Wednesday, May 11, 2005

Harman, inference and implication

Apologies for the long pause. Normal service -- whatever that might be-- is hereby resumed.

The third term is here. No teaching, so I should be dealing with a huge pile of marking and working on my PhD.

Does reading blog posts about the difference between inference and implication count?

Gillian at comments on a point that Gilbert Harman makes in the first chapter of Change in View -- and which has been in the back of my mind all through working on my PhD:

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:

  • Aren't you ignoring < insert recent result in psychology >?

  • Aren't you assuming that there is an analytic/synthetic distincton?

  • So you say, < insert one of the speaker's claims >, but isn't that just conflating inference and implication?

...The following claims are ubiquitous and false:

  • Logic is the study of the principles of reasoning.

  • Logic tells you what you should infer from what you already believe.

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.

1 comment:

Anonymous said...

Bulletin of Symbolic Logic. 12(2006) 353-354.

John Corcoran, Meanings of Inference, Deduction, and Derivation
Philosophy, University at Buffalo,
Buffalo, NY 14260-4150
Abstract: The verbs ‘infer’, ‘deduce’, and ‘derive’ used in logic are ambiguous; logicians use each with multiple normal meanings. Several of their meanings are vague in that they admit borderline cases. This paper juxtaposes, distinguishes, and analyzes several senses of these three-place action verbs, focusing on a constellation of recommended senses. In the sense to be recommended, the verb ‘infer’ is used for the epistemic activity of [a person] judging a proposition to be true by determining that it is a consequence of given propositions known to be true. The verb ‘deduce’ is used for the epistemic activity of determining that a proposition is a consequence of given propositions. Aristotle discovered that the same process of deduction used inferentially to draw a conclusion from premises known to be true is also used non-inferentially to draw a conclusion from premises whose truth or falsity is unknown, or even from premises known to be false. Applying his grasp of this point in the first few pages of Prior Analytics, he distinguished demonstrative from non-demonstrative deductions. He wrote: “Every demonstration is a deduction but not every deduction is a demonstration.” Inference, or demonstration, producing knowledge of the truth of its conclusion, and deduction, producing knowledge that its conclusion is logically implied by its premises, must both be distinguished from derivation, which consists in arriving at a string of characters by means of rule-governed manipulations starting with given strings of characters. Derivation by itself does not and cannot produce knowledge. No proposition can be inferred from a contradiction because no contradiction is known to be true. Every proposition can be deduced from a contradiction. And what can be derived from what depends upon which character-manipulating rules are allowed. This paper treats the relevant views of Aristotle, Boole, Frege, Lewis, Hilbert, Tarski, Church, and others.