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Papineau and Induction

October 30, 2012 — 1 Comment

a note from David Papineau “Reliabilism, Induction and Scepticism

The Problem of Induction – Problem? What problem?

Papineau suggests that there are different kinds of circularity (the problem of induction being a circular argument – induction to justify induction). There is a difference that needs to be distinguished between premise circularity and rule circularity. An argument is premise circular if its conclusion is contained amongst its premises. An argument is rule circular if it uses a rule of inference to arrive at a conclusion about that very rule of inference (induction for example).


How do we naturalize the normative?

A normative claim is a claim that one is justified in doing something. Normative claims are evaluative rather than factual. Naturalism emphasizes the empirical. When we talk about a normative aim, we need to justify that this aim is worthy of being pursued. Simply ‘making sense’ (coherent) is not enough – truth conducive.

How can an evaluative claim be derived from an empirical one?

Quine’s naturalized epistemology is characterized as placing itself in the school of psychology; that is, to describe a physical human subject – how humans produce beliefs. Epistemology then becomes a science. It addresses the questions of how justified belief works, ignoring completely justification itself as a central epistemological question. It’s the ‘technology of truth-seeking’.

Kornblith sees epistemology as normative. Despite his naturalism he thinks there is such a thing as epistemic justification. However, normativity is not the topic of the book, this is just a background context for the aims of the book (see chpt 1 notes – Inductive Inference and its Natural Ground) The stated focus of the book is investigating the reliability of our inductive inferences, and their relationship to the causal structure of the world. However, if our inductive inferences are reliable, then this reliability leads to a normative philosophy i.e. we should use this reliable method of inductive inference. So should not the source of normativity (a response to Quine) be part of the focus of the book?

If Kornblith assumes that truth is valued, that the goal of inductive inferences is to seek truths about the world, then he is positing a normative philosophy, just without a comprehensive establishment of what it is that inductive inference is reliable with regards to. Epistemic norms are a means to an end.

Notes from: Joel Pust – Induction, Focused Sampling and the Law of Small Numbers

This paper is a response to Kornblith‘s defense of the use of the Law of Small Numbers (Judgmental bias which occurs when it is assumed that the characteristics of a sample population can be estimated from a small number of observations or data points). Pust is claiming that this argument fails for the following reasons: the sort of inferences Kornblith seeks to justify are not really inductive inferences based on small samples, but rather knowledge based deductive inferences, and secondly that Dorrit Billman’s computational model upon which Kornblith builds some of his argument is not sufficient for this purpose.

Firstly, Kornblith’s defense of the use of the Law of Small Numbers is characterized as reliabilist.

“We have built-in biases in our processing of visual information and such presuppositions bring perceptual errors with them. However, the simple fact that our perceptual mechanisms are biased has no implications for their reliability without the further claim that such biases are inappropriate for our environment.” (Pust, p90)

Our inferential reasoning, like our perceptual mechanisms, whilst prone to making mistakes is nevertheless generally quite relaible. Our inferential mechanisms depend upon the assumption that the world contains natural kinds. With regard to the Law of Small Numbers, Kornblith cites Tversky and Kahneman (K, p90) claiming that we tend to draw inductive inferences on the basis of extraordinarily small samples. The key question becomes how to evaluate this tendency (K, p90). Tversky and Kahneman assert that this tendency is inappropriate, whereas Kornblith points out the question of reliability is far more subtle and complex.

1) Is presdiction from a small sample always unreliable?
2) Is the logic of statistical inference a reasonable standard against which to measure the appropriateness of our inferences?

” […] when a population is uniform with respect to a certain property, a generalisation based on a single case will be reliable indeed.” (Pust, p92)

Imagine that you are observing an unknown species of bird lay an egg. Based on this one observation, and the background knowledge that all birds in existence that have been observed thus far lay eggs, you can infer based on one very small sample that this unknown bird will always lay eggs. This ties in with Quine’s notion of projection. Projection seems to tie in with background knowledge to provide a solid base upon which to infer based on small samples.

Kornblith: we do have “a sensitivity to those features in objects which tend to reside in homeostatic clusters; and a tendency to project those characteristics which are indeed essential to the real kinds in nature.” (K, p95)

This also ties in with the ‘naturalisation’ of Kornblith’s epistemology. Kornblith’s reliabilist argument rejects the notion that the only justified inferential procedures are those that are relaible in any possible world. The justifiedness of a belief is a function of the actual world: actual world reliability of the process (evolution) that produced the justified inferential procedures.


Pust’s summary of Kornblith’s argument:

“The Aim: To provide a reliabilist defense of TLSN.
(1) Inductive generalizations based on small samples (or the single case) will be reliable if the features selected do, in fact, generally co-occur.
(2) In order for such an inferential tendency to be reliable, then, we must possess a sensitivity to those properties of natural kinds that are highly correlated. In other words, we must be able to detect what property correlations obtain.
(3) Though some experimental data shows that we are rather poor at detecting covariation when a single pair of properties covaries, Billman’s research on focused sampling shows that we are good at detecting property covariation when the properties in question also covary with a number of others that jointly covary. In short, when properties are ‘clustered’, we are quite adept at detecting their correlations by engaging in focused sampling.” (Pust, p95)

The main criticism, referring to the bird example above, is that Kornblith;s assertion of small sample sizes misses altogether crucial premises. i.e ‘new species of bird lays an egg’ (based on 1 observation) needs to be a conjunct with ‘all members of a biological species reproduce in the same manner’, such that:

premise: An observed new species of bird lays an egg.
premise: All members of a biological species reproduce in the same manner.
concl: New species of bird will always reproduce via laying eggs.

This is a deductive inference, even if the premise themselves were arrived at inductively; knowledge based deduction. This could be construed as ‘prior knowledge’ plus ‘observations’ equals ‘new knowledge’.

Kornblith’s descriptors ‘sensitivity’ and ‘intuitive grasp’ for his assertion of our evolved inductive reasoning mechanisms in this new light possibly, and most likely, correlate with background knowledge. Pust redesign’s Kornblith’s argument such that we have inductive inferences drawn from the law of large numbers (we develop knowledge of the world based on large scale observations) and then based on this background knowledge are able to make deductive inferences on the basis small samples.

1) Kornblith’s natural kinds are constituted by unobservable properties. This seems to have been critiqued as a return to Platonic ideals, or some kind of out-dated metaphysics, though I do not see this notion of unobservables in this light. If an unobservable is a homeostatic cluster, a gene, a chemical compound, a DNA strand, then it is induced by science to be of the physical world (metaphysics – what is the world that we may know it – in philosophy). If evolution is intoriduced to the argument, these are definitely not ideals as they are in a state of change and relationship to the environment. This is foremost a metaphysical theory (though, if it is a theory that purports to describe things in the world that can be empirically observed and tested, is it not a physical theory??)

2) There are real kinds in nature, Locke’s real essences.

3) Epistemology: this all relates to using induction to justify belief. However, always watch for using induction to justify induction. If Kornblith uses IBE about the success of science to justify induction, and IBE is a form of induction, is there a circular problem developing? I would argue that this does not need to be defined as circular, but rather that inferential inductive arguments are satisfactory so long as they are successful, as they have been thus far, until such a time as they are unsuccessful. You could take Thomas Kuhn’s paradigm shifts as a model for mapping this out. Also, watch for a priori arguments. IBE is comparative. It looks at alternative explanations, determining the best explanation for the given data. This can be used to frame the ‘satisfactory’ comment: once the data changes i.e. science is unsuccessful, induction can be argued as unjustified. However, the character of science, defined as Popper and Kuhn might put it, that it seeks to best explain the given data (explanatory, risky conjectures and refutations, and paradigmatic), science becoming ‘unsuccessful’ is highly unlikely.

4) Natural kinds and their apparent existence in the world show that inductive inference is reliable. Natural kinds can be argued for via Richard Boyd’s Homeostatic Property Cluster (HPC) account of natural kinds. The real kind structure of nature is what underlies the reliability of inductive inference. HPC is not committed to the existence of a single correct classificatory system in each scientific domain.

5) updating Locke: Locke assumed that Natural Kinds had to have all properties in common. Kornblith (in light of science) asserts that some properties are essential to natural kinds, others are non-essential, and members of natural kinds need only share the essential (HPC). Locke assumed that we couldn’t discover real essences. The advance of science has allows us now to discover ‘unobservables’. Given the success of science, or nominal kind classifications reflect real differences in kind found in nature.

6) Philosophy of science: realism vs. anti-realism. Kornblith’s argument for real kinds and the success of science reflect a traditional argument for scientific realism. Success of science is measured by empirical, explanatory, technological successes. The best explanation for this success is that scientific theories are (approximately) true and the entities they posit exist. This is IBE of an observed fact: success of science.

7) Kornblith’s view of Natural Kinds asserts that there are real divisions in nature. This runs counter to Locke who asserts that there are no chasms or gaps in nature.

8) Reductionism: special sciences reduce to physics and/or chemistry. Kornblith rejects this. Biological kinds may be composed of physical stuff, but biological kinds do not reduce to chemical or physical kinds. This seems anti-intuitive to me. I would have thought that a biological kind i.e. a reptile, would at some point reduce to a chemical kind i.e. DNA chemical makeup unique to reptiles. From Kornblith:

“Consider a particular dog, Fido. Fido is entirely physically composed … Nevertheless, even if we were to have an atom by atom description of Fido at this moment, Fido could not be identified with this collection of atoms. If we were to remove a single atom from the collection, we would not have the same collection; but we would, in all likelihood, still have the same dog.” (K, p 54 – 55)

But what if a change was made at the DNA level, at the time of conception and development of fetus, a change could be significant enough to entirely remove Fido from his natural kind grouping. So perhaps at the level of the atom kinds are indistinguishable, i.e. atoms are all alike, but at the chemical level kinds are entirely distinguishable.

Also, the question arises, am I identifiable with the matter that makes me up? Alternatively, how significant is the loss of particles and atoms in dry skin, or when I cut myself and lose blood? Do I really lose a part of myself? So perhaps there is a difference between the atoms that constitute the matter that you are, and the process of formation at the beginning, in DNA or whatever else, that determines what you are, what hair color you will have or deformities or eye color. I would have to argue that I am identical with the DNA blueprint that constitutes my physical makeup; it gives me my blue eyes, my brown hair, my height, my general physique. In this sense I argue for reductionism. But, am I identical with the atoms that come together to constitute the matter that holds me together? No. There is a temporal factor to this reductionism to do with conception and evolution.

Also, natural kinds is not about individual entities, it is about groupings.

Quick quote from T. E. Wilkerson; I think this has some bearing on Kornblith’s assumptions about natural kinds…

“… because there are no real essences that make rubbish rubbish, and tables tables, I cannot even in principle make sound inductive projections about rubbish as such or tables as such.
… the phrase as such is crucial. Obviously I can make safe predictions about the behavior of my table or rubbish heap under certain circumstances… But the point is that, in making my predictions, I am exploiting the fact that every object, or quantity of stuff, will belong to at least one natural kind, even if it also belongs to one or more non-natural kinds.” (p30)

i.e. all inductive inferences are safe (reliable) if they describe the behavior of natural kinds.

What is IBE?

Simply, IBE is using logical inference to create a hypothesis that accounts for reliable data, or seeks to explain relevant evidence i.e. the lawn/street etc is wet in the morning, therefore IBE would lead us to hypothesize that it rained last night. IBE also seeks to make the most economic explanation, hence the use of the word ‘best’ in the title.

Kornblith employs IBE to argue from success of science to existence of natural kinds. This raises the question of induction (the success of science can be accounted for by natural kinds, using IBE as the method to make such a hypothesis).

IBE: a form of inference in it’s own right, rather than a form of induction or deduction.

Problems with IBE:

Putting Inference to the Best Explanation in its Place – T Day & H Kincaid

“Within epistemology, IBE is used in at least two ways: as a fundamental rule of belief revision or as a strategy for showing that a favored account of justification has the needed ties to truth.” (p272)

Harman claims that all inductive inference is IBE. IBE as the basic rule of justification is useful for foundationalists. i.e. Moser, for whom foundations are subjective non-conceptual contents, non-propositional experiences that can justify propositions when the propositions are the best explanation for non-conceptual contents. IBE also appeals to truth; just think of Kornblith’s argument for the success of science, or propositions that hold up in comparison with the natural over time.

Van Fraassen sees IBE as worthless. He asserts that it makes us ‘incoherent’:

“… any IBE will work only given some hypotheses to choose from. However, unless we that the relevant contenders probably contain the truth, then inferring to the best explanation does not up the odds that we are picking the true one. Moreover, our current science is just one of many possible accounts of the world, most of which we cannot even state and most of which of course must be false. Thus our own current views must be taken as a random member of the total possible explanations, and thus as probably not true. Thus even if our current theories were the best explanation, that would be no ground for taking them to be true.” (p274)

There is no detailed explanation of IBE by its defenders or detractors. This chapter points out two basic approaches to explanation: unification and causation. If we understand IBE as unification, then 1) IBE collapses into nothing more than coherence with the totality of belief and evidence, thus making IBE redundant and uninformative; or 2) IBE is defeasible, limited argument strategy. If explanation is the citing of causes, then likewise IBE is a defeasible, limited argument strategy.

Day and Kincaid suggest a different form of inference, a kind of precursor to IBE: “On the causal interpretation, IBE traded on our background knowledge about causal processes to warrant an inference to one hypothesis over another. This suggests that IBE does not name a fundamental pattern of inference but that it is instead an instance of another, more general inference strategy. That strategy infers to warranted beliefs from background information and data. When those background beliefs essentially involve claims about explanation and those claims ground inferences from the data to new beliefs, this general inference strategy becomes IBE.” (p282)

“In short, appeals to the best explanation are really implicit appeals to substantive empirical assumptions, not to some privileged form of inference. It is the substantive assumptions that do the real work.” (p282)


IBE is useful, but must be evaluated within a context. In general, context of an argument is everything that goes into determining the adequacy of the inference (except for syntax and semantics); background knowledge, internal vs. external evidence, and purposes. Purpose refers to whether the conclusion is intended to fit into an overall doxastic system. Imagine taking an argument to a fellow specialist, who shares a set of assumptions and background knowledge, vs. to a skeptic.

Internal/external: the most internal standpoint allows only the facts that are to be explained as evidence (in the case of the wet lawn and street, only the wetness is to be used as evidence), whereas the most external standpoint is to ask skeptical questions and find evidence that responds to them (the sense data of the observer is incorrect; Descartes demon).

With contextual factors in mind, it can be seen that depending on the availability of background knowledge, or the presence of a common tradition, IBE the force and success of a given IBE can vary in different contexts.

Is Kornblith using IBE in a contextual way?

Scientific realism suggests we have good evidence that current science is in large part approximately true. IBE is used to draw this conclusion. Anti-realists deny this, and argue that IBE begs the question and that realism is not the best explanation for scientific success.

On anti-realists: “In fact, they need a well-confirmed theory of science. Such a theory would have to explain the rise and fall of scientific theories, the practice of science, and so forth, without invoking realist assumptions. That theory would also have to meet reasonable criteria for good science […] needless to say, anti-realists have no such theory.” (p292)

On realists: “To build successfully an IBE argument for realism, they need (1) to show that anti-realist explanations of science are empirically inadequate and (2) to give a clear account of when scientific success argues for realism. They must achieve the first task to show that realism is the best explanation […] Realists need to take on to take on the second task because we have good evidence that false theories sometimes have been predictively successful.” (p292)

It needs to noted and remembered that this discussion itself must be broken into its own specific contexts. Any theory or argument must be (or will likely be) piecemeal. Science is enormous in its scope and its breadth of claims. A ‘unified’ argument for either realism or anti-realism would be powerful, but unlikely. Any combination of both realist and anti-realist outcomes is possible.

The concept of a ‘real kind’, being a collection of unobservable properties, united in nature, jointly responsible for observable properties by which we can classify objects into kinds, is the causal structure in the world required for inductive knowledge to be possible. It is a foundation for inductive inference. Hence the importance of determining the arguments for conventionalism and realism.

Homeostatic Property Clusters:

A concept suggested by Richard Boyd: “Scientific Realism and Naturalistic Epistemology” (1981) & “Realism, Anti-Foundationalism and the Enthusiasm for Natural Kinds” (1991)

“Organisms are so structured as to maintain themselves in certain states.” (Kornblith, p35)

So homeostasis means a cluster of properties, perhaps cells, or biological systems, which work together so as to maintain themselves even the face of changes in the environment. A self maintenance program. These self-maintenance ‘parts’ are unobservables. They give rise to the salient observable properties which draw attention. For Locke, this would be the arrangement of ‘insensible’ parts.

“A natural kind is a cluster of properties which, when realized together in the same substance, work to maintain and reinforce each other, even in the face of changes in the environment.” (Kornblith, p35)

A key point to understand is that not just any arrangement of ‘parts’ is possible. By understanding the details of arrangement of insensible parts (i.e. chemistry) we understand why some arrangements are stable and others not. For instance, H2O is a possible molecule, but HO2 is not. The clustering of observable properties is a direct result of configurations which are possible at the unobservable level. This is the path to explaining what it is about the world that makes it knowable.

“Because there are natural kinds, and thus clusters of properties which reside in homeostatic relationships, we may reliably infer the presence of some of these properties from the presence of others. In short, natural kinds make inductive inference possible…” (Kornblith, p36)

A problem arises:

Remember that in nature we have real kinds, and nominal kinds. Real kinds correspond to homeostatic clusters of unobservables, and nominal kinds are the abstract Idea to which the real kind/essence is attached. However, invoking philosophy of science and turning to unobservables, the question arises whether they are real properties in nature or merely nominal. Therefore we need an account for which unobservable, homeostatic clusters are real, and not nominal. Therefore the argument is postponed by homeostatic clusters, and not concluded.

Kornblith does not worry about such objections:

“Were the postulation of such underlying properties and relationships unrelated to the predictive, explanatory and technological successes of science, there would indeed be reason to think that appealing to such unobservables is nothing more than a sham. But in light of the intimate relationship between the postulation of unobservable structure and the various successes of science, one can no longer reasonably doubt the real existence of such structures.” (Kornblith, p41)


Kornblith suggests that the success of science is the direct result of the postulation of unobservable structure that underlies appearances (essence).