Ph 346   Fall 2015                                                                               David Banach

Philosophy of Science

They did not want to look on the naked face of chance, so they turned themselves over to science. As a result they are released from their dependence on chance; but not from their dependence on science.

                                                Hippocratic treatise, On Science

All is Number.



All things which can be known have number; for it is not possible that without number anything can be either conceived or known.



Mathematics is the language with which God has written the universe.



No more fiction for us: we calculate; but that we may calculate, we had to make fiction first.



Man tries to make for himself in the fashion that suits him best a simplified and intelligible picture of the world; he then tries to some extend to substitute this cosmos for the world of experience, and thus overcome it. This is what the painter, the poet, the speculative philosopher, and the natural scientist do, each in his own fashion. Each makes this cosmos and its construction the pivot of his emotional life ... to find ... the peace and the security which he cannot find in the narrow whirlpool of personal experience.

                                                Albert Einstein


And here are trees and I know their gnarled surface, water and I feel its taste. These scents of grass and stars at night, certain evenings when the heart relaxes‑how shall I negate this world whose power and strength I feel? yet all the knowledge on earth will give me nothing to assure me that me that this world is mine. You describe it to me and you teach me to classify it. You enumerate its laws and in my thirst for knowledge I admit that they are true. You take apart its mechanism and my hope increases . . . .  But you tell me of an invisible planetary system in which the planets gravitate around a nucleus. You explain this world to me with an image. I realize then that you have been reduced to poetry: I shall never know . . . .  That science that was to teach me everything ends up in hypothesis, that lucidity founders in a metaphor, that uncertainty is resolved in a work of art. What need had I of so many efforts? The soft line of these hills and the hand of evening on this troubled heart teach me much more . . . . I realize that if through science I can seize phenomena and enumerate them, I cannot, for all that, apprehend the world.

                                                Camus, The Myth of Sisyphus


The need to understand is an attempt to recover what one has lost.

                                                Peter Hoeg, Smilla's Sense of Snow



The Course: This course examines scientific knowledge: what it is, how it is reached, what it reveals about the world we live in, and what role it plays in human life. We will look at the origins of the idea of science and how it arose and what implications it has for human life and human culture. The course will concentrate on the role that mathematics has played in science and how this has affected the development of science.  Some of the basic issues to be considered are:

     1. What is Number?: What is the nature of mathematical reality and how does it relate to the world we live in?

     2. Infinity: How does infinity manifest itself in the phenomena of the natural world, and what artifices have science and mathematics devised to describe infinity?

     3. Time: What is time? How has science attempted to use mathematics to describe the structure of events and the causal relationships that govern them?

     4. Realism: Do the mathematical structures used by science reflect that nature of reality independent of human perception, or does it reflect the structure of human consciousness or the contributions of our  conceptual schemes?

     5. Perception: Do we perceive reality directly? What role does observation have in Science?

     6. Science and the Meaning of Human Life: How does science arise from the problems of human life? What implications do the theories of science have for the meaning of human existence? What role does science and technology play in human life?



These issues will be discussed in the context of historical and contemporary examples. We will look at the origins of  mathematics and science in Greece, from Pythagoras through Zeno, Plato, Euclid, and Archimedes. Will also look at the application of these ideas to Astronomy in Ptolemy. Copernicus, Galileo, and Newton. The second half of the course will concentrate on illustrations from more modern work in quantum theory and relativity, geology, and evolutionary theory. Contemporary topics to be considered are:

                A. The nature of space-time in Special and General Relativity.

                B. The reality of sub-atomic particles in quantum theory and String Theory. 

                C. The facts of evolution: the evidence for evolutionary theory.

                D. The implications of evolutionary theory for our conception of  human consciousness and for the meaning of human existence.

                E. Conceptions of time in Science and their development in the history of Geology.

                F. Modern mathematical treatments of infinity and their application in the sciences.

                G. The influence of science and technology on our conception of time. Phenomenological accounts of the implication of science on human consciousness and human life.






Thomas Kuhn: The Structure of Scientific Revolutions
Peter Hoeg,  Borderliners.
Daniel Dennett,  Darwin’s Dangerous Idea

Julia Diggins, String, Straightedge, and Shadow

Readings on  Web page


Office: Bradley House 309                               Office phone: 641-7062

personal webpage:

course webpage:


Grading: Your grade will be determined as follows:

20%-- Midterm Exam

35%-- Final Exam

20%-  Assignments (There will be four. You must do the either the first or two of the last three. They can be found on our webpage)

25%-- Participation and Quizzes

Exams: There will be one midterm exam at the end of the first major section of the class. The final exam will be comprehensive. 

Grade Scale:

A --- 93 and above              C- -- 70 to 72

A- -- 90 to 93                        D+ -- 67 to 69

B+ -- 87 to 89                       D --- 60 to 67

B --- 83 to 87                        E --- below 60

B- -- 80 to 83           

C+ -- 77 to 79

C --- 72 to 77


Makeups: In order to makeup an exam you must have a written excuse for missing the exam. The exam must be made up within one week of your return to school (i.e., the last date covered by your excuse.) Quizzes may be made up without excuse within one week with a 20% penalty. Late assignments suffer a 10% penalty for each class meeting lat