Mathematics and the Mind: An Introduction into Ibn Sīnā’s by Hassan Tahiri

By Hassan Tahiri

This booklet examines how epistemology was once reinvented via Ibn Sīnā, an influential philosopher-scientist of the classical Islamic global who used to be recognized to the West by way of the Latinised identify Avicenna. It explains his conception of information within which intentionality acts as an interplay among the brain and the realm. This, in flip, led Ibn Sīnā to differentiate an operation of intentionality particular to the iteration of numbers.

The writer argues that Ibn Sīnā’s transformation of philosophy is among the significant phases within the de-hellinisation flow of the Greek historical past that was once trigger through the arrival of the Arabic-Islamic civilisation. Readers first know about Ibn Sīnā’s exceptional research into the concept that of the quantity and his feedback of such Greek notion as Plato’s realism, Pythagoreans’ empiricism, and Ari

stotle’s belief of existence.

Next, assurance units out the fundamentals of Ibn Sīnā’s conception of information wanted for the development of numbers. It describes how intentionality seems to be key in displaying the ontological dependence of numbers in addition to much more severe to their construction.

In describing some of the psychological operations that make mathematical items intentional entities, Ibn Sīnā built strong arguments and refined analyses to teach us the level our psychological lifestyles depends upon intentionality. This monograph completely explores the epistemic measurement of this idea, which, the writer believes, may also clarify the particular genesis and evolution of arithmetic by means of the human mind.

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Extra resources for Mathematics and the Mind: An Introduction into Ibn Sīnā’s Theory of Knowledge

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4 (p. 243, § 2) And why were the Greek doctrines of the three disciplines (physics, mathematics and metaphysics) not sound? ” 5 This criticism seems to particularly target the Greek notion of number. In this context, Ibn Sīnā reviews the various doctrines of the Greeks regarding the existence of numbers and differentiates two main groups: the first one claimed that numbers have separate existence like Plato while the second is represented by two factions: on the one hand Pythagoras and his followers who adopted the idea that objects are constituted by numbers and on the other hand Aristotle, and his disciples, who thought numbers are potentially in re.

20 2 Ibn Sīnā and the Reinvention of Epistemology For al-Fārābī, whose appreciation of arithmetic is reminiscent of that of the nineteenth century German mathematician Gauss (1777–1855), pure number theory is queen of the sciences. In his next paragraph, he explains that the science of theoretical number involves studying numbers as a structure by examining their properties, such as the property of being even or odd, their relationships and the various operations that can be performed on them. 20 This distinction is of paramount importance for two reasons: firstly, in itself because of its modernity and, secondly, 20 Al-Fārābī does not put arithmetic and geometry on the same epistemic level since his description of geometric objects is substantially different from the one he previously provides for the natural numbers.

The Number 1, on the other hand, or 100 or any other Number, cannot be said to belong to the pile of playing cards in its own right, but at most to belong to it in view of the way in which we have chosen to regard it; and even then not in such a way that we can simply assign the Number to it as a predicate” (Frege 1884, p. 29, § 22). And he further says: “Some writers define Number as a set or multitude or plurality. […] These terms are utterly vague: sometimes they approximate its meaning to “heap” or “group” or “agglomeration”, referring to a juxtaposition in space, sometimes they are so used as to be practically equivalent to “Number”, only vaguer.

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