2.8 Occam’s Razor and the Assumption of a “Closed World”
Prediction always involves an element of defeasibility. If one predicts what will, or what would, under some hypothesis, happen, one must presume that there are no unknown factors that might interfere with those factors and conditions that are known. Any prediction can be upset by such unanticipated interventions. Prediction thus proceeds from the assumption that the situation as modeled constitutes a closed world: that nothing outside that situation could intrude in time to upset one’s predictions. In addition, we seem to presume that any factor that is not known to be causally relevant is in fact causally irrelevant, since we are constantly encountering new factors and novel combinations of factors, and it is impossible to verify their causal irrelevance in advance. This closed-world assumption is one of the principal motivations for McCarthy’s logic of circumscription (McCarthy 1982; McCarthy 1986).
3. Varieties of Approaches
We can treat the study of defeasible reasoning either (i) as a branch of epistemology (the theory of knowledge), or (ii) as a branch of logic. In the epistemological approach, defeasible reasoning can be studied as a form of inference, that is, as a process by which we add to our stock of knowledge. Alternatively, we could treat defeat as a relation between arguments in a disputational discourse. In either version, the epistemological approach is concerned with the obtaining, maintaining, and transmission of warrant, with the question of when an inference, starting with justified or warranted beliefs, produces a new belief that is also warranted, given potential defeaters. This approach focuses explicitly on the norms of belief persistence and change.
In contrast, a logical approach to defeasible reasoning fastens on a relationship between propositions or possible bodies of information. Just as deductive logic consists of the study of a certain consequence relation between propositions or sets of propositions (the relation of valid implication), so defeasible (or nonmonotonic) logic consists of the study of a different kind of consequence relation. Deductive consequence is monotonic: if a set of premises logically entails a conclusion, than any superset (any set of premises that includes all of the first set) will also entail that some conclusion. In contrast, defeasible consequence is nonmonotonic. A conclusion follows defeasibly or nonmonotonically from a set of premises just in case it is true in nearly all of the models that verify the premises, or in the most normal models that do.
The two approaches are related. In particular, a logical theory of defeasible consequence will have epistemological consequences. It is presumably true that an ideally rational thinker will have a set of beliefs that are closed under defeasible, as well as deductive, consequence. However, a logical theory of defeasible consequence would have a wider scope of application than a merely epistemological theory of inference. Defeasible logic would provide a mechanism for engaging in hypothetical reasoning, not just reasoning from actual beliefs.
I am convinced that moral principles are contributory rather than absolute. I don’t like the term ‘particularist’; it sounds like a matter of arbitration when you put it that way; I am very reasonable about what considerations I allow to contribute to my moral judgments. I would prefer to call my morality contributist. I wonder if it makes sense to say that utilitarians are a subset of contributists.
I found the Defeasible Reasoning SEP page because I found this thing talking about defeasible reasoning, which I found because I googled ‘contextualist Bayesian’.
Interesting stuff from the Stanford Encyclopedia of Philosophy:
2.8 Occam’s Razor and the Assumption of a “Closed World”
Prediction always involves an element of defeasibility. If one predicts what will, or what would, under some hypothesis, happen, one must presume that there are no unknown factors that might interfere with those factors and conditions that are known. Any prediction can be upset by such unanticipated interventions. Prediction thus proceeds from the assumption that the situation as modeled constitutes a closed world: that nothing outside that situation could intrude in time to upset one’s predictions. In addition, we seem to presume that any factor that is not known to be causally relevant is in fact causally irrelevant, since we are constantly encountering new factors and novel combinations of factors, and it is impossible to verify their causal irrelevance in advance. This closed-world assumption is one of the principal motivations for McCarthy’s logic of circumscription (McCarthy 1982; McCarthy 1986).
3. Varieties of Approaches
We can treat the study of defeasible reasoning either (i) as a branch of epistemology (the theory of knowledge), or (ii) as a branch of logic. In the epistemological approach, defeasible reasoning can be studied as a form of inference, that is, as a process by which we add to our stock of knowledge. Alternatively, we could treat defeat as a relation between arguments in a disputational discourse. In either version, the epistemological approach is concerned with the obtaining, maintaining, and transmission of warrant, with the question of when an inference, starting with justified or warranted beliefs, produces a new belief that is also warranted, given potential defeaters. This approach focuses explicitly on the norms of belief persistence and change.
In contrast, a logical approach to defeasible reasoning fastens on a relationship between propositions or possible bodies of information. Just as deductive logic consists of the study of a certain consequence relation between propositions or sets of propositions (the relation of valid implication), so defeasible (or nonmonotonic) logic consists of the study of a different kind of consequence relation. Deductive consequence is monotonic: if a set of premises logically entails a conclusion, than any superset (any set of premises that includes all of the first set) will also entail that some conclusion. In contrast, defeasible consequence is nonmonotonic. A conclusion follows defeasibly or nonmonotonically from a set of premises just in case it is true in nearly all of the models that verify the premises, or in the most normal models that do.
The two approaches are related. In particular, a logical theory of defeasible consequence will have epistemological consequences. It is presumably true that an ideally rational thinker will have a set of beliefs that are closed under defeasible, as well as deductive, consequence. However, a logical theory of defeasible consequence would have a wider scope of application than a merely epistemological theory of inference. Defeasible logic would provide a mechanism for engaging in hypothetical reasoning, not just reasoning from actual beliefs.
I am convinced that moral principles are contributory rather than absolute. I don’t like the term ‘particularist’; it sounds like a matter of arbitration when you put it that way; I am very reasonable about what considerations I allow to contribute to my moral judgments. I would prefer to call my morality contributist. I wonder if it makes sense to say that utilitarians are a subset of contributists.
I found the Defeasible Reasoning SEP page because I found this thing talking about defeasible reasoning, which I found because I googled ‘contextualist Bayesian’.
Googling ‘McCarthy Logic of Circumscription’ brought me here; very neat.