Revisiting Popper – the scientific method

May 31, 2012 — Leave a comment

From the Stanford Encyclopedia of Philosophy:

“[…] if a theory is incompatible with possible empirical observations it is scientific; conversely, a theory which is compatible with all such observations, either because, as in the case of Marxism, it has been modified solely to accommodate such observations, or because, as in the case of psychoanalytic theories, it is consistent with all possible observations, is unscientific.”

This is a cold, dis-passionate view to establish a method for critiquing the rise of new sciences and ideologies in the 20th century (and obviously prior centuries as well). It does not assert that what is unscientific may not one day become scientific, nor that an unscientific theory or observation may not be enlightening. Popper is addressing demarcation. To separate out that which is and is not scientific.

Induction and Deduction

Induction according to the Oxford English dictionary is defined as follows: “The process of inferring a general law or principle from the observation of particular instances”. The Stanford On-line Encyclopedia explains that induction is not opposed to deduction. Induction has undergone a semantic/lexical change in meaning through the 20th century. Induction used to refer to simply the inference of a conclusion from a set of instances i.e. A is a white swan, B is a white swan, therefore all swans are white. Induction has been refined to not infer from observation nor particulars and does not lead to general laws or principles.

enumerative induction or universal inference; inference from particular instances:

a1, a2, …, an are all Fs that are also G,

to a general law or principle

All Fs are G.

A weaker form of enumerative induction, singular predictive inference, leads not to a generalization but to a singular prediction:

1. a1, a2, …, an are all Fs that are also G.

2. an+1 is also F.

Therefore,

3. an+1 is also G.

Singular predictive inference also has a more general probabilistic form:

1. The proportion p of observed Fs have also been Gs.

2. a, not yet observed, is an F.

Therefore,

3. The probability that a is G is p.”

taken from the Stanford Encyclopedia

Induction is used to estimate the validity of a set of observations as evidence for a statement/proposition about the whole to which they refer.

Deductive, on the hand, works to establish validity and soundness in an argument/proposition by making statements about whether the premises are true or false. Logic uses deductive reasoning.

The deductive procedure:

a) formal: testing the internal consistency of the theoretical system to see if it involves any contradictions.
b) semi-formal: the axiomatising of the theory to distinguish between its empirical and its logical elements.
c) comparing the new theory with existing theories to determine whether it constitutes an advance upon them. One theory is deemed better than another if it has greater empirical data and greater predictive power than its rival.
d) empirical application of the conclusions derived from the theory to test whether it is true. Corroboration does not equal verification, but does prove validity.

Popper argues that induction is never actually used by the scientist destabilizes the Newtonian/Baconian insistence on the primacy of pure observation. Popper argues that all observation is selective and theory laden and that there are no pure or theory-free observations (a characteristic of Heideggerian thought). Popper inserts falsifiability in induction’s place. Falsifiability is not concerned with the origin or nature of the evidence gathered, as Popper argues it is easy to obtain evidence for any viewpoint. Falsifiability simply requires that the theory or conclusion be testable and be conceivably false. Any corroborative evidence should count scientifically only if it is the result of a genuinely risky prediction. Therefore, Popper’s scientific method takes on the characteristic of refutation. The best way to test is to search for refutation as it is logically impossible to conclusively verify a universal proposition by reference to experience. One falsification refutes the theory. The falsification does not need adjusting (as in the case of Marxism), but rather the theory/universal proposition (characteristic of science).

“[…] while advocating falsifiability as the criterion of demarcation for science, Popper explicitly allows for the fact that in practice a single conflicting or counter-instance is never sufficient methodologically to falsify a theory, and that scientific theories are often retained even though much of the available evidence conflicts with them, or is anomalous with respect to them.” Stanford Encyclopedia

Popper recognizes the very human, problem-solving orientation of science and therefore the importance of intuition, subjectivity and the imagination. It does not matter how a theory is arrived at, but rather how it can be tested and falsified/refuted. This view was endorsed by Einstein:

“There is no logical path leading to [the highly universal laws of science]. They can only be reached by intuition, based upon something like an intellectual love of the objects of experience.” Stanford Encyclopedia

This focus on the human characteristic of the scientific endeavor places special emphasis on the role played by the independent creative imagination in the formulation of theory.

Popper on pseudo-science and the personalities it attracts:

“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.” (Popper in Conjectures and Refutations, p35)

Probability

“[…] with increasing content, probability decreases, and vice versa; or in other words, that content increases with increasing improbability.” (p 218)

“This trivial fact has the following inescapable consequences; if growth of knowledge means that we operate with theories of increasing content, it must also mean that we operate with theories of decreasing probability … Thus if the aim is the advancement or the growth of knowledge, then a high probability cannot possibly be our aim as well: these two aims are incompatible.” (p218)

“And since a low probability means a high probability of being falsified, it follows that a high degree of falsifiability, or refutability, or testability, is one of the aims of science – in fact, precisely the same aim as a high informative content.” (p219)

Truth and Content: Verisimilitude vs Probability

on the credibility of science:

“We hold that this ideal can be realized, very simply, by recognizing that the rationality of science lies not in its habit of appealing to empirical evidence in support of its dogmas – but solely in the critical approach: in an attitude which of course, involves the critical use, among other arguments, of empirical evidence (especially in refutations).” (p229)

Popper is not interested in theories being secure, certain, or probable. Theories that can be tested for mistakes, in order to learn from said mistakes, and therefore improve are the desirable approaches to science: they allow for falsifiability.

“Thus the very idea of error – and of falsifiability – involves the idea of an objective truth as the standard of which we may fall short.” (p229)

Fallibilism: we can never be completely certain about factual issues.

Scientific Change: Conjecture and Refutation

Conjecture: stage 1 of a two step cycle of scientific change. A conjecture is a hypothesis that describes and explains something in the world/universe. A good conjecture is a bold one that takes many risks.

Refutation: the hypothesis is subjected to critical testing in an attempt to show that it is false.

A new conjecture should not be a reaction to falsification in an attempt to avoid the problems revealed by earlier testing. This would lead to an ad-hoc theory, lacking justification and eventually coherence.

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