Journey of mathematical language’s relationship with truth in Islamic civilization

In the ancient philosophy-science tradition, the sciences are categorized into three levels based on their relation to the sublunar and supralunar realms: lower sciences (‘ulum-i adna), intermediate sciences (‘ulum-i awsaṭ), and higher sciences (‘ulum-i a’la). Natural sciences, which concern the sublunar world, are considered lower; mathematical sciences, which pertain to the supralunar world limited by the lunar sphere and the celestial sphere, are regarded as intermediate; and theological sciences, which address the realm beyond the cosmos, are seen as higher, as explained by Turkish academic Ihsan Fazlıoğlu. In this context, during the 1290s, the Maragha School of Mathematics and Astronomy constructed a new astronomy with a strongly mathematical character, which reached its peak in the 1400s with the Samarkand School of Mathematics and Astronomy. Throughout this process, the correspondence between mathematical knowledge and truth and existence became the subject of intense debate. Fazlıoğlu examines this complex process in his book “Deep Structure: The Conceptual Framework of Islamic-Turkish History of Philosophy and Science.”

At the center of the debate lies the idea that “since mathematical entities and models do not exist in the external world (in actuality), they cannot be the subject of belief, and thus cannot pertain to knowledge (‘ilm) that provides the cause and essence (form).” While natural objects exist both in the mind and in the external world in a dynamic, moving form, mathematical objects are abstracted from matter and are motionless – hence they are classified as intiza’i (abstract) sciences. Consequently, the question of whether mathematical models and inferences can provide knowledge about truth, and if so, whether that knowledge is reliable, has led to a significant tension.

Astronomy, however, has carried this tension to a different level. Although it is based on the abstract language of mathematics, it is concerned with the conditions of natural objects that exist in the external world in a dynamic and moving form. As stated: “This is why, despite addressing the same subjects, astronomy – relying on observation (ḥiss) and geometry (wahm) – describes, from a mathematical standpoint, that the celestial spheres have such configurations and states; whereas natural philosophy explains why the celestial spheres have these particular configurations and states. In short, astronomy, through its mathematical dimension, employs the “burhan al-inni” (“argument from effect to cause”), while through its reliance on natural philosophy, it brings in the “burhan al-limmi” (“argument from cause to effect”).

The tension in question arises from the relationship between the “mutaḫayyila” – formed with the support of internal and external senses – and the ma’qul, that is, the reality of things. Moreover, as mentioned earlier, truth must be able to integrate knowledge of both the sublunar and supralunar realms. Ibn Sina, commonly known in the West as Avicenna, resolves this tension by uniting the sublunar and supralunar worlds through the “active intellect” (‘aql al-fa’al): “The mutaḫayyila, which emerges under the influence of the wahima (estimative faculty), produces a distorted version of external reality when compared to the truth constructed by the mutafakkira, which is governed by reason. Therefore, for the intellect to produce demonstrative knowledge (‘ilm burhani) concerning sensible corporeal existents, the process must not only involve input from the internal and external senses – that is, from below – but also include a component that comes from above, namely from the active intellect, which provides essences and causes in their pure form. The active intellect thus corrects the distortions caused by the mutaḫayyila; through the illumination (fayd) of the active intellect, the rational faculty distinguishes the intelligible (ma’qul) from the imagined (mawhum), enabling the formation of a sound conception. Therefore, in this process governed by the active intellect, it is indeed possible to know the truth of things, and such knowledge is unaffected by the distortions of the mutaḫayyila.”

Subsequently, the enrichment of Illuminationist (Ishraqi) philosophy and the expansion of the boundaries of Peripatetic (Mashsha’i) philosophy – along with al-Ghazali and especially Fakhr al-Din al-Razi’s adoption of the theory of the nafs (soul) in the acquisition of knowledge in place of the active intellect – as well as the new approaches introduced by theologians (mutakallimun), and by thinkers such as Nasir al-Din Tusi, Najm al-Din al-Katibi, and Sadr al-Din al-Qunawi, gradually weakened the foundational ground of Ibn Sina’s use of the active intellect as a solution to the epistemological tension. This shift led to a rupture which, in Fazlıoğlu’s words, marked a transition “from the unity of truth to the plurality of methods, from a paradigmatic system to a perspective-based system.” In other words, as the number of methods and solutions increased, the relative dominance of earlier, more limited approaches declined, reducing them to the status of just one method among many. For instance, although Ibn Sina’s method, centered on the active intellect, once formed the core of the dominant paradigm, it eventually became just one of several perspectives proposed to address the same epistemological problem. This significant rupture, which in fact helped ease existing tensions, also granted legitimacy to multiple perspectives, thus facilitating the broader and more central placement of the Ahl al-Sunna tradition within the Muslim intellectual and social landscape.

Once again, at this critical juncture – namely, in the transition from paradigm to perspective and in legitimizing multiple perspectives – Sayyid Sharif plays a pivotal role. In other words, his classification of the methods of attaining knowledge granted legitimacy to these diverse viewpoints. As he states: “However, the ultimate aim of all these intellectual activities is to attain knowledge of God. There are two methods to obtain such knowledge: one is naẓar (rational inquiry), the other is kashf (intuitive unveiling). If a thinker engages in naẓar based on a revealed source, he is a theologian (mutakallim); if he engages in naẓar without grounding it in revelation, he is a Peripatetic (Mashsha’i), that is, a follower of Ibn Sina. Similarly, in kashf, if the thinker draws upon revelation, he is a “arif” (sufi); if he does not consider revelation, he is an Illuminationist (Ishraqi).” In this way, theologians, Peripatetic philosophers, Sufis, and Illuminationist thinkers all come to be evaluated as addressing the same absolute reality, while differing in the methods and principles they employ. This perspective thus provides a framework in which these traditions can coexist with intellectual legitimacy, as explained by Turkish academic Ömer Türker.

On the other hand, Sayyid Sharif, drawing on his equal mastery of both rational (‘aqli) and transmitted (naqli) sciences, resolves the tension between mathematics and natural philosophy in relation to truth: “Although mathematical entities and models are imaginal (wahmi) – that is, they do not exist in the external world – they are, at the very least, consistent (mutabiq) with real-world facts and phenomena in terms of their judgments (ahkam). Therefore, the knowledge they provide about such facts and phenomena is certain (yaqini). Moreover, even if these mathematical models do not exist externally in a visible (‘ayni) form, they do exist in terms of “nafs al-amr” (“objective reality”). In this way, Sayyid Sharif bridges the philosophical divide by affirming the epistemological legitimacy of mathematics, acknowledging its abstract nature while also affirming its correspondence to empirical reality through the lens of nafs al-amr.

In fact, Nasir al-Din Tusi, the founder of the Maragha School of Mathematics and Astronomy, also attempted to establish a framework for using the concept of nafs al-amr in place of the active intellect. Sayyid Sharif, especially through his commentary on al-Iji’s foundational work al-Mawaqif, went beyond al-Iji’s limitations regarding mathematical knowledge and opened a new horizon. In doing so, he provided a firm and legitimate foundation for the theological-mathematical approach of the Samarkand School of Mathematics and Astronomy. Sayyid Sharif also related this development to moral values: “Through mathematical inquiry, one discovers the states of the celestial spheres and the Earth, along with the subtle wisdom and miraculous design within them. Upon recognizing the grandeur of the Originator who created them, one is filled with awe and says – Sayyid Sharif here quotes a verse that would later be widely cited: “Our Lord, You have not created this in vain.”

Therefore, following the first rupture described above – namely, the transition from paradigm to perspective – the second rupture, shaped by Sayyid Sharif, linked the mental activity of abstraction to nafs al-amr, thereby eliminating the distinction between what exists in the external world and the considerations (i’tibarat) that exist in nafs al-amr. In Fazlıoğlu’s words: “Moreover, nafs al-amr has come to stand out as an ontologically independent category that guarantees both the existence of mathematical objects and models and the certainty of mathematical knowledge concerning nature.”

In this second rupture, which secured the legitimacy of mathematical knowledge, Ibn Sina’s earlier solution based on the active intellect was expanded through the concept of nafs al-amr. Introduced into intellectual circulation by Sayyid Sharif, the term nafs al-amr has since been used by different schools of thought with various meanings – such as “God’s knowledge,” “divine knowledge,” “the first intellect,” “the active intellect,” “the space of thought,” or even “the universal set.” Ali Tusi contributed to this intellectual journey by adding a new layer of meaning to nafs al-amr. According to this approach, nafs al-amr encompasses not only the natural objects of the external world but also the human mind. It includes all true judgments found in both the external world and the mental or conceptual space.

In fact, beginning with Nasir al-Din Tusi, the relationship between mathematics and the transcendent values that once helped secure its legitimacy gradually began to weaken. As Fazlıoğlu emphasizes, the Aristotelian-Avicennian metaphysical and physical principles that had traditionally underpinned astronomy – an enterprise grounded in mathematics – were gradually reduced through Tusi’s efforts. Within this framework, Shams al-Din al-Kishi, the teacher of Qutb al-Din al-Shirazi, sought to develop a more logical framework for the concept of nafs al-amr, one stripped of its cosmic associations. This intellectual legacy was further advanced by his student, Qutb al-Din al-Shirazi, who took it to the next level – going so far as to assert “that mathematical knowledge is more valuable than metaphysical and physical knowledge.” In this way, mathematical knowledge gradually moved step by step toward a structure more akin to its modern form.

Thus, through two foundational ruptures, the relationship between mathematical knowledge and truth was secured, and its legitimacy was established. The next step, as Fazlıoğlu emphasizes, was mathematical precision – that is, the further reinforcement and consolidation of mathematics. In this context, the Samarkand School of Mathematics and Astronomy, which inherited the intellectual legacy of the Maragha School, made highly significant contributions to the development of calculative mathematics. For example, one of its most prominent figures, Jamshid al-Kashi, worked on reinventing decimal fraction calculation and succeeded in determining the value of pi to the sixteenth decimal place.

Therefore, in contrast to the philosophical-scientific tradition of al-Andalus, which insisted on the kitabi (textual, scriptural) approach, the Eastern Islamic world – by taking the takwini (cosmological, created) realm into account – was able to develop mathematics through the Maragha and Samarkand Schools of Mathematics and Astronomy, and transferred this accumulated knowledge to the Ottoman world, where it evolved into a new stage. The mathematical precision inherited in Istanbul through Ali Qushji was applied within the Ottoman Empire to financial affairs, and over time, accounting mathematics became significantly more precise. Moreover, mathematical precision reached its peak in the early sixteenth century through the works of Mirim Çelebi and Taqi al-Din al-Rasid. In short, the epistemological legitimacy granted to mathematics by al-Ghazali continued to expand. Within this historical continuity, mathematical knowledge – whose legitimacy had been gradually reinforced – eventually came to be regarded as capable of providing knowledge about the external world that was at least as accurate as that of natural philosophy.