A third realm ontology? Naṣīr al-Dīn Ṭūsī and the nafs al-amr

ABSTRACT

The standard interpretation of Avicenna's correspondence theory of truth posits that propositions either correspond to what exists extramentally or otherwise their truthmaker is mental existence. An influential post-Avicennian philosopher, Naṣīr al-Dīn Ṭūsī (d. 1274) points to the insufficiency of the above division of propositions and their respective truthmakers. He mentions the possibility of conceiving false propositions, such as ‘One is not half of two’ and postulates the necessity of the existence of another truthmaking domain for their true counterparts which he calls nafs al-amr. It is where objective and timeless entities, such as mathematical propositions, are located. While some claim that Ṭūsī's identification of this domain with the first Separate Intellect is a testimony to his Avicennian convictions, Ṭūsī's solution is a conspicuous departure from Avicenna that not only helps him remedy the insufficiency of Avicenna's theory of truth but is consistent with his critique of Avicenna's theory of God’s knowledge.

KEYWORDS:

• Avicenna
• Naṣīr al-Dīn Ṭūsī
• correspondence theory of truth
• third realm
• Nafs al-amr

Naṣīr al-Dīn Ṭūsī (1201–1274) is considered an Avicennian hardliner who tried to re-establish and strengthen Avicenna's original positions vis-à-vis Fakhr al-Dīn Rāzī's (d. 1210) and other theologians’ more polemical engagement.¹ To an extent, this historiographical assessment can be challenged by an engagement in philosophical scrutiny of his doctrines.² One conspicuous example will be presented in the course of this article. This is Ṭūsī's understanding of correspondence theory of truth. On Ṭūsī's interpretation of Avicenna, the latter posited that propositions either correspond to what exists extramentally or otherwise their truthmaker is mental existence. Ṭūsī found this solution insufficient, arguing for the necessity of a third truthmaker, the nafs al-amr. The exact nature and ontological status of this additional truthmaker will be analysed here in detail. Although Ṭūsī's solution was almost universally rejected by later thinkers, the problem he postulated paved the way for a further development of Islamic metaphysics.³

Ṭūsī's entire argument consists of three parts. The first part was presented in the influential theological summa, Tajrīd al-iʿtiqād (“The Epitome of belief”). There, the problem of false judgements is brought up. The whole argument is laid down in an independent treatise called Ithbāt al-ʿaql al-mufāriq (“Proof of the [Existence] of the Separate Intellect”). In this work, Ṭūsī's understanding of the objective reality of truth is used to prove the existence of the Separate Intellect, as he finds other proofs unsatisfactory (Ṭūsī, Tajrīd al-ʿaqāʾid, 95). It is only within this treatise that an ontologically distinct, additional domain is posited.

I will start by analysing the initial part of the argument as found in the Tajrīd, where Ṭūsī postulates the insufficiency of Avicenna's theory (Section 1). Here, he refrains from making explicit ontological commitments to a third world because his primary focus is on addressing the problems inherent to mental existence itself, proposing original solutions along the way. I will then look at Ṭūsī's other works, notably Sharḥ al-Ishārāt, to trace the gradual development of the notion of nafs al-amr that led Ṭūsī to the subsequent reformulation of this concept in ontological terms (Section 2). In Section 3, I will present the argument in its full form. The question of whether the argument leads to the formulation of a third world ontology will be worked out in Section 4. In some significant ways, Ṭūsī's theory is similar to that of Frege who postulated a third realm of eternal truths and did it for similar reasons as Ṭūsī. Given the succinctness of Ṭūsī's account, Frege's theory offers a useful hermeneutical tool. Lastly, I will present some objections against Ṭūsī's theory (Section 5). I will not engage with a set of objections that do not challenge the ontological character of the nafs al-amr, and only reject its equation with the Separate Intellect. Instead, I will focus on the second type of objections which attack the postulation of a third truthmaking domain and argue instead that one can be realist about objectivity and necessity of truths without committing oneself to the belief in their eternal existence.

1. The insufficiency of Avicenna's theory of truth

In a section of the Tajrīd al-iʿtiqād devoted to non-existence, Ṭūsī discusses various operations the intellect can perform on it, such as conceptualization and judgement. These intellectual operations include conceiving two contradictories and predicating their contradiction (i.e. negation of one, affirmation of another), or conceptualization of non-existence. He deals with difficulties associated with such operations. For example, conceiving two contradictories together and judging them as such does not lead to the absurdity of the coincidence of contradictories, because contradiction relates to their essence only, and not to the correspondence of the conceived form with the external reality or lack thereof.⁴

The mind can also conceive of the non-existence of all things, the non-existence of itself or even the non-existence of non-existence by creating forms that represent them and then removing these forms. Here, Ṭūsī addresses the notion that something cannot exist under any circumstances, neither in reality nor even as a concept or in the imagination which leads to the well-known paradox of the absolute non-existence (see Lameer, Ghayr al-maʿlūm). It can be explained as follows. The judgement on the absolute non-existent is that it is not subsistent. This necessitates contradiction because the subject of this judgement is the absolute non-existent and it is judged by the impossibility of judgement upon it. Thus, the absolute non-existent is described by the impossibility of judgement upon it, and – simultaneously – by the validity of judgement upon it, hence the contradiction. In other words, the absolute non-existent is characterized by the impossibility of making judgements about it, yet the very act of making judgements on it involves a contradiction because it simultaneously affirms and denies the possibility of judgement (Ṭūsī, Tajrīd, 69). The answer Ṭūsī gives is that the mind can imagine that non-existence has some intelligible form which is distinct from the form of existence and then conceive its negation. The non-existence is subsistent⁵ because one has its concept in their mind, i.e. removal of both mental and external subsistence, and it is also the counterpart of existence because it is its negation. No contradiction obtains here because the judgement that non-existence is the removal of both mental and external subsistence as something that can be conceptualized is different from non-existence as the counterpart of existence, i.e. as something not subsistent extramentally.⁶

The premise whereby Ṭūsī refutes the above problems is the difference between forms of things existing extramentally and forms of things that exist mentally, the intelligibles, which do not share many of the concomitants of extramental things.⁷ This is why, as in the examples above, contradictories taken as cognitive forms are not contradictory, or why non-existence – as an intelligible – can be subsistent and a kind (qism) of existence, even if extramentally they are counterparts (qasīm). Ultimately, however, Ṭūsī runs into a problem he cannot remove by recourse to the doctrine of mental existence. This is the problem of false judgements:

If the mind’s judgment of the mind-independent things is by virtue of what is like them [i.e. insofar as both the subject and predicate of that judgment are mind-independent], then there must be mutual correspondence [between the mind-independent subject and predicate and the proposition] for [the proposition] to be true. Otherwise, it is not [i.e. the judgment is not true in view of the correspondence of both its subject and predicate to external reality]. In such case, [the judgment] is true in view of the correspondence with what is in the nafs al-amr, because of the possibility of conceiving false things.

(Ṭūsī, Tajrīd, 70)

Let us unpack this customarily succinct argument. According to the standard correspondence theory of truth, propositions either correspond to what exists extramentally or otherwise their truthmaker is mental existence. An example of the first type of proposition is ‘Human is an animal’. This proposition is true by virtue of both its subject and predicate existing extramentally and having an existential relation so that the judgement of the mind can be true, i.e. the cognitive relation corresponds to it. In the other two kinds of propositions mental existence plays a role and correspondence to what exists extramentally is not necessary. An example of the first kind is ‘Human is possible’, where the predicate ‘possible’ is an intellectual matter corresponding to the subject ‘human’, regardless of whether that subject exists in the external reality or not. The second kind of proposition is when the mind makes a judgement on intelligible matters by an intellectual judgement, such as when one says: ‘Possibility is opposite of impossibility’. In this case, the judgement’s correspondence to what exists extramentally is not necessary, because there is no possibility and impossibility in the extramental world (Kashf al-murād, 53; Tasdīd al-qawāʿid, 2:200–201; al-Sharḥ al-jadīd, 315–16). Since in both cases correspondence to extramental world is not possible, the truthmaker of such propositions must be the mind.⁸

Ṭūsī finds this theory insufficient and shows why the mind cannot be the truthmaker of all such propositions. This is because the mind can conceive of a false proposition and judge it as true. To take the above examples, the false propositions would be, respectively: ‘Human is necessary’ and ‘Possibility is not opposite to impossibility’. If the mind were the truthmaker of such propositions, then they would have to be true since there is a mental form that corresponds to them. This is why, the conclusion goes, propositions like ‘Possibility is opposite of impossibility’ are true by virtue of their correspondence with what is in nafs al-amr. False propositions are false because they do not correspond to anything that exists in nafs al-amr.

It is crucial to note that so far, the phrasing and the treatment of the issue avoid any additional ontological commitments. One possible reason is that Ṭūsī tried not to antagonize the readers of the summa with concepts that might provoke controversy or disagreement. Therefore, he wanted to steer clear of contentious concepts or theories that could alienate some of his audience. Another likely explanation is that the treatise where Ṭūsī identifies nafs al-amr with the Separate Intellect by an appeal to a third realm was written later than the theological summa. This would explain why in the Tajrīd Ṭūsī does not mention the nafs al-amr argument in his list of arguments for the existence of Active Intellect.⁹

Therefore, depending on the relative chronology of the two works and/or their different readership, two interpretations of nafs al-amr emerge, which will influence Ṭūsī's overall stance on problems of mental existence. According to the first interpretation, nafs al-amr should be understood as a spectrum concept that refers to how a thing is by virtue of its very self. So understood, nafs al-amr encompasses all entities, regardless of whether they are (1) mind-independent, (2) mind-dependent but mind-independently possible, or (3) mind-dependent and entirely contingent upon human perception that may not exist independently of it (like impossible things).¹⁰ Based on this understanding of nafs al-amr, non-existence can be conceptualized as having some form in the mind and its negation can be conceived within nafs al-amrs’ scope. The object and its modality are judged within their inherent context. For example, we take ‘The number five is even’ as such, and we can say it is false in the sense that it is not grounded in mind-independent reality (where 5 is odd), but the statement is true when considered within the context of its mental existence. This has the advantage that it can be taken as the subject of certain second order propositions about it. Thus, we can truly say: ‘“The number five is even” is false’ (cf. Ahmed, Palimpsests of Themselves, 215, fn. 88).

On a different interpretation, which can be called essentialist, nafs al-amr denotes the true essence (dhāt) of a thing, either not yet manifest in extramental reality, or one that can be discovered as true. In this sense, falsehoods are outside nafs al-amr. When it comes to a human knowers’ perception, two things may happen. First, the perceived thing may have an essential nature independent of the perceivers’ perception, such as ‘The number five is odd’ and the perception matches the true nature of five. Second, the perception might be of something that does not correspond to any essential nature, e.g. ‘The number five is even’. Such a thing lacks an essence that can be proven or correctly perceived because it does not exist in nafs al-amr (also al-Ṭihrānī, Tawḍīḥ al-murād, 95–96). For this interpretation not to collapse into the first one, a few additional caveats must be attached. One is the cui bono of the argument: if Ṭūsī advocates for something that preserves the essential natures of things and serves as their grounding principle, this understanding of nafs al-amr is a better one. Second, this interpretation better accounts for certainty of God’s knowledge, rather than being a theory directed at human knowers. Put differently, Ṭūsī would argue here for an externalist theory of knowledge in the sense that (1) nafs al-amr is a mental content external to the human mind, and (2) justification is not necessarily a condition of human knowledge (cf. what I say below).

The first interpretation of nafs al-amr better accounts for human knowledge and helps solve various problems of mental existence as it grounds mental considerations in the thing itself, the second is geared toward the explanation of God’s certain and eternal knowledge, as it grounds all truths, be they mental or extramental, in a supra-reality fully available only to Him. Without acknowledging these ontological and theological concerns (as well as rejecting certain premises of Ṭūsī's full argument presented in Section 3), the theory presented in the Tajrīd can be successfully reduced to the first interpretation. Historically, this is indeed what happened after Ṭūsī. It is instructive, however, that the second, third-realm interpretation was not lost even on some early readers of the Tajrīd; I will engage with some of them in Section 5. The second remark I want to make is that Ṭūsī warns about the conflation of truth with its psychological assertion. Ṭūsī's objective can thus be expressed as his anti-psychologism along the lines postulated by Frege.¹¹ Ṭūsī, like Frege, wants to differentiate between the psychological underpinning of our theory of truth as opposed to the theory of truth itself. Frege writes that logic discovers laws of thought. These, however, should not be understood in analogy to laws of nature, where they would be generalizations of ‘thinking as a mental occurrence’. Such generalizations would render them psychological laws dealing with the assertion (of truth/falsity) and the process of thinking (Frege, Thought, 289–90). So, rather than being empirical generalizations, logical laws are normative principles guiding our pursuit of truth.

This goes contrary to the tradition of Avicennian epistemology which orders propositions according to the strength of the intellect’s assent to them (and other principles such as the medium of assent). Famously, the hierarchy starts from the primary concepts or propositions to which a sound mind necessarily assents. Then there are judgements based on intuitions of the soul, and so on (cf. Avicenna, al-Shifāʿ: al-Burhān, I.4, 63–67). All this is described in purely psychological terms as the influence of a judgement on the soul (Avicenna, Burhān, I.4, 63), decisiveness of judgement (Avicenna, Burhān, I.4, 64), etc. For example, conjecture is defined as an inclination of the soul toward one of the sides of a proposition without decisive intellectual judgement that the other side cannot be true.¹² One could say that these psychological terms can be parsed in logical terms, e.g. the soul’s inclination to take some proposition as true amounts to that proposition’s greater likelihood of being true (given a certain set of background propositions). Indeed, Avicenna points out the difference between logic and psychology. However, Ṭūsī's example which shows that someone might be convinced that certain propositions are true despite them being actually false, underscores the fallibility inherent in this cognitive process. Consequently, the standard theory, which relies solely on mental existence as the determinant of truth, proves inadequate in explaining these instances of erroneous judgement.

In any case, on the standard account, knowledge is understood as a decisive assertion of truth (ḥukm jāzim yaqīn). With the bivalence of truth and falsity, knowing is described as an assertion of one of them – by the necessity of the intellect, the act of will, or other psychological processes. With the passage from the Tajrīd quoted above, Ṭūsī seems to say that we do make false judgements (perhaps even with the decisive assertion that they are true). Therefore, we need something beyond our minds that acts as a guarantor of truth.

2. Ontologising nafs al-amr: from Avicenna to Ṭūsī

In this section, let us follow Ṭūsī's other texts to see how he arrives at his full-blown theory. Nafs al-amr or al-amr fī nafsihi, as it is sometimes used, literally means the thing itself. This non-technical use of the term is attested in both Avicenna and Ṭūsī, where fī nafs al-amr means simply ‘in itself’.¹³ However, any attempt beyond this to render the Arabic expression by one phrase is virtually impossible, not least because of the changes of meaning this expression underwent from Avicenna to Ṭūsī and other authors after him.

Generally, when we scrutinize the text of Ṭūsī's commentary, we see that he uses the term much more often than Avicenna. This is in part because he often substitutes Avicenna’s fī nafsihi by fī nafs al-amr. For example, one of the technical meanings in which Avicenna uses fī nafsihi can be rendered as ‘as it really is’, or ‘actually’. In one passage, Avicenna refutes the atomists by pointing out that the continuity of the body is confirmed by the senses and says, “Rather, [the body] is in actuality (fī nafsihi) as it is to the senses”, which Ṭūsī explains:

Sensation judges that the body is continuous. According to the opinion of the two groups [of atomists mentioned previously], affirming divisible parts is an intellectual, non-sensible matter. When this is invalidated, it is correct [to say] that the body is actually (fī nafs al-amr) continuous, just like it is to the senses.

(Avicenna and Ṭūsī, Sharḥ al-Ishārāt, 2:165)

The point that Ṭūsī makes here is that the thing which appears continuous to the senses is actually continuous, it is in reality as it appears. This duality of representation and reality is highlighted in an alternative interpretation of how Avicenna uses the concept of nafs al-amr. According to al-Sāwī, nafs al-amr is equivalent to extramental reality, in contrast with the thing taken in consideration with something else, in which case a false statement can be made (al-Baṣāʾir al-naṣīriyya, 179). This sense may be corroborated by what Avicenna writes in the logical part of the Ishārāt, where he describes the relation of the predicate of a proposition to its subject. He says that it can be a relation of existential necessity, possibility, and impossibility. As Avicenna writes, the predicate must have one of the following relations to the subject:

(…) a relation of necessary existence in the extramental reality (fī nafs al-amr), such as ‘animal’ when we say ‘Human is an animal’ or ‘Human is not an animal’; or a relation where the existence or non-existence [of the predicate] is not necessary, such as ‘a writer’ when we say: ‘Human is a writer’ or ‘Human is not a writer’; or a relation where the non-existence [of the predicate] is necessary, such as ‘stone’ when we say: ‘Human is a stone’ or ‘Human is not a stone’.

(Avicenna and Ṭūsī, Sharḥ al-Ishārāt, 1:261)

Avicenna appears here to equate nafs al-amr with extramental reality, as in his examples both the subjects and predicates of the propositions refer to things existing in concrete reality. Only by referencing these concrete realities can one ascertain the truth of the propositions. Notably, the sentence ‘Human is an animal’ is used by Ṭūsī's commentators to illustrate those propositions that are true by virtue of both their subject and predicates’ correspondence to extramental reality, involving no correspondence to mentally existing objects. It is possible (although one can only speculate) that Ṭūsī was inspired by this exact passage. In any case, he explicates Avicenna's passage further:

He says, “And by ‘matter’ we mean, for example, the state which belongs to the animal in relation to the human extramentally (fī nafs al-amr) and to which the term ‘necessity’ applies, regardless of whether we say: ‘Human is an animal’ or ‘Human is not an animal’”. We know with certainty that this relation – if we want to capture it – does not change by reason of its affirmation or negation, and it is what is meant as ‘necessity’ in both cases [i.e. affirmation and negation] (…) Know that the matter is not the mode (al-jiha). The difference between them is that the matter is that relation as it exists extramentally (fī nafs al-amr) and the mode is what is understood and conceptualised when we think about the relation of this proposition’s predicate to its subject, regardless of whether it is uttered or not, and regardless of whether it corresponds to the matter or not.¹⁴

(Avicenna and al-Ṭūsī, Sharḥ al-Ishārāt, 1:261–62)

Ṭūsī makes use of Avicenna's idea that something is true regardless of our propositional attitude toward it. He goes further than Avicenna, though. In the logical part of the Ishārāt Avicenna says that the truth value of every proposition is determinate, and if it seems indeterminate in some possible propositions it is only due to the limitations of human knowers. Ṭūsī explains that this also obtains in future contingents:

Truth and falsity may negate [each other], as in the matters of necessity and impossibility, and may not negate [each other], as in the possible matter, especially the future one. What has occurred in the past and the present became determined, whether as existent or non-existent, so true and false [propositions] are determined according to the correspondence [to this extramental reality] or lack thereof, even though in relation to us, due to our ignorance, they might not be determined. As for the future [contingent matter], there is a controversy regarding whether the indetermination of one of its two sides is in the nafs al-amr, or in relation to us. The majority of philosophers think that it is also like this in the nafs al-amr. The verification rejects [the possibility that future contingents are indeterminate in themselves], because originated things depend in themselves on causes by which they become necessary, and without which they become impossible, and those causes end with the First Cause that is necessary in itself, as explained in theology.¹⁵

(Avicenna and al-Ṭūsī, Sharḥ al-Ishārāt, 1:300)

The indetermination of future contingents is only relative to us, but in reality, in the nafs al-amr, they are determined. Ṭūsī explains this determination by introducing the Principle of Sufficient Reason which dictates that everything that exists is causally determined and necessary. However, since future contingents are not yet existentiated and thus not yet determined in the same way past and present things are, their determination has to be somewhere over and above the realm of the already existentiated things. In other words, because their truth value is determined, there needs to exist a truthmaker to which our judgements about them correspond. This is the important step Ṭūsī makes toward ontologising the nafs al-amr.

3. Nafs al-amr as the separate intellect

The next step is taken by Ṭūsī in a short treatise written to provide a convincing proof of the existence of the Separate Intellect as he finds existing proofs lacking (cf. Ṭūsī, Tajrīd, 95). The proof he advances is the epistemological need for an intelligible truthmaking domain for true propositions which he then identifies as the First Separate intellect. The treatise presents three interconnected arguments: (1) argument from correspondence for the existence of the nafs al-amr, (2) argument for the nature of the nafs al-amr, (3) argument for its equation with the First Separate Intellect.

The significance of Ṭūsī's argument has not gone unnoticed (Spiker, Things as They Are, 29). One can approach it critically in two ways. The first is a careful analysis of the totality of the argument to challenge some or most of its premises. This in fact has been done by many commentators who take the treatise to present one argument. The other approach is to take the first part of the whole argument, i.e. the epistemic part, without accepting Ṭūsī's ontological solution. In my reading, the first part of the argument can and should be treated separately – in fact, this is what Ṭūsī does in the Tajrīd. In what follows, I will present the whole three-part argument in a schematic way to discuss its ontological concomitants in Section 4 and objections to its first part in the final section.

1.	Argument from correspondence for the existence of nafs al-amr

[P1] True judgements correspond to what is in the nafs al-amr. False judgements do not correspond to what is in the nafs al-amr. This includes judgements such as ‘The diagonal of the square is not commensurate with its side’ and judgements that no mind has even thought.

[P2] Correspondence obtains between two things that are different in individuation and united in that by which correspondence occurs.

[P3] True and false judgements share the fact of mental existence.

[C] So, true judgements correspond to the nafs al-amr that is different than mental existence, viz. something that subsists outside our minds, while false judgements do not.

Ṭūsī claims that all three premises are intuitive or otherwise beyond doubt. He shows that the nafs al-amr cannot be mental existence because both true and false propositions exist mentally, while only one of them is true.¹⁶ What strengthens this conclusion are the cases of compound ignorance, i.e. when a person does not know something but is certain that they do. Next, nafs al-amr cannot correspond to the physical existence either. This is because Ṭūsī mentions that nafs al-amr contains – and as exemplary entities – mathematical propositions such as ‘The diagonal of the square is not commensurate with its side’, or primary logical propositions, e.g. ‘One is half of two’. Moreover, we do not doubt that there are true propositions no mind has ever thought. If we were to identify the nafs al-amr with physical existence, some of our judgements would lack their truthmaker. Since we need to reject the physical and mental existence as possible truthmakers that can account for all true propositions, a truthmaker that is somehow different from the two needs to be existent. Note here that the argument works on the assumption that individuation should be understood in the strong sense of being a different kind of existence, which Ṭūsī takes to be self-evident. For the argument to bring the desired conclusion Ṭūsī must equate concrete reality of physical particulars with the whole extramental realm. So, the argument works this way: some statements have their truthmakers in concrete reality (e.g. ‘Human is an animal’), some in mental existence (‘Human is possible’). These two do not account, however, for all true statements. These remaining statements correspond to nafs al-amr which must perforce be a different kind of existence, because of P2.

2.	Argument for the nature of nafs al-amr

So far, Ṭūsī has determined that the truthmaker of some judgements cannot be mental existence (because of the possibility of false judgements) and suggested that their truth cannot be determined either by virtue of their correspondence to the physical realm (because of their intelligible character). The exact nature of the nafs al-amr is determined in a disjunctive syllogism that is presented directly after the first argument for its existence.

[DS] The extramentally subsistent nafs al-amr is either:

• self-subsistent: in position or not in position,

• represented in another: in position or not in position.

The nafs al-amr cannot be self-subsistent and in position because: (1) true judgements, such as mathematical propositions, are neither in time nor matter. (2) Knowledge of correspondence obtains after awareness of the corresponding things qua corresponding things. We do not doubt that correspondence occurs although we may be ignorant about the exact nature of the corresponding things in themselves, including whether they are in position or not. So, the corresponding things are not necessarily material. And even if they are, we do disregard their materiality when we take them as relate in our judgements. If I know that the whole, which is the judgement, is immaterial, I must know that its parts are immaterial too. So, correspondence must be immaterial. (3) We perceive the judgements that are in our minds only by our intellect, while we perceive things that are in position only by the senses. The correspondence between the intelligibles and the sensible things qua sensible things is impossible.

Further, the nafs al-amr cannot be self-subsistent and not in position because it would be the Platonic Forms. Ṭūsī does not offer an argument for the rejection of Platonic forms, but simply assumes the matter is settled in favour of their non-existence. Finally, the nafs al-amr cannot be represented in another which is in position because what is represented in it would share its nature, while it has been shown that it has to be immaterial. By exhaustion of all other options, true judgements must be represented in another which is immaterial.

3.	Argument for the equation of nafs al-amr with the 1st separate intellect

[P1] The substratum in which the nafs al-amr subsists cannot be potential because correspondence cannot obtain between something that is actual and something potential (our possible mental judgements).

[P2] The substratum in which the nafs al-amr subsists cannot be destroyed or changed (including become actual) or be in time because true judgements are eternally and unchangeably true. If the substratum of true judgements were capable of change, judgements subsisting in it could subsist without it and this is impossible.

[C1] The substratum where true judgements subsist must be immaterial, unchangeable and eternally actual. Such a thing is either the Necessary Existent or its first emanation, the First Separate Intellect.

[P3] This substratum must also include actually existent infinite multiplicity and be receptive of multiplicity that is represented in it.

[P4] There can be no multiplicity in the essence of the Necessary Existent, nor can He have a potential aspect.

[C2] The nafs al-amr cannot be the Necessary Existent. Therefore, it must be the First Separate Intellect.

The motivation driving Ṭūsī's C2 are his views on God’s knowledge and his critique of Avicenna's theory. Namely, he rejects two corollaries of Avicenna's theory of God’s knowledge. First, God cannot be the immediate source of things, as it would introduce multiplicity into His essence. Second, God is an absolutely simple being, thus He cannot have both active and passive, receptive aspects. However, according to Ṭūsī's critique, Avicenna's theory implies that God’s essence produces (multiple) intelligible forms and is also receptive of them. (See also Avicenna and al-Ṭūsī, Sharḥ al-Ishārāt 3:281–85.) Part of Ṭūsī's solution to the problems stemming from Avicenna's account is his theory that the Necessary Existent knows the objects of His knowledge as subsistent in the nafs al-amr.¹⁷

Before moving further, I would like to recapitulate what has been established so far, so that the important corollaries of Ṭūsī's theory can come to light. The first function Ṭūsī reserves for the nafs al-amr is to be the truthmaker for true judgements whose truth could not be guaranteed otherwise. This refers first and foremost to mathematical and logical truths, ensuring the objectivity of science. However, true, scientific judgements are far from constituting the full extension of the nafs al-amr. The second role Ṭūsī envisions for it stems from the identification of the nafs al-amr with the First Separate Intellect, which is the immediate object of God’s knowledge. To be perfect and complete, divine knowledge must include all events past, present and future.¹⁸ As Ṭūsī writes, God’s knowledge has as its object “the form of the world that corresponds to all its universal and fixed, particular things, renewing and passing by, individuated by a specific time, according to how existence is, and without any change in it” (Avicenna and Ṭūsī, Sharḥ al-Ishārāt, 3:288). Ṭūsī often illustrates this with an image of a scroll that is fully unfolded in front of God, present to Him in an atemporal and fully actualized way.¹⁹ The necessitarianism of this account can hardly be missed; interestingly, however, Ṭūsī strengthens it by his assertion that “that same form would correspond to other worlds if such worlds could exist, like this world” (Avicenna and Ṭūsī, Sharḥ al-Ishārāt, 3:288). Ṭūsī agrees here with Avicenna that there can be only one actual world, nevertheless, he presents a counterfactual conditional that quantifies over all possible worlds: if other worlds were possible, they would necessarily be identical in all their aspects to this world. Islamic scholars universally accept that knowledge consists of conceptualisations (Sg. taṣawwur) and judgements (Sg. taṣdīq), and Ṭūsī identifies both with the nafs al-amr in an unprecedented way.

4. A third world?

What do we talk about when we say, ‘The diagonal of the square is not commensurate with its side’?²⁰ Certainly, we do not want to communicate only the content of our thoughts, like when we say, ‘I feel cold’. Neither do we say something like, ‘It is my opinion that the diagonal of the square is not commensurate with its side’. We do not refer either to our experience of sensory data, as in ‘I see a sheep grazing in the meadow’. With the example of mathematical truths, Ṭūsī draws attention to the mind-independency of such judgements. They are true regardless of whether we think them or not and independent of our assertion of their truth; therefore, he suggests, such judgements must be eternally and necessarily true.

Frege’s theory is a parallel in a number of ways. For one, Ṭūsī's theory, as I tried to show, is driven by anti-psychologist concerns quite similar to those of Frege. Both thinkers see the difference between assertion of truth and its determination as grounds for postulating a truthmaker beyond mental existence. Second, Frege’s theory is better developed, thus promising to illuminate Ṭūsī's theory. Lastly, the solutions postulated by both played an important role historically and philosophically. However, while both theories were widely discussed, their reception was different. After Ṭūsī, attempts were made not so much to discard the theory of the nafs al-amr as an unplausible and ontologically costly solution but rather, while rejecting Ṭūsī's particular conclusions, to give it other explanations, seen as more acceptable but still ontologically robust, e.g. to equate the nafs al-amr with Platonic forms. Frege’s ideas about the third kingdom, on the other hand, were almost universally criticized; and these criticisms can be directed both against Ṭūsī and later theoreticians of the nafs al-amr doctrine.

While Ṭūsī pointed out that mental existence cannot be the truthmaker of a number of judgements because of the possibility of conceiving false judgements, Frege argued for a similar point from the difference between ideas and thoughts. Under ideas, he subsumed various objects of one’s inner world: sense-impressions, creations of imagination, sensations, feelings and moods, inclinations, and wishes. Ideas shared, in his view, four essential characteristics: (1) they are not material, (2) they are had, (3) they need a bearer, (4) every idea has one bearer.²¹ Ideas, then, overlap with the realm of mental existence in the Islamic philosophy jargon.

Thought, on the contrary, is not a subjective act of thinking, but the objective content of a sentence which can be shared by several persons. It contains the sense (Sinn) of a sentence.²² The reference of a sentence (Bedeutung), on the other hand, is its truth value. We are driven to it by the pursuit of truth. The sentence ‘Odysseus was set ashore at Ithaca while sound asleep’ has a sense, but no reference, since the name Odysseus, and hence the whole sentence, has no reference. For Frege, semantics of sentences and names is the same because in both we distinguish the objective sense and the reference. The reference of a name is a specific object, and the reference of a sentence is its truth value. The True and the False are, then, individual objects (Frege, “On Sense and Reference”, 62–63). This difficult concept received an ontological interpretation in Łukasiewicz; the two abstract referents of Frege’s sentences, i.e. the True and the False, are equated with being and non-being. Different true sentences correspond to different aspects of Truth or being. The relation of thought to Truth is therefore the relation of sense to reference.²³ This ontological interpretation can be successfully reconciled with Ṭūsī's solution. His equation of nafs al-amr with the First Separate Intellect (and not any other intelligible being lower on the emanationist scale) achieves a similar goal, as the First Intellect contains the whole being and within it, all of its aspects.

In the final step of his argument, and one that is strikingly similar to what Ṭūsī does, Frege demonstrates the difference between ideas and thoughts with the example of mathematicians talking about the Pythagorean theorem. The theorem is one and the same for all of them, contrary to one of the characteristic of ideas: (4) having only one bearer. We cannot reasonably say that the Pythagorean theorem is mine or hers, the way we say, e.g. ‘I see this green’. So, when I judge the Pythagorean theorem to be true, I refer to some reality outside my inner world, unlike when I say: ‘My vision of this green is true’. This also means that, unlike ideas in (3), thoughts do not require a bearer because there would be no science common to many (Frege, “Thought”, 301). The conclusion is that thoughts are not objects of either external or mental world, hence, a third realm has to exist (Frege, “Thought”, 302).

For Frege, the thought which expresses the Pythagorean theorem is true timelessly and independently of its assertion by anyone (Frege, “Thought”, 302). For Ṭūsī, too, the content of the First Intellect consists not only of discovered truths (i.e. proven and self-evident truths) but also of undiscovered or even undiscoverable truths. This means that we apprehend thoughts, we do not produce them.²⁴

On Frege’s view, Truth cannot be understood as correspondence; Truth is a particular, abstract object, thus something non-relative, atemporal and undefinable, while correspondence is a relation (Frege, “Thought”, 291). If indeed, like Łukasiewicz wants, Truth is to be equated with being, it cannot be defined precisely for the reason why being cannot be defined: it cannot be reduced to something simpler. Judgement, then, does not consist of establishing a correspondence between two corresponding things but grasping the eternal and immutable Truth, that is, connecting with the objective realm (Frege, “On Sense and Reference”, 65). This also means that thought can be causally effective in the material realm because it can be grasped and taken to be true (Noonan, “Fregean Thoughts”, 20).

If I am right in demonstrating these important parallels between Ṭūsī and Frege, then this potentially puts a strain on Ṭūsī's insistence on defining truth in terms of correspondence for reasons similar to those that compelled Frege to reject the correspondence theory of truth. However, this is difficult to ascertain because the focus of Ṭūsī's theory of the nafs al-amr is on God’s knowledge and he is not primarily interested in demonstrating how other thinking subjects gain epistemic access to truth.

The main difference between the two thinkers is that Frege argued for the self-subsistent third realm, contrary to Ṭūsī who presented an argument against the nafs al-amr being self-subsistent. The question is, then, does Ṭūsī offer a third-world ontology? Interestingly, Ṭūsī was asked this very question by his disciple, the well-known Shiʿi theologian, al-Āllāma al-Ḥillī (d. 1325). Al-Ḥillī mentioned the standard understanding of the nafs al-amr as either mental or external subsistence and inquired which one is the truthmaker of true judgements, to which Ṭūsī answered that it cannot be either of them, but rather one should understand truth as correspondence with a third entity beyond them, i.e. the Separate Intellect (Ḥillī, Kashf al-murād, 53–54). In a different place, however, Ṭūsī was untroubled by making an opposite claim and subsuming mental existence under external existence. Mental forms, he explained, as representations of extramental objects have mental existence in the human minds or the celestial intellects. However, they also have extramental existence because they exist as accidents in a subject, i.e. the human mind or the celestial intellect, which itself has extramental existence (Ṭūsī, “Sharḥ Masʾalat al-ʿilm”, 91). Ṭūsī suggests here that, fundamentally, all that exists, exists extramentally.

In the final section of this paper, I will mention that Ṭūsī's commentators raised similar questions about the ontological status of the nafs al-amr and offered some solutions. Here, I would like to point to a possible interpretation of Ṭūsī's theory in terms of modalities of being. They are introduced into Ṭūsī's theory with his concept of the systematic modulation of being (tashkīk al-wujūd), where God’s proper existence is differentiated from the existence which applies to all the contingent beings and is predicated in a modulated way (Ṭūsī, Tajrīd, 69). Modulation can be according to substantiality and accidentality, posteriority and priority, or more and less (Ṭūsī, Tajrīd, 65; “Sharḥ Masʾalat al-ʿilm”, 91–92). On this theory, the First Intellect and its content, i.e. the nafs al-amr could be seen as a different mode of being from what is above (the Necessary Existent) and below (the world of material particulars), having a unique position in a cosmological order in which being decreases, i.e. becomes more and more differentiated, with the descending levels of emanation. Perhaps the two contradictory claims Ṭūsī makes about the ontological status of the nafs al-amr can be reconciled by his concept of modulation, which does not allow for separate realms of being but still makes room for distinguishable categories of things: material, mental, and those belonging to the nafs al-amr.²⁵

5. Objections

Ṭūsī's solution was not well received. Commentators on both of Ṭūsī's works, the Tajrīd and the Ithbāt al-ʿaql al-mufāriq, challenged almost all of Ṭūsī's premises. I will mention here only one type of them, i.e. those against there being an additional truthmaker for true judgements different from both mental and external existence.

Ḥillī challenged his teacher’s theory in his presence. The gist of his critique, as he recounts it, is that adding the Separate Intellect as a third truthmaker does not solve the problem of false judgements. It is because philosophers argue for its existence from the difference between inattentiveness and forgetfulness. Similarly to the intelligible forms of sensible things, false judgements, just like true ones, may be forgotten and then remembered (which is a case of inattentiveness and not forgetting). The very fact that they can be remembered anew is because the Active Intellect acts as a storehouse for the rational soul and restores universal judgements to it, provided that its readiness for them remains (Ḥillī, Kashf al-murād, 53–54). In other words, in the absence of the currently thinking individual, it is the Intellect that thinks them. Therefore, the problem of false judgements is not solved by postulating the Active Intellect as an additional truthmaker. It is difficult to estimate how damning Ḥillīs’ challenge was because he overlooks that Ṭūsī's main incentive was the explanation of the possibility of God’s knowledge. Instead, Ḥillī shifts the explanatory demand to the possibility of knowledge acquisition by human knowers, which was not Ṭūsī's concern.

Be that as it may, one still might want to explain how humans can acquire true knowledge. Dawānī is believed to have offered a solution to Ḥillīs’ objection against such possibility. Ḥillīs’ objection could be removed by stipulating that the Separate Intellect does not make the connection between the terms of false judgements but only preserves the terms as concepts, while in the case of true judgements it is responsible for both preserving them and assenting to them (Mullā Ṣadrā, Asfār, 7:277, cf. also Spiker, Things as They Are, 59).

The first part of Dawānīs’ argument may be correct, at least in that it is consistent with Avicenna's view that the Active Intellect is a source of concepts only, so its role in the restoration of false judgements does not pose a problem. The judgement is construed by an imaginary conjunction of images, the conceptual counterparts of which are stored in and come from the Active Intellect. It is, however, mysterious, on Dawānīs’ account, why the Active Intellect is only a source of concepts for false judgements, and a source of not only concepts that make up true judgements but the true judgements themselves. Moreover, Ṣadrā observes that Dawānī falsely assumes a parallel between the connection of two terms made by the Active Intellect, which is necessary and complete, and the connection made by the mind, which is always weaker and tentative (Mullā Ṣadrā, Asfār, 7:277–78).

Shams al-Dīn Kīshī (l. 7th//13th c.)²⁶ posed a different challenge to Ṭūsī's theory. To recap, Ṭūsī's proof begins by establishing that true judgements correspond to nafs al-amr, whereas false judgements do not. This correspondence necessarily exists between entities differing in individuation. Since both true and false judgements exist within the realm of mental existence, then true judgements correspond to the nafs al-amr that is different from mental existence, while falsehood does not have this correspondence.

Kīshī challenged the second premise that the two things in a relation of correspondence have to differ in individuation with two arguments. The first is that what is sufficient for correspondence is a difference of aspect or consideration. An example of such a difference are two universal concepts of definition and definiendum that are not individuated, even though the mind judges that there is correspondence between them. So, correspondence can obtain between two things which are not different individuals.²⁷

The second argument in support of Kīshīs’ stance against [P2], and one that he deems the strongest (Kīshī in Ṭūsī et al., Risālat ithbāt al-ʿaql, 12) is this: if our judgements about the impossibility of the impossibilia are true, they have to correspond to what is in nafs al-amr (as in [P1]), but impossibilia cannot exist in the nafs al-amr, let alone be numerically distinct individuals. So, we can make true judgements even though one of the concepts we use does not have individuation in the strong Ṭūsian sense of the word, as a different kind of existence. What we have is the correspondence within mental existence, between two individual mentally existent individuals (Kīshī in Ṭūsī et al., Risālat ithbāt al-ʿaql, 15). Hence, Ṭūsī's understanding of difference in individuation between a predicative statement and the world is contrary to the truth of many judgements on natural phenomena that involve impossible things.

Kīshī argues that positing a separate, abstract entity that would be knowledge itself, existent outside the mind, is not necessary. Rather, what is necessary is the extramental existence of the correlate of knowledge – the known thing, contrary to compound ignorance which has no such extramental correlate. What is sufficient, then, is the correspondence of the cognitive form with its correlate, regardless of whether this correlate exists extramentally, like with our judgement ‘Fire is hot’, mentally, like with our judgement ‘Knowledge and compound ignorance exist in the mind’, or whether it is neither of them like ‘God’s partner is impossible to exist in nafs al-amr’. The correlate is how the thing is in itself, not in relation to something else or taken in consideration with something else (Kīshī in Ṭūsī et al., Risālat ithbāt al-ʿaql, 17). A similar response is given by Jurjānī who claims that what is meant by the nafs al-amr is ‘the thing itself as it is in itself’ (nafs al-shayʾ fi ḥadd dhātihi), that is, regardless of our assessment of it:

And the meaning of [a thing] existing in itself is that its existence is not according to one’s consideration and supposition. Rather, it exists [in itself] if one ignores every consideration and assumption; and this existence is either extramental or mental.

(Iṣfahānī and Jurjānī, Tasdīd al-qawāʿid, 2:201)

Jurjānīs’ and Kīshīs’ understanding of nafs al-amr is close to the spectrum interpretation – nafs al-amr refers to the way the thing is, irrespective of mental operations we perform on it. In essence, their conception of nafs al-amr aligns with Frege’s notion of thoughts: they are not subjective acts of thinking but rather objective, context-free contents of sentences (their sense). However, akin to Fregean sense, Kīshīs’ and Jurjānīs’ nafs al-amr lacks reference and truth value. Consequently, these thinkers are still unable to elucidate, for example, the driving forces behind individuals’ scientific pursuits.

A different approach was attempted by a much later thinker, Shams al-Dīn Gīlānī (d. ca. 1654). In his commentary, he challenged only [P2], i.e. the premise that corresponding things should differ in individuation in the strong sense of the word. Put differently, he asserted the impossibility of there being an eternal realm or entity that serves as the truthmaker for true judgements. He rejected [P2] on the basis that the whole world and all beings, except God, are originated, a thesis which he demonstrated elsewhere.²⁸ Consequently, he argued that the requirement for individuation in correspondence is not necessary, or more precisely – it cannot be true. He posited that a differentiation in aspect is sufficient for establishing correspondence between propositions and their referents. According to Gīlānī, since everything apart from God is originated, nothing in the created order existed in eternity. So, everything except God is non-existent in eternity, and it is known that non-existent qua non-existent cannot be attributed with anything at all. This means that even judgements like ‘One is half of two’ can be both eternally true and false, because asserting the eternal truth of ‘one’ and ‘two’ would imply their presence in eternity, which contradicts the principle that everything except God is originated. Thus, no positive judgement on eternal truths is possible (Gīlānī in Ṭūsī et al., Risālat ithbāt al-ʿaql, 68).

Gīlānī then defines truth of a judgement as its fixed attribute and qualification. So, if the object of the judgement is originated, so must be the truth that is an attribute of this judgement (Gīlānī in Ṭūsī et al., Risālat ithbāt al-ʿaql, 69). Truth, then, is a quality supervening on a judgement. As far as I know, Gīlānīs’ conceptualization of truth as a quality supervening on a judgement is his novel and innovative approach. It helped Gīlānī to effectively link the ontological status of objects (being originated) with the epistemological status of truth (as an attribute of judgements). This means that truth is not an independent, eternal quality but is contingent upon the originated nature of its objects. Thus, truth itself is originated, and by this Gīlānī avoids the theological problem of positing eternal truths that could imply the pre-existence of things other than God, which seems to be his primary philosophical concern. That said, Gīlānī still fails to show how we can know the difference between false and true judgements.

A more successful answer, I believe, would be to show that thoughts supervene on the human activity of thinking and infer from this how true ones can remain true. In one way, a true judgement – if it was once uttered – remains true. But this is a characteristic it shares with false judgements, which also have this kind of eternity. What differentiates true and false judgements is that the true ones can be repeatedly affirmed and remain true, as a perpetual present. To clarify, the repetition of a true judgement continually corresponds to the reality it describes, ensuring its perpetual truth. For example, the judgement ‘Water boils at 100°C at sea level’ remains true every time it is asserted, as it consistently matches the reality. In contrast, a false judgement, such as ‘The Earth is flat’, does not withstand scrutiny when repeated. Repetition reveals its falsehood because it fails to correspond to reality. Thus, false judgements cannot be perpetually repeated and remain false in the same manner because they can be falsified.

This solution has the advantage of showing that truths of science do not have to differ much from truths of reason. Scientific truths, like rational truths, can be consistently verified through repeated observations and corroboration. Of course, such an understanding of true judgements is epistemically quite humble, as we can never be certain if our judgements will not be falsified. It is also possible for false judgements to be repeated and appear to remain false. However, the majority of them do not have the same enduring quality and can ultimately be proven wrong. Despite its limitations, this solution is still a step forward in comparison with Ṭūsī's theory, which was not interested with our epistemic access to truth and perhaps in some cases made such an access impossible.

6. Conclusion

Ṭūsī noticed a problem of false judgements that questioned the standard correspondence of truth and remained a lasting challenge in the history of Islamic philosophy. His solution was to show that true judgements must exist eternally and independently of our thinking. In this article, my aim was twofold. Firstly, I presented a close reading of Ṭūsī's texts that hopefully avoids anachronistic interpretations of his theory of nafs al-amr in light of later authors. Instead, I offered what I believe to be a more faithful reconstruction of Ṭūsī's argument as the postulation of an additional truthmaker beyond the realm of material particulars and mental existence. Ṭūsī's argument relies on two critical considerations: firstly, the premise that correspondence can only occur between ontologically distinct entities, giving rise to three truthmaking domains. Secondly, the existence of the first domain, that of nafs al-amr, relies on additional metaphysical assumptions Ṭūsī holds concerning God’s knowledge, necessitarianism, and the principle of plenitude. This distinguishes Ṭūsī's approach from subsequent tradition that employs the concept of nafs al-amr to address logical and epistemological issues concerning mental existence. A fact that further corroborates this conclusion is that Ḥillī, one of Ṭūsī's closest students, attests to the notion of an additional truthmaker in Ṭūsī's thought. Ḥillīs’ conspicuous dissent from his master’s ideas and the severity of the anti-Ṭūsian reaction suggest that they may in fact stem from the rejection of his inflated ontology. My second aim was to probe some of the attempts to refute Ṭūsī's challenge. I argued that they failed to address the problems of the nature of true and false judgements and eternal truths adequately. The final proposed solution, while imposing limitations on human knowledge, improves upon Ṭūsī by avoiding ontological inflation of his theory, while showing the possibility of cognitive access to truth.

Acknowledgements

I would like to express my sincere appreciation to Yusuf Daşdemir, Jari Kaukua, and Francesco Zamboni from the University of Jyväskylä for their insightful feedback on early versions of this article. I am also grateful to the participants of the 11th colloquium of the International Society for the History of Arabic and Islamic Science and Philosophy (SIHSPAI) for their critical comments, which contributed to the improvement of my arguments on this complex philosophical topic.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Academy of Finland [grant number 340923].

Notes

1 This took the form of a competition over the correct understanding of Avicenna’s imperative of verification (taḥqīq), where Rāzī argued that verification meant adhering to Avicenna’s demonstrative method, while Ṭūsī argued that it should consist of defending Avicenna’s philosophical positions, see Wisnovsky, “Avicennism and Exegetical Practice”.

2 Also note that in one place Ṭūsī states that his responsibility as a commentator is to expose other philosophers’ mistakes and provide an explanation of Avicenna’s doctrines as faithfully as possible without rejecting or supporting them (cf. Ṭūsī and Shahrastānī, Muṣāriʿ al-muṣāriʿ, 4). For Ṭūsī’s similar critique of Rāzī’s approach and the statement of his own purpose, see Avicenna and al-Ṭūsī, Sharḥ al-Ishārāt wa-l-tanbihāt, 1:112. In another place in the Ishārāt, Ṭūsī admits that he has to restrain himself from bringing all critical points he has against Avicenna’s views on God’s knowledge, for he pledged at the beginning of the commentary that he would not do that (cf. Sharḥ al-Ishārāt wa-l-tanbihāt, 3:283).

3 Some of these developments, especially in their Akbarian formulations in Ottoman times, are discussed in Spiker, Things as They Are.

4 Al-Ṭūsī, Tajrīd, 69. See also al-Ḥillī, Kashf al-murād, 51; al-Iṣfahānī and al-Jurjānī, Tasdīd al-qawāʿid, 194; al-Qūshjī and al-Dawānī, Sharḥ Tajrīd al-ʿaqāʾid, 310–11. This solution was also suggested by al-Abharī in response to Rāzī’s arguments about the existence of impossible objects, see Benevich, “The Reality of the Non-Existent Object of Thought”, 49.

5 The term I translate here as ‘subsistent’ is thābit (Nominal form: thubūt). It traces back to the Muʿtazilī usage, where thubūt is a concept broader than existence (wujūd), as it encompasses both existence and being an object of knowledge (maʿlūm). Knowing confers distinction and determination. In this way, things can have a kind of reality or subsistence but do not possess existence independently; rather, through being known, they attain a state of being and determination, while still remaining non-existent in themselves. In logic and philosophy, thubūt can refer to the state of a proposition being established as true or existent. For Ṭūsī and his interpreters, the term in the context of the present discussion refers to the state of being mentally established. It encompasses the idea that the mind can conceive of both existents and non-existents and attribute a form of determination to them within the realm of mental existence. This determination in the mind does not imply external existence but rather denotes the mental state of being conceived and fixed within the realm of thought.

6 Tajrīd, 69; Kashf al-murād, 52; Tasdīd al-qawāʿid, 2:196–97; al-Sharḥ al-jadīd, 313. Ṭūsī’s solution is similar, and might have been inspired by that of Rāzī (cf. Benevich, “The Reality of the Non-Existent Object of Thought”, 40–41.

7 Tajrīd, 64. This is explicated and accepted by Iṣfahānī in Tasdīd al-qawāʿid, 2:194. Qūshjī rejects this premise (al-Sharḥ al-jadīd, 312).

8 This exact exposition of the theory is not explicitly found in Avicenna’s works, but to an extent it can be reconstructed from various elements of his writings. Avicenna explains that mentally existent things fall into two categories: those conceived from external reality and those existing in the mind without any correspondence to external reality. Things in the second category, which exist solely in the mind and have no correspondence to external reality, can only have mental truthmakers. They include secondary intelligibles (subject of logic) and concepts like ‘existent’, ‘thing’ and modal concepts, which are self-evident and primary, thus require no material abstraction or preparation. Their mental existence is sufficient because, even without a basis in external reality, they can still be the subjects of metaphysical and logical analysis (cf. Avicenna, al-Shifāʾ: al-Ilāhīyāt, I.2, 12.11–13.9; I.4, 26.3–5). See also Marmura, “Avicenna’s Chapter on Universals”, 34–56. Similarly, we can make judgments about not yet existing future and past events, al-Shifāʾ: al-Ilāhīyāt, I, 5, 34.1–10. Finally, Deborah Black, in her analysis of Avicenna’s minor treatise “Letter on the Soul”, addressed the issue of how unreal forms or fictional beings, like phoenixes, lacking concrete instantiations, can exist in human intellects. Since the agent intellects only know what is necessarily concomitant to their essence and do not engage with impossibilities, the impossible propositions do not have a corresponding reality in the agent intellects’ knowledge. So, their truth or falsity is determined solely within the mind. However, as Avicenna explains, fictional forms depend on sensation and imagination to become intelligibles, as the intellect processes and renders imagined forms intelligible (cf. Black, “Avicenna on the Status of Fictional Beings”, 425–53). It is important not to conflate Avicenna’s theory with its later formulations. Therefore, I use the expression ‘standard theory of correspondence’ to refer to what Ṭūsī identified as the received understanding present in post-Avicennian philosophy, rather than the theory as expressed by Avicenna himself.

9 This was suggested by Qarāmalikī in the Introduction to Ṭūsī et al., Risālat ithbāt al-ʿaql al-mujarrad, xxvi.

10 Most scholars of post-Ṭūsian traditions refer to this meaning. For İhsan Fazlioglu, nafs al-amr includes mental and extramental reality (“Between Reality and Mentality”, 28). The important aspect in which nafs al-amr, in his analysis, aligns with Ṭūsī’s position is that in both falsehoods do not exist in nafs al-amr. That said, the major reorientation among post-Ṭūsian thinkers can be culled from the diminishing role of the Active Intellect as a guarantor of certain knowledge (Fazlioglu, “Between Reality and Mentality”, 24). Hasan’s analysis is in line with this understanding of the concept, see Hasan, “Foundations of Science in the Post-Classical Islamic Era”. Although Hasan is one of very few scholars to mention Ṭūsī’s entire argument, he disregards some of its crucial premises which – as I will elaborate on in Section 3 – convince me of the ontological reading of nafs al-amr (Hasan, “Foundations of Science in the Post-Classical Islamic Era”, 111–15). Similarly, in Ahmed’s analysis, nafs al-amr is a polysemic term with multiple meanings, all connected by the notion of how a thing is by its very nature. This polysemy allows for the most expansive scope for the nafs al-amr, including the actual, the concrete, the mind-independent, the Active Intellect, or mental considerations of the intellect (Ahmed, Palimpsests of Themselves, 77). The broadening of the term arises from a further shift towards epistemology and logic. Logicians analyzed by Ahmed solve various logical puzzles by recourse to mental considerations. As a consequence, they grapple with how affirmative propositions can correspond to anything mind-independent at all if objects of knowledge are mentally considered entities. Yet, logicians often make truth-valued statements about them.

11 I do not attempt in this article to give a comparative analysis of Ṭūsī’s and Frege’s ideas. Such an analysis would have to account for, among other things, to what extent Ṭūsī reiterates a correspondence theory of truth, while Frege clearly challenges it, arguing that truth can be given no definition (cf. Frege, “The Thought”, 291). Instead, I use Frege to illuminate Ṭūsī’s characteristically elliptical way of arguing, perhaps most importantly, his anti-psychologist intuitions that prove remarkably close to those of Frege.

12 Avicenna and al-Ṭūsī, Sharḥ al-Ishārāt, 1:357. For the hierarchy of judgments on the decreasing scale of certainty, see Ṭūsī, Tajrīd, 104–5.

13 For example, when discussing Avicenna’s arguments against atomists, Ṭūsī mentions that Avicenna did not only wish to refute specific claims of the atomists but the whole doctrine in itself, fī nafs al-amr (Avicenna and al-Ṭūsī, Sharḥ al-Ishārāt wa-l-tanbihāt, 2:154).

14 Ṭūsī applies a similar reasoning to the division of necessary conditional syllogisms that are either true by virtue of their material premises (by nature) or are true a priori, cf. Avicenna and al-Ṭūsī, Sharḥ al-Ishārāt, 432.

15 Cf. other fragments where Ṭūsī makes similar points: Avicenna and al-Ṭūsī, 1:387, 394.

16 There is a potential problem here introduced by the Liar Paradox as a challenge to the correspondence theory of truth. Specifically, the paradox may work against Ṭūsī because it requires the coexistence of truth and falsity in the nafs al-amr, and Ṭūsī cannot resort to saying that they are merely mental objects, as he clearly excludes this option here. Without explicitly linking the Liar Paradox with his own argument equating nafs al-amr the Separate Intellect, he gave a solution to the paradox. Ṭūsī refers to Abharī’s presentation of the paradox where a statement like ‘Each of my statements now is a lie’ creates a logical contradiction. Ṭūsī’s response proposes a solution to the paradox by stating that correspondence requires a distinction between a predicative statement and its subject. In such cases, truth and falsehood obtain: when a statement corresponds to its subject, its contradiction does not, and vice versa, leading to a mutual necessity of contradiction. However, if a statement is self-referential, truth and falsehood become inconceivable, as correspondence does not obtain. Thus, with a statement about its own falsity, correspondence and lack thereof are inconceivable, rendering judgment about its truth or falsehood absurd because such statements defy truth conditions. See Qarāmalikī, “Burhān-i ḥaqāʾiq-i nafs al-amrī”, 59–69 (esp. 64–67). Note that Ṭūsī uses a similar move in premise 2. The reader might also want to consult the rich literature on the Liar Paradox in Islamic philosophy, e.g. Alwishah and Sanson, “The Early Arabic Liar”; Zarepour, “Abharī’s Solution to the Liar Paradox”; El-Rouayheb, “The Liar Paradox in Fifteenth-Century Shiraz”; Daşdemir, “A Fifteenth-Century Ottoman Solution to the Liar Paradox”.

17 The intricacies of Ṭūsī’s theory cannot be addressed here in any sufficient manner. I refer to my forthcoming article on the topic.

18 Ṭūsī, “Sharḥ Masʾalat al-ʿilm”, 99–100. Cf. also the previous discussion on future contingents.

19 Ṭūsī, “Ajwibat masāʾil Fakhr al-Dīn Muḥammad b. ʿAbd Allah Bīyārī”, Ṭūsī, “Sharḥ Masʾalat al-ʿilm”, 99.

20 Cf. Ṭūsī, “Ithbāt al-ʿaql al-mufāriq”, 479.

21 Frege, “The Thought”, 299–300. See also Frege, “On Sense and Reference”, 59–61.

22 E.g. if someone does not know that the morning star has the same reference as the evening star, the sentence ‘The evening star is a body illuminated by the Sun’ will not be the same as ‘The morning start is a body illuminated by the Sun’. We may believe that one thought is true and the other false, see Frege, “On Sense and Reference”, 62.

23 Cf. “Two different, true sentences, e.g. ‘2 times 2 is four’ and ‘Warsaw is located on the Vistula river’, differ only in their content, and refer to the same object, viz. Truth, similar to the expressions ‘2 times 2’ and ‘3 plus 1’ which differ only in their content but refer to the same object, that is, number 4. All true propositions refer to one and the same object, namely, Truth, and all false propositions denote one and the same object, namely, Falsehood. I regard Truth and Falsehood as individual objects in the same sense as numbers 2 or 4. We have as many different names for one Truth as there are true propositions, and as many different names for one Falsehood as there are false propositions. Ontologically, truth corresponds to being, falsehood – to non-being”, Łukasiewicz, “Logika dwuwartościowa”, 190.

24 Cf. what Frege says in this regard: “The work of science does not consist of creation but of the discovery of true thoughts”, Frege, “Thought”, 308.

25 Ṭūsī’s position would align, then, with predecessors like Avicenna, Suhrawardī, and possibly ʿUmār Khayyām and Abū l-Barakāt al-Baghdādī in their shared view that mental beings should not be excluded from ordinary existence. Khayyām, notably, expands upon Avicenna by using the analogy of existence to elucidate the connection between mental and extramental realms, cf. Benevich, “Representational Beings: Suhrawardī (d. 1191) and Avicenna’s Mental Existence”, 310.

26 He was a contemporary of Ṭūsī and corresponded with him. See Ṭūsī et al., Risālat ithbāt al-ʿaql al-mujarrad, liii–lvii.

27 Ṭūsī et al., Risālat ithbāt al-ʿaql al-mujarrad, 13–14. Other commentators pressed on this point as well, cf. Ṭūsī et al., Risālat ithbāt al-ʿaql al-mujarrad, 49 (Dawānī), 66–67 (Gīlānī), 78 (Ardabilī).

28 I.e. in another treatise entitled Ithbāt ḥudūth al-ʿālam (“Proving the origination of the world”).