TA Diaries – Week 2
This term I am TAing HPS250 – Introductory Philosophy of Science. Since I’ve decided to put a lot more effort into designing lessons than I have previously, I will be relating my experiences here in the hope that they might be useful for others and that it will help me improve my teaching in the future. You can read the first instalment here:
I really like how our instructors, Agnes Bolinska and Hakob Barseghyan, have designed the course this term. In particular, I like that they have selected readings which span the major developments in philosophy of science during the 20th century while also speaking directly to each other. I’m also very happy with how they have designed the grading scheme for the course. Students receive marks for the final essay, an essay proposal, a short summary / critique assignment, and 5-minute multiple choice quizzes in tutorials. I think exams are a pretty bad method of evaluation in general, but especially so for a subject like philosophy. Philosophy takes time—you need to think about a problem carefully, not just write down the first 300 words that occur to you in response to an exam question.
Anyways, for the first assignment students had to write a 3-page paper where the first two pages responded to one of the readings from the first five weeks of class and the last page criticized one point made in that reading. For the second tutorial, which would be the third week of class, I decided to do a mini version of that assignment. I presented the students with an argument taken from Nelson Goodman’s “The New Riddle of Induction”:
How do we justify a deduction? Plainly, by showing that it conforms to the general rules of deductive inference. An argument that so conforms is justified or valid, even if its conclusion happens to be false. An argument that violates a rule is fallacious even if its conclusion happens to be true. To justify a deductive conclusion therefore requires no knowledge of the facts it pertains to. Moreover, when a deductive argument has been shown to conform to the rules of logical inference, we usually consider it justified without going on to ask what justifies the rules. Analogously, the basic task in justifying an inductive inference is to show that it conforms to the general rules of induction. Once we have recognized this, we have gone a long way towards clarifying our problem.
Yet, of course, the rules themselves must eventually be justified. The validity of a deduction depends not upon conformity to any purely arbitrary rules we may contrive, but upon conformity to valid rules. When we speak of the rules of inference we mean the valid rules – or better, some valid rules, since there may be alternative sets of equally valid rules. But how is the validity of rules to be determined? Here again we encounter philosophers who insist that these rules follow from some self-evident axiom, and others who try to show that the rules are grounded in the very nature of the human mind. I think the answer lies much nearer the surface. Principles of deductive inference are justified by their conformity with accepted deductive practice. Their validity depends upon accordance with the particular deductive inferences we actually make and sanction. If a rule yields inacceptable inferences, we drop it as invalid. Justification of general rules thus derives from judgments rejecting or accepting particular deductive inferences.
This looks flagrantly circular. I have said that deductive inferences are justified by their conformity to valid general rules, and that general rules are justified by their conformity to valid inferences. But this circle is a virtuous one. The point is that rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either.
All this applies equally well to induction. An inductive inference, too, is justified by conformity to general rules, and a general rule by conformity to accepted inductive inferences. Predictions are justified if they conform to valid canons of induction; and the canons are valid if they accurately codify accepted inductive practice.
I broke the students up into random groups of four by putting numbers on index cards and shuffling them. I want to make students talk to different people in the class each week, rather than just hanging out with their friends. This should also make it slightly more likely that they’ll stay on topic rather than gossiping. I gave them ten minutes to read, summarize, and come up with a criticism of the passage. This passage was a little long, but I wanted to have them look at something that was not from any of the class readings because I thought that would be too much of an advantage for doing the assignment. I wanted them to learn skills that would help them with the assignment, not what they should actually say in the assignment. It turned out to be really difficult to find a self-contained, short argument that was related to the course material in some way.
This passage is nice in that Goodman writes clearly and without too much jargon, but it is difficult to actually extract a deductive argument from it. We’d been encouraging students to hunt articles for premises and see how they support the authors’ conclusions, but this isn’t a task that is as straightforward as we might like to believe. How might we break the above into a deductive argument?
- Deductions are justified by being in accord with valid deductive rules.
- Inferences are justified if they follow the standard set by deduction.
- Inductions follow inductive rules.
- If the rules of induction are valid, then inductions that follow them are justified (1&2&3).
- Deductive rules are shown to be valid by according with accepted deductive practice.
- Inductive rules can be shown to be valid in the same way as deductive rules.
- There are inductive rules that accord with accepted inductive practice.
- Those rules of induction are valid (5&6&7).
- Inductions that follow the rules of induction are justified (4&8).
That’s pretty convoluted and we still haven’t dealt with Goodman’s circularity argument, arising from the fact that “accepted practice” means “inferences that we consider justified”.
On the positive side, I think this exercise did help students to critically read an argument and try to extract premises and conclusions. Since Goodman’s argument was met with healthy skepticism on their part, I think it also helped reinforce the weight of Hume’s problem. When you see how crazy the arguments attempting to refute Hume are, Hume starts to seem a lot more reasonable. There was also a lot of good discussion in the groups and the students were generally pretty willing to speak after we brought everyone back together.
On the negative side, the students spent too long reading and the argument was too difficult to extract. The first argument you show students in philosophy shouldn’t be one that the author himself admits is circular! If I do a similar exercise in the future I’ll definitely try to find a better passage.
In the Thursday tutorial I had a major disaster. I came to school about half an hour before class to print out copies of the Goodman passage, but one printer was out of ink and the other was having major problems. I spent like 25 minutes wrestling with it before acknowledging defeat, so I had to wing that tutorial with basically no planning. It was pretty ugly. So much for my credibility with that group!
