Sunday, October 21, 2012

The Logic of Scientific Discovery

Opposing to inductive logic as the methodology of science, Karl Popper proposes the theory of the deductive method of testing. In his book The Logic of Scientific Discovery, he argues that scientific hypothesis should be empirically tested and falsified in cases. It is easy to test the validity of a chain of logical reasoning. Just break it up into many small steps, each easy to check by anybody who has learnt the mathematical or logical technique of transforming sentences.

Falsifiability as essence of science
Popper argues that what distinguishes the empirical science from pseudo-science is that the former theory intrinsically falsifiability.

I shall certainly admit a system as empirical or scientific only if it is capable of being tested by experience. These considerations suggest that not the verifiability but the falsifiability of a system is to be taken as a criterion of demarcation. In other words: I shall not require of a scientific system that it shall be capable of being singled out, once and for all, in a positive sense; but I shall require that its logical form shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientific system to be refuted by experience.(18)

The reason why he emphasizes falsifiability, not verifiability, is that it is not possible to prove something in empirical science. Through the history, every scientific theory has been denied by the new facts and then updated. Popper took a radical example to explain his idea: Let us suppose that the sun will not rise tomorrow. Should such a thing occur, science would have to try to explain it, i.e. to derive it from laws. Existing theories would not merely have to account for the new state of affairs: our older experiences would also have to be derivable from them. (250)

Granted, the best thing is that we can just jump into immortal truth, but that will not come true forever. That is why human beings have taken paths that seem to be beating around the bush.

Probability of hypothesis and probability of events
Popper also strictly differentiates probability of hypothesis from probability of events. He argues that probability of hypothesis should not exist in science, although probability of events do and contribute for testing the validity of hypothesis.

Hypotheses regarding probabilities are not verifiable because they are universal statements, and they are not strictly falsifiable because they can never be logically contradicted by any basic statements. (259) I believe that physics uses probability statements only in the way which I have discussed at length in connection with the theory of probability; and more particularly that I uses probability assumptions, just like other hypotheses, as falsifiable statements. (260)

Science in evolutionary process
Popper believes that the essence of science is its falsifiability and thus its evolutionary process which lasts forever. One driving force of the evolution is craving for the truth, although the goal will never be attained. Another driving force is ones intuition: although new facts have always transformed science, those facts do not come to those who passively experience it; it comes to someone who believes in his/her anticipation, idea, speculative thought and so on. In other words, the facts that change the world are visible to only those who want to do it.

Science is not a system of certain, or well-established, statements; nor is it a system which steadily advances towards a state of finality. Our science is not knowledge (episteme): it can never claim to have attained truth, or even a substitute for it, such as probability.
  Yet science has more than mere biological survival value. Although it can attain neither truth nor probability, the striving for knowledge and the search for truth are still the strongest motives of scientific discovery.
  Marvelously imaginative and bold conjectures or anticipations of ours are carefully and soberly controlled by systematic tests. Once put forward, none of our anticipations are dogmatically upheld. Our method of research is not to defend them, in order to prove how right we were. On the contrary, we try to overthrow them. Using all the weapons of our logical, mathematical, and technical armoury, we try to prove that our anticipations were false in order to put forward, in their stead, new unjustified and unjustifiable anticipations, new rash and premature prejudices, as Bacon derisively called them.

The advance of science is not due to the fact that more and more perceptual experiences accumulate in the course of time. Nor is it due to the fact that we are making ever better use of our senses. Out of uninterpreted sense-experiences science cannot be distilled, no matter how industriously we gather and sort them. Bold ideas, unjustified anticipations, and speculative thought, are our only mans for interpreting nature: our only organon, our only instrument, for grasping her.

The old scientific ideal of episteme of absolutely certain, demonstrable knowledge- has proved to be an idol. The demand for scientific objectivity makes it inevitable that every scientific statement must remain tentative for ever. It may indeed be corroborated, but every corroboration is relative to other statements which, again, are tentative. Only in our subjective experiences of conviction, in our subjective faith, can we be absolutely certain.  (Page 278 280)

The idea proposed in this book is still the fundamental idea in problem solving in business fields. We always begin with a hypothesis when we tackle problems. After coming up with the hypothesis, we test it by collecting facts and checking the chain of reasoning. If we find the facts or logical fallacies which reject the hypothesis, we turn down the original one and try to find out the new.

What this book is missing unfortunately is how the motivation and intuition that change the structure of science come to us. People now are striving to find out the more systematic way to get to the world-changing idea. Granted, that part is not the scope of this book, but I just wanted to know how Popper thought of the process of the idea generation.

Karl Popper, The Logic of Scientific Discovery, Routledge (2nd edition), 2002/3/29

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