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Iqbal traces the Muslim revolt against Greek logic across five centuries — from al-Naẓẓām's principle of doubt, through Ghazālī, Suhrawardī, Ibn Taimiyyah, Ibn Ḥazm, and Abū Bakr al-Rāzī — and argues that their critical work gave rise to the method of observation and experiment. The experimental method, he insists, was not a European discovery: it travelled to Europe through Ibn al-Haytham, Roger Bacon, and the Muslim universities of Spain.
Section 4 stated the anti-classical thesis in its most explicit form: the spirit of the Qur'an is 'essentially anti-classical,' and the failure of the attempt to read the Qur'an through Greek categories was the precondition for Islam's genuine intellectual achievement. Section 5 now supplies the evidence — a rapid survey of Muslim thinkers who challenged Greek logic and developed alternative methods of reasoning, culminating in the claim that the experimental method itself has Islamic origins.
The section advances through three movements. First, Iqbal identifies the revolt against Greek philosophy as manifesting 'in all departments of thought' but focuses on the criticism of Greek logic as its most revealing expression, since 'dissatisfaction with purely speculative philosophy means the search for a surer method of knowledge.' He traces this search from al-Naẓẓām's formulation of doubt as the beginning of knowledge, through Ghazālī's amplification of the principle (which 'prepared the way for Descartes' Method'), and notes Ghazālī's limitation: despite his methodological radicalism, he remained 'on the whole a follower of Aristotle in Logic.'
Second, Iqbal pivots from Ghazālī's limitation to the thinkers who went further. The Qur'an itself, in Sūrah al-Shu'arāʾ, establishes a proposition 'by the method of simple enumeration of historical instances' — an inductive rather than deductive procedure that Ghazālī overlooked. Suhrawardī al-Ishrāqī and Ibn Taimiyyah undertook a 'systematic refutation of Greek Logic.' Abū Bakr al-Rāzī criticised Aristotle's first figure in an objection later reformulated by John Stuart Mill. Ibn Ḥazm emphasised sense-perception as a source of knowledge. Ibn Taimiyyah demonstrated that 'induction is the only form of reliable argument.' Together, these thinkers developed the intellectual infrastructure for the method of observation and experiment.
Third, Iqbal insists that this method was 'not a merely theoretical affair' — it produced practical results in psychology (al-Bīrūnī's discovery of reaction-time, al-Kindī's law of proportional sensation) and transmitted itself to Europe through Roger Bacon, whose Opus Majus is 'practically a copy' of Ibn al-Haytham's Optics. Europe, Iqbal charges, has been 'rather slow to recognize the Islamic origin of her scientific method,' though recognition has finally come — and he prepares to cite Briffault's Making of Humanity in evidence.
This is the most historically dense section of Lecture V, naming over a dozen thinkers across five centuries. Its argumentative purpose is to demonstrate that the anti-classical thesis is not a philosophical abstraction but a historical reality: Muslim thinkers actually did revolt against Greek logic, actually did develop inductive and experimental methods, and actually did transmit those methods to Europe. The section reads as a brief for a case that Iqbal considers proven but insufficiently acknowledged.