Archives For Logic

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.

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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.

So…

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.

Quine – Natural Kinds

October 25, 2012 — 4 Comments

Notes on Quine’s famous paper: Natural Kinds

Quine, Willard Van Orman. 1969. Natural Kinds. in Ontological Relativity and Other Essays: Columbia Univ. Press.

The paper starts with a problem for induction: “What tends to confirm an induction?” He relates Hempel’s puzzle of the non-black non-ravens and Goodman’s puzzle of the grue emeralds to an innate sense we have for similarity and sorting into kinds. First of all, we need to understand projection. The grue problem: this has been difficult for me to get my head around and it seems to have some complex logic problems, not to mention much discussion across the net around its implications and predicates. All emeralds studied before 2013 are green, so induction would suggest that all emeralds are green. Simple enough. However, at time t all emeralds turn blue but we do not know this yet. An emerald that has turned from green to blue is grue. So all emeralds studied after time t in 2013 will be grue and hence blue. The predicate green is projectable, the predicate grue is not, as who is to know that the emeralds are going to change color? Some discussions on this have broadened the context to suggest other precious stones change color in the same fashion creating a precedent and likelihood that emeralds will change color, therefore can you use induction to conclude that all emeralds are grue?

A projectable predicate counts towards the confirmation of all x‘s are z‘s. Quine uses projectability to solve the black raven, non-black non-raven problem. ‘Black’ and ‘raven’ are projectable, though ‘non-black’ and ‘non-raven’ are not. Hence, the raven problem is not an induction problem as induction only runs in the same direction as projectability. However, the proposition ‘all non-black things are non-ravens‘ is still lawlike, as it is logically equivalent to ‘all x are y‘.

“A projectable predicate is one that is true of all and only the things of a kind. What makes Goodman’s example a puzzle, however, is the dubious scientific standing of a general notion of similarity, or of kind.” (p116)

Quine then turns his attention from projectability to the problem of determining a ‘property’ as we need to sort kinds via their common properties. The point of projectability was to first outline how we might have confidence in our inductions about kinds in a temporal setting. He then illustrates how fundamental the notion of similarity or kind is to our thinking, yet how alien it is to logic and set theory. The non-logical roots of similarity and kind are important.

“One part of the problem of induction, the part that asks why there should be regularities in nature at all, can, I think, be dismissed. That there are or have been regularities, for whatever reason, is an established fact of science; and we cannot ask better than that. Why there have been regularities is an obscure question, for it is hard to see what would count as an answer. What does make clear sense is this other part of the problem of induction: why does our innate subjective spacing of qualities accord so well with the functionally relevant groupings in nature as to make our inductions tend to come out right? Why should our subjective spacing of qualities have a special purchase on nature and a lien on the future?” (p126)

Quine turns to Darwin and suggests that people’s innate spacing of qualities is a gene-linked trait, and that successful inductions will have become predominate through natural selection. He asserts that he is not generalising or creating a priori arguments. He wants to demonstrate that the ‘innateness’ he is describing is not an argument against empiricism. Rather than innate ideas (rationalists – continental) he is describing innate capacities (empirical – Darwin). He sees philosophy as continuous with science, with no external vantage point (no foundationalism – Quinean holism). Therefore all scientific findings that are at present plausible can be used a specificity in philosophy as elsewhere.

Important: Kornblith departs from Quine on this point. He asserts that we can survive without our cognitive capacities being accurate; see chpt 1.

He next acknowledges inductions conspicuous failures. He uses the sense-input data we have as humans as an example, primarily color. We are well aware of our sense data limitations, yet in spite of an array of inductive errors made in such a context we have still been successful. This boils down to the human condition whereby our limitations have helped us survive on one hand, i.e. color is helpful at the food gathering level, but on the other are insignificant to such activities as broader theoretical science. So there is a dynamic existence and use of sense data and innate similarity biases. Essentially, it is the achievement of the species to have risen above, using inductive inference, his sensory limitations and sensory space. Induction has allowed a trial and error process of theorizing and therefore has a definite temporal quality/factor that needs to be included in any justification discussion of induction:

“A crude example is the modification of the notion of fish by excluding whales and porpoises. Another taxonomic example is the grouping of kangaroos, opossums, and marsupial mice in a single kind, marsupials, while excluding ordinary mice. By primitive standards the marsupial mouse is more similar to the ordinary mouse than to the kangaroo; by theoretical standards the reverse is true.” (p128)

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)

Important:

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

Kornblith finds three contrasting views sitting side by side in Book III of An Essay Concerning Human Understanding (Locke). He sees this as a great strength in Locke as Locke was struggling with his reason and empiricism and certain intuitions that did not necessarily add up. With regard to natural kinds Kornblith asserts that these seeming contradictions are problems for us all; they are universal contradictions which pull us in different directions on this issue. These three views are broadly Kornblith’s own interpretation of Locke, and direct reference to their presence in the text is not made. This is a window to the larger, more contemporary discussion.

The key question: are there real kinds in nature? or do we (humans) impose them on nature for the benefit of our own understanding?

1) Conventionalist: no real kinds in nature. This is appealing as it lumps the burden of proof to the realist. Though ultimately, it seems a bit hard to swallow once you update the conversation to include evolution, chemistry, biology etc.

2) There may be real kinds in nature, but what they are is unknowable by us (locke’s official position): this seems to me to be like the worm trying to perceive the elephant. This is also a particularly British empiricist view.

3) There are real kinds in nature and what they are can be known by us. This is known as corpuscularianism. This is realism.

Two Arguments for Conventionalism:

This is an analysis of Book III, chpt vi of Locke’s Essay. It seems to be essentially a linguistic argument, pre-linguistics. Locke discusses how a word is capable of referring to kinds of things i.e. a signifier (word – cat), signified (kind – cat) and referent (an actual cat).

The question of whether something is or is not a cat just amounts to the question of whether it does or does not answer to the idea one associates with the term ‘cat’.” (Kornblith, p18)

This seems simple enough. Locke, however, being pre-Nietzsche and pre the proper onslaught of scientific industry and culture relates these connections to metaphysical concepts:

“The measure and boundary of each Sort, or Species, whereby it is constituted that particular Sort, and distinguished from others, is that we call its Essence, which is nothing but that abstract Idea to which the Name is annexed: So that every thing contained in that Idea, is essential to that Sort.” (III, vi, 2)

Such an apparent linguistic argument seems to invoke much later philosophical thought such as that of Derrida’s differance and drift let alone any conflicts with scientific realism. This raises the interesting question of how to read linguistic or hermeneutic philosophy with regard to scientific realism. Where do they cross over, are they at odds (of course different views from different philosophers produce different contrasts). Never-the-less, this is Locke’s picture of conventionalism. One key argument he makes is a priori, the other empirical:

a priori – the essential properties of an object derive not from features of the object itself, but only from the idea associated with soem term used to pick it out. No empirical facts are called upon for this argument.

empirical – (pre-evolutionary biology, or plain modern biology) ‘irregular and monstrous births’ observed in animals give us reason to doubt whether Nature designs things by reference to a model; a regulated, established essence. Also, there are no great chasms or gaps in Nature. Rather, things differ from one another by a series of small steps. Instances might be birds that live on the ground, fishes that have wings, sea creatures that inhabit the land etc.

Essentially, modern science makes it easy to reject these sets of arguments for conventionalism. At what point does the categorization of beings stop? For instance, all animals (incl. humans) could be in the Kind named ‘built from DNA’ which would most definitely have to be an essence and therefore a negation of conventionalism.

Kornblith sees the study of these two arguments as essential. Locke himself did not fully explore the relationship of these two arguments or recognize questions that they seem to bring to the fore. Namely: our traditional taxonomy, whether there are gaps between its groupings or instead merely differences of degree – whether our taxonomy is the only possible taxonomy, or whether it is, instead, merely one among many.

As to why these questions remain important in this context, in light of scientific realism and modern advances in science and philosophy, I am not yet sure.

Chapter 3 response:

Kornblith responds to the a priori argument, being a conceptual argument, by widening the scope and introducing an empirical dimension.

“It seems to me, however, that the argument is better understood as an inference to an explanation: the idea that some properties are essential to a kind and others are not can be fully explained by way of our conceptual activity, and no other explanation seems even possible. Essential properties are thus best explained as merely a product of the way we think about the world, and there is nothing to be gained by postulating the existence of real kinds. When put in these terms, the argument does not appear to be a conceptual argument at all, and it may be defeated by offering empirical considerations which would suggest an alternative explanation of the apparent existence of essential properties of kinds.” (Kornblith, p46)

He is of course referring to advances and successes in science since the time of Locke.

“Natural Kinds” Philosophy 63 (1988) pp 29 – 42

The problem of Natural Kinds is that there is no agreement anywhere about a doctrine for how to determine natural kinds. Certain paradigm examples have agreement: the kinds oak, stickleback and gold are natural kinds, and the kinds table, nation, and banknote are not. Wilkinson identifies two conditions which must be fulfilled to categorize a natural kind:

1) the notion of a natural kind must be tied to that of real essence.

2) 2) members of natural kinds, and the corresponding real essences, lend themselves to scientific investigation.

Natural kind predicates are also inductively predictable. It is easy to predict the behavior of the lump of stuff in front of me if I am able to determine it is oak. Alternatively, it is impossible to inductively predict the behavior of a nation. Also, any single object/entity might belong to one natural kind and numerous non-natural kinds. This does not effect the concept of inductive predictability as you are making your inductive predictions based on membership to a natural kind.

Distinguishing Between Natural Kinds and Non-Natural Kinds

A natural kind relates directly to the science that studies the real essence. For instance, ‘clouds’ do not have real essence, thereby a meteorologist does not study a real essence as such. Gases and water vapor do have real essence and so the chemist studies more precisely the natural kind. Likewise, a geographer or geologist might study a cliff, but the cliff does not have real essence. Instead it is the rock or granite, the realm of the physicist/chemist. See Locke on real and nominal essences.

“Meaning and Reference” from A W Moore (ed), Meaning and Reference (Oxford U P 1993) pp 150 – 161

If the meaning of a term is a concept, the implication is that meanings therefore are mental entities. Frege asserted that meanings were public domain, that a meaning could be the same for for more than one person, and by people at different times. Hence, meanings are identified as abstract entities, though ‘grasping’ these entities is an individual, psychological act. Putnam traces the intension/extension relationship in meanings back through medieval philosophy. He sites Carnap who “accepted the verifiability theory of meaning, the concept corresponding to a term provided a criterion for belonging to the extension.” (Putnam, p150)

Theory of meaning came to rest on two assumptions:

1) knowing the meaning of a term came is a matter of a certain psychological state

2) the meaning of a term determines its extension

Putnam rejects this outright as a false theory.

Is Meaning in the Head?

Putnam asserts that meaning is matter of conditions established by knowledge. He uses an elaborate science fiction example of the changing meaning of water over time. On an identical planet called twin earth, he suggests that everything is the same, even our own dopplegangers. However, the one difference is that water is not made of H2O, it is made of some alternative we can call XYZ. In 1590, water was the clear liquid substance found in rivers, oceans etc and between Earth and Twin Earth water could be identified as the same: x is the same liquid as y. In 1950, water on Earth is H2O and water on Twin Earth is XYZ. The relation ‘is the same as‘, which is the central logic relation, is theoretical and may require an indeterminate amount of scientific investigation. Or to make an example closer to home, (hypothetically) in Sydney people refer to Beech trees as Elm trees and Elm trees as Beech trees, and in Melbourne Beech trees are Beech trees, Elm trees are Elm trees. It follows that the Sydney-sider and the Melbourne do not have different meaning extensions to their terms because of a particular difference in their psychological states, but because of linguistic hiccup. Meanings are not in the head.

Putnam invokes a cultural and social aspect to meaning in the context of linguistics:

“We may summarise this discussion by pointing out that there are two sorts of tools in the world: there are tools like a hammer or a screw driver which can be used by one person; and there are tools like a steamship which require the co-operative activity of a number of persons to use. Words have been thought of too much on the model of the first sort of tool.” (p156)