philosophy and the sciences - phil. sci. course

Inductive Logic Deductive and Inductive Logic What is Reasoning? Example: The first theorem Euclid’s Elements provides a good example of the kind of reasoning that people admire. Suppose we construct a triangle in the following way: 1. Draw a circle centered at point A. Mark a point B on the circumference and draw a line from A to B. Draw a second circle centered at B that passed through A. Mark one of the points at which the circles intersect as B and draw lines from C to A and from C to B. Theorem: All the sides of the triangle ABC are of equal length. Proof: Let |AB| denote the length of the line segments AB, and so on. Step 1: |AB| = |AC| because they are radii of the circle centered at A. Step 2: |BA| = |BC| because they are radii of the circle centered at B. Step 3: |AB| = |BA| because AB and BA denote the same line. Step 4: |AC| = |BC| because they are each equal to the same thing (viz. |AB| ). Step 5: Therefore, |AB| = |AC| = |BC| by steps 1 and 4. Definition: An argument is a list of statements, one of which is the conclusion and the rest of which are the premises. The conclusion states the point being argued for and the premises state the reasons being advanced in support the conclusion. They may not be good reasons. There are good and bad arguments. Tip: To identify arguments look for words that introduce conclusions, like "therefore", "consequently", "it follows that". These are called conclusion indicators . Also look for premise indicators like "because" and "since". Remark: Each of the five steps in the proof to Euclid’s first theorem is an argument. The conclusions in steps 1 to 4 are called intermediate conclusions, while the conclusion in step 5 is the main conclusion. http://philosophy.wisc.edu/forster/220/notes_1.html (1 of 6) [08.04.2007 17:07:55] Inductive Logic Question: All arguments, or sequences of arguments, are examples of reasoning, but is every piece of reasoning an argument? A perceptual judgment such as "I see a blue square", or the conclusions of scientific experts reading in X-rays, or looking through a microscope, may be examples of reasoning that are not arguments. They are derived from what Kuhn called tacit knowledge, acquired through training and experience (e.g., knowing how to ride a bicycle). It is not easily articulated, and is not stated in any language. The Difference between Good and Bad Arguments In logic, we assume that any reasoning is represented as an argument, and the evaluation of an argument involves two questions: 1. Are the premises true? 2. Supposing that the premises are true, what sort of support do they give the conclusion? Answers to question 2: Compare the following arguments. 1. All planets move on ellipses. Pluto is a planet. Therefore, Pluto moves on an ellipse. 2. Mercury moves on an ellipse. Venus moves on an ellipse. Earth moves on an ellipse. Mars moves on an ellipse. Jupiter moves on an ellipse. Saturn moves on an ellipse. Uranus moves on an ellipse. Neptune moves on an ellipse. Therefore, Pluto moves on an ellipse. Definition: An argument is deductively valid if and only if it is impossible that its conclusion is false while its premises are true. Examples: Argument 1 is deductively valid, while argument 2 is not. Remark on terminology: The notion of deductively validity is such a central and important concept in philosophy, that is goes by several names. When an argument is deductively valid, we say that the conclusion follows from the premises, or the conclusion is deduced from , or i nferred from , or proved from the premises. Or we may say that the premises imply , or entail , or prove the conclusion. We also talk of deductively valid arguments as being demonstrative . All these different terms mean exactly the same thing, so the situation is far simpler than it appears. What’s possible? The sense of "impossible" needs clarification. Consider the example: 3. George is a human being. George is 100 years old. George has arthritis. Therefore, George will not run a four-minute mile tomorrow. http://philosophy.wisc.edu/forster/220/notes_1.html (2 of 6) [08.04.2007 17:07:55] Inductive Logic Suppose that the premises are true. In logic, it is possible that George will run a four-minute mile tomorrow. It is not physically possible. But logicians have a far more liberal sense of what is "possible" in mind in their definition of deductive validity. Argument 3 is not deductively valid on their definition. So, argument 3 is invalid. Key idea: In any deductively valid argument, there is a sense in which the conclusion is contained in premises. Deductive reasoning serves the purpose of extracting information from the premises. In a non-deductive argument, the conclusion ‘goes beyond’ the premises. Inferences in which the conclusion amplifies the premises is sometimes called ampliative inference. Therefore, whether an argument is deductively valid or not, depends on what the premises are. ‘Missing’ premises?: We can always add a premise to turn an invalid argument into a valid argument. For example, if we add the premise "No 100-year-old human being with arthritis will run a four-minute mile tomorrow" to argument 3, then the new argument is deductively valid. (The original argument, of course, is still invalid). Definition: An argument is inductively strong if and only if it is improbable that its conclusion is false while its premises are true. Remember: This definition is the same as the definition of "deductively valid" except that "impossible" is replaced by "improbable." The degree of strength of an inductive argument may be measured by the probability of that the conclusion is true given that all the premises are true. The probability of the conclusion of a deductively valid argument given the premises is one, so deductively valid arguments may be thought of as the limiting case of a strong inductive arguments. Ampliative arguments have an inductive strength less than one. The probability of the conclusion given the premises can change from person to person, as it depends on the stock of relevant knowledge possessed by a given person at a given time. Summary: In response to question 2, we may give answers like "the argument is valid", "the arguments is inductively strong" or "the argument is inductively weak." Exercise: Discuss the following examples (all statements are understood to refer to the year 1998): 4. There are multi-celled organisms living on Mars. Therefore, there is intelligent life on http://philosophy.wisc.edu/forster/220/notes_1.html (3 of 6) [08.04.2007 17:07:55] Inductive Logic Mars. 5. There are multi-celled organisms living on Mars. Therefore, there are single-celled organisms living on Mars. 6. There are multi-celled organisms living in Lake Mendota. Therefore, there is intelligent life living in Lake Mendota. 7. There are multi-celled organisms living in Lake Mendota. Therefore, there are single- celled organisms living in Lake Mendota. Nevertheless, in logic, it is assumed that the answer to question 1 is relevant to the evaluation of an argument. But it is a question that needs to be asked in addition to question 2. So, if the premises of an inductively strong argument are false, then logicians are forced to say that the argument is not a good one. It is confusing to say that an inductively strong argument is a weak argument, but this is how the terms are defined . Tip: Defined terms must be used as defined. You can’t use the term differently just because you don’t agree with the definition. Different Kinds of Ampliative Argument Definition: Any argument that is not deductively valid, or deductively invalid, is called an ampliative argument. The term refers to the fact that the conclusion of such argument goes beyond, or amplifies upon, the premises. Remark on terminology: Again the notion of ‘invalid’ is so common and central, that it goes by many names. Other terms commonly used are inductive and non-demonstrative. I prefer ‘ampliative’ because it reminds us that the conclusion ‘goes beyond’ the premises, and it does not have the bad reputation that sometimes goes along with the word ‘induction.’ Here are a variety of examples of ampliative arguments: Simple enumerative induction goes from a list of observations of the form "this A is a B" to the conclusion "All A’s are B’s". The example Hume made famous is like this: 8. Billiard ball 1 moves when struck. Billiard ball 2 moves when struck. Billiard ball 3 moves when struck… Billiard ball 100 moves when struck. Therefore, all billiard balls move when struck. Some ampliative arguments go from general statements to general statements: http://philosophy.wisc.edu/forster/220/notes_1.html (4 of 6) [08.04.2007 17:07:55] Inductive Logic 9. All bodies freely falling near the surface of the Earth obey Galileo’s law. All planets obey Kepler’s laws. Therefore, all material objects obey Newton’s laws. Others go from general statements to specific statements: 10. All emeralds previously found have been green. Therefore, the next emerald to be found will be green. Conclusion: To understand empirical science we need to understand ampliative inference. Two Kinds of Science? A Priori and Empirical? 1. A priori science, like Euclid’s geometry, is where the conclusions are deduced from premises that appear to be self-evidently true. 2. In empirical science, like physics, conclusions are based on observational data. ● This is similar to the distinction between pure mathematics and applied mathematics. The distinction is not always sharp. Ever since Einstein rejected the use of Euclidean geometry in his new physics at the turn of the 20 th century, it seems that a priori sciences cannot tell us anything about the real world. The focus of recent philosophy of science is on the empirical sciences. ● A priori sciences contain the strongest form of reasoning, at the expense of telling us less about the real world. Introduction to the Demarcation Problem Definition: In philosophy of science, we refer to what we already know directly through observation as the empirical evidence (we are open-minded about the possibility that some of these ‘facts’ are mistaken). See Exercise 1. All of empirical science uses ampliative arguments. Hume made the same point in a different way. He pointed that in example 8, it is possible that the premises are true and the conclusion is false. No matter how many instances of a generalization we observe, it does not prove that the generalization is true. What is the difference between science and pseudoscience? You often hear that science is based on the ‘facts’ while pseudoscience is not. Or you say that religious belief is based on faith, whereas scientific belief is not. Unfortunately, both scientific and non-scientific reasoning go beyond the facts. So, can we tell them apart? http://philosophy.wisc.edu/forster/220/notes_1.html (5 of 6) [08.04.2007 17:07:55] Inductive Logic Argument: 1. The demarcation between science and pseudoscience depends only the nature of the reasoning used. 2. Genuine science involves ampliative inference. 3. Pseudoscience involves ampliative inference. 4. Therefore, there is no demarcation between science and pseudoscience. The problem of demarcation is to say what is wrong with this argument. (Question: what are the two things that can be wrong with an argument?) Review of Central Definitions and Remarks on Terminology Definition: An argument is deductively valid if and only if it is impossible that its conclusion is false while its premises are true. Remark: The notion of deductively validity is such a central and important concept in philosophy, that is goes by several names. When an argument is deductively valid, we say that the conclusion follows from the premises, or the conclusion is deduced from , or i nferred from , or proved from the premises. Or we may say that the premises imply , or entail , or prove the conclusion. We also talk of deductively valid arguments as being demonstrative . All these different terms mean exactly the same thing, so the situation is far simpler than it appears. Definition: Any argument that is not deductively valid, or deductively invalid, is an ampliative argument . The term refers to the fact that the conclusion of such argument goes beyond, or amplifies upon, the premises. Remark: Again the notion of ‘invalid’ is so common and central, that it goes by many names. Other terms commonly used are inductive and non-demonstrative. I prefer ‘ampliative’ because it reminds us that the conclusion ‘goes beyond’ the premises, and it does not have the bad reputation that sometimes goes along with the word ‘induction.’ http://philosophy.wisc.edu/forster/220/notes_1.html (6 of 6) [08.04.2007 17:07:55] Demarcation Demarcation: Popper, Kuhn and Lakatos Last modified on Friday, September 18, 1998.  Malcolm R. Forster, 1998 The Problem The difference between science and non-science has practical ramifications for society: ● Parapsychology includes the study of such alleged phenomena as telepathy, clairvoyance, and precognition. In 1969 the American Association for the Advancement of Science (AAAS) admitted the Parapsychology association as an Affiliate member. Should they have done that? ● In Arkansas, U. S. A., there were attempts to have the biblical story of creation taught in schools alongside evolutionary theory (after earlier attempts to ban evolutionary theory failed). They argued that creationism is a just as much a science, and therefore deserves equal time. ● The Merriam-Webster's Collegiate ® Dictionary defines creation science n (1979): creationism; also : scientific evidence or arguments put forth in support of creationism. Should an authoritative dictionary presuppose that creationism is a science? ● Freudian psychology has a poor reputation in scientific circles. Is it a pseudoscience? ● Immanuel Velikovsky and Erich van Daniken wrote best sellers Worlds in Collision and Chariots of the Gods , which angered many scientists. Are these examples of pseudoscience. ● Thor Heyerdahl launched the Kon-Tiki expedition to support his theory that the polynesians migrated from South America. Was he a pseudoscientist? ● Gould wrote a book called The Mismeasure of Man about the IQ debate, and phrenology, which purported to predict the criminal nature of people from their skull shape and other characteristics. ● IQ testing has been used to screen children from entering high school, or college, in many countries for many years. Does it predict future academic performance reliably? Is there really such a thing as intelligence? ● Chemistry grew out of alchemy. One’s a science and the other is not. What’s the difference? ● The label 'science' carries a high degree of authority, and people need to understand when the label, and the authority, are deserved. Is there any clear difference between an unscientific study and a scientific one? ● More generally, an understanding of what science is carries us a step closer to telling the difference between good and bad science, and the limits of good science. If we understand how science works, we can be better and more informed use of scientific expertise. http://philosophy.wisc.edu/forster/220/notes_2.html (1 of 9) [08.04.2007 17:08:14] Demarcation If we wanted to know which subjects were generally accepted as science, we would probably find a fairly sharp and clear division between two categories. But we are interested in more than that! We want to understand the general characteristics of science that are different from pseudoscience. That is actually surprisingly difficult and controversial. Exercise: Critically evaluate the following characterization of science (from the Encyclopedia Britannica ): any system of knowledge that is concerned with the physical world and its phenomena and that entails unbiased observations and systematic experimentation. In general, a science involves a pursuit of knowledge covering general truths or the operations of fundamental laws. Examples of Science and Pseudoscience The key to understanding Popper's demarcation criterion is to compare two examples. The first, Popper thinks is typical of science, while the second is typical of pseudoscience. Example (a): Einstein's prediction of the bending of star light. For over 200 years prior to Einstein, Newtonian physics had enjoyed a period of unprecedented success in science. Many scientists thought that Newton's theory was the end of science, and many philosophers not only believed that Newton's theory was true, they thought that it was necessarily true. They sought to explain why Newton's theory had to be true. All that began to change with Planck's 1900 introduction of the idea that energy comes in small discrete packages (the quantum hypothesis) and Einstein's discovery of the special theory of relativity in 1905. Einstein's special theory of relativity was a way of reconciling some inconsistencies between the wave theory of light and Newtonian mechanics. Instead of modifying the wave theory, he modified some of the fundamental assumptions used in Newtonian physics (like the assumption that simultaneity did not depend on a frame of reference, and that the mass does not depend on its velocity). However, Einstein's special theory of relativity said nothing about gravity. Einstein's general theory of relativity was his theory of gravitation, which he had published by 1916. Many scientists were impressed by the aesthetic beauty of Einstein's principles, but it was also important that it be tested by observation. For most everyday phenomena, in which velocities are far smaller than the speed of light, there is no detectable difference between Einstein's prediction and Newton's prediction. What we needed was a crucial experiment in which Einstein and Newton made different predictions. In 1916, there were successful tests of Einstein's special theory. But crucial tests of the general theory were harder to come by. One such case was provided by the bending of starlight by the gravity of the sun. The period from 1900 to at least 1916 was a period of revolution in physics, and Eddington's confirmation of Einstein's prediction in 1919 helped to complete the change in physics. "The idea that light should be deflected by passing close to a massive body had been suggested by the British astronomer and geologist John Michell in the 18th century. However, Einstein's general relativity theory predicted twice as much deflection as Newtonian physics. http://philosophy.wisc.edu/forster/220/notes_2.html (2 of 9) [08.04.2007 17:08:14] Demarcation Quick confirmation of Einstein's result came from measuring the direction of a star close to the Sun during an expedition led by the British astronomer Sir Arthur Stanley Eddington to observe the solar eclipse of 1919. Optical determinations of the change of direction of a star are subject to many systematic errors, and far better confirmation of Einstein's general relativity theory has been obtained from measurements of a closely related effect namely, the increase of the time taken by electromagnetic radiation along a path close to a massive body." ( Encyclopedia Britannica) "The theories involved here were Einstein's general theory of relativity and the Newtonian particle theory of light, which predicted only half the relativistic effect. The conclusion of this exceedingly difficult measurement that Einstein's theory was followed within the experimental limits of error, which amounted to +/-30 percent was the signal for worldwide feting of Einstein. If his theory had not appealed aesthetically to those able to appreciate it and if there had been any passionate adherents to the Newtonian view, the scope for error could well have been made the excuse for a long drawn-out struggle, especially since several repetitions at subsequent eclipses did little to improve the accuracy. In this case, then, the desire to believe was easily satisfied. It is gratifying to note that recent advances in radio astronomy have allowed much greater accuracy to be achieved, and Einstein's prediction is now verified within about 1 percent." (Encyclopedia Britannica) "According to this theory the deflection, which causes the image of a star to appear slightly too far from the Sun's image, amounts to 1.75 seconds of arc at the limb of the Sun and decreases in proportion to the apparent distance from the centre of the solar disk of the star whose light is deflected. This is twice the amount given by the older Newtonian dynamics if light is assumed to have inertial properties. If light does not have such properties, as is generally accepted now, the Newtonian deflection is zero." (Encyclopedia Britannica) Reconstruction of the example: Philosophers need a general characterization of the example: Let E be a statement of the prediction made by Einstein's theory. E states the direction that the starlight will be observed at the time at which the star was to be observed by Eddington. Let T be a statement of the general principled in Einstein's general theory of relativity. Let A be the conjunction of all auxiliary statements used to derive, or deduce, E from T . That is to say, the argument with T and A as premises, and E as the conclusion, is deductively valid. Symbolically, we may write this as: T & A ⇒ E . A will include assumptions like "the sun is spherical ball of mass M ", "there are no other bodies close by to add to the sun's gravitational field," "If the sun were not present, then the star would be seen in the direction such-and-such," "the effect of stellar aberration on the direction of light is such-and-such," and so on. http://philosophy.wisc.edu/forster/220/notes_2.html (3 of 9) [08.04.2007 17:08:14] Demarcation Example (b): Adler's 'individual psychology'. Compare the following two (hypothetical) explanations of human behavior. (1) E 1 : A man pushes a child into the water with the intention of drowning it. (2) E 2 : A man sacrifices his life in an attempt to save the child. Popper claims that Adler's 'individual psychology' can explain both of these behaviors with equal ease. Let T be Adler's theory, let A be the auxiliary assumption that the man suffered feelings of inferiority (producing the need to prove to himself that he dared to commit some crime). Then T & A 1 ⇒ E 1 . Let A 2 be the auxiliary assumption that the man suffered feelings of inferiority (producing the need to prove to himself that he dared to rescue the child). Now T & A 2 ⇒ E 2 . Definition: Let us say that a theory T predicts an event E if and only if there are auxiliary assumptions that have either been used successfully in other predictions, or are the simplest and most obvious assumptions that one would make in the situation, and that T & A ⇒ E . If there exists auxiliary assumptions such that T & A ⇒ E , where A is some ad hoc assumption that is introduced in light of the evidence E itself, then theory T merely accommodates E . In example (a), Einstein's theory predicts the observational evidence, while in example (b), the theory is merely accommodates the evidence. Popper describes the difference by claiming that Einstein's theory is falsifiable, whereas Adler's theory is not. Remark: Popper also claims that the problem with Adler's theory is that it is too easily verified: "the world was full of verifications of the theory." Adler may have seen it like that, but was he right? My feeling is that mere accommodations do not count as verifications at all. Hence, I think that a verificationist could account for the difference between these two examples as well as, if not better than, a falsificationist. Discussion Question: How does our previous distinction between ampliative inference and deductive inference enter into these examples, if at all. Popperians tend to think that there is no need for ampliative inference in science at all. Why might they think that? Are they right? Popper's Path to his Demarcation Criteria (Curd and Cover, pages 1-10) To understand a philosophical theory, like Popper's demarcation criterion, it is useful to see why simpler alternative proposals do not work. Proposal 1: Science is distinguished by its empirical method. That is, science is distinguished from pseudoscience by its use of observational data in making predictions. http://philosophy.wisc.edu/forster/220/notes_2.html (4 of 9) [08.04.2007 17:08:14] [...]... inventing theories They can come in a dream or they can be constructed from the data—it does not matter Rather, the essence of science is about how predictions are deduced from the theories This way of viewing science is known as hypothetico-deductivism The difference between science and pseudoscience rests solely on the 'deductive' part of the process Kuhn’s Characterization of Science Thomas Kuhn makes the. .. the prediction E0 from model M0 and E0 proves to be false, then the scientist does not blame T, but instead moves to M1, because it is next on the ordered list, and so on Scientists now predict E1 because M1 & B ⇒ E1 And so on There is no falsifiability of the theory, but it can still make predictions Thus, the idea of a heuristic may save the distinction between accommodation and prediction, and thereby... Thus the forelimbs of such widely differing mammals as humans, bats, and deer are homologous; the form of construction and the number of bones in these varying limbs are practically identical, and represent adaptive modifications of the forelimb structure of their common early mammalian ancestors Analogous structures, on the other hand, can be represented by the wings of birds and of insects; the structures... The evolution of horses ● ● Fact to be explained: In the lineage leading up to the modern genus Equus, of which the horse is a species, the fossil record shows that the ratio of molar tooth height to length increases over time, and that there is an acceleration in the rate of change through time Assumption 1: The environment changed In the Miocene period, Merychippus and its descendents abandoned the. .. distribution of plants and animals, and later knowledge has reinforced his observations For example, there are about 1,500 species of Drosophila vinegar flies in the world; nearly one-third of them live in Hawaii and nowhere else, although the total area of the archipelago is less than onetwentieth the area of California There are also in Hawaii more than 1,000 species of snails and other land mollusks that... (unpredicted wobbles) in the motion of the outermost planet known at the time (Uranus) They postulated that these might be caused by a hitherto unknown planet Based on that conjecture they recalculated the solutions to Newton's equations, and fit the solutions to the known data for Uranus That fit even predicted the position of the postulated planet, whereupon Neptune was seen for the first time once telescopes... Laudan, is whether evolutionary theory is better supported by the evidence than creationism Debating the scientific status of the theories is a red herring Arguments that Creationism is a Pseudoscience (Kitcher) Argument 1: Scientific theories make predictions (= observational consequences deduced from the theory) If the predictions prove to be false, then the theory is false That is, scientific theories... nucleotides, and all of the various proteins are synthesized from different combinations and sequences of the same 20 amino acids, although several hundred other amino acids do exist The genetic "code" by which the information contained in the nuclear DNA is passed on to proteins is everywhere the same Similar metabolic pathways are used by the most diverse organisms to produce energy and to make up the cell... However, we must now decide whether to count statements of background evidence, prior observations, and data, as auxiliary assumptions They are auxiliary in the sense that they are needed in order to make predictions In the Le Verrier-Adams example it would be impossible to predict the position of the postulated planet without making use of the observed positions of Uranus, and the other planets Let use refer... 17:09:06] Evolution the mirror ophrys (Ophrys speculum) The colouring so closely resembles that of the female wasp Colpa aurea that males of the species are attracted to the flower and pick up pollen during their attempts at copulation E.S Ross DOBZHANSKY: Between 1920 and 1935, mathematicians and experimentalists began laying the groundwork for a theory combining Darwinian evolution and Mendelian genetics . us anything about the real world. The focus of recent philosophy of science is on the empirical sciences. ● A priori sciences contain the strongest form of reasoning, at the expense of telling. is the conclusion and the rest of which are the premises. The conclusion states the point being argued for and the premises state the reasons being advanced in support the conclusion. They. nothing to do with the status of the theory as scientific. There are no scientific or unscientific ways of inventing theories. They can come in a dream or they can be constructed from the data—it