a guest post by Carter Gillies
April 29 is the anniversary of Wittgenstein’s death. Somehow that seems important to me, in the wake of having just been told I’ve got cancer. Wittgenstein died from prostate cancer, but he worked on his ideas until the last days of his life. I will take that as inspiration. In the time that is left me there is something I still have to do. This one theme that occupies my thoughts and is seemingly given to me alone to hash out. I apologize if I repeat myself…..
The Role of Measures
You hold in your hand a ruler, or a yardstick, and approach a length of wood. Placing the measure alongside the board you read off “9 3/4 inches”. You approach something else and take its measurement. And so on and so forth. This, among other things, is how we learn to measure. This is what we call ‘measuring’.
So the picture we have of measuring is often simply putting ourselves in the position to take a reading, and it seems everything around us is equally subject to finding its measurement. But say one of the objects you make the comparison with is another ruler or yardstick. Can we measure the length of a yardstick with a ruler? Is that called ‘measuring’?
The problem is that measuring has two parts, and it almost seems as though we were blind to one of them. We obsess with getting our results, but somehow it often appears that we lose touch with what it is to measure and what does the measuring. The thing to be measured is an empirical question, results to be determined, and yet the measure itself stands outside that. The role of measures, rather, is something else. And not respecting the measure for a measure at least sometimes has unfortunate consequences.
For instance, the myth of Procrustes tells the tale of travelers visiting Procrustes’ inn and being guaranteed that the bed for overnight stays would fit them. Normally we measure the fit of the bed by how well we, the person, can comfortably lie in it. The person measures the bed. But Procrustes had another idea. His bed was one size, and it was used to measure the guests instead. The myth dramatizes this upending of normal practice by having Procrustes stretching out too short travelers and lopping off the excess of too tall ones. A grisly solution!
In other words, it matters what gets used as the measure.
Sometimes it makes sense to measure measures. We have needs that are external to particular measures and it makes sense to subject them to some relevant comparison. In today’s world it seems almost everything can be measured in some way. In fact, we are typically so overwhelmed with consequences that things often only seem justified if they can be measured for the right value. Does the Philosophy department deserve more funding or less? Are the arts worth supporting with tax dollars? The question is, is our rush to measure necessarily the right way to look at a thing, or are we continuously and blithely jumping into Procrustes’ bed, mistaking the measure for the thing measured.
In getting my head around this issue I am focused on measures specifically, but Wittgenstein noticed this difference in perhaps more general terms. He talked a great bit about ‘hinges’ in On Certainty, but in general his discussion there seems to be an attempt to show the difference between what things operate empirically for us, and those which do not. His beef with British philosopher G. E. Moore that sets off the notes compiled as the book is specifically an objection that the things Moore claims to ‘know’ are in fact no such thing. They are not the sorts of things we subject to doubt, and we do not test them for proof. They are things we have set aside from the stream of empirical questioning.
Nor are they things we simply see, as if reading them straight off from the world. Rather, they are placed in our lives in positions about which the rest flows. Just as hinges hold fast so that the door may rotate about, such things operate as the still points removed from the trials of empirical indecision. And they do so not from the necessity of their own nature as much as that they are placed there through the practices and history of our patterns of life.
In other words, we often choose how to measure the world rather than the world necessarily dictating its own terms. And it has to be said that the measures are not one thing either. If measuring is a practice it has practical purposes. Or, it is simply what we do. There are different uses and a variety of ways they get applied in our lives, and from the outside some of them may seem to not make much sense.
I remember being struck by Wittgenstein’s observation in the early part of Remarks on the Foundations of Mathematics:
How should we get into conflict with truth, if our foot rules were made of very soft rubber instead of wood and steel? – “Well, we shouldn’t get to know the correct measurement of the table.” – You mean: we should not get, or could not be sure of getting, that measurement which we get with our rigid rulers. So if you had measured the table with the elastic rulers and said it measured five feet by our usual way of measuring, you would be wrong; but if you say that it measured five feet by your way of measuring, that is correct. – “But surely that isn’t measuring at all!” – It is similar to our measuring and capable, in certain circumstances, of fulfilling ‘practical purposes’. (A shopkeeper might use it to treat different customers differently.) RFM I §5b
In other words, as Wittgenstein might entreat us, we measure as part of the lives we lead, because of the specific forms of life we are involved in. It is THAT which we ought to more properly acknowledge.
What is the difference between loving someone because of their endearing qualities and appreciating a person’s qualities because we love them? What thing measures what? How often do we find that qualities which would be a turn off in others are especially appealing in those we love? We simply see them differently.
What is the difference between holding that a box is strong and therefor will contain these things, and determining that a box is strong because it can contain these things? The boundary of what we take as empirical seems to depend on the difference between what we accept and what we feel needs testing, proof, or justification. We go throughout our daily life not subjecting every possible thing to every possible doubt. Some things simply hold fast and are not questioned unless exceptional circumstances impress that need on us.
You walk into a room and there are several people sitting and standing around a table looking at playing cards. There are two observations. That something is a game, and the kind of game it is. That people are playing is not doubted, but it is a mystery whether there are two players or four, for instance, what rules are being enforced, the objectives, and what winning moves, if any, there are.
That something is being played as a game is often beyond doubt, that it IS a game, but the specifics can still be determined. We don’t test that it is a game. That stands before us as accepted. That is the necessary starting point. If we doubted that there might not be much to hold onto. And yet the nature of the game is in doubt. Our empirical investigations only begin after we have framed the question properly, anchoring our questions in what we already accept.
But there are grey areas. You walk into a contemporary gallery and see a pile of clothes on the floor. Did someone leave their laundry out by mistake? Is it Art? Or simply bad art? It might even be ‘good’ art…..
The point is that when we learn what things are, what roles they have in our lives, some aspects are left in question and others are removed from doubts and from testing, and indeed from justifications too.
I just poked my nose back into Remarks on the Foundations of Mathematics, and one consistent theme is that calculations, like 12 x 12, are not empirical. That is, they are not experiments we simply determine values for. So many things can have the appearance of being empirical, and this impresses itself on us. But that impression may have more to do with our obsession with ‘results’, and the unfortunate lack of awareness we seem to have for what is other than empirical…… Consider,
If 2 and 2 apples add up to only 3 apples, i.e. if there are 3 apples there after I have put down two and again two, I don’t say: “So after all 2 +2 are not always 4”; but “Somehow one must have gone”. RFM I§157
Severin Schroeder explains this as well as I ever could in his essay “Mathematics and Forms of Life” in the Nordic Wittgenstein Review 2015:
when on the basis of my experience with nuts and apples etc. I put forward the sum ‘2 + 2 = 4’ it is not presented as an empirical generalization, but as a rule or norm of representation, which means that it is made immune from empirical falsification. We will insist on it even where experience seems to contradict it: in that case we declare our experience as inaccurate. We say that something else must have happened that we didn’t see. However, even though no conflicting experience can falsify a mathematical proposition, repeated conflicting experiences can undermine its usefulness. If putting together pairs of apples frequently resulted in more or fewer than 4 apples, we would have to say that our arithmetic was not applicable to apples; as, in fact, it is not applicable to drops of water (one and one make one) or measures of different liquids (one quart of alcohol and one quart of water yield only 1.8 quarts of vodka). https://www.nordicwittgensteinreview.com/article/view/3357
Schroeder’s example of the drops of water reminds me of what I have been thinking about heap paradoxes. For instance, a $20 bill cut in quarters is not 4 parts of $5 each. We do not treat money as divisible in that way. There is a difference between treating something as subject to experiment, testing, manipulation, etc., and treating it as a measure in itself. We can count the money, yes, but each bill is an indivisible measure of value in its own right.
And similarly with heaps and bald people. Those are determinations we make as easily as we identify something as a game (my example above). We don’t need to prove that a person is bald, merely see them as such. A heap is a heap without the need for testing. Call it a ‘norm of representation’ rather than an empirical question determined by counting grains or hairs. The two roles are, in this case, distinct.
In our daily life we remove certain things from the uncertainties. We could change the way we behaved and put ‘bald’ and ‘heap’ back among the testable things. That is of course possible, but this difference is only ever an example of the contingency of cultural practices. What WE do with certain things in our daily life.
We could, for instance, also officially accept parts of $ bills as legitimate currency (In Medieval England cut pennies [farthings] were accepted practice to make change).
Life could play out in those different ways. It could be other than it is in important ways. Which is why Wittgenstein so often resorted to testing our assumptions by imagining a different form of life. The still points we assume could get overturned and some other variable things stiffen and form new references.
From On Certainty:
94. But I did not get my picture of the world by satisfying myself of its correctness; nor do I have it because I am satisfied of its correctness. No: it is the inherited background against which I distinguish between true and false.
95. The propositions describing this world-picture might be part of a kind of mythology. And their role is like that of rules of a game; and the game can be learned purely practically, without learning any explicit rules.
96. It might be imagined that some propositions, of the form of empirical propositions, were hardened and functioned as channels for such empirical propositions as were not hardened but fluid; and that this relation altered with time, in that fluid propositions hardened, and hard ones became fluid.
97. The mythology may change back into a state of flux, the river-bed of thoughts may shift. But I distinguish between the movement of the waters on the river-bed and the shift of the bed itself; though there is not a sharp division of the one from the other.
98. But if someone were to say “So logic too is an empirical science” he would be wrong. Yet this is right: the same proposition may get treated at one time as something to test by experience, at another as a rule of testing.
99. And the bank of that river consists partly of hard rock, subject to no alteration or only to an imperceptible one, partly of sand, which now in one place now in another gets washed away, or deposited.
Last observation. Another way of looking at these differences is that some can be identified as ‘deliberative’ in nature while others are more ‘automatic’. An interesting parallel can be drawn to the work of Daniel Kahneman, who perhaps unsurprisingly studied Wittgenstein in grad school. In his book Thinking, Fast and Slow, Kahneman distinguishes between two types of mental approach to things, and these seem to roughly (not precisely) illuminate part of that difference Wittgenstein was intent on showing us. Kahneman identifies them as follows:
System 1: Fast, automatic, frequent, emotional, stereotypic, unconscious. Examples (in order of complexity) of things system 1 can do:
- see that an object is at a greater distance than another
- localize the source of a specific sound
- complete the phrase “war and …”
- display disgust when seeing a gruesome image
- solve 2+2=?
- read a text on a billboard
- drive a car on an empty road
- come up with a good chess move (if you’re a chess master)
- understand simple sentences
- connect the description ‘quiet and structured person with an eye for details’ to a specific job
System 2: Slow, effortful, infrequent, logical, calculating, conscious. Examples of things system 2 can do:
- brace yourself before the start of a sprint
- point your attention towards the clowns at the circus
- point your attention towards someone at a loud party
- look out for the woman with the grey hair
- dig into your memory to recognize a sound
- sustain a higher than normal walking rate
- determine the appropriateness of a behavior in a social setting
- count the number of A’s in a certain text
- give someone your phone number
- park into a tight parking space
- determine the price/quality ratio of two washing machines
- determine the validity of a complex logical reasoning
- solve 17 x 14
Kahneman is, of course, mostly interested in how we get into trouble by treating slow deliberative issues with fast thinking, and Wittgenstein was simply pointing out the difference in roles, regardless of speed and duration, i.e. not an interest in mental states or mental processes (his frequent example of 12 x 12 being non-empirical, that is, not an experiment, points to an important difference in their motives). But it is interesting to consider the flip-side of Kahneman’s concern, that we can mistakenly be deliberative when an issue is more properly non-empirical. That was G. E. Moore’s problem. It is our pernicious temptation to jump into Procrustes’ bed. And it seems to plague us throughout our lives, and without our understanding what the issue actually is…..
Food for thought, I hope.