The concept of rational goat, in contrast, would clearly be logically impossible for Avicenna. Some considerations made below suggest that goatstag is physically impossible only.

4.2.1 Logically Impossible: The Absolute

Avicenna says little about the logically impossible. After all, in his metaphysics he focuses on essences insofar as they exist in re in the world. Yet he does seem to need it. Indirect proofs may assume the logically impossible. Arithmetic talks about the greatest positive integer, and then proceeds to prove that it cannot exist. Geometry proves that Bryson’s project of squaring the circle is logically impossible.^[101] Logically impossible types may be constructed directly from combinations of quiddities in themselves: the rational goat; the four-sided triangle.

On the other hand, Avicenna says

As for the Platonic Forms, peace be upon them! They are empty sounds and names not having a sense.^[102]

He accepts Aristotle’s objections to the Forms. The conception of a Form is incoherent and hence logically impossible. Avicenna admits that Forms are names. Hence, they appear in written and spoken language. How about in the mental language, as senses? Avicenna himself makes judgments about them. Perhaps by “not having a sense,” Avicenna means here that such names are not first intentions pointing to things outside of the mind. I am inclined to go this way, and say that Avicenna recognizes logically impossible objects. For, as mentioned, they have use in indirect proofs in science.

Avicenna might allow also for logically impossible individuals. In saying, “Let n be the largest positive integer,” I am assuming, by ekthesis, that n, an individual constant, is this individual number, to which I then add 1 so as to demonstrate the impossibility.^[103]

Avicenna has a theory that, once the intellect, purified by dialectic, intuits quiddities in themselves, it, in cooperation with the imagination, can generate intelligible individuals – well, here, unintelligible individuals. I discuss this theory further below.

4.2.2 Physically Impossible: The Hypothetical

In On Interpretation 11, Aristotle discusses why the inference from “Homer is a poet” to “Homer is” is fallacious. Avicenna offers two readings of it. First, “Homer” refers to something existing, in re, in the past and not in the present: a past poet. The reference is ampliated, as with “eclipse”: statements about the moon having eclipses should be understood as restricted to the times when the moon is eclipsed.^[104] On the second reading, “Homer” refers to something never existing in re but to a figment of the imagination, a phantasm, existing only in intellectu, like the griffin or Cookie Monster.^[105] Taken in this way, subject terms may have existential import, but only to imaginary individuals existing in intellectu.

In the same passage, Aristotle worries about the inference from “what is not is thought about” to “what is not is.”^[106] The Greek and Latin tradition tended to take chimeras and griffins as not-beings, examples of what is not. These would be imaginary beings, which do not ever exist in re, or, perhaps, cannot ever exist in re. Avicenna also gives an analysis of “Homer is a poet” along these lines, where Homer is a not-being, a mythical being.

Avicenna has an example of an imaginary being similar to the griffin, the “anquā” (عنقا), often translated as “griffon” [read: griffin] in the Wehr dictionary and in translations of “Ibn Arabi’s Al-Anqa” al-Mughrib (The Fabulous Gryphon).^[107] Druart notes

The famous translator from Greek or Syriac into Arabic, Ishâq ibn Hunayn, had already used this “anquā” to translate the word “sphynx” in Aristotle’s Physics at 208a29f and Avicenna’s predecessor, the philosopher/logician al-Fârâbí (870-950) had added the “anquā” as an example of a fabulous animal parallel to that of the famous “goat-stag” in his Long Commentary on Aristotle’s De Interpretatione, ^[108]

So this “anquā” was a standard example of a not-being. Avicenna says about it that this expression is a name signifying a sense in the imagination, while not having existence in individuals.^[109]

However, Druart makes a strong case that Avicenna has an idiosyncratic sense of “anquā.” In several passages, Avicenna takes it to mean a human being able to fly like a bird. He then says: “but this thing [, i.e., the ‘anqâ’,] is impossible (muḥāl) as one knows with a minimum of reflection.”^[110] The combination of flying and human being is “impossible.” Avicenna, I would say, uses “muḥāl” here to mean “absurd” or “impossible” physically; he hardly ever uses it to mean “impossible” in the logical sense. This becomes important, as noted above.

Druart goes on to note that in the Letter on the Disappearance of the Vain Intelligible Forms after Death (The Letter on the Soul), Avicenna says,

Now among the impossible forms, there are some which have this characteristic, for example, the belief that the “Anquā” Mughrib exists in concrete singulars. Whoever admits its existence in concrete singulars also admits that it can be more than one individual. He, therefore, believes something universal and this thing is intelligible.^[111]

So Avicenna admits that things like anquā are imaginary individuals, existing in intellectu but not in re, instances of the imaginary species of “anquā.” Thus he recognizes physically impossible individuals and types. Indeed, elsewhere Avicenna groups the phoenix and heptagonal house together.^[112] As discussed next, Avicenna claims that there never are heptagonal houses, but surely they are possible – physically or even actually. The phoenix is a mythical beast, along the lines of griffins and “anquā.” At the least, such objects are not logically impossible.

4.2.3 Actually Impossible

Actually impossible objects include the cut up cloak, which in fact was never cut up, and the sea battle that never took place, although it did. As with physically impossible individuals, the imagination constructs such individuals from elements of sense perceptions. Avicenna’s theory allows also for actually impossible types, like the sea battle in the Antarctic Ocean in the twentieth century, assuming that there were none.

Avicenna’s famous example of the heptagonal house might be an instance of the actually impossible. Given the laws of nature, materials, and carpenters in the world, heptagonal houses seem physically possible, both the type and the individual. Yet, Avicenna says, no heptagonal houses exist, ever.

Avicenna speaks of the universal 1) as being predicated in actuality of many, like human being, and 2) as being predicated of a sense that by its nature could be predicated of many, like the heptagonal house, even though it never is so predicated, and 3) as being predicated of a sense such that it could be predicated of many, although in actuality it is predicated only of one, like the Sun or the Earth.^[113] The second way gives something that is physically possible but actually impossible. The third way too can be taken thus, although Avicenna says that the impossibility of many Suns come from general hypothetical conditions of the world – and then would be physically impossible. For Avicenna speaks of this third type in the mode of manī’, typically used for the logically impossible but here being extended to the physically possible. Avicenna speaks of the second type in the mode of muḥāl, typically used for the physically impossible.^[114]

5 Conclusions

Contingent nonexistent objects may exist at other times or be unactualized potentialities of things existing in re now.
As thought and talked about, all impossible objects exist in intellectu.
The impossible, in the sense of “necessary not” may be: logical or physical.
The logically impossible has its basis in the quiddities in themselves combined in various ways. Such give logically impossible types. From these the imagination may generate logically impossible individuals.
The physically impossible has its basis in quiddities in re and their combinations. From such physically impossible types, the imagination may generate physically impossible individuals.
The actual impossible concerns the physically impossible, plus additional postulates about the state of the world beyond the logical principles, with additional hypothesis about which individuals exist at a certain time and place. Given all those assumptions, certain individuals and types are impossible then and there.

Compared to a modern theory of nonexistent objects, like that of Terence Parsons, Avicenna does not fare so badly. Parsons has all objects, necessary, possible, actual, and impossible, in a single domain, rather like that of the quiddities in the mind. He admits that they “are,” such that they may take the existential quantifier. However, they do not exist in the robust sense, the E! predicate, which he takes to be a “watered-down” version of the existential quantifier. He admits various applications of his theory of nonexistent objects, to fiction, myth, fantasies, and dreams, and, in particular, to impossible objects like round squares. He makes these interpretations and applications on a pragmatic, ad hoc basis. Avicenna has a more systematic account and supplies a metaphysical foundation for the genres of nonexistent objects that he recognizes. This modern theory has the advantage in the precision and power of its syntax; Avicenna’s has the advantage in its semantics and ease of applying the formal model to the world.

Although Parsons speaks of medieval theories of nonexistent objects as being under a paradigm different from the one of his theory, I hope to have shown their congruences. Instead, view them as being under the same paradigm or research tradition, with some differences.

Funding information: Author states no funding involved.
Author contribution: The author confirms the sole responsibility for the conception of the study, presented results and manuscript preparation.
Conflict of interest: Author states no conflict of interest.

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Received: 2024-04-01

Revised: 2025-03-20

Accepted: 2025-03-21

Published Online: 2025-05-16

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