Popper’s Objective Knowledge

KR Popper Objective Knowledge: an evolutionary approach Revised Edition OUP 1979 (original 1972)

An addendum to his well-known  Logic of Scientific Discovery.

Preface

“… I regard the commonsense theory of knowledge as a subjectivist blunder. This blunder has dominated Western philosophy. I have made an attempt to eradicate it, and to replace it by an objective theory of essentially conjectural knowledge.”

1. Conjectural Knowledge: My solution of the problem of induction

Critical method

Common formulations of the problem of induction assume:

“that the future will be like the past – an assumption which I, for one, regard as mistaken … “

Popper notes that Hume’s objection to induction applies equally well to probabilistic inference.

“Why … do reasonable people often expect, and believe, that instances of which they have no experience will conform to those of which they have experience? …

    Hume’s answer … is: Because of ‘custom or habit’; that is, because we are conditioned, by repetitions and by the mechanism of the association of ideas; a mechanism without which … we could hardly survive.”

Popper asks:

“Can a preference, with respect to truth or falsity, for some competing universal theories over others ever be justified by such ’empirical reasons’?

… Yes; … if we are lucky … our test statements may refute some – but not all – of the competing theories … .”

But notes:

“… we must regard all laws or theories as hypothetical or conjectural … .”

“… my answer … is in agreement with the following somewhat weak form of the principle of empiricism: Only ‘experience’ can help us to make up our minds about the truth or falsity of factual statements.”

Popper discusses various grounds for preferring some conjectures or hypotheses to others.

“… the theoretician will be especially interested in finding the best testable of the competing theories in order to submit it to new tests. … this will at the same time be the one with the greatest information content and the greatest explanatory power. …  If it survives its tests, it will also be the best tested … . ”

“… the new theory, although it has to explain what the old theory explains, corrects the old theory, so that it actually contradicts the old theory: it contains the old theory, but only as an approximation. …

    The method described may be called the critical method.

There is no assurance that we shall be able to make progress towards better theories.”

“… preferability cannot be a probability in the sense of the calculus of probability”

Which theory should we prefer for practical action, from a rational point of view?
… the best tested theory.

… This will be ‘rational’ in the most obvious sense of he word … .”

Comments

Popper’s thinking behind the following are not clear to me. They seem wrong: 

  • Popper thinks it ‘rational’ to pick out a single ‘best’ theory, rather than (say) identifying all credible theories. If rationality is so poor, maybe we should aim for something more reasonable.
  • The new method has to ‘explain what the old theory explains’, yet if all that one has is the old theory, one does not know what it explains. One would need to know not only what the old theory was but also the range of experiments that it explained and, for example, the range of phenomena which it explained as ‘random’ that might conceivably have a more deterministic explanation.
  • The new theory is regarded as an approximation to the old. This is often the case, but some new theories (such as Copernicus’s) seem more revolutionary, and the difference is significant, for example to Kuhn’s account of science. Popper seems concerned with gradualist evolution.

A more technical quibble is that Popper supposes that whatever corroborates a theory corroborates an implication of that theory. But suppose that we have corroborated “all swans are white” and then discover Australia. “All Australian swans are white” is corroborated in one sense, but not in another. Perhaps we need to distinguish between objective and subjective corroboration.

Psychology

“It was first in animals and children, but later also in adults, that I observed the immensely powerful need for regularity – the need which makes them seek for regularities; which makes them sometimes experience regularities even where there are none; which makes them cling to their expectations dogmatically … . ”

“… expectations may arise without, or before, repetition … they could not arise otherwise because repetition presupposes similarity, and similarity presupposes a point of view – a theory or an expectation.”

“… the main difference between Einstein and an amoeba … is that Einstein consciously seeks for error elimination. He tries to kill his theories: he is consciously critical of his theories which … he tries to formulate sharply rather than vaguely.”

“… a pragmatic belief in the results of science is not irrational, because nothing is more ‘rational’ than the method of critical discussion, which is the method of science. And although it would be irrational to accept any of its results as certain, there is nothing ‘better’ when it comes to practical action: there is no alternative method which might be said to be more rational.”

“… all languages are theory-impregnated … “

Comments

My reading of this is that Popper intends much of his theory to apply to a wide range of pragmatic, rational, action. Yet much else seems to assume more of a laboratory setting. Hence the scope is not entirely clear. Can one be scientific about choosing a car?

The notions of pragmatism and rationality, and hence Popper’s account of science, seem deeply impregnated with assumptions. They seem correct in so far as they are negative about what went before, or some simplistic notions that are still with us. They seem reasonable about some paradigmatic activities of science. But many areas that we commonly regards as science, such as climate science, do not seem to fit. At least, Popper seems to be making implicit assumptions that we should check.

Popper assumes that ‘practical action’ must be based on a single theory. But sometimes we might be able hedge across theories, doing something that will be satisfactory whichever theory is true. Or we might have a main activity based on one theory with supplementary theories that aim to test the theory (before it is too late) or which otherwise ‘hedge’. It is not that Popper discounts such situations, but that he appears not to consider them.

In particular, we might look for a method that is still critical but does not focus on ‘the best’, but on the range of credible theories. Technically, this is a minor change to the critical method.

2. … an Argument for Commonsense Realism and against the Commonsense Theory of Knowledge

This predated chapter 1, and largely overlaps it.

“My thesis is that realism is neither demonstrable nor refutable. … but it is arguable and the weight of arguments is overwhelmingly in its favour.”

Thus one should reject anything that is inconsistent with realism, and may as well accept realism as a working hypothesis, if it helps to reduce ambiguity. Popper cites an argument of Winston Churchill’s, that the ability to predict eclipses gives a ‘cross-bearing’ on the issue of the reality of the sun. More generally, Popper builds on Tarski. Perhaps alluding to the Banach-Tarski paradox he says:

“I do not think that … logical probability … can ever be numerically determined, expect in certain limiting cases (such as 0 and 1). … in actual application we depend on … non-metrical and … qualitative or general logical grounds … .”

 Popper comments on the pre-scientific ‘bucket’ theory of mind, in which ‘information’ fills the mind and is processed to become ‘knowledge’.

“Among the many things which are wrong with the bucket theory of mind are the following:
   (1) Knowledge is conceived of as … thing-like entities …
   (2) Knowledge is …in us: … information that has reached us, and which we have managed to absorb.
    (3) There is immediate or direct knowledge … .”

    “Almost everything is wrong in the commonsense theory of knowledge. But perhaps the central mistake is the assumption that we are engaged in what Dewey called the quest for certainty.”

“… some of the most succesful animals have disappeared, and … past success is far from ensuring future success.”

“… The existence of an environment with a certain structure is empirical. That this environment changes, but not too fast for long periods of time, and not too radically, is empirical … there is nothing in logic which explains [this].”

“… there is no sense organ in which anticipatory theories are not genetically incorporated. … what can be absorbed (and reacted to) as relevant input and what is ignored as irrelevant depends completely upon the innate structure (the ‘programme’ (sic) ) of the organism.”

Popper introduces his ‘three worlds’ model.

“Main thesis: our conscious subjective knowledge (world 2) depends upon world 3 [the logical content of books etc.], that is to say on linguistically formulated theories.”

 “… We do not act on  repetition or ‘habit’, but upon the best tested of our theories … – the best among competing theories … .”

Of Kant:

“… we have no reason to believe ‘that those instances of which we have had experience [are likely to] resemble those, of which we have had experience’.

Comments

This adds more detail to Ch. 1. Popper builds on Tarski, but Tarski only seeks to eliminate wrong theories, not to identify the ‘best’.

3. Epistemology Without a Knowing Subject

Popper takes an objective view of knowledge, distinguishing between production and structure, with the latter being more important to their reflexive relationship. Thus he regards theories and assertions as more important than designation of terms, concepts, meanings and definitions. His notion of the development of (scientific) knowledge is built around demonstration and criticism. A stronger logic is appropriate for the latter than the former.

“… the scientist … neither knows or believes. …”

    “Nowhere has the subjectivist epistemology a stronger hold than in the field of  the calculus of probability. … this amounts to … certain knowledge in the subjective sense. This is a consequence which few Bayesians … will cherish.
    This subjective interpretation of the probability calculus … springs from the same epistemic philosophy which attributes to the statement ‘I know that snow is white’ a greater epistemic dignity than to the statement ‘snow is white’.
    I do not see any reason why we should not attribute still greater epistemic dignity to the statement ‘In the light of all the evidence available to me I believe that it is rational to believe that snow is white.’ … ”

“… the subjective theory of knowledge has entered science on a broad front. The original point of entry was the subjective theory of probability. But the evil has spread into statistical mechanics, the theory of entropy, into quantum mechanics, and into information theory.”

It is said that in 1967 Mario Bunge was expecting a ‘turn of the tide’.

“… science begins with problems, and proceeds to competing theories which it evaluates critically. …
    In most cases, and in the most interesting cases, the theory will ultimately break down and thus raise new problems. … ”

“… selection is a two-edged sword: it is not only the environment that selects and changes us – it is also we who select and change the environment, mainly by discovering a new ecological niche.”

“… organic systems may be looked at as the objective products or results of tentative behaviour which was ‘free’ – that is, not determined – within a certain realm or range circumscribed or bound by its internal situation … and its external situation … . Ill-success rather than success leads then by natural selection to the comparative fixation of the successful way of reacting. …”

Comments

 Popper is dismissive of subjective notions of knowledge, which seem unpersuasive. Why should I trust me own or anyone else’s subjective views? Instead he has a notion of generating and critiquing competing hypotheses. In the short run the best hypotheses so far are selected, and may be refined. In the long-run one may need a more radical change. This formulation seems realistic in the short run without relying on subjective assessments or ad-hocism (such as Ockham’s razor) and in the long-run anticipates and amplifies on Kuhn’s paradigm shifts. 

4. On the Theory of Objective Mind

Popper develops his ‘three worlds’ concept, and the problem of ‘understanding’. He clearly focuses on scientific knowledge, which he regards as problem solving while taking account of the limitations of language.

Comments

While much of Pepper’s accounts can be read as concerning knowledge in general, it is clearer here that his focus is specifically on the development of science.

5. The Aim of Science

Popper regards the aim of science as being to provide ‘the’ explanation, rather than to identify possible explanations. He also amplifies his notion of ‘approximation’. It is that one theory is a special case of another. But the earth-centric theory of epicycles is not a special case of Copernicus’s sun-centric theory, and Copernicus does not ‘explain’ the earth-centric theory: it’s correction is radical, not gradualist. It thus seems that Popper is considering ‘ordinary’ progress, not revolutionary change.

“… the discovery of structural laws of the kind we are seeking … [is] almost impossible. … In spite of this, science has been almost miraculously succesful … .  This strange fact cannot, I think, be explained without proving too much.”

6. Of Clouds and Clocks

Popper has an example of a cloud of gnats. He imagines them flying in arbitrary directions, but turning towards the apparent centre if they get too isolated.

“… this whole can be used to dispel the … ‘holistic’ belief that the ‘whole’ is always more than the mere sum of its parts.”

The bulk of the discussion is about indeterminism.

“… I shall try to show that indeterminism is not enough.”

”    My theory … consists of a certain view of evolution as a growing hierarchical system of plastic controls, and a certain view of organisms as incorporating … [possibly] exosomatically – this growing hierarchy of plastic controls.

    Error-elimination may proceed either by the complete elimination of unsuccessful forms … or by the (tentative) evolution of controls which modify or suppress unsuccessful organs, or forms of behaviour, or hypotheses.

….

…. the problems (or problem situations) which the organism is trying to deal with are often new, and arise themselves as products of evolution. The theory thereby gives implicitly a rational account of … ‘creative evolution’ or ’emergent evolution’

… each organism is all the time engaged in problem-solving by trail and error; that it reacts to new and old problems by more or less chance-like … trials which are eliminated if unsuccessful.”

In a footnote, Popper remarks:

“That we can only choose the ‘best’ of a set of competing hypotheses … means that we choose the one which appears, in the light of the discussion, to come ‘nearest to the truth’.

He goes on to show a model of plastic control. In a soap bubble both the surface and the trapped are indeterministic while controlling each other. Hence plastic controls do actually exist.

Comments

Popper refers to Bergson, Whitehead and Smuts‘ notions of holism and of creative evolution. The difference doesn’t seem so very substantial, although Popper’s account does seem more accessible. In the gnats there are short-term (free) and long-term (keep together) dynamics. The whole is not the sum of the short-term behaviours, but only arises from the fact that the gnats in the middle will tend to keep together if and when they find themselves near he edge. Moreover, the long-term behaviour needs to be strong-enough compared to the short-term behaviour. Even then it is not obvious that the swarm will be sustained, and will not split. So it it not clear that it is not a holistic whole. Even if it is, it is not fatal to the views of Bergson et al if there are non-holistic wholes, as long as there are important holistic wholes.

Popper regards science as being concerned with universal laws, which cannot apply to emergent evolution, or to anything temporary. It would be scientific to develop a theory of clocks that includes their stopped and working modes, and one could apply that scientific model to describe a particular clock as working, but this would be outside of Popper’s scope. However, his ideas seem to invite an application to the growth of knowledge beyond science

Again, Popper insists on finding the single best hypothesis, whereas his theory of evolution would merely suggest eliminating the bad hypotheses. Or are we regard some hypothesis as bad simply because there is some other hypothesis which is very slightly better, under circumstances in which such a small difference is not significant. For example, if we toss a coin once to yield heads do we choose the hypothesis that the coin is double-headed? Or do we reject the hypothesis that the coin is double-tailed and leave open th hypothesis that it is fair or fair-ish?

7. Evolution and the Tree of Knowledge

“I believe that theory – at least some rudimentary theory or expectation – always comes first.
… we do not start from observations but from problems … . … the growth of knowledge proceeds from old problems to new problems, by mean of conjectures and refutations.”

“…
Once a new … tendency or disposition, or a new skill … has evolved … , this fact will influence the effects of natural selection in such a way that previously unfavourable (though potentially favourable) mutations become actually favourable if they support the newly established tendency. But this means that the evolution of the executive organs will become directed by the tendency or aim, and thus become ‘goal directed’.

Popper discusses mutations that either improve general capability, or which specialize.

”    The point here is that mutations of the central structure will be leading.”

“… I offer [this conjecture] as no more than a possible line of thought.”

Popper goes on to suggest that while large mutations might generally be harmful, large deviations in behaviour might not be harmful, and might lead to a preference for new niches, which then leads further evolution.

Comments

These speculations provide some interesting insights which might be applied – conjecturally – to all kinds of evolution. We should anticipate all kinds of deviancy so long as there is a short-term niche, and hence ‘expect the unexpected’. On the other hand, if we are overly conforming we will lack the creativity to compete and also the insight to see the potential for others’ deviancy.

8. A Realist View of Logic, Physics and History

“… we should propose many theories as attempts to solve some given problem, and that we should critically examine each of our tentative solutions. We then find that each gives rise to new problems; … The decisive point is, of course, always: how well does our theory solve its problems… ?
    At any rate, one of the things that we wish to achieve is to learn something new. … the theory is progressive if … it has really made a difference to the problem we wanted to solve ; that is, if the newly emerging problems are different from the old ones.”

Popper applies a similar notion of emergence to natural evolution.

“What characterizes the [scientific] theory is that it is offered as a solution to a scientific problem … within the realm of problems and solutions belonging to the scientific tradition.”

“… if … there is no complete theoretical understanding of life possible in physical terms, then we might speak of life as an emergent property of physical bodies, or of matter.

… I think it quite likely that there may be no reduction possible; it is conceivable that life is an emergent property of physical bodies.

    I call bad reduction or ad hoc reduction the method of reduction by merely linguistic devices … . …

    This second kind of reduction or the use of Ockham’s razor is bad, because it prevents us from seeing the problem. …”

On behaviourism Popper says:

“They do not realize that all observation involves interpretation in the light of theories, and that what they call ‘observable’ is what is observable in the light of pretty old-fashioned and primitive theories.”

On emergence:

“… growth of knowledge … cannot be predictable by scientific means. For he who could so predict … our discoveries of tomorrow could make them today; which would mean … an end to the growth of knowledge.
… unpredictability has always been considered the salient point of emergence; and it seems to me that … the growth of knowledge must be unpredictable in principle. “

Popper distinguishes between the demonstrative (positive) and empirical (critical) sciences, and between mathematics as a demonstrative science as applied mathematics, used within other sciences.

”    Although I am an opponent of pragmatism as a philosophy of science, I gladly admit that pragmatism has emphasized something very important: the question of whether a theory has some application, whether it has, for example, predictive power. … “

Comments

Popper introduces the notion of emergence, which seems not very different from that of Bergson, Whitehead and Smuts. The critical feature, for Popper, is that emergence cannot be explained within his conception of science (or perhaps at all).

Popper is critical of Ockham’s razor and other ad-hoc means of selecting one theory among many candidates. But he does see a theory as a solution to a problem, and hence only needs one. Here Popper seems to be supposing that there is a static real problem to which one already has a partial solution, which one is simply trying to improve. Many of our current problems are not like this: often we lack even a clear initial understanding and the problems are emergent, perhaps driven by our own behaviour.

Popper places mathematics as a demonstrative science, which usage is currently very common, but which has come in for criticism, e.g. in financial mathematics. But any demonstrative science can be used in a critical (’empirical’) role by demonstrating the possibility of a contrary theory. Thus the value of much complexity theory is not so much in the models as models to be applied computationally, but as counter-examples to simplistic theories. For example, in showing that economic systems need not be stable (Keynes).

Popper refers approvingly to ‘The pernicious Influence of Mathematics on Science’ as a criticism of mathematics. This was written by a mathematician, citing Keynes in decrying the use of ‘pseudomathematics’ and providing an example of how mathematics can be used demonstratively to critique pseudomathematics. My interpretation is that mathematics can be misused, and that mathematicians and scientists, at least, need to understand the proper role of mathematics in support of science and how to avoid such misuse.

9. Comments on Tarski’s Theory of Truth

Popper notes that a notion of truth may be valid even if there is no possible decision rule for it. He sketches out a definition of verisimilitude, the relative gain in the ‘truth content’, which he takes as the aim of science. This allows one to claim that a given theory is more truth-like or more nearly true than another while recognizing that it is probably not absolutely true.

Comments

We do not have to suppose that the findings of science are real, only that – in some sense – they are most like reality. Thus while we might act as if they were true, we should not be unduly surprised if they are not.

Appendix 1: The Bucket and the Searchlight

Popper expands on his concepts of hypothesis, observation and test.

“… The process of learning consists largely in … corrections; … in the elimination of certain [disappointed] expectations.”

”    The various horizons of expectations differ, of course, not only in their being more or less conscious, but also in their content. Yet in all these cases the horizon of expectations plays the part of a frame of reference: only their setting in this frame confers meaning or significance on our experiences, actions and observations.
    Observations, more especially, have a very peculiar function within this frame. They can, under certain circumstances, destroy even the frame itself, if they clash with certain expectations. In such a case they can have an effect … like a bombshell. This … may force us to reconstruct, or rebuild, our whole horizon of expectations; … we may have to correct our expectations and fit them together again into something like a consistent whole. … in this way our horizon of expectations is raised to and reconstructed on a higher level, and that we reach in this way a new stage in the evolution of our experience. …  ” 

Science is seen as primarily aiming at predictions, and depends upon bold hypotheses critical tested. Its technical applications have their own approaches to problem-solving, resembling those of science but not identical, and draw upon the theories of science as reasonable  approximations to truth.

Comments

Popper sees science as having coherent expectations, corresponding to a single frame. The theory may change slightly, or occasionally may undergo a paradigm shift, as in Kuhn’s theory. Popper views changes to the frame as being on a ‘higher level’ to changes to a theory within a frame. This is reminiscent of Whitehead’s model in Process and Reality.

Popper’s views on induction suggest that we should read the ‘expectations and ‘frames’ as relating to the theory rather than necessarily being ours. But then if – as Popper suggests – we are pragmatic we act as if the expectations and frames are our own, which seems contradictory. I think that Popper here has in mind only short-term actions. We may continue to try out alternative frames and to test the theory, thus treating the ‘expectations’ more as ‘pragmatic extrapolations’ than as beliefs. My view is that one might also hedge theories and frames.

Appendix 2: Supplementary Remarks (1978)

Popper notes some residual technical difficulties in defining the ‘contents’ of theories and verisimilitude.

Comment

I find Popper’s details hard to follow. This appendix seems to excuse the effort. Popper’s continual reference to measurement and precision suggests that in practice the hypotheses will be statistical, in which case Good’s Good Thinking may supply some technical underpinning to Popper’s metaphysics.

Comments

Popper is concerned with scientific reasoning, looking for universal laws. He is seeking the best possible current theory based on (theory-laden) observations to date. His work is useful as a criticism of alternatives, such as that one observes reality, or that reality is socially constructed. On the positive side, his work seems reasonable as long as one accepts the limitation of always seeking to identify a single best theory.

Popper notes that you don’t understand the scientific method until you have tried to tackle typical problems for yourself. But in my view you don’t understand a topic, such as quantum mechanics, if you only understand one theory. As Popper notes, there have been multiple theories that were equally consistent with the available experimental observations but which made testably different predictions for experiments that were not then practical. It seems to me that it is only by understanding the range of such theories, and the extent to which other theories have been considered, that I can come to understand their subject. This seems even more important in areas outside science, such as criminal justice and economics. Fortunately, it seems easy to adapt Popper’s approach: rather than selecting the theory nearest the truth one accepts all theories that are near the truth (in Popper’s sense), perhaps weeding out ones that are trivial variations and highlighting differences that could credibly become significance.

Some such work as Jack Good’s (above) could usefully supply the details for statistical theories, to create a firm base from which one might develop a more general sound approach to ‘objective knowledge’.

Dave Marsay 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: