A Concise History of Mathematics for Philosophers (Elements in the Philosophy of Mathematics) by John Stillwell (PDF)

Description

This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I really enjoyed reading this. Some of the early history of math (antiquity through 19th century) was very well covered and I thought the major themes up to that point were well-represented (non-euclidean geometry, imaginary numbers, set theory, Cantor’s diagonal, dealing with continuum, etc). Oddly, several interesting developments such as chaos theory and computation were mostly left out.But nonetheless, a great read and I appreciated the high-level perspective.

⭐For studying mathematical philosophy

⭐In the super intellectual critical examination of the Bible circles, they’ve come to say that the comparative mythologists . . . that Jesus Christ is just a redo, an analogy of many sungods that came before him – Osirus, Dionysus, Mithras . . . is “parallelomania.” Even though there’s explicit statements from early “Christian apologists” that state that Jesus Christ is analogous to all the previous sungods! So, the Critical Biblical scholars have been calling the evidences they can come up for showing Jesus Christ is a redo, or took on Pagan holidays, the “calculation theory.”They go and look at early Christian efforts to find the date of Jesus birthdays in Christian and others calendars, and they don’t exactly find much. Although they do find some pretty heroic efforts! Anyways. seems to me, that today’s Mathematicians have a “calculation theory” of Mathematics.They say mathematics starts with numbers, and any effort to understand the nature and origins of mathematics beyond that is “philosophical mumbo jumbo.” – or, something to that effect.David Oker’s “Gospel of Truth – Mathematics as the Holistic Viewpoint” explains the nature and origins of Mathematics, and shows how this understanding explains all the philosophical blind alleys of history.- John Stillwell states this book is not about Mathematical foundations – maybe so. But, I can’t help noting that the Mathematicians “Foundations” debate is all “the calculation theory” of Mathematics. The real foundations of mathematics resides in an understanding of the nature and origins of Mathematics. That of understanding how abstraction works, and Jacob Bronowski’s deeper penetration into the nature of all knowledge “The Origins of Knowledge and Imagination.”

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