Longing to be Loosed from the Limits of Logic?

We've all had the experience of having a student who advances some version of the "logic is just our way of thinking" thesis.

Here's a way I've developed to handle it that I've come to like and find effective. Actually, it's a refinement which is the result of a linguistic turn brought on in part by studying with Henry Kyburg. I'll use the second-person as if I'm addressing the student.

"That's an interesting-sounding suggestion, but I don't think I understand what you mean. [Student talks about Eastern philosophy not being "binary" or "bound by logic" and the deepest truth "transcend logic".] Hmmm, again it sounds interesting, but some logic comes rather built-in to language. For example, the meaning of "and" is captured by this chart [puts up truth-table for conjunction]. That's just what "and" means. An even simpler word is "not" [puts up truth-table for negation]. That's just what "not" means in ordinary language [maybe not in math, but that's another story]. And the thing is, when you put those two together you get an interesting principle called the Law of Non-Contradiction [puts up truth-table for LNC]. This principle says that in no case can a contradiction be true. That principle is the cornerstone of logic [it's not an axiom, but you know what I mean]. Most of the forms of reasoning we'll use in this class are based on this simple principle. If something implies a contradiction, we have to reject it. In a valid argument, affirming the premises but not the conclusion is contradictory. Now if you think that you or someone else has access to truths not expressible in language, I'm not going to argue with you, but please note that by it's very nature we can't discuss it. So this class is going to be taught in English and we'll discuss the topics in English as well.

Now, I know there's a bit of tweaking there, but nothing, I think, disingenuous or philosophically misleading. It leaves enough open ended not to totally shut them down, but it makes it clear that it's a dead end as a topic for class discussion.

Introducing Modal Operators to Intro Students

I find it pretty much impossible to teach philosophy at any level without using and mentioning modality. I also have terrible handwriting and am lazy, so symbols are really handy. Since I mostly teach intro type stuff I can't go crazy on the symbols, but this year I'm once again using a strategy I've found to work in the past and thought I'd pass it on.

I introduce possible worlds by talking about stories about the way things could have been--which, a la Adams, is in fact how I tend think of them--then I tell them that I'm going to use a box with an 'N' in it to stand for necessities things that must be true in any story and I write [N] in front of some necessary statements to make the point. Then I introduce a diamond with a 'P' in it--

--to stand for statements which could be part of some story. Gradually throughout the class the 'N''s and 'P''s get smaller and smaller until the disappear. By the end of the semester the box and the diamond are part of their vocab and they automatically understand them. The strategy generalizes more or less to other symbols as well.

A bit more on qualitative epistemic status concepts

I've been reading a lot lately on the idea of "acceptance" in theories of nonmonotonic logic. To accept something is often taken as being to accept it as "practically certain". There's always some statement about how the quest for certainty is a fool's errand and so on, but then it's often replaced by this vague close cousin. I haven't yet seen why practical certainty is A. much more likely to be acquired, B. very valuable in it's own right. It seems to me that whether practical certainty is something to be sought is a matter that will depend on a number of factors. Given an agent with a broad distribution of degrees of utilities--which I assume is most of us--a broad range of degrees of certainty will be important. For an agent--somewhat like me--with typically well-defined and extreme utilities fairly low probabilities are frequently sufficient for decisive action. So I'm not too bothered by the fact that I don't seem to be practically certain of much of anything.

What's the use of belief?

Justification looms ever larger as the central concept in epistemology from my point of view. I've long since stopped being very interested in knowledge: it just doesn't seem to feature in the explanation of very much I'm interested in or, frankly, very much at all as far as I can tell. Williamson's gambit is, to be sure, the best there is, but, though brilliant, his arguments don't move me (problem could be with me of course). Then I realized that I had very little clue what belief was. There is an *excellent* survey of theories of belief by Paul Weirich called "Belief and Acceptance" in the Kluwer Handbook of Epistemology. Paul there argues that there is no need to replace belief with acceptance, since degree of belief can explain both belief and acceptance. In at the apex of a crescendo of eloquence he concludes
"Although acceptance may find roots n the conventions of inquiry, its fruit already grows on the branches of a theory of belief" (518).Not bad for a logician, eh? I'm not sure I'm convinced--I dropped belief for acceptance a while ago--but my problem recently is that I don't see much utility at all in any qualitative doxastic attitude. A bit more below the fold.
Continue reading "What's the use of belief?"
Posted by Trent Dougherty at 10:23 AM Comments (0) TrackBack (0)
-->
January 18, 2006

Velleman on Counterfactuals: Bass Ackwards?
J. David Velleman at NYU has a neat online, interactive introduction to logic called Blogic. It has many virtues including--pedagogically--an introduction to Boolean connectives which meets students where they are: web searches, and--with respect to content--philosophically interesting logical topics like probability and modal logic, the latter including sections on subjunctive conditionals. That material includes a page with an array of worlds: the world designated actual at the center surrounded by the remaining array. The array is meant to, and does, provide a visual aid in determining the truth value of a token subjunctive conditional. It worked off and on in IE Explorer 6.0.2 but seemed always to work in Mozilla Foxfire 1.0.3. The interesting thing is that you can hit a button which "shuffles" the array, redistributing the P, ~P, Q, and ~Q worlds about which the text says this:
When the realm of possibility is arranged in *this* manner, the statement "If p were true, then q would be true" is *no longer true* in application to the actual world. [Emphasis added.]
There's no suggestion that the referent of "actual world" has changed. This strikes me as getting it backwards: the array depends on facts about the actual world. I.e. it's facts about the actual world which generate the metric which orders other possible worlds dictating the structure of the array. You can't just plop the actual world down into another array as you would cut a face out of a picture and paste it on another body. That is, the following seems to me to be the case.
CFN Necessarily, if A is an array of possible worlds centered on world W, then W has A essentially.
(I often worry about redundancy using "necessarily" and "essentially" in the same sentence, but I don't *think* I've done that here.) This could just be an instance of me being persnickety. It could be a harmless heuristic. Still, it would be easy to correct: just change the language above, dropping talk of actuality--after all, we can ask what subjunctives conditionals are true at any world--to something like:
When we go to a different world, different facts will hold and so the surrounding worlds will be ordered differently. Click here and check to see whether the conditional is true in this world as well.
I think that would get the order of explanation right without hurting the pedagogical value of these neat illustrations.

Knowledge, Lotteries, and the Future

I often hear people concede skepticism about the future quite easily when pressed to defend a principle about knowledge. A recent example is Dretske in response to John Hawthorne in the Contemporary Debates book. John presses him on an example having to do with a future event and Dretske response blithely "I'm a bit of a skeptic about the future" (p. 44). I've seen it in print a couple of times and I hear it fairly often in discussions with epistemologists. I say I'm going to Italy next summer. You challenge this, and I respond "Very well, I'm planning on going to Italy." Sounds good right? I want to explore that a bit.