The best way to introduce this four volume set is a quote from the author in the introduction of Volume 1; He says,
I have tried in this book to show the range of mathematics, the richness of its ideas and multplicity of its aspects. It presents mathematics as a tool, a language and a map; as a work of art and an end in itself; as a fulfillment of the passion for perfection. It is seen as an object of satire a subject for humor and source of controversy;… As an activity which has driven men to frenzy and provided them with delight. It appears in broad view as a body of knowledge made by men, yet standing apart and independent of them. In this collection, I hope, will be found material to suit every taste and capactiy.
Philip Jourdain was a British mathematician and “follower of Bertrand Russell” Although he lived a short life that was impacted by physical illness he managed to make a significant contribution the the field of Mathematics. The author credits Jourdain with having the rare ability of being able to communicate complex ideas in a simple manner. Over the next few days we will discuss his book The Nature of Mathematics. This book isn’t really a collection of equations and methods but more of a discussion of how and why these methods grew up. Newman compares Jourdains book with AN Whitehead’s Introduction to Mathematics and Mathematics for the General Reader by E.C. Titchmarsh which he recommends as classics for non mathematicians. the strength of Jourdains book over the other two is that he uniquely enlightens us on the relationship between logic and mathematics.
Transcript: Philip Jourdain states that the best way to become acquainted with new ideas is to study the way in which knowledge about them grew up. his book The Nature of mathematics is an attempt to convey the development of less discussed concepts like the negative number and logic. He writes that a big part of mathematics as well as the natural sciences is lessening the load we have to carry physically or mentally so we can focus our attention on unexplored areas of possible inquiry. This wouldn’t be possible, for example, if we had to memorize long chains of reasoning that go into the development of every math equation. Instead math and science provide shortened methods for getting what we want done without having to think through every step involved
What is the philosophy of computer science? What is philosophy? What is science? What does “the philosophy of” even mean? From the name computer science, we know that it is a scientific study of something, but of what is computer science a scientific study of. Most people use computers day in and day out, and have a pretty good understanding of what a computer is, but how is this understanding different from a computer scientist’s understanding of computation. What is computation? What are algorithms? What is the difference between hardware and software? What is the relationship between engineering and programming? Computation theory is said to lie at the intersection of mathematics and philsophy. This book covers some of the topics mentioned.
When the author writes about “African Philosophy”, he is referring to contemplation of topics such as truth as justice, social order, inner balance, the cosmos, and the ultimate destiny of humanity, that has taken place on the African continent over the course of the last 5000 years. Obenga mentions the different centers of thought on the continent over the millenia(Egypt, Carthage, Cyrene, Hippo, Timbuktu, Gao, Dejenne) but makes it clear that his focus is on the Pharonic period of ancient Egypt which he sees as a distinctly African culture, that makes its presence felt to this day in the culture and personality of the black African. He cites Flavius Josephus in emphasizing the impact that Ancient Egyptian thought had on Greek thinkers like Pherecydes, Pythogras, and Thales… especially in how they saw the cosmos and divine matters. He recommends a study of the different traditionally African cultures to gain a better understanding of Ancient Egypt and vice versa to gain an understanding of the origin of these cultures.
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Transcript The Pyramids were venues for religious rites and tomb temples dedicated to kings that were defied after their death. A text now know as the pyramid texts was found in the tomb of King Unas and a few of his successors. The text is a mythological description the origin of the universe and the universe before its creation. The author writes:…
What makes the Ancient Egyptian account of creation relatively unique to many of the accounts that came later on is the concept of Nwn. Nwn was not a creator God, nor void, nor chaos. But a watery abyss which already contained everything that would later be included in creation. In this account matter existed before creation as “water”. This “water” would later gain consciousness and come into being as the different forms of creation. The author contrasts this with other creation myths, like Platos in which the being responsible for creation existed prior to the world he would go on to create. In ancient Sumer, Enki ,creator of life, brings order to a chaotic world that was already formed. The origin of the world that he brings order to is left unexplained. The author goes on to talk about the Bible, the Laws of Manu, and the Popol Vuh. The creators in all of these myths are independent and separate from their creation. In the Ancient Egyptian myth the author states, “idea emerges, endowed with power, from matter.” According to the author, 2000 years later the stoics would offer a spermatic explanation that echoed the watery nature of the ancient egyptian “idea”. The eternal nature of matter is very similar to contemporary explanations for creation in which matter always existed in some form.
Transcript: Obenga reitterates that the idea of matter before creation and predating the demiurge is uniquely Ancient Egyptian in the world of creation myths. A universe that existed before the current universe FROM which and WITHIN which all of creation, space, time, life and death are projected was ahead of its time. (Old kingdom 2780 – 2260). According to Plato’s explanation 2000 years later God does not explicitl create the matter which he would go on to shape. Chaos already existed but the activity of God was absent from chaos. God is seen as responsible for the reconfiguration of preexisting elements from a chaotic state to a harmonius one. Aristotle would later express a view closer to that of the Old Kingdom by stating that the uborn constitution existed before the birth of the world. According to Saint Augustine(453 – 430 BC) God creates matter from nothing at the same time that he is creating his works..these views differ greatly from the Ancient Egyptian one in which God emerges as the creator, itself uncreated, from the preexisting primal matter. The author states that the leap from unbaked bricks and wood to Pyramids over the course of 500 years is a reflection of the impact that their world view had on their behavor.
Transcript: Obenga states that the concept of Nwn, that primal sea of water from which and within which all of creation, and creator emerge is one that links the myths of pharonic Egypt to the rest of black Africa. The author mentions the Malian dogon, the Barbara and Akan of west Africa, and Bantu speaking people of Central, East, and South Africa as groups of people whose mythological relationship with water is similar to that of pharonic Egypt. Easterly origins and water as the venue of primal creation are the recurring themes that tie the different myths together. Obenga posits that these myths served as a way of understanding the African environment in which water plays a recurring vital and vitalizing role in the lives of the different agrarian peoples. A world of continuous creation in which rituals are a way of keeping pace with the cosmos. Obenga writes, “into the heavy constraints of existence in the real world, Nwn infuses historical meaning and human intelligence, here and now.
Transcript: Obenga states that The primal egg is another symbol that acts as a thread in the cosmogonies of black African cultures starting with pharonic Egypt where it is said to contain the breath of life at the dawn of the earth. The Bambara of Mali make use of this symbolism in their initiation rituals which serve the purpose of integrating human beings into the cosmos. In the Fali culture of Northern Cameroon homes are built as physical representations of a mythology in which the first home represents the egg from which the earth/other homes emerge to become the home for humanity. In this culture Obenga writes, “the house, is a self-contained reflection of the of the life of the universe” Among the Abure of ivory coast there is legend of a time when a special egg served to tell time…Being full at sunrise and drained of its yolk at midday. This egg was said to give indications of when to start the day,stop for lunch, and stop work. Obenga writes that in addition to its ties to the cosmos the egg is a symbol of completeness, perfection, and wholeness…purity, youth, and life…the world about to be born from it.
Obenga continues his analysis of the impact that the works of early pharonic Egypt had on those of the early greek philosophers. He posits that the concepts that were being discussed in Miletus at around 700BC about the origins of creation had a lot of similarities to those found in works like the Pyramid texts which date to as early as 2000 years earlier. Obenga states that Thales’ ideas about a world created out of water or Anaximanders Indeterminate Infinite (creation out of matter that is like no substance known by man) evoke concepts that are found throughout the Egyptian literature. Obenga mentions Classical physics as having had a major impact on our perception of a world devoid of spirit. In the Ancient Egyptian world view he writes, “there is no opposition beteween matter and spirit…Life is immanent in matter.” Obenga gives Water as an example of a substance(matter)…that is equipped with a “spiritual” germinating force. Through this line of reasoning Obenga advocates for reconsidering the labeling of Ancient Egyptian philosophy as religion…heseesthe the “gods” of ancient Egypt as ways of understanding the living world.
Overgaard, S., Gilbert, P., & Burwood, S. (2013). An Introduction to Metaphilosophy (Cambridge Introductions to Philosophy). Cambridge: Cambridge University Press.
Rough Transcript: Philosophers examine subjects that claim to provide knowledge and understanding about the world. Part of the examination process is asking what a subject is and how it goes about providing that knowledge and understanding. Philosophy itself claims to provide knowledge and understanding about the world; Should it not then put itself through the same examination process as other subjects? Metaphilosophy is the inquiry into the nature of philosophical questions and the methods adopted in answering them… According to Colin McGinn it is ‘perhaps the most undeveloped part of philosophy’.One of the traps of being a philosopher is taking for granted our world view and Not putting it under scruitny. Is it necessary for every philosopher to do this? This book will dive deepr into this these topics
Rough Transcript: what is philosophy? When we ask what philosophy is, should we simply give a descrption of what philosophers today do on a day to day basis? In that case Philosophy hasn’t always been what philosophy is currently. Does this mean that we shouldn’t count philosophers of the past as philosophers? Philosophy has changed a lot since the days of Plato, yet most people would consider him a philosopher…so should we then just describe what they SHOULD be doing instead? There is no consensus currently on what philosophy is or what it ought to be. Is this a problem? Is this the reason that it isnt making the kind of progress that 1the other sciences are making? Is it the origin of new sciences or is it a part of science? Should we be looking to philosophy for the answers to the big questions in life, or should it simply help us understand what we already kn1ow? Has science solved all of the problems that philosophy is good for? Do we have anything left to discover which science alone cant discover with time. Are we at the doorstep of knowing-it-all? There are those who think so.
Transcript: With the success of science over the past century there has been a rise in influential thinkers who have declared that philosophy is dead. One such person is Stephen Hawkig. It is hard to argue that there is a more effective way of finding out facts about the world and coming up with explanations of how the world works than science. With the introduction of systemized methods of observation and experimentation the world changed. Before these methods were introduced, most philosophers were speculating about ideas without having to put them to the test. Afterwards, the topics that philosophers were merely contemplating became the subjects of scrutiny by scientists. This scrutiny led to a lot of insight and progress…Some which philosophers were involved in. Lately however scientists appear to be carrying the torch when it come to progress, while philosophers are left to speculate about the topics which are unobservable and unmeasurable. Is this all that is left for a philosopher to do? If so, is anything wrong with that?
Compared to science, Philosophy appears to have made very little progress over the course of the last few centuries. Several reasons have been put forth as to the reason why? One of them is: philosophers lack the capacity to achieve consensus. Progress requires a group to agree that the ideas put forth in the past are good enough to get us where we need to go… and all that is left to do is refine those agreed upon ideas until we get there. Refining ideas, that are decent ,does tend to yield results…one example is that we gain a better understanding of the nature of the problem over time and another is that we develop better and better ways of dealing with obstacles that surround that specific problem. The authors cite progress made in logic with the formalization of symbolic logic as one of the great examples of this process at work in philosophy. Is this a special case, and if so is progress possible in the other branches of Philosophy?
Are philosophers overly crictical…should philosophers change their behavior to mirror that of scientists so that they can deliver similar outcomes. What would it even look like for philosohy to make rapid progress? And Would the topics being discussed be philosophical in nature if achieving consensus quickly was possible? Or, is the role of Philosophy in the world inherently different from that of science? Overgard and Co point out that even though the modes of arguments in philosophy aren’t uniquely adversarial they should facilitate disagreement. Philosophers are expected to be comfortable with disagreement and be more interested gaining insight in discourse than victory. If a philosopher is employing slights of hand to get ahead is she really a philosopher? Whether the criticisms of philosophers are valid or not, their disagreements do tend to make the price of maintaining certain positions clearer and clearer over time…so anyone that wishes to defend a particular position can easily find out what they are getting themselves into…this can be seen as a progress of sorts
Overgaard and Co authors discuss a thought experiment in which Aristotle time travels to a present day university. He attends classes given by the different departments to get a taste for the amount of progress that has occurred over the millenia. He attends physics lectures and is baffled by the concepts being discussed, cosmology? Same thing? Biology? Same thing. Things take a turn when he starts attending Philosophy lectures. Not only does he understand, but he is able to make insightful contributions to the discourse when it comes to topics like metaphysics and ethics. The progress made by science is pretty much undeniable. But what role is left for philosophers like Aristotole to play in a world dominated by the undeniable greatness of science? Some philosophers have turned to ontological naturalism…a world view in which there are no super natural forces, disembodied, or immaterial spirits directing the course of events…therefore there is nothing that is not observable and accessible through the methods of the emperical sciences. Ontological naturalist philosophers accept as fact that the identification and description of reality is best left to the natural sciences , not speculative metaphysics. Overgaard and company posit that the idea that there is nothing left for philosophers to do in this world would only need to be true if there was a commitment to methodolical naturalism. The view that the only way to say something meaningful about the world is by employing the methods of the natural sciencs.
Overgaard and company go on to discuss whether ontological naturalism and methodological naturalism must necessarily go hand in hand. They use Wittgenstein to show that intuition and outside of the box thinking can lead to accurate insights. Although what Wittgenstein was doing in his studies on language might seem anthropological in nature, and therefore scientific,, he never went around setting up experiments or observing people to gain his insights. Infact he never utilized the methods provided by science at all. He simply acknowledged facts about the world which were being taken for granted by a particular world view, and as a result was able to give a more complete description of it. Overgaard and company state that this is explicitly the role that Wittgenstein saw for philosophers. Not offering up theories or explanations about the world, but a more complete description that takes into account even the most basic assumptions. In Wittgenstein’s own words, “Don’t think, but look!” He argues that clarifi is the role of Philosophy and the discovery of new facts will do little to resolve problems that are conceptual in nature.
How valuable are the descriptions that science gives us about the world when compared to the image of the world that we see when we look out? Overgaard and company use a quote from Eddington’s the nature of the physical world to make the point that, the world that the average person sees when they look out, is just as important to acknowledge in our theories, as our scientific descriptions… that is if we want our theoretical understanding of the world to have any relation to the world that we know then we need to incorporate a common sense approach. What we see, hear, taste, smell, and feel need be incorporated into scientists’ explanations of the world and vice versa. This approach would leave significant room for philosophers to operat; A philosopher’s input would be just as crictical to our understanding of the world as the periodic table in this world view… all without having to abandon naturalism. But at what cost are we ignoring science’s revelations about reality just appeal to the familiarworld in which we exist?
Earlier in this series we broadly defined ontological naturalism as the view that the natural world is all that exists…there are no supernatural or unobservable entities influencing the way in which events unfold in this world view. This outlook is usually coupled with methodological naturalism which limits the way in which we can go about attempting to gain knowledge…to science. There is arguably no better way to describe and explain events and phenomena in the natural world than science. Science gives us a detached access to reality that is independent of our limited senses As the methods deployed by scientists are refined over time…is there any room for philosophers to make contributions without abandoning the traditional methods of Philosophy. Overgaard and company state that once science and theology which were at one time intertwined with philosophy started traveling down their own paths philosophy was left with the task of understanding people. Are the detached classifications and explanations of love given by science, for example, satisfying enough to a person who has fallen in love….or is explaining love to this person the role of the humanities…and if so is philosophy in particular a part of the humanities? Or Is philosophy a second order discipline that reflects on how we represent reality itself through our language, ideas, and perceptionas.
