It is sensible in the philosophy of the quantitative sciences to distinguish between three kinds ... more It is sensible in the philosophy of the quantitative sciences to distinguish between three kinds of hypothesis. The main goal of this chapter is to explain why the distinction is philosophically useful. 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 d...
The debate between William Whewell and John Stuart Mill is not only hard in the sense that both s... more The debate between William Whewell and John Stuart Mill is not only hard in the sense that both sides are difficult to understand, but the issue itself is unresolved. Whewell's idea of predictive tests is similar to the method of cross validation in statistics and machine learning, except that Whewell applies it in a hierarchical way at multiple levels. Or at least, that is how Whewell argues that hypothesis testing works in science. In contrast, the received view of theory testing is that the confirmation of rival hypotheses is measured by their degree of fit with the total evidence, provided that the rival hypotheses are equally simple. However, there is a growing realization that predictive tests are stronger in many ways. What this suggests is that the history of science could be used as a source of examples against which theories of learning may be tested. The purpose of this paper is to explain and highlight some of the features of Whewell's theory of hypothesis testin...
We find ourselves agreeing with much of what Kruse says in his reply to Why Likelihood?, and we... more We find ourselves agreeing with much of what Kruse says in his reply to Why Likelihood?, and we appreciate his clarification on other points. Boik, on the other hand, believes there is a satisfactory Bayesian solution to the problem of model selection. He also believes that the Akaike solution is flawed. We discuss these two points in sections 2 and 3. In addition, we disagree with Boik about several points of interpretation. We discuss these in section 1.
Recent approaches to causal modelling rely upon the causal Markov condition, which specifies whic... more Recent approaches to causal modelling rely upon the causal Markov condition, which specifies which probability distributions are compatible with a directed acyclic graph (DAG). 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 1 Introduction 2 The Causal Markov Condition 3 Faithfulness 4 Frugality 4.1 Basic independences and ...
According to one definition, a general philosophy of science seeks to describe and understand how... more According to one definition, a general philosophy of science seeks to describe and understand how science works within a wide range of sciences. This does not have to include every kind of science. But it had better not be confined to a single branch of a single science, for such an understanding would add little to what scientists working in that area already know. Deductive logic is about the validity of arguments. An argument is valid when its conclusion follows deductively from its premises. Heres 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 t...
This chapter examines four solutions to the problem of many models, and finds some fault or limit... more 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 Poppers 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.
Recent approaches to causal modeling rely upon the Causal Markov Condition, which specifies which... more Recent approaches to causal modeling rely upon the Causal Markov Condition, which specifies which probability distributions are compatible with a Directed Acyclic Graph (DAG). 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.
Statisticians and philosophers of science have many common interests but restricted communication... more Statisticians and philosophers of science have many common interests but restricted communication with each other. This volume aims to remedy these shortcomings. It provides state-of-the-art research in the area of Philosophy of Statistics by encouraging numerous experts to communicate with one another without feeling ���restricted��� by their disciplines or thinking ���piecemeal��� in their treatment of issues. A second goal of this book is to present work in the field without bias toward any particular statistical paradigm. Broadly speaking, ...
] published a theorem that appears to be stronger than the Bell (1964) theorem in a way that is m... more ] published a theorem that appears to be stronger than the Bell (1964) theorem in a way that is more significant than the other variations of Bell's theorem that have been published in the 50 years since Bell's theorem. Colbeck and Renner themselves do not relate their theorem directly to Bell's theorem, so here I present a version of the Colbeck-Renner theorem that makes the relationship explicit.
It is sensible in the philosophy of the quantitative sciences to distinguish between three kinds ... more It is sensible in the philosophy of the quantitative sciences to distinguish between three kinds of hypothesis. The main goal of this chapter is to explain why the distinction is philosophically useful. 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 d...
The debate between William Whewell and John Stuart Mill is not only hard in the sense that both s... more The debate between William Whewell and John Stuart Mill is not only hard in the sense that both sides are difficult to understand, but the issue itself is unresolved. Whewell's idea of predictive tests is similar to the method of cross validation in statistics and machine learning, except that Whewell applies it in a hierarchical way at multiple levels. Or at least, that is how Whewell argues that hypothesis testing works in science. In contrast, the received view of theory testing is that the confirmation of rival hypotheses is measured by their degree of fit with the total evidence, provided that the rival hypotheses are equally simple. However, there is a growing realization that predictive tests are stronger in many ways. What this suggests is that the history of science could be used as a source of examples against which theories of learning may be tested. The purpose of this paper is to explain and highlight some of the features of Whewell's theory of hypothesis testin...
We find ourselves agreeing with much of what Kruse says in his reply to Why Likelihood?, and we... more We find ourselves agreeing with much of what Kruse says in his reply to Why Likelihood?, and we appreciate his clarification on other points. Boik, on the other hand, believes there is a satisfactory Bayesian solution to the problem of model selection. He also believes that the Akaike solution is flawed. We discuss these two points in sections 2 and 3. In addition, we disagree with Boik about several points of interpretation. We discuss these in section 1.
Recent approaches to causal modelling rely upon the causal Markov condition, which specifies whic... more Recent approaches to causal modelling rely upon the causal Markov condition, which specifies which probability distributions are compatible with a directed acyclic graph (DAG). 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 1 Introduction 2 The Causal Markov Condition 3 Faithfulness 4 Frugality 4.1 Basic independences and ...
According to one definition, a general philosophy of science seeks to describe and understand how... more According to one definition, a general philosophy of science seeks to describe and understand how science works within a wide range of sciences. This does not have to include every kind of science. But it had better not be confined to a single branch of a single science, for such an understanding would add little to what scientists working in that area already know. Deductive logic is about the validity of arguments. An argument is valid when its conclusion follows deductively from its premises. Heres 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 t...
This chapter examines four solutions to the problem of many models, and finds some fault or limit... more 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 Poppers 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.
Recent approaches to causal modeling rely upon the Causal Markov Condition, which specifies which... more Recent approaches to causal modeling rely upon the Causal Markov Condition, which specifies which probability distributions are compatible with a Directed Acyclic Graph (DAG). 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.
Statisticians and philosophers of science have many common interests but restricted communication... more Statisticians and philosophers of science have many common interests but restricted communication with each other. This volume aims to remedy these shortcomings. It provides state-of-the-art research in the area of Philosophy of Statistics by encouraging numerous experts to communicate with one another without feeling ���restricted��� by their disciplines or thinking ���piecemeal��� in their treatment of issues. A second goal of this book is to present work in the field without bias toward any particular statistical paradigm. Broadly speaking, ...
] published a theorem that appears to be stronger than the Bell (1964) theorem in a way that is m... more ] published a theorem that appears to be stronger than the Bell (1964) theorem in a way that is more significant than the other variations of Bell's theorem that have been published in the 50 years since Bell's theorem. Colbeck and Renner themselves do not relate their theorem directly to Bell's theorem, so here I present a version of the Colbeck-Renner theorem that makes the relationship explicit.
Notes on Thomas Kuhn's The Structure of Scientific Revolutions, 1970 edition, 21 single-spaced p... more Notes on Thomas Kuhn's The Structure of Scientific Revolutions, 1970 edition, 21 single-spaced pages.
Notes on Thomas Kuhn's famous book The Structure of Scientific Revolutions, 1970 edition. This v... more Notes on Thomas Kuhn's famous book The Structure of Scientific Revolutions, 1970 edition. This version is 41 single-spaced pages.
The Principle of Common Cause is generalized to the idea that that correlated phenomena (not just... more The Principle of Common Cause is generalized to the idea that that correlated phenomena (not just correlated events) are indicators of a common cause. Examples in which the correlation between sets of variables do not reduce to pairwise correlations (Bernstein’s paradox) prove that it is strictly more general, in an interesting way. It is also explained how the generalized principle (like the original corrected version of Reichenbach’s principle) follows from the Causal Markov Condition, which is the main axiom of the structural theory of causation (aka Bayes causal nets).
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