Friday, December 10, 2010

Loading the directions for the Chis Squared analysis was a little troublesome. Check the links below for clear images if you have trouble reading the post below.

For a PDF of the directions in the post:

For a clear Chi Squared Table:

For an image of the Chi Squared formula:

Chi Squared Analysis

Here are the directions for your Chi Squared Analysis in your fly lab write up.

1. The purpose of doing a statistical test:
a. Data varies from expected results
b. We need to know if variation is expected
c. Conduct statistical analysis to know:
i. If data falls within random variation
ii. Suggests we should find an alternative hypothesis

2. The purpose of the Chi squared test is to determine if your results vary significantly from expected numbers.

3. Steps of the Chi Squared Test:
a. State your NULL HYPOTHESIS (the null hypothesis states that your data do not differ significantly from your expected results).
b. Figure out expected ratios for data
c. Compile your data
d. Find the difference between the observed and expected number of each phenotype.
e. Square the differences from step 4.
f. Divide the squared differences from step 5 by the expected number of each phenotype.
g. Add the resulting values to determine a Chi Squared Value

4. To complete the former steps:
a. Use a table like this:

Phenotype Observed (o) Expected (e) 0-e (o-e)^2
Red eyes 51 50 1 1
White eyes 49 50 -1 1

Then add the values in the (o-e)^2 column. This is your Chi Squared value.

5. Using a Chi Squared Table:
a. Determine a Chi Squared value as shown above.
b. Determine the Degrees of freedom (# of phenotypic classes -1)
c. Determine acceptable level of probability—for the fly lab, use p>0.05 (for a discussion of p value, see point 6)
d. Find your Critical Value (the number in the cell where your degrees of freedom and p value intersect). See the table below.
e. If your calculated Chi Squared value is less than the critical value, accept your null hypothesis (there is no significant difference between observed and expected results).
f. If your Chi Squared value is equal to or greater than the critical value, propose an alternative hypothesis.

6. Determining a p value
a. The p value is the probability that the difference between your observed and expected values is due to chance alone.
b. In biological research, we generally accept p > 0.05. A p value of 0.05 means that the results we observed would be due to due to chance 5% of the time.

7. Interpreting Your Results:
a. Check your calculated Chi Squared value.
b. Compare it to the Critical Value from the table.
c. If your calculated Chi Squared value is less than the critical value, accept your null hypothesis (there is no significant difference between observed and expected results). For your flies, this means that your data match your prediction about the F2 phenotypes.
d. If your Chi Squared value is equal to or greater than the critical value, propose an alternative hypothesis. In your paper, make a suggestion about how the data you collected occurred that is different from your original hypothesis.

8. Chi Squared Table:

9. A practice problem:

Thomas Morgan did the following dihybrid cross: grey X black bodies and normal X vestigial wings. Grey bodies and normal wings are dominant.
• The cross can be symbolized: b+b vg+vg X bb vgvg, where b+ is grey body, b is black body, vg+ is normal wings and vg is vestigial wings.

• For this cross, he observed the following phenotypic ratios:
Grey-Normal: 965
Grey-Vestigial: 206
Black-Normal: 185
Black-Vestigial: 944

Answer the following questions:

What are the expected phenotypic ratios for a normal dihybrid cross?
If these traits normally show 20% recombination, what are the expected phenotypic ratios?
What is your null hypothesis?
What is your Chi Squared value?
How many Degrees of Freedom are there?
If we accept 90% probability, what is the critical value?
Should we accept or reject you null hypothesis?

Tuesday, October 12, 2010

Watson and Crick

One of the most important discoveries in modern genetics was that DNA exists as a double helix. James Watson and Francis Crick published this finiding in Nature in the April 25, 1953 issue. They followed their initial paper with another that detailed a mechanism for DNA replication.

Here is a copy of their original paper for your reading pleasure (it's only a page long, and well worth taking a look at as a peice of scientific history).

Genetics Vocabulary List

Here is a list of vocabulary terms that you might find useful when studying the chapters on genetics (Chapters 13-17 are listed here). All answers can be found in your textbook. The list may look long and daunting, but most of the terms will be much easier to remember after we go over the topics in class.

Chapter 13- Meiosis and Sexual Life Cycles

Asexual reproduction
Sexual Reproduction
Life cycle
Somatic cells
Homologous chromosome
Sex chromosome
Alternation of generations
Chiasmata (singular=chiasma)
Independent assortment
Crossing over

Chapter 14-Mendel and The Gene Idea

P generation
FX generation (x=1, 2, etc)
Test cross
Incomplete dominance
Multiple alleles
Polygenic inheritance
Norm of reaction
Multifactorial characters
Cystic Fibrosis
Sickle Cell Anemia
Huntington’s disease
Chorionic villus sampling

Chapter 15- The Chromosomal Basis of Inheritance

Chromosome theory of inheritance
Thomas Morgan
Drisophila melanogaster
Linked genes
Sex linked genes
Wild type
Genetic map
Sex chromosome
Duchenne Muscular Dystrophy
Barr body
Down syndrome (Trisomy 21)
Genomic imprinting

Chapter 16- The Molecular Basis of Inheritance

Frederick Griffith
Oswald Avery
Hershey & Chase
Erwin Chargaff
Double helix
Hydrogen bonding
Semiconservative model of DNA replication
Origin of replication
Replication fork
DNA polymerase
Parallel and anitparallel strands
3’ end
5’ end
Single Strand Binding Protein
Leading strand
Lagging strand
Okazaki fragments
Mismatch repair
Excision repair

Chapter 17- From Gene to Protein

One gene-one enzyme (polypeptide) hypothesis
Beadle and Tatum
Messenger RNA (mRNA)
Primary transcript
Template strand
Triplet code
TATA box
Transcription factor
RNA polymerase
Transcription initiation complex
5’ cap
Poly (A) tail
RNA splicing
Small nuclear RNA (snRNA)
Transfer RNA (tRNA)
Aminoacyl-tRNA synthetase
Ribosomal RNA (rRNA)
P site
A site
E site
Large and small ribosomal subunits
Start codon
Stop codon
Peptide bond
Signal peptide
Point mutation
Base pair substitution
Missense mutation
Nonsense mutation
Frameshift mutation
Ames test

Thursday, August 19, 2010

Summer Assignment Three - Biology and the Chemistry of Life


We shift gears now to what you will recognize as a more traditional introduction to a science class. This will be the last assignment before I see you in the classroom. It may seem like a lot but it is not very "meaty" and I suspect much of it you already know or are familiar with so it should be easily digestible.

By having you do these lessons before school begins we make time to cover all the heavy duty AP material and labs before the exam in May. That may seem a long ways off but time will fly.

So go to which is a University of California open access AB Biology course. From what I have read and seen of it you may want to use it throughout the school year as a study supplement. When you get there you will find a Moodle page that has links to lessons. You will be doing the first six and they are due the first day of school. Here is what I want you to do:

Lesson 1, Biology and Biologists - Read the Introduction, watch Play Media, and do the Review Questions

Lesson 2, The Chemical Basis of Life - Watch Play Media, and do the Review Questions

Lesson 3, Water and Life - Watch Play Media, and do the Review Questions

Lesson 4, Acids, Bases, and Buffers - Read pdf Acids, Bases, and Buffers, and do the Review Questions

Lesson 5, Organic Molecules - Review the pdf Reference Sheet, Watch Play Media, and do the Review Questions

Lesson 6, Macromolecules - Watch Play Media, and do the Review Questions

What to turn in? For each lesson Review Questions, on a piece of paper write the question number and the letter of the answer you selected. It should look like this-

Lesson 1 Review Questions
#1 - d
#2 - a
#3 - c
and so on......

Feel free to ask questions as they come up by responding to this post. I do my best to respond within a day. Remember, these are due the first day of school.

When school begins we will take time discuss Ziman, Popper, and see how you did on the six lessons. I am looking forward to the year but make no mistake, you will be challenged to be the best student you can be. This class is what a student intending to major in biology would take their first year of college.

Mr. Baker

Wednesday, August 11, 2010

Blog Assignment Two - Karl Popper

This week we wrap-up our look at the nature of science with another classic in the cannon of the philosophy of science, “Science: Conjectures and Refutations” by Karl Popper. This essay is meaty so take your time to digest what it has to offer.

But first, some vocabulary -

1. Induction: inferring a general conclusion or principle from particular instances (from specific to general). The theory of plate tectonics (general principle) is inferred from many individual evidences (specifics).
2. Deduction: inference in which the conclusion about particulars follows from general principle (from general to specific). Sherlock Holms used deduction. Fingerprints are unique to the individual (general principle) so if the suspect’s fingerprints are on the knife, he held the knife (specific).
3. Demarcation: to set apart, distinguish

Distinguishing science from pseudo-science:

Finding truth through science is an empirical process based on inductive reasoning. It is different from other “truth” finding activities such as astrology and tarot card reading, which are based on other principles. While induction does result in new knowledge it comes at a cost. The cost is that science is tentative and subject to revision. Due to the nature of science, two philosophical problems arise. The first problem is distinguishing science from pseudo-science also known as the problem of demarcation. For example, what makes astronomy science yet astrology not? The second problem is the logical problem of induction. In other words how can science find truth if it is always tentative and subject to revision?

The philosopher, Sir Karl Popper (1902-1994) addressed these problems in the essay you are about to read. In the essay he first distinguishes science from pseudo-science by solving the problem of demarcation. He then explores the logical problem of induction and concludes that it and the problem of demarcation are the same. The ideas presented in this essay likely are new to you. Your understanding will require careful attention to the essay, thoughtful responses to the questions, and careful discussion with your instructor. There are two primary objectives for this activity. First, you will learn what separates science from pseudo-science. Second, will be to understand how we can know a theory is true even if it is tentative and subject to revision.

I hope is that after reading these two essays you begin to appreciate the dimensions of science. As you have already discovered, science is not just doing experiments. It is much more – a grand achievement of the human mind that is capable of understanding the universe in which we live.

So sit back, relax, and enjoy Popper’s essay you will find the questions at the end of the essay.

Next week we begin looking at the chemistry of living things.

Karl Popper - Science: Conjectures & Refutations

Mr. Turnbull had predicted evil consequences, . . . and was now doing the best in his power to bring about the verification of his own prophecies. Anthony Trollope

When I received the list of participants in this course and realized that I had been asked to speak to philosophical colleagues I thought, after some hesitation and consultation that you would probably prefer me to speak about those problems which interest me most, and about those developments with which I am most intimately acquainted. I therefore decided to do what I have never done before: to give you a report on my own work in the philosophy of science, since the autumn of 1919 when I first began to grapple with the problem, "When should a theory be ranked as scientific?" or "Is there a criterion for the scientific character or status of a theory?"

The problem which troubled me at the time was neither, "When is a theory true?"nor, "When is a theory acceptable?" My problem was different. I wished to distinguish between science and pseudo-science; knowing very well that science often errs, and that pseudo-science may happen to stumble on the truth.

I knew, of course, the most widely accepted answer to my problem: that science is distinguished from pseudo-science or from "metaphysics" by its empirical method, which is essentially inductive, proceeding from observation or experiment. But this did not satisfy me. On the contrary, I often formulated my problem as one of distinguishing between a genuinely empirical method and a non-empirical or even a pseudo-empirica1 method-that is to say, a method which, although it appeals to observation and experiment, nevertheless does not come up to scientific standards. The latter method may be exemplified by astrology with its stupendous mass of empirical evidence based on observation-on horoscopes and on biographies.

But as it was not the example of astrology which led me to my problem I should perhaps briefly describe the atmosphere in which my problem arose and the examples by which it was stimulated. After the collapse of the Austrian Empire there had been a revolution in Austria: the air was full of revolutionary slogans and ideas, and new and often wild theories. Among the theories which interested me Einstein's theory of relativity was no doubt by far the most important. Three others were Marx's theory of history, Freud's psycho-analysis, and Alfred Adler's so-called "individual psychology."

There was a lot of popular nonsense talked about these theories, and especially about relativity (as still happens even today), but I was fortunate in those who introduced me to the study of this theory. We all-the small circle of students to which I belonged-were thrilled with the result of Eddington's eclipse observations which in 1919 brought the first important confirmation of Einstein's theory of gravitation. It was a great experience for us, and one which had a lasting influence on my intellectual development.

The three other theories I have mentioned were also widely discussed among students at that time. I myself happened to come into personal contact with Alfred Adler, and even to co-operate with him in his social work among the children and young people in the working-class districts of Vienna where he had established social guidance clinics.

It was during the summer of 1919 that I began to feel more and more dissatisfied with these three theories-the Marxist theory of history, psychoanalysis, and individual psychology; and I began to feel dubious about their claims to scientific status. My problem perhaps first took the simple form, "What is wrong with Marxism, psycho-analysis, and individual psychology? Why are they so different from physical theories, from Newton's theory, and especially from the theory of relativity?"

To make this contrast clear I should explain that few of us at the time would have said that we believed in the truth of Einstein's theory of gravitation. This shows that it was not my doubting the truth of those other three theories which bothered me, but something else. Yet neither was it that I merely felt mathematical physics to be more exact than the sociological or psychological type of theory. Thus what worried me was neither the problem of truth, at that stage at least, nor the problem of exactness or measurability. It was rather that I felt that these other three theories, though posing as sciences, had in fact more in common with primitive myths than with science; that they resembled astrology rather than astronomy.

I found that those of my friends who were admirers of Marx, Freud, and Adler, were impressed by a number of points common to these theories, and especially by their apparent explanatory power. These theories appeared to be able to explain practically everything that happened within the fields to which they referred. The study of any of them seemed to have the effect of an intellectual conversion or revelation, opening your eyes to a new truth hidden from those not yet initiated. Once your eyes were thus opened you saw confirming instances everywhere: the world was full of verifications of the theory. Whatever happened always confirmed it. Thus its truth appeared manifest; and unbelievers were clearly people who did not want to see the manifest truth; who refused to see it, either because it was against their class interest, or because of their repressions which were still "un-analysed" and crying aloud for treatment.

The most characteristic element in this situation seemed to me the incessant stream of confirmations, of observations which "verified" the theories in question; and this point was constantly emphasized by their adherents. A Marxist could not open a newspaper without finding on every page confirming evidence for his interpretation of history; not only in the news, but also in its presentation-which revealed the class bias of the paper-and especially of course in what the paper did not say. The Freudian analysts emphasized that their theories were constantly verified by their "clinical observations." As for Adler, I was much impressed by a personal experience. Once, in 1919, 1 reported to him a case which to me did not seem particularly Adlerian, but which he found no difficulty in analysing in terms of his theory of inferiority feelings, although he had not even seen the child. Slightly shocked, I asked him how he could be so sure. "Because of my thousandfold experience," he replied; whereupon I could not help saying: "And with this new case, I suppose, your experience has become thousand-and-one-fold."

What I had in mind was that his previous observations may not have been much sounder than this new one; that each in its turn had been interpreted in the light of "previous experience," and at the same time counted as additional confirmation. What, I asked myself, did it confirm? No more than that a case could be interpreted in the light of the theory. But this meant very little, I reflected, since every conceivable case could be interpreted in the light of Adler's theory, or equally of Freud's. I may illustrate this by two very different examples of human behaviour: that of a man who pushes a child into the water with the intention of drowning it; and that of a man who sacrifices his life in an attempt to save the child. Each of these two cases can be explained with equal ease in Freudian and in Adlerian terms. According to Freud the first man suffered from repression (say, of some component of his Oedipus complex), while the second man had achieved sublimation. According to Adler the first man suffered from feelings of inferiority (producing perhaps the need to prove to himself that he dared to commit some crime), and so did the second man (whose need was to prove to himself that he dared to rescue the child). I could not think of any human behaviour which could not be interpreted in terms of either theory. It was precisely this fact-that they always fitted, that they were always confirmed-which in the eyes of their admirers constituted the strongest argument in favour of these theories. It began to dawn on me that this apparent strength was in fact their weakness.

With Einstein's theory the situation was strikingly different. Take one typical instance-Einstein's prediction, just then confirmed by the findings of Eddington's expedition. Einstein's gravitational theory had led to the result that light must be attracted by heavy bodies (such as the sun), precisely as material bodies were attracted. As a consequence it could be calculated that light from a distant fixed star whose apparent position was close to the sun would reach the earth from such a direction that the star would seem to be slightly shifted away from the sun; or, in other words, that stars close to the sun would look as if they had moved a little away from the sun, and from one another. This is a thing which cannot normally be observed since such stars are rendered invisible in daytime by the sun's overwhelming brightness; but during an eclipse it is possible to take photographs of them. If the same constellation is photographed at night one can measure the distances on the two photographs, and check the predicted effect.

Now the impressive thing about this case is the risk involved in a prediction of this kind. If observation shows that the predicted effect is definitely absent, then the theory is simply refuted. The theory is incompatible with certain possible results of observation-in fact with results which everybody before Einstein would have expected. This is quite different from the situation I have previously described, when it turned out that the theories in question were compatible with the most divergent human behaviour, so that it was practically impossible to describe any human behaviour that might not be claimed to be a verification of these theories.

These considerations led me in the winter of 1919-20 to conclusions which I may now reformulate as follows.

(1) It is easy to obtain confirmations, or verifications, for nearly every theory-if we look for confirmations.

(2) Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory-an event which would have refuted the theory.

(3) Every "good" scientific theory is a prohibition: it forbids certain things to happen. The more a theory forbids, the better it is.

(4) A theory which is not refutable by any conceivable event is nonscientific. Irrefutability is not a virtue of theory (as people often think) but a vice.

(5) Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability; but there are degrees of testability; some theories are more testable, more exposed to refutation, than others; they take, as it were, greater risks.

(6) Confirming evidence should not count except when it is the result of a genuine test of the theory; and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory. (I now speak in such cases of "corroborating evidence.")

(7) Some genuinely testable theories, when found to be false, are still upheld by their admirers-for example by introducing ad hoc some auxiliary assumption, or by re-interpreting theory ad hoc in such a way that it escapes refutation. Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering, its scientific status. (I later described such a rescuing operation as a "conventionalist twist" or a "conventionalist stratagem.")

One can sum up all this by saying that the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability.


I may perhaps exemplify this with the help of the various theories so far mentioned. Einstein's theory of gravitation clearly satisfied the criterion of falsifiability. Even if our measuring instruments at the time did not allow us to pronounce on the results of the tests with complete assurance, there was clearly a possibility of refuting the theory.

Astrology did not pass the test. Astrologers were greatly impressed, and misled, by what they believed to be confirming evidence_so much so that they were quite unimpressed by any unfavourable evidence. Moreover, by making their interpretations and prophecies sufficiently vague they were able to explain away anything that might have been a refutation of the theory had the theory and the prophecies been more precise. In order to escape falsification they destroyed the testability of their theory. It is a typical soothsayer's trick to predict things so vaguely that the predictions can hardly fail: that they become irrefutable.

The Marxist theory of history, in spite of the serious efforts of some of its founders and followers, ultimately adopted this soothsaying practice. In some of its earlier formulations (for example in Marx's analysis of the character of the "coming social evolution') their predictions were testable, and in fact falsified.2 Yet instead of accepting the refutations the followers of Marx reinterpreted both the theory and the evidence in order to make them agree. In this way they rescued the theory from refutation; but they did so at the price of adopting a device which made it irrefutable. They thus gave a "conventionalist twist" to the theory; and by this stratagem they destroyed its much advertised claim to scientific status.

The two psycho-analytic theories were in a different class. They were simply non-testable, irrefutable. There was no conceivable human behaviour which could contradict them. This does not mean that Freud and Adler were not seeing certain things correctly: I personally do not doubt that much of what they say is of considerable importance, and may well play its part one day in a psychological science which is testable. But it does mean that those "clinical observations" which analysts naively believe confirm their theory cannot do this any more than the daily confirmations which astrologers find in their practice.3 And as for Freud's epic of the Ego, the Super-ego, and the Id, no substantially stronger claim to scientific status can be made for it than for Homer's collected stories from Olympus. These theories describe some facts, but in the manner of myths. They contain most interesting psychological suggestions, but not in a testable form.

At the same time I realized that such myths may be developed, and become testable; that historically speaking all-or very nearly all-scientific theories originate from myths, and that a myth may contain important anticipations of scientific theories. Examples are Empedocles' theory of evolution by trial and error, or Parmenides' myth of the unchanging block universe in which nothing ever happens and which, if we add another dimension, becomes Einstein's block universe (in which, too, nothing ever happens, since everything is, four dimensionally speaking, determined and laid down from the beginning). I thus felt that if a theory is found to be non-scientific, or "metaphysical" (as we might say), it is not thereby found to be unimportant, or insignificant, or "meaningless," or "nonsensical." it cannot claim to be backed by empirical evidence in the scientific sense-although it may easily be, in some genetic sense, the "result of observation."

(There were a great many other theories of this pre-scientific or pseudoscientific character, some of them, unfortunately, as influential as the Marxist interpretation of history; for example, the racialist interpretation of history-another of those impressive and all-explanatory theories which act upon weak minds like revelations.)

Thus the problem which I tried to solve by proposing the criterion of falsifiability was neither a problem of meaningfulness or significance, nor a problem of truth or acceptability. It was the problem of drawing a line (as well as this can be done) between the statements, or systems of statements, of the empirical sciences, and all other statements-whether they are of a religious or of a metaphysical character, or simply pseudo-scientific. Years later-it must have been in 1928 or 1929-I called this first problem of mine the "problem of demarcation. " The criterion of falsifiability is a solution to this problem of demarcation, for it says that statements or systems of statements, in order to be ranked as scientific, must be capable of conflicting with possible, or conceivable, observations....


Let us now turn from our logical criticism of the psychology of experience to our real problem-the problem of the logic of science. Although some of the things I have said may help us here, in so far as they may have eliminated certain psychological prejudices in favour of induction, my treatment of the logical problem of induction is completely independent of this criticism, and of all psychological considerations. Provided you do not dogmatically believe in the alleged psychological fact that we make inductions, you may now forget my whole story with the exception of two logical points: my logical remarks on testability or falsifiability as the criterion of demarcation; and Hume's logical criticism of induction.

From what I have said it is obvious that there was a close link between the two problems which interested me at that time: demarcation, and induction or scientific method. It was easy to see that the method of science is criticism, i.e. attempted falsifications. Yet it took me a few years to notice that the two problems-of demarcation and of induction-were in a sense one....

I recently came across an interesting formulation of this belief in a remarkable philosophical book by a great physicist-Max Born's Natural Philosophy of Cause and Chance.5 He writes: "Induction allows us to generalize a number of observations into a general rule: that night follows day and day follows night . . . But while everyday life has no definite criterion for the validity of an induction, . . .science has worked out a code, or rule of craft, for its application." Born nowhere reveals the contents of this inductive code (which, as his wording shows, contains a "definite criterion for the validity of an induction"); but he stresses that "there is no logical argument" for its acceptance: "it is a question of faith"; and he is therefore "willing to call induction a metaphysical principle." But why does he believe that such a code of valid inductive rules must exist? This becomes clear when he speaks of the "vast communities of people ignorant of, or rejecting, the rule of science, among them the members of anti-vaccination societies and believers in astrology. It is useless to argue with them; I cannot compel them to accept the same criteria of valid induction in which I believe: the code of scientific rules." This makes it quite clear that "valid induction" was here meant to serve as a criterion of demarcation between science and pseudo-science.

But it is obvious that this rule or craft of "valid induction" is not even metaphysical: it simply does not exist. No rule can ever guarantee that a generalization inferred from true observations, however often repeated, is true.(Born himself does not believe in the truth of Newtonian physics, in spite of its success, although he believes that it is based on induction.) And the success of science is not based upon rules of induction, but depends upon luck, ingenuity, and the purely deductive rules of critical argument.

I may summarize some of my conclusions as follows:

(1) Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure.

(2) The actual procedure of science is to operate with conjectures: to jump to conclusions-often after one single observation (as noticed for example by Hume and Born).

(3) Repeated observations and experiments function in science as tests of our
conjectures or hypotheses, i.e. as attempted refutations.

(4) The mistaken belief in induction is fortified by the need for a criterion of demarcation which, it is traditionally but wrongly believed, only the inductive method can provide.

(5) The conception of such an inductive method, like the criterion of verifiability, implies a faulty demarcation.

(6) None of this is altered in the least if we say that induction makes theories only probable rather than certain.


If, as I have suggested, the problem of induction is only an instance or facet of the problem of demarcation, then the solution to the problem of demarcation must provide us with a solution to the problem of induction. This is indeed the case, I believe, although it is perhaps not immediately obvious.

For a brief formulation of the problem of induction we can turn again to Born, who writes: ". . . no observation or experiment, however extended can give more than a finite number of repetitions"; therefore, "the statement of a law-B depends on A-always transcends experience. Yet this kind of statement is made everywhere and all the time, and sometimes from scanty material.'

In other words, the logical problem of induction arises from (a) Hume's discovery (so well expressed by Born) that it is impossible to justify a law by observation or experiment, since it "transcends experience"; (b) the fact that science proposes and uses laws "everywhere and all the time." (Like Hume, Born is struck by the "scanty material," i.e. the few observed instances upon which the law may be based.) To this we have to add (c) the principle of empiricism which asserts that in science, only observation and experiment may decide upon the acceptance or rejection of scientific statements, including laws and theories.

These three principles, (a), (b), and (c), appear at first sight to clash; and this apparent clash constitutes the logical problem of induction.

Faced with this clash, Born gives up (c), the principle of empiricism (as Kant and may others, including Bertrand Russell, have done before him), in favour of what he calls a "metaphysical principle"; a metaphysical principle which he does not even attempt to formulate; which he vaguely describes as a "code or rule of craft"; and of which I have never seen any formulation which even looked promising and was not clearly untenable.

But in fact the principles (a) to (c) do not clash. We can see this the moment we realize that the acceptance by science of a law or of a theory is tentative only; which is to say that all laws and theories are conjectures, or tentative hypotheses(a position which I have sometimes called "hypotheticism") and that we may reject a law or theory on the basis of new evidence, without necessarily discarding the old evidence which originally led us to accept it.7

The principles of empiricism (c) can be fully preserved, since the fate of a theory, its acceptance or rejection, is decided by observation and experiment_ by the result of tests. So long as a theory stands up to the severest tests we can design, it is accepted; if it does not, it is rejected. But it is never inferred, in any sense, from the empirical evidence. There is neither a psychological nor a logical induction. Only the falsity of the theory can be inferred from empirical evidence, and this inference is a purely deductive one.

Hume showed that it is not possible to infer a theory from observation statements; but this does not affect the possibility of refuting a theory by observation statements. The full appreciation of the possibility makes the relation between theories and observations perfectly clear. This solves the problem of the alleged clash between the principles (a), (b), and(c), and with it Hume's problem of induction....

1. This is a slight oversimplification, for about half of the Einstein effect may be derived from the classical theory, provided we assume a ballistic theory of light.
2. See for example, my Open Society and Its Enemies, ch. 15, section iii, and notes 13-14.
3. "Clinical observations," like all other observations, are interpretations in the light of theories; and for this reason alone they are apt to seem to support those theories in the light of which they were interpreted. But real support can be obtained only from observations undertaken as tests (by "attempted refutations"); and for this purpose criteria of refutation have to be laid down beforehand; it must be agreed which observable situations, if actually observed, mean that the theory is refuted. But what kind of clinical responses would refute to the satisfaction of the analyst not merely a particular analytic diagnosis but psycho-analysis itself? And have such criteria ever been discussed or agreed upon by analysts? Is there not, on the contrary, a whole family of analytic concepts, such as "ambivalence" (l do not suggest that there is no such thing as ambivalence), which would make it difficult, if not impossible, to agree upon such criteria? Moreover, how much headway has been made in investigating the question of the extent to which the (conscious or unconscious) expectations and theories held by the analyst influence the "clinical responses" of the patient? To say nothing about the conscious attempts to influence the patient by proposing interpretations to him, etc.) Years ago Iintroduced the term "Oedipus effect" to describe the influence of a theory or expectation or prediction upon the event which it predicts or describes: it will be remembered that the causal chain leading to Oedpus' parricide was started by the oracle's prediction of this event. This is a characteristic and recurrent theme of such myths, but one which seems to have failed to attract the interest of the analysts, perhaps not accidentally. (The problem of confirmatory dreams suggested by the analyst is discussed by Freud, for example in Gesammelte Schriften,i 111, 1925, where he says on p. 314: "If anybody asserts that most of the dreams which can be utilized in an analysis . . . owe their origin to [the analyst's] suggestion, then no objection can be made from the point of view of analytic theory. Yet there is nothing in this fact,"he surprisingly adds, "which would detract from the reliability of our results.']
4. The case of astrology, nowadays a typical pseudo-science, may illustrate this point. It was attacked, by Aristotelians and other rationalists, down to Newton's day, for the wrong reason-for its now an accepted assertion that the planets had an "influence" upon terrestrial ("sublunar") events. In fact Newton's theory of gravity, and especially the lunar theory of the tides, was historically speaking an offpsring of astrological lore. Newton, it seems, was most reluctant to adopt a theory which came from the same stable as for example the theory that "influenza"epidemics are due to an astral "influence." And Galileo, no doubt for the same reason, actually rejected the lunar theory of the tides; and his misgivings about Kepler may easily be explained by his misgivings about astrology.
5. Max Born, Natural Philosophy of Cause and Chance, Oxford, 1949, p. 7.
6. Natural Philosophy of Cause and Chance, p. 6.
7. I do not doubt that Born and many others would agree that theories are accepted only tentatively. But the widespread belief in induction shows that the far-reaching implications of this view are rarely seen.
Source: Karl Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (New York: Harper Torchbooks, 1963), pp. 33-39, 52-55.

Your Assignment:

1. What makes a theory scientific?
2. Explain why in Popper’s view Marx’s theory of history, Freud’s psycho-analysis and Alfred Adler’s “individual psychology” are not science. Please provide at least one example from the reading in your explanation.
3. Explain why Einstein’s theory of relativity is science.
4. What is the danger of ad hoc theories?
5. In your words, explain how the problem of demarcation solved?
6. What is the logical problem of induction?
7. How does Popper solve the problem of induction?