An Introduction to the Philosophy of Science

This is an incredible book packed with abstract and sophisticated ideas told simply and clearly. The author explores how abstract ideas are the foundation for science (since they allow us to quantify and organize experience), and how we apply them. What I liked about it is that it wasn't just a book packed with scientific facts, but explored and examined ideas thoroughly. I highly recommend it if you're interested in the philosophy of science or philosophy in general.

There are lots of books on philosophy and the sub category known as the philosophy of science. Science is the primary interest to me and, regards philosophy, I want to know how and why it is that we know what it is we think we know. I.e., epistemology is of interest. In this regards, while other books on philosophy have come and gone or remained on my bookshelf unreferenced, I have clung to Carnap's since purchasing over a decade ago. Praise be to Dover. Perhaps a future printing of these 300 pages might also include a Glossary addendum.The context of my interest in philosophy arose long ago in terms of Evolution (the theory of common descent); a radio report in the mid-1980s regards Evolution that didn't make sense; and my own prior college education that was rich with science, mathematics, and engineering. While Carnap doesn't write much directly regards Evolution, he does give justification to the science that I know, an empirically based science that confirmed the validity of my prior formal and continuing informal education.FACTS VERSUS LAWS --- The radio report, the details of which are long forgotten, was that some Evolutionist now thought of Evolution as a "fact." I have since learned that the association of Evolution with fact was strongly promoted in a paper by Julian Huxley in the early 1960s and the association of "fact" with "evolution" and Darwin's ideas goes back even further to soon after Darwin wrote. That inappropriate idea has thus long caught on amongst the idealogs of Evolution. As rich as my higher education had been in physics, chemistry, organic chemistry, and associated laboratory courses, all I knew regards natural history is what I had absorbed in high school biology where Darwin's theory was briefly taught as a theory. Of course we all thought Evolution to be a true theory just as Newton's or some other. My education had led me to believe, and I continue to believe, that scientific theories, even true theories, are theories and that facts are facts. Facts, by definition, are considered to be true. Theories, on the other hand, are never considered to be facts even though they may or may not be so well confirmed so as to be considered to be "true." In science, "fact" is not a synonym for "a truth" or "true", etc. Thus, theories such as Newton's Theory of Motion, Einstein's Theory of Special Relativity, etc., may be well confirmed to the point of being considered "true." But even then it is important, in science, to maintain the integrity of the distinct notion of "fact." Again, in this view, no theory, no matter how well confirmed, is ever a fact. One might think of the analogy to a game of baseball. The game itself is never considered to be the baseball. Similarly, a theory or law of gravity is not equivalent to the observations of a falling apple.Carnap's book is one of the few philosophy books that I have come across that even addresses, without a whole lot of ambiguity, the notions of facts, laws, and theories in science. Furthermore, while some might think that positivism is dead, if positivism is the label that is attached to Carnap and apparently it is, then my belief is that positivism is and ought to be alive and well. If, as some philosophers seem to argue, the symbolic language of positivism isn't appropriate to modern science then, certainly, update the symbolics while not throwing out the proverbial baby with the proverbial bath water. Mathematics has long been considered to be the universal language of the sciences. Surely, mathematical symbolism and logic is thus preferable to any philosophical symbolism and logic especially if the latter can't be easily transformed across disciplines. Surely, implementing the former ought not be problematical to the latter but rather seen as an enhancement to both science and philosophy.According to Webster's dictionary the relevant definition of "positivism" is:"3. a system of philosophy that is based solely on the positive data of sense experience; empiricism; especially, [also P-}, a system of philosophy organized by Auguste Comte, which is based solely on positive, observable, scientific facts and their relations to each other and to natural law; it rejects speculation on or search for ultimate origins."In other words, "seeing is believing." But don't tell Evolutionists you agree with Ptolemy on this. They might have theoretical problems and their conscious may lead them to need to do a general recall on many of their books. Of course, we need to give adequate consideration to the idea of verification. It is important that our observations are correct observations. Verification of facts is one of the hallmarks that distinguishes rigorous science from, say, eyewitness testimony which can often be erroneous.In the world of more modern science some caveats, or at least cautions, regards observations and observables are in order regards quantum and relativistic realities: (1.) At the micro-level of quanta and quantum waves and (2.) Regards quantum entanglements as associated with the macro-world. (It wouldn't be a surprise if quantum entanglements were causal regards biological mimicry between, for example, some species of flowering orchids and their insect pollinators.) (3.) At cosmic distances and relativistic velocities, the speed of light becomes a factor in attempting to understand what it is we are actually observing.One might balk at reading of limits placed on philosophy (and science) by positivism regards the "speculation on or search for ultimate origins." But I have come to see that such a limit does make sense in terms of natural science. Furthermore, such a thought seems to be very much in line with the thoughts of Kurt Godel ([1931], 1992) whose theorem proved that within any system of logic there are limits to what can be proved and disproved within the system. E.g., scientists now believe that the universe (i.e., the empty space between galaxies) is expanding faster than the speed of light. Therefore, can we possibly ever hope to know anything regards the "starry sky" we observe that lies beyond our own galaxy? Where precisely are those stars --- exactly, "now!"? Do those stars even continue to exist? Where does philosophy intersect with theology?Thus, it is well understood that modern "empirical science" is not equivalent to "The Empirical School." (Some label such an extreme view as "scientism.") That is, most scientists would not suggest that all "truth" comes but from empirical science. See also note 1 below regards a prediction of Comte that failedWell, enough with unknowable and possibly knowable cosmology. What does Carnap say that we can best define as knowable "fact" as that word is defined or ought to be defined by empirical science? Carnap very well tells us. For example, Carnap writes(p.230):"Some physicists may even speak of the law of thermal expansion, Ohm's law, and others, as facts. Of course, they can then say that empirical laws explain facts, but the word `fact' is being used here in two different ways. I restrict the word to particular, concrete facts that can be spatiotemporally specified, not thermal expansion in general, but THE expansion of this iron bar observed this morning at ten o'clock when it was heated. It is important to bear in mind the restricted way in which I speak of facts. If the word `fact' is used in an ambiguous manner, the important difference between the ways in which empirical and theoretical laws serve for explanation will be entirely blurred."My guess is that Carnap would want to know not just that the bar expanded at ten o'clock when it was heated, he would want to measure by how much it expanded and by how much it had been heated. These all would be facts of science. Thus, as Carnap further states, in considering "facts," it is not the general law of thermal expansion that is of interest or some theory explaining the laws and facts. Rather the facts are the specifics of the particular spatiotemporal event.Well done, Carnap! Well done.LAWS AND THEORIES --- While Carnap is quite straight forward in making the distinction between facts and laws and, in doing so, quite relevant to what is generally seen as the actual practices of science as might be discussed in the general literature (and as taken from my own education and experience), Carnap's further discussion regards "empirical laws" versus "theoretical laws" and in regards to "theory" itself seem to me to be less evident outside of this book. Carnap writes (P.226):"Empirical laws, in my terminology, are laws containing terms either directly observable by the senses or measurable by relatively simple techniques. [....]"There is no commonly accepted term for the second kind of laws, which I call THEORETICAL LAWS. [....] A theoretical law is not to be distinguished from an empirical law by the fact that it is not well established, but by the fact that it contains terms of a different kind. The terms of a theoretical law do not refer to observables even when the physicist's wide meaning for what can be observed is adopted. They are laws about such entities as molecules, atoms, electrons, protons, electromagnetic fields, and others that cannot be measured in simple, direct ways."Fortunately, unlike many philosophers, Carnap does throughout his book provide concrete examples for which his terminologies might apply. Even so, I tend to think that where Carnap's thinking might get somewhat lost in the above as applicable to modern research is in the determination of distinctions between entities that are "measureable by relatively simple techniques" and those that "cannot be measured in simple, direct ways." Carnap would probably have agreed that looking through a microscope at a microbe is simple and direct enough to qualify as an observation, an indirect observation. But it is not so clear where the line is drawn between simple and direct observation and the non-observable. For example, these days it is easy enough to purchase a simple EMF meter to measure the intensity of electromagnetic fields, i.e., small but relevant portions of the infinite EMF spectrum. Are EMFs thus observable or non-observable? Actually, Carnap addresses this issue somewhat:"If there is a static field of large dimensions, which does not vary from point to point, physicists call it an observable field because it can be measured with a simple apparatus. But if the field changes from point to point in very small distances, or varies very quickly in time, perhaps changing billions of times each second, then it cannot be directly measured by simple techniques. Physicists would not call such a field an observable. [....]"Clearly, the distinction between what is considered an observable and a non-observable is somewhat subjective and dependent on the apparatus and norms of the day. Who knows, perhaps since Carnap wrote a more sophisticated apparatus might have been developed or will be developed that can objectively measure even very small distances and rapid variations. Presumably, scientists would then label these measurements as being measurements of observables.Carnap also very well discusses theories in general and the importance of deriving empirical laws from theoretical laws. He discusses some ideas that most scientists would probably not encounter: the role of correspondence rules bridging theoretical and empirical laws; the so-called Ramsey Sentence; the philosophical dichotomy between analytic (inclusive of logic and mathematics) and factual (information of the real world; physics) truth. And he even touches on quantum thinking and statistical laws. There is much in this book to think and rethink about, much that is relevant to actual scientific practice, and perhaps some that is not so relevant.STATISTICS: DATA ANALYSIS AND DEVELOPMENT OF THEORIES ---- Traditionally, one manner of division for academic science has been to with divisions of two broad categories, "experimental / empirical" and "theoretical science." A third category is also relevant, "data analysis." It would seem that many of the poor results from otherwise good experimental / empirical research falls into this later category. For example, experimental science might generate valid data regards the question "Is a particular vitamin or mineral supplement good, bad, or indifferent prescription for the general population?" Or, "Is drinking coffee good, bad, or indifferent to overall health?" The credibility of science becomes strained in answering such questions much less more complicated ones (such as the significance or insignificance of human activities regards global warming.) The public often might come to the conclusion that "If you don't like the current answer, just wait a few months and research will conclude the opposite." Unfortunately, enormous research biases have seemed to come into play concerning issues of analysis, more so than in primary narrowly focused research. Such questions, due to the quantity of variables involved, might not be answerable even with ideal research. Research biases have only added to the difficulties. While various neutral organizations do as well as they can, often via newsletters, in presenting the relevant output from analysis by those doing the primary research, much more might be done in terms of eliminating any biases. It makes no sense to depend on research from those who have a vested interest in the end results and re-patents thereof.Given the importance of statistics to appropriate evaluation of scientific data, it is no wonder that Carnap devotes several chapters to the subject. Carnap gives but passing reference to the contributions of Reverend Thomas Bayes who "made an important contribution" (in a 1763 paper) to the "classical thinking" that was developed by Jacob Bernoulli (1654-1705) and later by the mathematician and physicist Pierre Simon de LaPlace. It is unfortunate that Bayesianism isn't discussed as its prevalence in modern day thought and the controversies invoked would seem to be highly relevant. Carnap does briefly discuss the contributions of other founders of what has become modern statistics. In addition to his early chapters titled "Induction and Statistical Probably" and "Induction and Logical Probability," his last chapters, Part VI, explore "Beyond Determinism" and delve into the statistical and (long believed) indeterminate nature of quantum physics. (See not 2 below for a modern view towards more determinate understandings of quantum realities.)OTHER MATTERS: In Part I, Carnap covers, as already discussed, "facts," "laws," "theories," and statistics. Also in Part I is an obviously important discussion regards "The Experimental Method." Part II is devoted to "Measurement and Quantitative Language" which, among others, has an important chapter regards "Three Kinds of Concepts in Science" which are classificatory, comparative, and quantitative. Part III, "The Structure of Space," discusses Euclidean and Non-Euclidean geometry as leading up to Einstein's Relativity Theory. Part IV, somewhat philosophical in nature, is "Causality and Determinism." But even in philosophy, Carnap seems to remain well grounded in reality. Some of the ideas in Part V, "Theoretical Laws and Theoretical Concepts" have been discussed above. I am also finding the discussion regards "Correspondence Rules" could be relevant to non-science subjects also, namely, economics. It would seem, for example, that appropriate correspondence rules have long been missing associating the financial economy (monetary policy and often physical policies) and what might be termed the real world economy of actual goods, services, resources, etc. The final part, Part VI, is "Beyond Determinism" and is the discussion regards quantum physics. Regards the Heisenberg Uncertainty Principle, Carnap, writing in 1966 or before, tells us (p.284):"[....] I believe it is fair to assert that it would take a revolutionary change in the basic structure of present-day physics to remove this feature. Some physicists today are convinced (as was Einstein) that this feature of modern quantum mechanics is questionable and may some day be discarded. That is a possibility. But the step would be a radical one. At the moment, no one can see how the uncertainty principle can be eliminated." (Again, see note 2 below.)Each time I pick this book up, I find more to think about. I look forward to further rereads.---------------------------UPDATE OF 05/17/'13 ----- Carnap verses Fleck: In an attempt to discover how there can be such a wide disparity between understandings of what is considered a "scientific fact," I have been keeping an eye out for relevant explications thereof and believe I have found one. I obtained a copy of Ludwik Fleck's GENESIS AND DEVELOPMENT OF A SCIENTIFIC FACT ([1935, 1979], 1981). After reading the following, I began to wonder if I had misunderstood Rudolph Carnap's views. Referring to Carnap and others of his view, Fleck writes (p.50):"To these epistemologists trained in the natural sciences, for instance, the so-called Vienna Circle including Schlick, Carnap, and others, human thinking ---- construed as an ideal, or thinking as it should be ---- is something fixed and absolute. An empirical fact, on the other hand, is relative. Conversely, the philosophers previously mentioned with a background in the humanities construe facts as something fixed and human thought as relative. It is characteristic that both parties relegate that which is fixed to the region with which they are unfamiliar."I would have thought that just the opposite would apply. That is, it didn't occur to me that Carnap thought that "An empirical fact [....] is relative." But then I recalled that this is about the time that Einstein's relativity theory was just beginning to be widely understood and accepted and, although Newton long ago also had a relativistic understanding, perhaps Fleck and those in the humanities that he credits as taking his view weren't yet aware of the significance of "fact" within its own context, i.e., its frame of reference. I don't know but clearly the views differ.Carnap, Einstein, and Newton all understood that if you stand on the Moon, hold an apple in one hand and then drop the apple, the apple will drop towards the Lunar surface and not towards the Earth's surface. The facts associated with the apple (velocities, locations, mass, colors, etc.) can be said to be fixed but are so only as relative to each observer. The mathematics (correspondence rules, if you will) used to describe the motion of the falling apple can be said to be subjective in the sense that the variables input into the equations and conclusions of observations made, and even the extent or kind of equations and observations made, are observer dependent. For example, seen from a powerful telescope aboard an Earthbound space station, the mathematical description of the apple falling to the Moon's surface would surely require considerably more elaboration and different variables than those used by the Lunar astronaut. The facts observed from Earth or the Earthbound station would not be the same facts as those observed by the Lunarnaut. Nevertheless, when the equations from all remote observers are solved and other observations such as of color are considered, these data / facts ought to reconcile well with those facts considered by the Lunarnaut and provide an accurate (i.e., factual) description of the apple and its motion. Facts are facts and an apple is an apple.A further error (in my view) of Fleck's is in not recognizing the categorical difference between "fact" as a statement and other separate categories to which scientific laws and scientific theories are each separately put into. Fleck seems to believe that "fact" is in the same category as theory and is merely an adjective and substitute for the statement "true theory." Thus Fleck's understanding seems to me to make scientific (or empirical) "fact" more equivalent to the vernacular "fact" than Carnap would more appropriately, in my view, have it. This is seen with the very first words of the "Prologue" of Fleck's book where he defines "fact." Fleck writes (p.xxvii):"What is a fact?"A fact is supposed to be distinguished from transient theories as something definite, permanent, and independent of any subjective interpretation by the scientist. It is that which the various scientific disciplines aim at. The critique of the methods used to establish it constitutes the subject matter of epistemology."Thus, I suppose, like current Evolutionists who have been fond of comparing "evolution" to "gravity," Fleck apparently also would have said that gravity is a fact. Carnap would, I am sure and I agree, say that such a statement is inappropriate. The confusion is clear. What Fleck would better have written, in my view, is that which the various scientific disciplines aim at is "truth" as opposed to "fact." Facts, whether verified observations or valid results from experiments, are true (if they are indeed factual) but not everything that is true is considered to be a fact. Clearly, Fleck has failed to see the distinction between scientific / empirical fact and the vernacular. Read again Carnap's understanding of "facts" and also the same views of empirical scientists whose views Carnap has explicated and reinforced. Consider the views of those such as Einstein, Reichenbach, and the many others in science who have made great accomplishments.It needs to also be recognized, and this is a commonplace in laboratory research, that scientific facts become increasingly objective through repeated verification, first by the original researchers own repeated efforts but, more importantly, by the repeated independent observations by others. Theories and laws are then developed based on these facts and others. Carnap recognized this distinction such as when he distinguished between facts and laws. Carnap wrote in his own book (p.5):"When we use the word 'fact,' we will mean it in the singular sense in order to distinguish it clearly from universal statements. Such universal statements will be called 'laws' even when they are as elementary as the law of thermal expansion or, still more elementary, the statement, 'All ravens are black.' I do not know whether this statement is true, but, assuming its truth, we will call such a statement a law of zoology. [.....]"There is much more to better understand in both of these philosopher's short but intense books. Carnap does very well, in my view, in discussing law and distinguishes law from fact. Carnap also discusses "theory" at length and here more effort is required on my part to understand if Carnap differs from the now well accepted view that theories are explanations of facts, and laws. Meanwhile, Fleck has some great ideas concerning 'group think,' what he labels "Denkkollektive" (thought collective), and also "Denkstil" (thought style). Both of these terms remain highly relevant to working scientists and, while perhaps not equivalent, also transfer well to R. Buckminster Fuller's concept of "synergy."ADDENDA TO UPDATE, 05/18/'13 ------ It would be incorrect to infer from Fleck's book that all those who come from a humanities background, assuming that psychology is classified as a humanistic endeavor ---- it would be incorrect to infer total agreement by humanists with Fleck's understanding of empirical science and "fact." Clearly, acceptance of Fleck is not necessarily even the norm. One of the best explications of "fact" I have come across, one that correlates well with Carnap's, is from the field of psychology. Anthony M. Graziano and Michael L. Raulin, in their RESEARCH METHODS: A PROCESS OF INQUIRY (1989), in my view, do a great job of explicating "fact." Here are some selected quotes from pp.24-25. Emphases are those of the authors:"In scientific research empirical observations constitute the facts of research. In a somewhat circular fashion, FACTS are those events that can be directly, empirically observed. Each scientific discipline has its own particular kinds of facts. In psychology, observed facts include the physiological structures of the subjects, the physical conditions around them, the behavior of other organisms including the researcher, and, of course, the subject's own behavior: The major category of fact that is observed in psychology is the BEHAVIOR OF ORGANISMS. [....] OBSERVATION is the empirical process of using our senses to recognize and to note factual events."In addition to studying behavioral facts, psychologists also study memory, emotion, intelligence, attitudes, values, creativity, thinking, perception, humor, and so on. These are not behavioral events. They are not directly observable and thus are not facts."Note that the word "directly" is not here juxtaposed against 'indirectly' with the latter used in the same manner as one might write that a researcher indirectly observes a microorganism with the use of a microscope or a planet with the use of a telescope. Such indirect observations, when objectively verified, are also considered to be scientific facts. (Ideally, it would seem, slightly nuanced but different truth-levels might be associated with direct observations, indirect observations via instrumentation, and experimental results.) The authors further explain their understanding of scientific facts in a discussion of the distinction between facts and inferences (constructs) from facts:"Making an inference is a process that is engaged in by the researcher, with the inference residing in the researcher and not in the subject. The process involves the researcher's rational activity of tentatively accepting the sensory data (the observations) as true and then drawing from them an idea (inference) about nonobservable events. [.....] This is an extremely important point! Those non observable inferred events such as gravity, electricity, intelligence, memory, anxiety, perception, id, and ego are all RATIONAL IDEAS THAT HAVE BEEN CONSTRUCTED BY THE RESEARCHER. They are not facts! Not surprisingly the ideas constructed in this way by the researcher are called constructs." (Emphasis is that of the authors; note that Carnap explicitly refers to the same "constructs" with his alternative terminology, "theoretical terms.")And so it is!---------------------------Review Notes:1. P.A. Cox in his THE ELEMENTS: THEIR ORIGIN, ABUNDANCE, AND DISTRIBUTION ([1989], 1994) reports that positivist philosopher Comte, above, believed it would never be possible to ever know the composition of the Sun or other celestial bodies. In 1835, Comte wrote:"We understand the possibility of determining their shapes, their distance, their sizes and motions, whereas never by any means will we be able to study their chemical composition, mineralogic structure, and not at all the nature of organic beings living on their surface."Well, apparently "never" is not such a very long time (I am being facetious; only a paradigmist would redefine words so as to justify their paradigm) as researchers have indeed quite satisfactorily been able to discover --- thanks especially to the discovery of mass spectrometry by Aston in 1921 --- the elemental composition of even bodies far removed from our own solar system. Now, if we can just spot those little green (or blue? or red?) folks on Mars who are endowed with enough green (blue or red) foliage that eating for the purposes of vitamin C ingestion and all other nutrients is entirely unnecessary. Obviously these Martians are making use of nanotechnology to slightly strengthen the strong nuclear force. This allows the Martians to manufacture helium from readily available hydrogen in sufficient quantities to cause themselves to be light enough (without being explosive) to move around. Even with the reduced Martian gravity --- about 1/3 that of Earth --- the increase in buoyancy is quite useful. (End of my facetiousness.)2. A SUBJECTIVE VIEW OF OBJECTIVE QUANTUM REALITY: The June 2013 issue of "Scientific American" has a very interesting article titled "Quantum Weirdness? It's All in Your Mind" by the theoretical particle physicist, Hans Christian von Baeyer. Physicists have been developing a model, called Quantum Bayesianism, QBism for short. QBism aims to eliminate the paradoxes of quantum physics that even Einstein had problems with. For instance, the notion that Schroedinger's Cat is both alive and dead at the same time becomes but a subjective understanding of the wave function and not an indication of reality itself. Albert Einstein, Kurt Godel, and Rudolph Carnap would surely be pleased to see our supposed understanding of quantum reality as being supposedly indeterminate become rather more determinate.

A cultural cornerstone. Must be read by those who are interested in science and its history.

Rudolf Carnap is my favorite of the Science philosophers. If you haven't read him, here is chance to read him, now.

Great book, well written

Dr. Robert Cormack of NMIMT (RIP) taught a course using this book.The chapter on the Ramsey Sentence is out of date but the rest holds up. I learned more about the philosophy of science with him and this book than I ever did in all my other courses.Tl;dr - science is about falsifiability of the hypothesis and using math to study the world around us. In a world where social media says that vaccines "cause" things or that the Earth is flat, this is a book that should be read and taught in every college.It's still a good read and you will learn a lot. 10/10 would take that class again.

Is this book still relevant, despite being a bit old? The answer isan unqualified YES. Why is this book the best introduction to thephilosophy of science ever written? Because it is the result of acollaberation between Rudolf Carnap (a philosophical giant) and MartinGardner--the celebrated columnest who gave us so many years of"Mathematical games," during Scientific American's golden years.Because it was co-written by a professional writer of popularmathematics, it is probably the only philosophy of science book whichcan be read and understood by the interested lay person. But becauseit is based on a series of lecture notes from one of the worldsall-time great philosophers of science, it doesn't "wimp out" on thetechnical level. If you read it you will be brought to the forefrontof philosophy of science, at least as understood by the later logicalpositivists.In short, a remarkable collaberation by two men who were at the top oftheir game. Thank God for Dover. For ten bucks you can buy a pricelessbook.