mathematical logics vs philosophical logics

From a comment I just wrote to jcreed.

Another thing I asked Pfenning about was the proper interpretation of sentences in Linear Logics (it might as well have been about non-monotonic logics, or para-consistent logics (thanks to quale for the reminder)). My inclination would be to say that these are "logics" only in the mathematical sense, not in the philosophical sense (i.e. In what I call "philosophical logics", sentences are about real truth. In particular, excluded middle and monotonicity hold.). But when we talk about agents' beliefs, we are in an intensional context, and these two no longer need to hold.

If we claim that sentences of such logics are meaningful, then we should be able to translate them into sentences in philosophical logics, e.g. temporal logics, by jumping out of the agent, and into an outsider's "objective perspective". But I don't see anyone bothering to do this.

For an illustration of what I mean:

While non-monotonic logic can model an agent's belief revision, we know that sentences in this logic are not to be judged as modeling truth. When we see a pair of sentences like:
X |- Z
X, Y |/- Z

we know that |- can't possibly refer to truth (afterall, truth is monotonic). Instead, |- must refer to the agent's beliefs and reasoning processes. Furthermore, this formalism is vague about what refers to the agent's beliefs about facts, what refers to the agent's beliefs about what inferences are valid, or whether the agent's inferences follow this logic blindly, without reflection.

Therefore, if we want to use a true philosophical logic, we should write something like:
B( B(X) ||- B(Z) ) (agent believes that: belief in X, in the default case, justifies belief in Z)

B( B(X) /\ B(Y) ||/- B(Z) ) (agent believes that: belief in X, when accompanied by belief in Y, in the default case, does not justify belief in Z)

Real reasoning involves reflection. Logicians often don't care enough about reflection.

"Maths is Scruffy but Computable"

Edmund Furse's "Maths is Scruffy but Computable" is interesting, but not very rigorous

Some keywords:
* mathematics understanding
* experience-based learning
* learning heuristics


Here is his Why did AM run out of steam?

interview with Gian-Carlo Rota

"Mathematics, Philosophy, and Artificial Intelligence" is a dialogue with Gian-Carlo Rota on a variety of questions:

"There is a ratio by which you can measure how good a mathematician is, and that is how many crackpot ideas he must have in order to have one good idea. If it's ten to one then he is a genius."

spam

I wish GMail warned anyone whose email gets placed in the spam folder, and told them to look up my address on my website. Yes, I know that spammers would use this feedback to learn what kind of messages pass through the spam filter. But it's not like it's very hard to get this kind of feedback already.

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Why is it so hard for people to use BCC / create mailing lists? I wish email clients had an option, right next to "Compose Message" called "Create a Yahoo! mailing list, invite these same people, and Post Message".

Seriously, clients should give a big warning whenever the number of people in "To:" + "CC:" has more than 5 people.