Thursday, November 17, 2016

Why do we teach 1st-year philosophers intro logic?

Many undergraduate programs in philosophy have a logic requirement, and in many of these programs, that requirement is expected or even required to be fulfilled fairly early on in the program. My department is currently revisiting its core course requirements and looking at reducing the number of required courses in the first year, with the aim of making a more flexible program allowing students more ability to customise their courses to the topics that interest them. At the same time, we're planning to introduce a wholly new 1st-year course, which will be required, the Philosophical Skills course I've talked about earlier.

Right now, Intro Logic is a required 1st-year course for honors philosophy students, and one issue we're considering is whether it should remain one. Various suggestions are being put forward, including that it should remain one; that it should remain a 1st-year course but be an elective; that it should become a 2nd-year course; that every 1st-year student should know their truth tables and thus if Intro Logic isn't a required course, then basic propositional logic and truth-tables should be covered in the Philosophical Skills course; and more.

Of course, I'm a logician. Not only do I think Intro Logic should be a required course for all single honors philosophy students, I think it should be required for all joint honors students too. But this is just because it follows from the general claim that I think it should be a required course for all university students. Let's go back to the Middle Ages! :) So, I'm happy to admit that I have a biased viewpoint when it comes to discussing the question of whether Intro Logic should be a program requirement for philosophers.

Instead, I would like to talk about why we teach logic to 1st-year philosophers in the first place, because one thing that has come out of the discussion of the various options noted above is that I apparently have a very different view about what I want my 1st-year students to get from their Intro Logic class than some of my colleagues do.

It seems to me (and I hope very much I'm not grossly misrepresenting anyone) that many of my colleagues -- and probably lots of non-logician philosophers elsewhere -- think that one of the primary goals of an Intro Logic class is to teach students how to symbolise natural language arguments and determine whether they are valid.

Prior to these discussions, it would never have occurred to me that this could be one of the central goals of teaching logic. It's certainly a useful thing to teach, but I have always viewed symbolisation as a means to an end, and not an end in itself. The point of symbolisation is not to produce a symbolic representation that can be tested for validity, after which one then concludes that the argument in question is either good or bad (not the least of which because it completely ignores the soundness of the argument), but rather to hone the skills necessary to recognize when statements are ambiguous, and could be represented in more than one way, or where equivocal terms are being used, or what the scope of negation is, or what the suppressed premises are. It is the skills that you hone during the process by which you come up with your representation, not the end representation itself, that I want my students to learn. So that is one goal.

There is also the goal that I want them to be able to read contemporary analytic philosophy papers which use logical notation and understand what is being said, even if they don't have the means necessary to prove the statements or do anything with them formally. I just want them to be able to learn to read the language of logic, so that when faced with backwards E's and upside down A's, they can still extract content from the article. This is one reason why I make a point of alerting students to the different notation that is used for the same concepts, in hopes that they can develop a little translation vocabulary so that they can read Polish notation as well as infix notation, know what the horseshoe is as well as the arrow, know that the arrow can be ambiguous between strict and material implication. If that's the one skill they come away with from my course, I'll be happy. I'd rather they have this skill than know how to symbolise a propositional logic argument.

Another goal is, of course, directed to those students who might grow up to be logicians themselves. In an Intro Course, I feel it is a requirement of me as the teacher to ensure that I give them everything they need to gain a foundational understanding of the field -- where did logic come from? what is it aimed at? what is its historical development? -- as well as all the tools they would need to succeed in an advance course -- in particular, a clear understanding of the distinction between semantics and proof-theory, and an understanding of, if not yet the ability to prove, the importance of soundness and completeness. This is why 7 weeks into the term we've already read Aristotle and the Stoics, and bits from Roger Bacon and William of Sherwood, and why I hope to be able to include more of the medievals in future lectures. This is why I will regularly make side remarks about the narrowness of the scope of the logics we study in the Intro Logic so that they know what else is out there that they could go on to do -- everything we do is two-valued, but many-valued logics exist. Everything we do is non-modal, but modal logics exist. Everything we do is classical, but constructive logics exist. I want them to know that these things are out there.

But the primary goal, the one thing that I really want my students to come away with, is not any skill at symbolisation and truth-tables, but rather a method of thinking which involves minute and precise attention to detail and which involves an ability to reason from and manipulate definitions. When we did Aristotelian syllogistics a few weeks ago, I gave a relatively narrow definition of what counts as a syllogism. In last week's tutorial assignment, I then tested to see how well they'd picked up on just how narrow the definition was, by giving them a bunch of arguments, most involving categorical claims, to see if they could tell which are syllogisms and which are not. Many of them looked syllogistic, but failed for very precise reason: They had three premises instead of two; or had four terms instead of three; or had two terms instead of three; or lacked a quantifier on the subject term; or had the minor premise first. The logic you do in an intro course really is just an exercise in rule following -- I always tell my students that if they are able to read and follow the directions of a board game like Monopoly, they will be able to pass my intro course (and not only pass, but probably pass well). The thing with logic is that there is no room for error, you have to know what the rules and definitions are and when and where you can apply them. For a lot of students, nothing else have they ever studied required them to be this finicky about the details, and that is what I think is the primary goal of teaching 1st-year philosophers logic: To give them ample opportunity to develop and hone the skill of being a nit-picky finicky curmudgeon with a highly developed attention to detail. (We're grand fun at parties, you can well imagine.)

The first piece of philosophy that I ever read was Lewis Carroll's "What the Tortoise Said to Achilles", and what I remember thinking was "I want to do that. I want to learn to think like that." And that's what I want to teach my students.

That being said, I think it's clear why I'm in favor of retaining a logic requirement -- because these skills in precision of thought are transferable to every other area of philosophy. But more importantly, I do not think these goals can be obtained by simply having 2-3 weeks on propositional logic inserted into another general philosophical skills course: This attention to detail and level of precision is something that requires practice, lots of practice, over and over and over again until it becomes second nature. And practice simply takes more time than you get in 2-3 lectures.

Just as every logician ends up writing their own logic textbook because none of the ones out there do what they want them to do, I'm sure every logician has their own goals for teaching 1st-year philosophers introductory logic -- and I'm sure every non-logician philosopher who teaches the same course has their own goals. If you teach intro logic (as a required course or not), what do you think the point of it is?


  1. Just read this... Here is what I agree with: EVERY student should have intro logic (emphasis mine).

    To me - as a non-logician - logic should "hone skins necessary to recognize when statements are ambiguous", and to recognize "where equivocal terms are being used or what the scope of negation is, or what the supressed premises are." I think it important for students in every field to be abole to make equivocal statements and then to know how to clarify (unequivocate - is that a word?) them; to be able to make a variety of negations, to play with premises and how to supress them - or not.

    Absolutely they should be able to read current philosophical papers, otherwise how can they go further? So of course they should be introduced (Intro to...) to the language of logic (duh).

    Your paragraph beginning "Another goal is, of course, directed to those students..." has me in full agreement with each point and sub point mentioned. Each is like a window opening on a hither unseen vista which I lack experience or vocabulary to do justice to. Primarily I see this pargraph as pathways to the future, or ways forward, which in a world where many people wonder if they will have future employment, ought to be a vital consideration. If one does not know that a field of study exists, one is unlikely to stumble into that field of study. But if one KNOWS it is there, one can make plans and chart a path toward it. Skills like these are necessary in today's world.

  2. I think I agree with most or all of this, but would add that I think it varies somewhat depending on the environment at your institution, and the kind of background your students have had.

    For example: I tend not to spend a lot of time on history because my students are primed (because of US secondary education) to treat any mention of history as a list of facts to memorize, rather than as contextualizing a particular system (or better, as a way of figuring out what the system might be aiming at). I could fight to overcome that priming, but there's already so little time in a semester for introductory logic that it doesn't seem worth the investment to me. Which is a shame, because I think you're absolutely right about how valuable it can be when there's the right kind of uptake.

    Similarly, I think it matters what your students' lives are like. Logic in some ways requires a certain kind of quiet (or so it seems to me). If many of your students have full-time jobs, or kids, or both, there's only so much time and mental bandwidth they can devote to their first logic course. So while there's some ideal sense in which I think one of the goals of a first logic course should be to help students see logic as in some way playful and exploratory (i.e. as mathematical!), there are some contexts where so few students are going to be able to take advantage that it becomes a distraction rather than enrichment. This is doubly true if it's a university-wide requirement, since so many students might just want to survive the course with minimal investment.

    So then the goals have to shift to "what can I do that will be helpful to my students, but is reasonably achievable by the majority of them". And I think that might impact, say, whether it's productive to pursue meta-level questions about soundness and completeness. Because those ideas are most interesting and engaging when they bubble up organically. I also think it impacts what (if anything) to do with syllogistic logic, since I think one of the coolest things about syllogistic logics is how many of the results students can find on their own just by poking around and exploring. If you're not trying to take advantage of that feature, it might be better to just spend more time with propositional and predicate logics.

    I think all of that is compatible with what you say. Maybe it's just a question of emphasis. But that's the kind of thing I had in mind with my tweet about the answer being context dependent. In general I think the goals of a course come from the needs of the students maybe even moreso than facts about the subject, and that means different goals for different students.

    1. I cannot disagree with any of this! (Except perhaps the bit about needing quiet solitude for logic. I think ANY type of academic inquiry is difficult with small children around, and logic isn't necessarily distinct in this way. Also, I've managed to be a productive logician even with a child of my own. :) )

  3. Dear Sarah - super post and very helpful! I agree with you that we need to cover basic logic - pretty hard to even engage with lots of mainstream philosophy without it! However, I guess the problem is that lots of students just really don't like it, or find it seriously demotivating (as we know, lots of bright students scoring highly in other modules can really flounder, while sometimes the otherwise just 'okay' students, philosophically speaking, can do brilliantly). So, I wonder if we should run logic in a more substantial form than would be covered in the PhilSkills course (which looks great btw - saw your other posting) in first year after all, but that the way we attribute credit might not be based on assessment? Maybe we could have attendance-based credit, with mandatory completion of non-credit bearing 'assessments' - low-stakes mutiple-choice questionnaires or something...anyway, lots to think about!

    1. It's only in the UK where there is this weird formative/summative distinction that students aren't being assessed in logic courses by numerous homework assignments. If I were teaching in any other institution, I'd be doing what my advisor at UW-Madison did: Weekly homework assignments, which could be handed in with up to three people putting their name to the answer sheets, and one opportunity to redo the homework after it was marked. The best I can simulate this in the British system is with the weekly tutorial assignments, which are exactly of the same sort as they'll get on the summative assessments, but it's really hard to encourage people to work together (and even harder in my 3rd year class, because we've taught them too well to work individually (this is something else the philosophical skills course will try to change!)), and it doesn't give them the opportunity to do redos. While I understand the idea behind formative assessments, in that it allows students to explore and take risks, I really wish there was a way to make them still "count", i.e., at least be pass fail. Because too often people see "formative" and think "I can skip it, because it doesn't count to my grade".

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  5. Can you share the link to the course syllabus? What books and articles do you use with the students?

    1. I'm drafting the textbook as we go. It's at

      We started with the syllogistic, did a bridge week or two on the Stoics, and are now doing propositional logic. We'll do a few more weeks of that at the beginning of next term, and then head into predicate logic. At the end, we'll do 2-3 weeks on Buddhist logic and hopefully have 1-2 weeks left for some other fun things.