Wednesday, October 8, 2008

Classical Logic and Inconsistent but Non-Trivial Fiction

This is a short excerpt from my paper on "What You Don't Need Paraconsistency or Pluralism For." The basic claim of the paper, as mentioned in the last post, was that while it is certainly true that if dialetheism is right, classical logic is wrong, since rules like Disjunctive Syllogism won't be universally truth-preserving, none of the traditional (non-dialetheist) motivations for paraconsistency give the classical monist (i.e. the logical monist who thinks that classical logic is the correct logic) any reason to abandon that position in favor of either logical pluralism or paraconsistent monism, since they can happily accept the relevant claims and accommodate them in their classical monist framework. Here's the bit about fiction:

"Start with inconsistent fiction. That it is possible for the writers of fiction to create inconsistencies, whether on purpose (as in Graham Priest’s whimsical short story ‘Sylvan’s Box,’ in which Priest himself, appearing as a character, finds that the late Richard Routley owned a box that both contained and did not contain a statuette, at the same time and in the same sense) or, as is vastly more common, by accident, is clear enough. To take a classic example, in Arthur Conan Doyle’s Sherlock Holmes stories, Watson’s war wound is always referred to in the singular, strongly suggesting that he only has one of them, but sometimes it is on his left shoulder (and thus, presumably not on his right shoulder) and sometimes it is on his right shoulder (and thus not on his left shoulder). Moreover, in both the Conan Doyle case and the Priest case, not everything is true in the worlds of the stories. It is not true in the world of ‘Sylvan’s Box’ that Graham Priest agrees with everything in this paper, and it is not true in the world of Conan Doyle’s Sherlock Holmes stories that Professor Moriarty’s ultimate aim was to raise up Cthulu and Azathoth to destroy humanity.

"How can the classical monist make sense of this? Easily, and in pretty much the same way that a conscientious paraconsistentist would have to make sense of it. Regardless of what your view is on fictional characters--whether they have no ontological status at all, or are abstract objects, or are Meinongian objects that fail to have the property of existing but have all sorts of other properties, like ‘being referred to in philosophy papers’--statements like, for example, “Sherlock Holmes lives on 221B Baker Street” are, strictly speaking, false. Go to 221B Baker Street in London, and you will not find Holmes or Watson there, but a bank, one with a special employee in charge of responding to correspondence written to Holmes. To the extent that we regard such statements as true--and this is true regardless of our stance on the ontological status of fictional characters--it is because we read them as containing implicit fiction operators. Sherlock Holmes, if he exists as an abstract object, has, for example, the property of being written about by Arthur Conan Doyle, but he most certainly does not have the property of actually living on 221B Baker Street. He only has this property in fiction.

"Once we realize this, however, the apparent conflict between classical monism and our obvious ability to non-trivially reason about fictional inconsistencies disappears. If Dr. Watson had the property of both being written about by Arthur Conan Doyle and not being written about by Conan Doyle, in precisely the same sense, that would be a real contradiction symbolized as (α ∧ ¬α), that would indeed entail any and every β in classical logic. If, however, Dr. Watson has the property of having in his war wound on his left shoulder and having it on his right (i.e. not on his left) shoulder in fiction, then acknowledging that that’s true commits us not to (α ∧ ¬α), but F(α ∧ ¬α), which is a very different thing.

"When we extend classical logic, to include such operators I see no reason why we should mimic the rules about what goes on outside of them when we make the rules for what goes on within their scope. A classical monist can happily admit that there are cases where F(α ∨ β) and F(¬α) are both true, but F(β) is not. More radically still, we can allow inferences within the scope of the fiction operators to be not only ‘paraconsistent’ but non-adjunctive. That is to say, F(α) and F(¬α) need not always entail F(α ∧ ¬α). This preserves the intuitive difference between the ‘Sylvan’s Box’ case, in which it is true in the world of the story that the box is both empty and non-empty, and the Sherlock Holmes case, in which both ‘Watson’s war wound is on his left shoulder rather than his right shoulder’ and ‘Watson’s war wound is on his right shoulder rather than his left shoulder’ are both true, but ‘Watson’s war wound is on both of his shoulders’ does not seem to be true. Notice that even here, we have not revised classical logic one whit, as evidenced by the fact that even if F(α) and F(¬α) do not jointly entail F(α ∧ ¬α), they continue to jointly entail (F(α) ∧ F(¬α))."

Saturday, October 4, 2008

What You Don't Need Paraconsistency or Pluralism For

Yesterday, I gave a Miami Forum talk entitled "What You Don't Need Paraconsistency Or Pluralism For." Here's the abstract:

"If dialetheism is right, classical logic is wrong, at least for the context of reasoning about the domain of the inconsistent. As such, classical monism--the claim that there is One True Logic, and that logic is classical--must be rejected in favor of either paraconsistent monism or some sort of logical pluralism. Many paraconsistent logicians, however, reject the claim that there are real contradictions ‘out there in the world,’ but think that there are good reasons short of that to reject classical monism in favor of some sort of paraconsistent approach. I argue that standard defenses of this claim fail to hit their target, examining and rejecting claims that classical logic somewhow gets negation wrong, and showing how standard motivations for paraconsistency from inconsistent fiction, counterpossible conditionals and so on offered by Greg Restall, J.C. Beall, Newton Da Costa and others can be accommodated in a classical monist framework."