forall x, forsome x, forno x 
Today I received student comments from last term. Since it was the first time teaching with forall x, I asked a number of questions about the text itself. There aren't very many dust-jacket quality comments, but here is one: "Very clear. Not overly wordy. Great book to use."

The raw data looks like this:

Did the textbook explain matters clearly?
  yes         42
yes, but... 13
no 5

Did the textbook explain matters in sufficient depth?
  yes         37
yes, but... 9
no 13

Did the book provide enough practice problems of varying kind and difficulty?
  yes         45
yes, but... 1
no 10

Although I did not ask about it, 32 respondents said that there should be more solutions to practice exercises.

64 students responded, 2 of whom said that they had not used the book at all. I ignored incoherent responses such as "yes&no"; I counted answers like "mostly" as "yes, but..."

I also asked about lecture, and students were split in this regard. Many students said they would not have understood the book if they had not come to lecture. Others said that the book was a good study guide, filling in gaps and reinforcing things done in lecture. A few said that they were always confused by lecture and would be completely lost if it weren't for the book.

Altogether, the results are positive. I need to think more about adding to the solutions in the back of the book. I worry about making the book needlessly larger. Also, students can come to office hours to make sure they're getting it right. Hmm...

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forall x marches on 
A few random remarks about forall x:

(i) At the APA in December, I had a number of strange conversations about the book. People would say how great it was that I was making it available for free over the internet, but (they asked) what if someone used it as a course textbook? How did I plan on getting money from them?

I have tried to make the web page clearer on this point, but I fear that some people just don't quite get it. The book is available at no charge, which is to say that I'm not getting any money for it. There are too many logic textbooks already with an author, a publisher, a distributor, and a bookstore taking their cut at the expense of students who are basically a captive audience. Forall x is free because I think instructors should have the option of using a textbook that doesn't pass costs on to the students in that way.

(ii) Aaron Schiller is going to be using forall x at UCSD in the Spring. He prefers to use the squiggle for negation, the dot for conjunction, the horseshoe for conditional, and the triple bar for biconditional. No problem. Because all of the logical constants are defined in the style file, I only had to change four lines. I had an alternate version generated for him in a matter of minutes.

Actually, there was a complication... it was the dot. The default LaTeX bullet that I used the first time was a bit too big. Making an aesthetically satisfactory dot took some back and forth. Now that I know how to do it, it would be trivial to do again.

If you, the reader of this blog, are teaching a logic course and are looking for a textbook, note that forall x can be tailored to whatever symbols you like. (If you want to use the Staypuff Marshmellow Man as the symbol for disjunction, there might be some trademark issues.)

(iii) I ordered a copy from Lulu, a print-on-demand publisher. I was curious as to what their output looked like. It arrived this week, and the verdict is... cool.

At a cost of around ten bucks delivered, it comes as an immaculately printed, perfect-bound paperback. For an entire class, it makes more sense to take it to a local copy center-- but for a single copy, this is satisfactory.

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The d and the cog in d-cog 
Working on my distributed cognition paper, I have been thinking along these lines: We cannot treat the skin of an organism as the boundary of every cognitive activity in which the organism is involved; the boundaries of the cognitive system often must be drawn so as to include tools, parts of the environment, and other organisms. Two questions arise: (1) How far should the boundaries be pushed? (2) Why call the activity of these congeries 'cognitive'?

The answer to (1) will depend on the task we have in mind when we are describing the system. Consider doing long division with paper and pencil, a stock example of a d-cog activity. If we specify the task as long division, then the boundaries of the system need to include you plus the pencil and paper. We don't need to include the buckle of your belt, a nearby deep frier, or Olympus Mons. If we specify the task as doing a smaller division problem, writing down the outcome, carrying a digit, and so on, then the cognitive system just includes you.

Given the first specification, the task doesn't require there being paper at all; paper and pencil are part of the process that implements the task. Given the second, the task involves responding to and modifying the paper as part of the environment.

So, whether the process is distributed and how far depends on the task specification.

Ron Giere answers (2) by saying that 'cognitive' is just a term of art. D-cog might or might not be cognitive in an everyday sense, but it doesn't matter.

This only holds the problem at bay for a moment. We now need to ask what 'cognitive' means qua term of art.

I suggest in the paper that we can provide a rough and ready answer to this question in this way: Call an activity d-cog if (a) the task would count as cognitive if it were implemented in a single brain or mind and (b) the process that implements it actually extends beyond the boundary of a single organism. This allows us to leverage our ability to distinguish cognitive from non-cognitive tasks when considering individual cognition, extending the judgments to cover distributed cases which we might otherwise hesitate to call cognitive.

This handles long division, the examples offered by Ed Hutchins, and others besides. However, I am not sure that it will work in all cases. Nancy Nersessian and her collaborators have done extensive work on a specific research lab. The lab is studying blood vessels. She describes constructs and flow loops meant to simulate blood vessels. As she describes them, the constructs are 'mental models.' This language is partly just provocation, but she clearly thinks that the constructs are part of the cognitive system of the lab.

How should we specify the task that the lab is performing? Suppose we say that the task is learning about blood vessels. A single organism might pursue this task by constructing formal models and operating on them with its prodigious intellect. In so doing, the inquirer would learn about the models and-- if the models were sufficiently like real blood vessels-- learn about blood vessels as well. Certainly, this would be a cognitive task.

The scientists cannot do this, so they build physical models. They revise the physical models over time, much as the imagined inquirer would modify its formal models. And so the scientists learn about blood vessels.

Question (1) returns in this form: Does talking in this way make every experiment into part of the cognitive system that does the experiment? If so, then I think there is a problem. I want to say that many experiments are things we think about, rather than part of the system doing the thinking. Once we extend the cognitive system to include constructs and flow loops, how do we stop it from including everything?

I am not sure, but here is what I am thinking at the moment: The constructs are part of the system that implements the task of learning about blood vessels. Blood vessels are not part of that system, except in the trivial sense that the scientists themselves have blood vessels. Relative to this task specification, the scientists aren't thinking merely about the constructs. Rather, they are thinking about them qua models of blood vessels.

Suppose that a scientist is, on a given afternoon, working with a construct. If we characterize her task as learning about the construct, then we should not count the construct as part of the cognitive system. Since she relies on other instruments, then the process will still be distributed-- it just won't be distributed to the thing that she is trying to learn about.

I am tempted by this rule of thumb: If the task is learning about X, then don't include X as part of the process that implements the task.

It is only a rule of thumb, because it breaks down in cases of introspection. It also cannot clearly be applied to cases of mathematical inquiry.

The caveat about introspection has me worried that the rule of thumb is vacuous. We should only include X as part of the cognitive system if the cognition is introspective, but whether the cognition is introspective just depends on whether X is part of the cognitive system.

Hmm...

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Further reverberations in the echo chamber 
The mononymous Helmut blogs about my discussion of the wikipedia. He writes: "Ideally, other readers engage in a collective re-editing of each entry, and I like that ideal as a kind of Peircean community of inquirers." As he notes, the ideal, Peircean community doesn't include just anyone. It is open to anybody doing science, but they have to be doing science. People relying primarily on methods of tenacity or authority don't count.

There are serious criticisms of Peirce's claim that the scientific community will eventually come up with the truth. Browsing through recent issues of the Transactions, I can point to a solid paper by Ilya Farber [PDF] and another by Robert Meyers-- and that is only counting the papers authored by friends of mine. It is rarely noted, however, that his claim that the community' opinion will converge on the truth is only about the community for contingent reasons. Scientists need to work together because each human scientist is finite: not enough attention, not enough time. If there were a single inquirer with time and resources enough, then she could converge on the truth as well as an arbitrarily large community.

In this respect, Peirce thinks of scientific methods as definable in terms of a single individual. A scientific community is one in which each member considered individually employs those methods. Contrawise, real epistemic communities are as much defined by the structure of their social networks as by the individuals considered each in isolation.

The issue arises with respect to the wikipedia: Does the structure allow people who do know more to correct for people who know less, or does error swamp wisdom?

There is certainly something that touches on these issues in Peirce's corpus, but I'll leave the archival work as an exercise for the reader.

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Gossiping in the echo chamber 
More ruminations about the reliability of the wikipedia; cf. my earlier post Reliability on Wikipedia.

Meandering off-task this morning, I was browsing the wikipedia entry for Aldous Huxley. It claims that he wrote the original screenplay for Disney's Alice in Wonderland. The entry for Alice does not corroborate this, so I searched more broadly. About.com's encyclopedia makes a similar claim. Another website describes it as an uncredited contribution.

About.com's encyclopedia is covered by the GNU free document license. It is, for all appearances, a cut-and-paste from the wikipedia. So it repeats rather than corroborates.

The wikipedia seems to serve as a relay in this way: Someone, call them Alpha, says X on their webpage. Alpha or someone who has read Alpha's webpage writes X into a wikipedia entry. Other people read it and say X on the websites or in on-line discussions. Because the wikipedia is more often consulted than particular websites, this amplifies the usual echo chamber effect. Wikipedia also has an air of comprehensiveness and ubiquity that makes people less likely to acknowledge it specifically.

In my jargon, this makes sampling a less effective method than it would otherwise be.

Since this is simply a matter of curiosity for me, I could easily have accepted this without much scrutiny. If I had added it to my stock of beliefs, I could easily have done so without remembering where I had read it. If I recalled it later in some other context, I might rely on it because I believed it.

The worry about Huxley and Alice is just that the wikipedia can amplify ignorance or carelessness. Greater concerns arise when people start deliberately manipulating entries for their own ends. The defamation of John Seigenthaler seems to have been a practical joke, but more insidious manipulations are possible. Congress seems to be in on the act; congressional staffers are manipulating the entries on their bosses and their boss' adversaries [via ShortWoman].

UPDATE: Patrick Barkham has a clever piece in the Guardian about political spin of wikipedia entries.

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