Teaching The Teaching Workshop: The Analytic Synthetic Distinction

The Teaching Workshop: The Analytic Synthetic Distinction

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I find myself having to teach the analytic-synthetic distinction in almost every class, as the distinction arises in our readings. In an upper-level epistemology or metaphysics class, you have the time to explain the background of the distinction, why it is important, and how it has evolved. But in an introductory philosophy or introductory ethics class, you often have only 10 minutes or so to explain the distinction before you have to move on to the rest of the reading. What should I tell introductory philosophy students about the analytic-synthetic distinction? What should I say about why philosophers think this distinction is so important?


From Edgar Valdez:

I think it is important to remember that even though the initial discussion of the analytic-synthetic distinction can be dealt with in a few minutes, it is a lesson that requires reinforcement throughout the semester.  Invariably teaching the analytic-synthetic distinction first arises in my introductory courses around the same time as the introduction of the synthetic a priori, even if not the same day. This timing is usually helpful as the introductory remarks I have on the distinction are best situated in conjunction with some remarks on the a priori – a posteriori distinction. I emphasize that these are two different distinctions we can make regarding truth judgments and contrasting them often helps draw out the salient features. While the a priori – a posteriori distinction concerns how we are in a position to make certain judgments, the analytic-synthetic distinction is about the information contained in the judgment. Put another way, the first describes how we can say something, while the second describes the kind of thing we can say. I mention at this point that this kind of distinction sets up a battle that we will later consider between method and content as a way of emphasizing the distinction.

Before considering some examples, I go over two (for our purposes equivalent) ways of describing an analytic judgment: a judgment that is true by definition and a judgment whose predicate is contained within the subject. This language usually leads me to open the floor to any self-proclaimed grammar gurus to explain the difference between a subject and a predicate.  I resist the temptation to use mathematical judgments as examples (since they are the ones Kant will only complicate later when turn to the synthetic a priori) and stick to genus-species examples for analytic judgments. Among others, I regularly use “the cat is a mammal” and “the bachelor is a male.” This is the kind of information that is contained within the subject. In the sense of being true by definition, our very expression of what the subject is calls for expressing the predicate in question. A cat is a mammal that… A bachelor is a male that… Without getting into concept intension and extension, I explain the idea of a predicate being contained within a subject as meaning that the predicate is one of the concepts we would list if we were thinking of all the concepts we would need to establish the concept of the subject.

When it comes to synthetic judgments, I find adding visual predicates to the analytic examples to be the least ambiguous step. The cat is black. The bachelor is tall (and depending on the class, a reference to the television show might get some laughter).  Blackness and tallness are not predicates we would ever arrive at simply by considering our concepts of cat and bachelor. And of course, we can think of lots of cats that are not black, though they are no less cats. And likewise lots of short bachelors. Synthetic judgments add to the concept of the subject. At this point, I will do some quick etymology on the words analysis and synthesis to emphasize that in one case, we are breaking down the concept of the subject and in another we are putting something with the concept of the subject.

To talk about the importance of the distinction, I usually—with the help of Hume—explain that synthetic judgments often come at the cost of experience and that if we hope to maintain an a priori method, we are usually confined to analytic judgments. The examples I have chosen then set up a nice contrast between two kinds of possible explanations of the world. How different are the worldviews of those that think that philosophy should aspire to a posteriori synthetic judgments and those that think we should stick to a priori analytic judgments? Since introductory philosophy students tend to have empiricist tendencies, I jokingly ask them if they would want to sign up for the course where we discuss that all cats are mammals and all bachelors are male. Though, of course, that’s what we just did.

From Gillian Russell:

I may actually be the unique worst person in the world to answer this question, as I’ve reached a point where I need 5 hours to talk about Quine on the topic.  So I estimate that you’d want to reserve … let’s see about … 30 hours for the distinction more generally…

I think a common problem that intro students have with analyticity is seeing how it is different from necessity and a priority.  I suspect one reason for this is that the standard examples of such claims tend to be similar, and as a result adequately explaining the ideas requires more than just those examples.  They also need:  i) a short gloss for each term, ii) some examples of philosophers with motivated reasons for thinking they come apart or go together (e.g. positivists and Kant respectively), and iii) examples of views where analyticity is expected to do some heavy lifting (e.g. a priori knowledge or the linguistic doctrine of necessary truth).

With intro students I’d be happy to use the glosses below and suggest that they learn them off by heart.  I’d list them on a board off to the side (building up the list and the glosses as I went along) or on a class handout.

  • analytic — true in virtue of meaning alone
  • synthetic — true in virtue of both meaning and the way the world is
  • a priori — justification is independent of experience
  • a posteriori — justification dependent on experience
  • necessary — could not have been otherwise
  • contingent — could have been otherwise

Here are two things you can do in your ten minutes:

  1. Telling the Two-Factor Story.

You can introduce the analytic/synthetic distinction by telling the “two-factor” story, which goes a bit like this:

Normally, sentences are true in part because of what they mean, and in part because of the way the world is.  The sentence “snow is white” is true in part because snow is a certain colour (if it were black the sentence would be false) and in part because of what the sentence means (if “snow is white” meant what “2+2=5” means then the sentence would be false).  Normal sentences like that are called synthetic.

Analytic sentences, by contrast, are supposed to be special:  they are true in virtue of their meaning alone, and so no matter what the world is like they will be true.

Whether or not any such sentences exist is controversial, but a frequently discussed example is “all bachelors are unmarried”.    The idea is that the meaning of the words in this sentence is sufficient to guarantee its truth.  So a good way to remember what “analytic” means is to memorise the gloss “true in virtue of meaning.”

  1. Analyticity and A priori Knowledge.

The two-factor story is one way to introduce the bare distinction, but I also want to help students see why the distinction is important and how it differs from related distinctions.

So next I would introduce the distinction between a priori and a posteriori knowledge, giving putative examples of each, and being careful to use different examples from the ones used for analyticity (maybe “sugar dissolves in water” for the a posteriori and “2+2=4” for the a priori).  I would emphasise that the status of these examples is up for review later if we decide we’ve made a mistake (perhaps nothing is a priori?)

I’d then raise the question of how a priori knowledge is possible. We have some understanding of the mechanism that allows us to know that sugar dissolves in water: visual perception.  But how do we know things about numbers?

Analyticity might help us answer that question.   Why are we justified in thinking that “all bachelors are unmarried” is true?  It is not as if we went out and interviewed all the bachelors and asked them whether they were unmarried.  We seem to be able to know that it is true without perceiving any particular bachelors.  Perhaps that is because we know what “bachelor” means, and this tells that that in order to count as a bachelor, you have to be unmarried.  Our knowledge of the meaning of the sentence seems sufficient for knowledge of its truth.

Now,  if “2+2=4” and other a priori truths were like this, then we might be able to know their truth by understanding the symbols and words they contain:  just as you can know that all bachelors are unmarried without going out and surveying bachelors, so perhaps you can know that 2+2=4 without being able to perceive abstract objects like the number 4.   Analyticity might provide an epistemology for mathematics that explains how it can be a priori.

Is analyticity the only way we can get a priori knowledge? Some philosophers, such as the Logical Positivists, defended an affirmative answer to this question. (I’d encourage the enthusiastic students to take a look at Ayer’s Language, Truth and Logic, since this book is short and highly accessible.)

BUT not everyone agrees that all a priori knowledge is analytic.  Kant, for example, thinks that there is non-analytic a priori knowledge.   I’d give some of Kant’s examples of the synthetic a priori (e.g. every effect has a cause, 5+7=12, etc.) and quote the part of the 1st Critique where he denies that arithmetical claims are analytic.

Kant still thinks that arithmetic is a priori, so he is subscribing to the existence of synthetic a priori knowledge—a priori knowledge that is not analytic.  The question of exactly how  there could be synthetic a priori knowledge is a difficult one. But it’s a central question of the Critique of Pure Reason and leads Kant to some very interesting views about reality.

If you have time, you could give the class a list of 10 sentences and give them 5 minutes to divide them into analytic and synthetic. (e.g. “5+7=12,” “all green things are extended”.)  Then ask for votes on the answers and talk about the difficult or interesting cases.

Ten minutes are surely up even though there’s so much more to say! But I think this is a reasonable way to start.

Additional Resources:

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  1. If you are teaching intro to modern, or if your students can be assumed to have had intro to modern, it can be helpful to introduce the distinction historically through Leibniz and Kant. Leibniz wants to know, what relation needs to obtain between subject and predicate to make the judgment true and, as it turns out, the only answer he can come up with is concept containment. (At one point in the Arnauld correspondence he even says, “or else I don’t know what truth is”!) Kant thinks, clearly there are examples of true statements that don’t exhibit concept containment. The ones that exhibit concept containment are the analytic ones of course, but what relation might obtain between a subject concept and predicate concept to make a judgment true where there is NOT concept containment (i.e., a synthetic judgment)? Kant’s answer is, the subject concept and predicate concept must be joined in an object. (This, of course, sets up Kant’s theory of synthetic a priori judgments: the object in which the two concepts are joined must be somehow provided by the understanding itself, as in a geometric construction.)

    This may just be because I’m an early modern specialist, but I find this story about the context in which the distinction arose helpful for understanding what it is and what it does. Of course, not every class is an appropriate forum for covering Leibniz and Kant on truth!


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