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J from Blogosophy proposes that we use "in a manner of speaking" instead of "accoring to the fiction" as a prefix for fictional statements. This, J says, would also work for the problematic cases like "Sherlock Holmes consumed drugs that are illegal nowadays". I'm afraid I don't quite understand this operator. What are the truth conditions of "in a manner of speaking, p"?
It is controversial whether indicative conditionals with false antecedents are generally true. As far as I know, which really is not very far at all, it is equally controversial whether counterfactual conditionals with necessarily false antecedents are generelly true. What's interesting is the different kinds of counterexamples that are brought forward against these views. For indicatives, the counterexamples are indicative conditionals with false antecedents that nevertheless appear to be false, e.g. "if I put diesel in my coffee, the coffee tastes fine." For counterfactuals however, the alleged counterexamples (brought forward e.g. by Field in §7.2 of Realism, Mathematics & Modality, Katz in §5 of "What mathematical knowledge could be", and Rosen in §1 of "Modal fictionalism fixed") are counterfactual conditionals with necessarily false antecedents that appear to be true, e.g. "if the axiom of choice were false, the cardinals wouldn't be linearly ordered". Isn't this quite puzzling? How can the fact that some instances are true be a problem for a theory that claims that all instances are true?
This is part 2 of my comments on Fiction and Metaphysics.
Amie Thomasson argues that fictional objects are not as strange and special as one might have thought because they belong to the same basic ontological category as works of art, governments, chairs and other objects of everyday life. Doing without fictional entities, she says, would merely be "false parsimony" unless one can also do without other entities of this category.
I have three complaints.
Brian has made so many puzzling remarks about fictional characters being real but abstract that I've decided to read Amie Thomasson's Fiction and Metaphysics. Here is my little review.
Thomasson's theory, in a nutshell, is that the Sherlock Holmes stories are not really about the adventures of a detective who lives at 221B Baker Street, but rather about the adventures of a ghostly, invisible character who lives at no place in particular and never does anything at all. We don't find this written in the Sherlock Holmes stories because, according to Thomasson's theory, Arthur Conan Doyle simply doesn't tell the truth about Holmes. In fact the only thing he gets right is his name: That ghostly character he is telling wildly false stories about is really called "Sherlock Holmes".
Here comes the promised reply to Sam's reply to my previous posting. In that posting, I first suggested that some sentence S (in a given language) is analytic iff you can't understand it unless you believe it. Then I said that, "put slightly differently", S is analytic iff it is impossible to believe that not-S.
As Sam notes, the first definition implies that even very complicated analytic truths have to be believed in order to be understood, which might be somewhat unintuitive. I'm not sure how bad this is for lack of a clear example. Sam uses "the sum of the digits of the first prime number greater than 1 million is even", but this is not analytic, so here I can perfectly well admit that you may understand it without either believing or disbelieving it. He also mentions infinitely long sentences, but I don't believe there are any of those in ordinary languages.
Here at Humboldt University, there's a reading group about analytic philosophy (Sam already mentioned it). The flyer advertising this group describes analytic philosophy as a sort of new and fascinating kind of philosophy characterised by its perspicuity and ignorance of philosophical tradition. The funny thing is that the organisers of the reading group decided that we'll be discussing David Wiggins' Sameness and Substance Renewed. I don't want to know how much Hegel one has to read to find Wiggins perspicuous (and ignorant of philosophical tradition).
Some expression can't be properly understood unless one believes certain things: In some sense you don't understand "irrational number" unless you believe that no natural number is irrational; You don't understand "grandmother" unless you believe that grandmothers are female; Maybe you don't understand "cat" unless you believe that cats are animals.
This is all quite vague because "understanding" and "believing" are vague. I now want to suggest that a sentence is analytic iff you can't understand it unless you believe it. Analyticity is also vague, so the vagueness of the explicans is fine for this purpose.
I've made some slides about logic programming (PS) for my presentation next week in the logic seminar.
The following restriction might be a way out of the problems I mentioned in my last posting:
The gamma rule must not be applied if the result of its previous application has not yet been replaced by the Closure rule.
(The gamma rule deals with 
and 
formulae; the Closure rule is the rule that allows to replace dummy
constants by real constants iff that leads to the closure of at least one
branch.)
I'm half-way into programming a more efficient tree prover, based on free-variable tableaux. But now I'm not sure any more if this is really what I want.
The basic idea in free-variable tableaux is that you use dummy constants
to instantiate universally quantified formulas, and only replace these
dummy constants by real constants if this allows you to close a branch. In
automatised tableaux, this dramatically decreases the steps required for
certain proofs. For example, my old tree prover internally creates an
860-node tree to prove xy(Fxy 
zFzz) 
x y Fxy x Fxx, whereas a free-variable
system only needs 12 nodes.
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