God Is a Volitional Agent

Why Islam Is True E08: Infinity Is an Imaginary Concept

The strongest objection to the “Kalam Cosmological Argument” hides behind the seemingly complex uses of various kinds of infinities in modern mathematics.

In this episode, Shaykh Hamza explains the history and nature of modern mathematics, numbers, set theory, mathematical infinities, and the philosophy of mathematics, all in terms that anyone with a good high-school education can understand.

The straightforward conclusion of the explanation of these concepts is that modern mathematical infinities are completely unrelated to the “Kalam Cosmological Argument.”

Not only that, but the explanation also reveals several additional arguments that make the “Kalam Cosmological Argument” even stronger. This presentation is significantly longer than the other presentations in this series.


To help you navigate this episode, here are some markers of the different topics presented (click on the time to jump to the topic):

1:54 – Meaning of “Infinity is Imaginary”
5:13 – Meaning of “Physical Quantity”
9:48 – Numbers in Ancient Mathematics
16:26 – Algebra and Abstraction
21:54 – Cartesian Plane and Negative Numbers
24:41 – What is Modern Mathematics?
27:42 – Imaginary Numbers
31:31 – Negative and Imaginary Numbers in Modern Science
34:02 – Negative and Imaginary Numbers and Physical Quantities
42:13 – Potential Infinities Describe Physical Quantities
44:52 – Potential Infinities are Proof of Finitude
47:53 – The Second Kind of Mathematical Infinity
48:27 – The Foundations of Mathematics
50:52 – Philosophers of Mathematics do not Study Physical Quantities
52:03 – Dedekind Cuts
59:09 – The Purpose of Mathematical Infinities
59:54 – It is Impossible to Construct an Actual Infinity
1:03:05 – Actual Infinities and Modern Science
1:06:28 – Actual Infinities are Incoherent Concepts
1:08:28 – Inferring Real Infinities from Mathematics Begs the Question
1:19:32 – Cantor and One-to-One Correspondence
1:22:22 – A Kalam Argument from One-to-One Correspondence
1:27:01 – The Meaning of Cantor’s Transfinite Numbers
1:33:42 – Transfinite Numbers do not Describe Physical Quantities
1:43:20 – Summary of Why Transfinite Numbers are Imaginary Concepts
1:46:34 – Conclusion

About the Series

“Why Islam is True” is a series of 40 short presentations that analyze the claim, “Islam is true,” by dividing it into a series of sub-claims and then evaluating their truth by examining the evidence for them, as well as the evidence against them. As they do this, the presentations explain

  • the relationship between Islam and science
  • the fallaciousness of the arguments of contemporary atheists
  • the relationship between Islam and other faith-traditions
  • the role of prophecy in human history
  • the nature of life, death, and the human soul
  • and the purpose of human existence

While the presentations are all grounded in the traditional Islamic sciences—particularly the sciences of Islamic theology (‘ilm al-tawhid), Islamic logic (mantiq), Qur’anic exegesis (tafsir), and legal theory (usul al-fiqh)—their goal is to answer the questions that any open-minded and thinking graduate of a contemporary high-school or university—Muslim or not—would ask about Islam.

The conclusion of this series of presentations is that God does, in fact, exist. That the Prophet Muhammad, Allah bless him and give him peace, was, in fact, His messenger. That He did, in fact, teach us the purpose of our existence on earth. And that we will, in fact, be resurrected after our deaths to stand before and be judged by God.

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