Marcus Giaquinto traces the story of the search for firm foundations for mathematics. The nineteenth century saw a movement to make higher mathematics rigorous; this seemed to be on the brink of success when it was thrown into confusion by the discovery of the class paradoxes. That initiated a period of intense research into the foundations of mathematics, and with it the birth of mathematical logic and a new, sharper debate in the philosophy of mathematics. The Search for Certainty focuses mainly on two major twentieth-century programmes: Russell's logicism and Hilbert's finitism. Giaquinto examines their philosophical underpinnings and their outcomes, asking how successful they were, and how successful they could be, in placing mathematics on a sound footing. He sets these questions in the context of a clear, non-technical exposition and assessment of the most important discoveries in mathematical logic, above all Godel's underivability theorems. More than six decades after those discoveries Giaquinto asks what our present perspective should be on the question of certainty in mathematics. Taking recent developments into account, he gives reasons for a surprisingly positive response.

This comprehensive overview of the prediction game takes readers on a journey through the worlds of probability, chance and chaos, and investigates developmental biology, modern warfare, weather and climate prediction, mathematics, economics and games of chance.

We all long for certainty in life, yet things often don't go as we expect. When facing illness, job loss, strained relationships, and other struggles, our impulse is to question God and strive to fix things ourselves. In this book, Shelly Miller, a trusted ministry leader, explores how difficult times can actually be purposeful times of spiritual growth. Weaving the exodus story from the Bible with her own story, she shares how to focus on God rather than trying to overcome challenges in our own limited strength. Each chapter features a simple spiritual practice to help us enjoy the peace and security that is only possible through Christ. Uncertain seasons will soon be translated as an aha instead of an oh no.

The topic of certitude is much debated today. On one side, commentators such as Charles Krauthammer urge us to achieve "moral clarity." On the other, those like George Will contend that the greatest present threat to civilization is an excess of certitude. To address this uncomfortable debate, Susan Schreiner turns to the intellectuals of early modern Europe, a period when thought was still fluid and had not yet been reified into the form of rationality demanded by the eighteenth and nineteenth centuries. Schreiner argues that Europe in the sixteenth century was preoccupied with concerns similar to ours; both the desire for certainty -- especially religious certainty -- and warnings against certainty permeated the earlier era. Digging beneath overt theological and philosophical problems, she tackles the underlying fears of the period as she addresses questions of salvation, authority, the rise of skepticism, the outbreak of religious violence, the discernment of spirits, and the ambiguous relationship between appearance and reality. In her examination of the history of theological polemics and debates (as well as other genres), Schreiner sheds light on the repeated evaluation of certainty and the recurring fear of deception. Among the texts she draws on are Montaigne's Essays, the mystical writings of Teresa of Avila, the works of Reformation fathers William of Occam, Luther, Thomas Muntzer, and Thomas More; and the dramas of Shakespeare. The result is not a book about theology, but rather about the way in which the concern with certitude determined the theology, polemics and literature of an age.

Jesus claimed to be "the way and the truth and the life." But can we really accept this ultimate truth in an age of questioning, uncertainty, relativism and skepticism? In MORE Truth, young philosopher Kristi Mair explores whether Christians can be confident in the "truth" in our anything goes age.

This volume represents a radical departure from the current philosophical duopoly in the area of foundations of probability, that is, the frequency and subjective theories. One of the main new ideas is a set of scientific laws of probability. The new laws are simple, intuitive and, last but not least, they agree well with the contents of current textbooks on probability. Another major new claim is that the OC frequency statisticsOCO has nothing in common with the OC frequency philosophy of probability, OCO contrary to popular belief. Similarly, contrary to the general perception, the OC Bayesian statisticsOCO shares nothing in common with the OC subjective philosophy of probability.OCO The book is non-partisan on the scientific side OCo it is supportive of both frequency statistics and Bayesian statistics. On the other hand, it contains well-documented and thoroughly-explained criticisms of the frequency and subjective philosophies of probability. Short reviews of other philosophical theories of probability and basic mathematical methods of probability and statistics are incorporated. The book includes substantial chapters on decision theory and teaching probability, and it is easily accessible to the general audience

The world is full of people who are very certain--in politics, in religion, in all manner of things. In addition, political, religious, and social organizations are marketing certainty as a cure all to all life's problems. But is such certainty possible? Or even good? The Certainty of Uncertainty explores the question of certainty by looking at the reasons human beings crave certainty and the religious responses we frequently fashion to help meet that need. The book takes an in-depth view of religion, language, our senses, our science, and our world to explore the inescapable uncertainties they reveal. We find that the certainty we crave does not exist. As we reflect on the unavoidable uncertainties in our world, we come to understand that letting go of certainty is not only necessary, it's beneficial. For, in embracing doubt and uncertainty, we find a more meaningful and courageous religious faith, a deeper encounter with mystery, and a way to build strong relationships across religious and philosophical lines. In The Certainty of Uncertainty, we see that embracing our belief systems with humility and uncertainty can be transformative for ourselves and for our world.