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March 21, 2005

Inference vs Implication

When I was a graduate student at Princeton (many days ago), we used to joke that Gilbert Harman had only three kinds of question for visiting speakers:

These questions had a tendency to induce harmania in the subject and the inference/implication point, (which is what this post is really about) sometimes seems to me to have the following odd property: hardly anyone gets it if you explain it to them in conversation (I didn't get it that way), but everyone understands it if they read Chapter 1 of Change in View.

So naturally I want to try it out here. The following claims are ubiquitous and false:

Each overstates the responsibilities of logic, which is the study of what follows from what - implication relations between interpreted sentences; one can know the implication relations between sentences without knowing how to update one's beliefs.

Suppose, for example, that S believes the content of the sentences A and B, and comes to realise that they logically imply C. Does it follow that she should believe the content of C? No. Here are two counterexamples:

1. Suppose C is a contradiction. Then she should not accept it. What should she do instead? Perhaps give up belief in one of the premises, but which one? Logic does not answer the question - as we know from prolonged study of paradoxes - because logic only speaks of implication relations, not about belief revision.

2. Suppose she already believes not-C. Then she might make her beliefs consistent by giving up one of the premises, or by giving up not-C. Or she might suspend belief in all of the propositions and resolve to investigate the matter further at a later date.

Hence these questions about inference and belief revision - about what she should believe given i) what she already believes and ii) facts about implication - go beyond what logic will decide. That's not to say that logic is never relevant to reasoning or belief revision, but it isn't the science of reasoning and belief revision. It's the science of implication relations.

Convinced? Gil has a short and very clear discussion of this, and the pernicious consequences of ignoring it, in the second section of his new paper (co-authored with Sanjeev Kulkarni) for the Rutger's Epistemology conference.

Posted by logican at March 21, 2005 9:05 PM

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Gillian linked to a paper by Gil Harman and Sanjeev Kulkarni, which contains this nice explanation of the distiction between inference (reasoning) and implication (what follows from what). [Read More]

Tracked on April 11, 2005 2:43 PM