Scientific discovery is often regarded as romantic and creative - and hence unanalyzable - whereas the everyday process of verifying discoveries is sober and more suited to analysis. Yet this fascinating exploration of how scientific work proceeds argues that however sudden the moment of discovery may seem, the discovery process can be described and modeled. Using the methods and concepts of contemporary information-processing psychology (or cognitive science) the authors develop a series of artificial-intelligence programs that can simulate the human thought (...) processes used to discover scientific laws. The programs - BACON, DALTON, GLAUBER, and STAHL - are all largely data-driven, that is, when presented with series of chemical or physical measurements they search for uniformities and linking elements, generating and checking hypotheses and creating new concepts as they go along. "Scientific Discovery examines the nature of scientific research and reviews the arguments for and against a normative theory of discovery; describes the evolution of the BACON programs, which discover quantitative empirical laws and invent new concepts; presents programs that discover laws in qualitative and quantitative data; and ties the results together, suggesting how a combined and extended program might find research problems, invent new instruments, and invent appropriate problem representations. Numerous prominent historical examples of discoveries from physics and chemistry are used as tests for the programs and anchor the discussion concretely in the history of science. Pat Langley is an Associate Professor in the Department of Information and Computer Science at the University of California, Irvine.Herbert Simon is a Professor in the Departments of Psychology, Computer Science, and Philosophy at Carnegie-Mellon University. Gary L. Bradshaw is an Assistant Professor in the Department of Psychology and Institute of Cognitive Science at the University of Colorado, Boulder. Jan M. Zytkow is an Associate Professor in the Computer Science Department at Wichita State University. (shrink)

Traditional analyses of the curve fitting problem maintain that the data do not indicate what form the fitted curve should take. Rather, this issue is said to be settled by prior probabilities, by simplicity, or by a background theory. In this paper, we describe a result due to Akaike [1973], which shows how the data can underwrite an inference concerning the curve's form based on an estimate of how predictively accurate it will be. We argue that this approach throws light (...) on the theoretical virtues of parsimoniousness, unification, and non ad hocness, on the dispute about Bayesianism, and on empiricism and scientific realism. * Both of us gratefully acknowledge support from the Graduate School at the University of Wisconsin-Madison, and NSF grant DIR-8822278 (M.F.) and NSF grant SBE-9212294 (E.S.). Special thanks go to A. W. F. Edwards.William Harper. Martin Leckey. Brian Skyrms, and especially Peter Turney for helpful comments on an earlier draft. (shrink)

William Whewell’s philosophy of scientific discovery is applied to the problem of understanding the nature of unification and explanation by the composition of causes in Newtonian mechanics. The essay attempts to demonstrate: the sense in which ”approximate’ laws successfully refer to real physical systems rather than to idealizations of them; why good theoretical constructs are not badly underdetermined by observation; and why, in particular, Newtonian forces are not conventional and how empiricist arguments against the existence of component causes, and against (...) the veracity of the fundamental laws, are flawed. (shrink)

Recent approaches to causal modelling rely upon the causal Markov condition, which specifies which probability distributions are compatible with a directed acyclic graph. Further principles are required in order to choose among the large number of DAGs compatible with a given probability distribution. Here we present a principle that we call frugality. This principle tells one to choose the DAG with the fewest causal arrows. We argue that frugality has several desirable properties compared to the other principles that have been (...) suggested, including the well-known causal faithfulness condition. _1_ Introduction _2_ The Causal Markov Condition _3_ Faithfulness _4_ Frugality _4.1_ Basic independences and frugality _4.2_ General properties of directed acyclic graphs satisfying frugality _4.3_ Connection to minimality assumptions _5_ Frugality as a Parsimony Principle _6_ Conclusion Appendix. (shrink)

The simple question, what is empirical success? turns out to have a surprisingly complicated answer. We need to distinguish between meritorious fit and ‘fudged fit', which is akin to the distinction between prediction and accommodation. The final proposal is that empirical success emerges in a theory dependent way from the agreement of independent measurements of theoretically postulated quantities. Implications for realism and Bayesianism are discussed. ‡This paper was written when I was a visiting fellow at the Center for Philosophy of (...) Science at the University of Pittsburgh; I thank everyone for their support. †To contact the author, please write to: Department of Philosophy, University of Wisconsin–Madison, 5185 Helen C. White Hall, 600 North Park Street, Madison, WI 53706; e-mail: [email protected]. (shrink)

Wayne Myrvold (2003) has captured an important feature of unified theories, and he has done so in Bayesian terms. What is not clear is whether the virtue of such unification is most clearly understood in terms of Bayesian confirmation. I argue that the virtue of such unification is better understood in terms of other truth-related virtues such as predictive accuracy.

What has science actually achieved? A theory of achievement should define what has been achieved, describe the means or methods used in science, and explain how such methods lead to such achievements. Predictive accuracy is one truth‐related achievement of science, and there is an explanation of why common scientific practices tend to increase predictive accuracy. Akaike’s explanation for the success of AIC is limited to interpolative predictive accuracy. But therein lies the strength of the general framework, for it also provides (...) a clear formulation of many open problems of research. (shrink)

What has science actually achieved? A theory of achievement should define what has been achieved, describe the means or methods used in science, and explain how such methods lead to such achievements. Predictive accuracy is one truth-related achievement of science, and there is an explanation of why common scientific practices tend to increase predictive accuracy. Akaike's explanation for the success of AIC is limited to interpolative predictive accuracy. But therein lies the strength of the general framework, for it also provides (...) a clear formulation of many open problems of research. (shrink)

Sober (1984) has considered the problem of determining the evidential support, in terms of likelihood, for a hypothesis that is incomplete in the sense of not providing a unique probability function over the event space in its domain. Causal hypotheses are typically like this because they do not specify the probability of their initial conditions. Sober's (1984) solution to this problem does not work, as will be shown by examining his own biological examples of common cause explanation. The proposed solution (...) will lead to the conclusion, contra Sober, that common cause hypotheses explain statistical correlations and not matchings between event tokens. (shrink)

Ramsey, Stick and Garon (1991) argue that if the correct theory of mind is some parallel distributed processing theory, then folk psychology must be false. Their idea is that if the nodes and connections that encode one representation are causally active then all representations encoded by the same set of nodes and connections are also causally active. We present a clear, and concrete, counterexample to RSG's argument. In conclusion, we suggest that folk psychology and connectionism are best understood as complementary (...) theories. Each has different limitations, yet each will co-evolve with the other in an overlapping domain of 'normal' psychology. (shrink)

The theory of fast and frugal heuristics, developed in a new book called Simple Heuristics that make Us Smart (Gigerenzer, Todd, and the ABC Research Group, in press), includes two requirements for rational decision making. One is that decision rules are bounded in their rationality –- that rules are frugal in what they take into account, and therefore fast in their operation. The second is that the rules are ecologically adapted to the environment, which means that they `fit to reality.' (...) The main purpose of this article is to apply these ideas to learning rules–-methods for constructing, selecting, or evaluating competing hypotheses in science, and to the methodology of machine learning, of which connectionist learning is a special case. The bad news is that ecological validity is particularly difficult to implement and difficult to understand. The good news is that it builds an important bridge from normative psychology and machine learning to recent work in the philosophy of science, which considers predictive accuracy to be a primary goal of science. (shrink)

Curve-fitting typically works by trading off goodness-of-fit with simplicity, where simplicity is measured by the number of adjustable parameters. However, such methods cannot be applied in an unrestricted way. I discuss one such correction, and explain why the exception arises. The same kind of probabilistic explanation offers a surprising resolution to a common-sense dilemma.

The likelihood theory of evidence (LTE) says, roughly, that all the information relevant to the bearing of data on hypotheses (or models) is contained in the likelihoods. There exist counterexamples in which one can tell which of two hypotheses is true from the full data, but not from the likelihoods alone. These examples suggest that some forms of scientific reasoning, such as the consilience of inductions (Whewell, 1858. In Novum organon renovatum (Part II of the 3rd ed.). The philosophy of (...) the inductive sciences. London: Cass, 1967), cannot be represented within Bayesian and Likelihoodist philosophies of science. (shrink)

The paper provides a formal proof that efficient estimates of parameters, which vary as as little as possible when measurements are repeated, may be expected to provide more accurate predictions. The definition of predictive accuracy is motivated by the work of Akaike (1973). Surprisingly, the same explanation provides a novel solution for a well known problem for standard theories of scientific confirmation — the Ravens Paradox. This is significant in light of the fact that standard Bayesian analyses of the paradox (...) fail to account for the predictive utility of universal laws like All ravens are black. (shrink)

Van Fraassen has argued that quantum mechanics does not conform to the pattern of common cause explanation used by Salmon as a precise formulation of Smart's 'cosmic coincidence' argument for scientific realism. This paper adds to this list some common examples from classical physics that also do not conform to Salmon's explanatory schema. This is bad news and good news for the realist. The bad news is that Salmon's argument for realism does not work; the good news is that realism (...) need not demand hidden variables in quantum mechanics if they are not used in classical mechanics. Many correlations in physics are explained in terms of property identity (contra Salmon). This leads to a new argument against van Fraassen because the unified version of the theory obtained by identifying theoretical properties is always less empirically adequate. (shrink)

Classical mechanics is empirically successful because the probabilistic mean values of quantum mechanical observables follow the classical equations of motion to a good approximation (Messiah 1970, 215). We examine this claim for the one-dimensional motion of a particle in a box, and extend the idea by deriving a special case of the ideal gas law in terms of the mean value of a generalized force used to define "pressure." The examples illustrate the importance of probabilistic averaging as a method of (...) abstracting away from the messy details of microphenomena, not only in physics, but in other sciences as well. (shrink)

Skyrms's formulation of the argument against stochastic hidden variables in quantum mechanics using conditionals with chance consequences suffers from an ambiguity in its "conservation" assumption. The strong version, which Skyrms needs, packs in a "no-rapport" assumption in addition to the weaker statement of the "experimental facts." On the positive side, I argue that Skyrms's proof has two unnoted virtues (not shared by previous proofs): (1) it shows that certain difficulties that arise for deterministic hidden variable theories that exploit a nonclassical (...) probability theory extend to the stochastic case; (2) the use of counterfactual conditionals relates the Bell puzzle to Dummett's (1976) discussion of realism in quantum mechanics. (shrink)

This paper aims to show how Whewell's notions of consilience and unification-explicated in more modern probabilistic terms provide a satisfying treatment of cases of scientific discovery Which require the postulatioin component causes to explain complex events. The results of this analysis support the received view that the increased unification and generality of theories leads to greater testability, and confirmation if the observations are favorable. This solves a puzzle raised by Cartwright in How the Laws of Physics Lie about the nature (...) of explanation by the composition of causes. (shrink)

This chapter examines four solutions to the problem of many models, and finds some fault or limitation with all of them except the last. The first is the naïve empiricist view that best model is the one that best fits the data. The second is based on Popper’s falsificationism. The third approach is to compare models on the basis of some kind of trade off between fit and simplicity. The fourth is the most powerful: Cross validation testing.

Deductive logic is about the validity of arguments. An argument is valid when its conclusion follows deductively from its premises. Here’s an example: If Alice is guilty then Bob is guilty, and Alice is guilty. Therefore, Bob is guilty. The validity of the argument has nothing to do with what the argument is about. It has nothing to do with the meaning, or content, of the argument beyond the meaning of logical phrases such as if…then. Thus, any argument of the (...) following form (called modus ponens) is valid: If P then Q, and P, therefore Q. Any claims substituted for P and Q lead to an argument that is valid. Probability theory is also content-free in the same sense. This is why deductive logic and probability theory have traditionally been the main technical tools in philosophy of science. (shrink)

The distinction itself is best explained as follows. At the empirical level (at the bottom), there are curves, or functions, or laws, such as PV = constant the Boyle’s example, or a = M/r 2 in Newton’s example. The first point is that such formulae are actually ambiguous as to the hypotheses they represent. They can be understood in two ways. In order to make this point clear, let me first introduce a terminological distinction between variables and parameters. Acceleration and (...) distance (a and r) are variables in Newton’s formula because they represent quantities that are more or less directly measured. The distinction between what is directly measured and what it is not is to be understood relative the context. All I mean is that values of acceleration and distance are determined independently of the hypothesis, or theory, under consideration. I do not mean that their determination involves no kind of inference at all. For instance, acceleration is the instantaneous change in velocity per unit time, and this is not something that is directly determined from raw data that records the position of the moon at consecutive points in time. It is consistent with that raw data that the motion of the moon is actually discontinuous, so that the moon has no acceleration. So, there are definitely theoretical assumptions make about the moon’s motion that are used to estimate the moon’s acceleration at a particular time. But these assumptions are not unique to Newton’s theory. The same assumptions are also made by the rival hypotheses under consideration. In fact, the existence of quantities such as instantaneous acceleration is only called into question by the far more recent theory of quantum mechanics. Likewise, in the case of Boyle’s law, there is no controversy in viewing the volume of the trapped air as being determined in a way that does not make use of the theory that Boyle is introducing. (shrink)

Wayne Myrvold (2003) has captured an important feature of unified theories, and he has done so in Bayesian terms. What is not clear is whether the virtue of such unification is most clearly understood in terms of Bayesian confirmation. I argue that the virtue of such unification is better understood in terms of other truth-related virtues such as predictive accuracy.

Textbooks in quantum mechanics frequently claim that quantum mechanics explains the success of classical mechanics because “the mean values [of quantum mechanical observables] follow the classical equations of motion to a good approximation,” while “the dimensions of the wave packet be small with respect to the characteristic dimensions of the problem.” The equations in question are Ehrenfest’s famous equations. We examine this case for the one-dimensional motion of a particle in a box, and extend the idea deriving a special case (...) of the ideal gas law in terms of the mean value of a generalized force, which has been used in statistical mechanics to define ‘pressure’. The example may be an important test case for recent philosophical theories about the relationship between micro-theories and macro-theories in science. (shrink)

Type 1: This process occurs for half of the population. For this segment of the population, there is 10% chance of developing the disease. There is a test for the disease such that 90% of the people who have the disease in this case will test positive (event E), while the false positive rate is 10%, which means that there is a 10% chance of testing positive for the disease when they do not have the disease.

Kenneth Wilson won the Nobel Prize in Physics in 1982 for applying renormalization group, which he learnt from quantum field theory (QFT), to problems in statistical physics—the induced magnetization of materials (ferromagnetism) and the evaporation and condensation of fluids (phase transitions). See Wilson (1983). The renormalization group got its name from its early applications in QFT. There, it appeared to be a rather ad hoc method of subtracting away unwanted infinities. The further allegation was that the procedure is so horrendously (...) complicated that one cannot see the forest for the trees. The second allegation is justified in the applications that made it famous. But it is not true of the following example, which appears in Chowdhury and Stauffer (2000, 486-488). (shrink)

Although in every inductive inference, an act of invention is requisite, the act soon slips out of notice. Although we bind together facts by superinducing upon them a new Conception, this Conception, once introduced and applied, is looked upon as inseparably connected with the facts, and necessarily implied in them. Having once had the phenomena bound together in their minds in virtue of the Conception men can no longer easily restore them back to the detached and incoherent condition in which (...) they were before they were thus combined. The pearls once strung, they seem to form a chain by their nature. Induction has given them unity which it is so far from costing us an effort to preserve, that it requires an effort to imagine it dissolved — William Whewell, 1858. (Quoted from Butts (ed.), 1989, p. 143). (shrink)

Deductive logic is about the property of arguments called validity. An argument has this property when its conclusion follows deductively from its premises. Here’s an example: If Alice is guilty then Bob is guilty, and Alice is guilty. Therefore, Bob is guilty. The important point is that the validity of this argument has nothing to do with the content of the argument. Any argument of the following form (called modus ponens) is valid: If P then Q, and P, therefore Q. (...) Any claims substituted for P and Q lead to an argument that is valid. Probability theory is also content-free. This is why deductive logic and probability theory have traditionally been the main tools in philosophy of science. (shrink)

Suppose that the true structural equation is Y = X + U, where U is n(0,1), X is n(0,1), and X and U µ be the mean of X, y µ the mean of Y, x σ the standard deviation of are independent. Now let x..

There is an interesting problem concerning component causes posed by Cartwright (1983) in her book How the Laws of Physics Lie, which is easily explained in terms of a simple example. Consider a cup sitting on the table. Why doesn’t it move? The explanation given by Newtonian mechanics is that the cup is experiencing two forces-the downward force of gravity and the upward ‘elastic’ force of the table-and these two forces exactly cancel to produce a zero resultant force. This zero (...) resultant force then produces a zero acceleration, which ‘explains’ why the cup doesn’t move. This rather simple, yet typical, example of theoretical explanation raises a surprisingly deep puzzle: What justification is there for believing in the existence of the component forces if they are redundant to the explanation? For it does not really matter what size the component forces are so long as their resultant is zero. (shrink)

A and B in signaling games (Lewis 1969). Members of the population, such as our prehistoric pair, are occasionally faced with the following ‘game’. Let one of the players be the receiver and the other the sender. The receiver needs to know whether B is true or not, but only possesses information about whether A is true or not. In some environmental contexts, A is sufficient for B, in others it is not. The sender knows nothing about A or B, (...) but does know that A is sufficient for B in some environments. This is a higher-order signaling game in which both players can benefit from sharing the information that they possess. How does a communication strategy evolve, and is it evolutionarily stable? (shrink)

Puzzle solving in normal science involves a process of accommodation—auxiliary assumptions are changed, and parameter values are adjusted so as to eliminate the known discrepancies with the data. Accommodation is often contrasted with prediction. Predictions happen when one achieves a good fit with novel data without accommodation. So, what exactly is the distinction, and why is it important? The distinction, as I understand it, is relative to a model M and a data set D, where M is a set of (...) equations with adjustable parameters (i. e., M is a family of equations with no free parameters). Definition: Model M predicts data D if and only if either (a) all members of M fit D well, or (b) a particular predictive hypothesis is selected from M by fitting M to other data, and the fitted model fits D well. M merely accommodates D if and only if (i) M does not predict D, and (ii) the predictive hypothesis selected from M using other data does not fit D well. There will be cases in which a model M neither predicts nor accommodates D. These are the cases in which we are willing to say that data falsifies the model. So, the distinction between prediction and accommodation applies only when there is no falsification. (shrink)

What is induction? John Stuart Mill (1874, p. 208) defined induction as the operation of discovering and proving general propositions. William Whewell (in Butts, 1989, p. 266) agrees with Mill’s definition as far as it goes. Is Whewell therefore assenting to the standard concept of induction, which talks of inferring a generalization of the form “All As are Bs” from the premise that “All observed As are Bs”? Does Whewell agree, to use Mill’s example, that inferring “All humans are mortal” (...) from the premise that “John, Peter and Paul, etc., are mortal” is an example of induction? The surprising answer is “no”. How can this be? (shrink)

The Value of Good Illustrative Examples: In order to speak as generally as possible about science, philosophers of science have traditionally formulated their theses in terms of elementary logic and elementary probability theory. They often point to real scientific examples without explaining them in detail and/or use artificial examples that fail to fit with intricacies of real examples. Sometimes their illustrative examples are chosen to fit their framework, rather than the science. Frequently these are non-scientific examples, which distances the discussion (...) from its intended target. In the final analysis, philosophical discussions of explanation, confirmation, scientific realism, and the nature of theories are often too abstract, or too imprecise, or too disconnected with real science, to allow scientists to benefit from the discussion. This is a great loss for both parties. In my experience, working scientists are confronted with philosophical issues not only in their role as researchers, but also in their role as tertiary teachers of science. (shrink)

Section 2 will begin by formulating Reichenbach’s principle of common cause in a more general way than is usual but in a way that makes the idea behind it a lot clearer. The way that Salmon has pushed the principle into the services of scientific realism will be explained in terms of an example, van Fraassen objects, Salmon modifies his stand and van Fraassen rejoins - all in section 2. (See van Fraassen 1980, chapter 2).In this episode I think van (...) Fraassen right in claiming - against Salmon that there is no categorical imperative for common cause explanation, and I add my own examples in section 3. The first example ‘is the explanation of the correlation between the equilibrium positions of two objects on a balance in terms of their property of “mass” and the law of moments. (shrink)

Whewell, William (b Lancaster, England, 24 May 1794; d Cambridge, England, 6 March 1866) Born the eldest son of a carpenter, William Whewell rose to become Master of Trinity College, Cambridge and a central figure in Victorian science. After attending the grammar school at Heversham in Westmorland, Whewell entered Trinity College, Cambridge and graduated Second Wrangler. He became a Fellow of the College in 1817, took his M.A. degree in 1819, and his D.D. degree in 1844.

The central problem with Bayesian philosophy of science is that it cannot take account of the relevance of simplicity and unification to confirmation, induction, and scientific inference. The standard Bayesian folklore about factoring simplicity into the priors, and convergence theorems as a way of grounding their objectivity are some of the myths that Earman's book does not address adequately. 1Review of John Earman: Bayes or Bust?, Cambridge, MA. MIT Press, 1992, £33.75cloth.

Forster demonstrates that Hegel did not in fact ignore epistemology, but on the contrary he fought a tireless and subtle campaign to defeat the threat of skepticism. Forster's work should dispel once and for all the view that Hegel was naive or careless in epistemological matters. Along the way, Forster makes much that has hither to remained obscure in Hegel's texts intelligible for the first time.

Most contemporary accounts of the nature of faith explicitly defend what we call ‘the positivity theory of faith’ – the theory that faith must be accompanied by a favourable evaluative belief, or a desire towards the object of faith. This paper examines the different varieties of the positivity theory and the arguments used to support it. Whilst initially plausible, we find that the theory faces numerous problematic counterexamples, and show that weaker versions of the positivity theory are ultimately implausible. We (...) discuss a distinct property of faith that we call ‘true grit’, such that faith requires one to be resilient toward the evidential, practical, and psychological challenges that it faces. We show how true grit is necessary for faith, and provides a simpler and less problematic explanation of the evidence used to support the positivity theory. (shrink)

Are extreme beliefs constitutive of echo chambers, or only typically caused by them? Or are many echo chambers unproblematic, amplifying relatively benign beliefs? This paper details the conceptual relations between echo chambers and extreme beliefs, showing how different conceptual choice-points in how we understand both echo chambers and extreme beliefs affects how we should evaluate, study, and engage with echo chambering groups. We also explore how our theories of extreme beliefs and echo chambers shape social scientific research and contribute in (...) a practical way when treating these phenomena, focusing on examples of climate change scepticism. (shrink)