A Sophisticated Philosophy of Functions

We examine a much neglected work on the philosophy of artifacts and their functions. The author, Ruth Krauss, presents a bold and unapologetic view on artifactual functions. The presentation is concise, eloquent even, but is lacking the detailed arguments one expects from modern philosophical texts. Nonetheless, we believe that the view presented here should be taken as a foundation for further inquiry, a common point from which all other analyses are judged according to how they diverge from this origin.

We have reproduced1 the text below ("A Hole is to Dig", Ruth Krauss, 1952, with illustrations by Maurice Sendak, as reprinted in The World Treasury of Children's Literature). Before turning to the text, let us enumerate the central theses, which are more or less implicit in the treatment.

  1. An inclusive view of artifacts. One of the primary difficulties in the philosophy of artifacts is delineating the subject matter. What ought to count as an artifact? For Krauss, the answer is fairly clear. All those things one encounters in daily life are artifacts, whether man-made or natural. A face is no less artifactual than obvious human constructions. Indeed, Krauss's examples tend to the biological more than the artificial.

    What is one to make of this? First, that the distinction between biological and artifactual function is illusory, irrelevant for her purposes here. The biological organ, human invention and social construction all possess the same relation to their function, regardless of how that function has arisen. This relation is our next item.

  2. An artifact is defined by its function. An artifact, whether natural, social or artificial, is defined by its function. Krauss could not be clearer on this point, which is stressed in the subtitle: "A First Book of First Definitions".

    How something is used, what it is good for, is sufficient to explain what it is. On this view, ontology is teleology. If one explains what the thing is for, then there is nothing more to be said about what it is2. This view is particularly bold, given the final thesis.

  3. An artifact may have several unrelated proper functions. Artifacts are defined by their functions, but a single artifact may have several unrelated functions3. A hole is to dig, but it is also to sit in. These functions are evidently proper, since accidental functions are simply insufficient for the ontological role we see here. Thus, proper functions are not unique, even though they are defining.

    Krauss is unfortunately too brief on this point. Is something which is for digging a hole, or must it also be suitable for sitting in? Are artifacts defined by their conjoined functions or is it the disjunction? What about hypothetical functions ("Maybe you could hide things in a hole.")? Functions with contradictory ends ("A mountain is to go to the top. A mountain is to go to the bottom."4)? We must tread carefully here. Krauss is subtler than Nietzsche.

Clearly, the three main theses are ripe for further study. However, Krauss's exposition is as valuable in the narrow asides as in broad themes.

"Cats are so you can have kittens." No other scholar has expressed the evolutionary origin of biological function so concisely and clearly, omitting the tedious detail of second-order this and forward-looking that. But in so doing, she has playfully introduced a hint of infinity. "Cats are so you can have kittens" is a definition, but of what kind? Yes! It is a fixed point definition, definition by corecursion5. Our philosopher of artifacts was also a logician.

Ever playful, the author teases us with another definition: "A face is so you can make faces." Structurally similar to the preceding, just as clearly corecursive in nature and evidently about a biological artifact, but what to make of the analogy? Ought one view the function of faces as a biological function, arising through evolutionary process? Or is the similarity superficial and misleading? Again, Krauss tantalizes us with such questions, but the reader is left hungry for more.

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A Hole Is To Dig (1)
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(1) Ruth Krauss died in 1993. Thanks to Sonny Bono, Mickey Mouse and a remarkably easily purchased Congress, this means that the copyright on this book does not expire until the year 2063, by which time we will all have rocket cars and robot slaves. Or be slaves of robots. Whichever. Anyway, copyright will surely be retroactively extended long before that.

The point is that I may be exceeding my fair use rights by publishing images of Krauss's work on the web. Well, maybe that's not the point. Maybe the point is that retroactively extending copyright terms (in order to encourage deceased authors to retroactively write) is stupid and pandering to extremely profitable corporations and wealthy artists, some of whom made their profits on public domain works (*koff* Disney *koff* Bob Dylan *hack*). See this article for details.

But I digress. And rant. And slobber all over myself. Never mind.

And anyway, who will notice this page?

(2) On this point, the author teases us however. She writes "Toes are to wiggle. Ears are to wiggle." Thus, toes and ears are evidently indistinguishable. More on this in the subsequent footnote, but in defense of the toe/ear problem, let us point out that it's not as silly as Frege's Julius Caesar problem. Is Caesar a number? Come on.

Relatedly, we see the role of malfunction arise here. My ears do not wiggle. Thus, they do not fulfill their primary purpose. They are broken ears. Or broken toes. Whatever.

(3) Here we see an out regarding the toe/ear problem. Toes and ears may have other functions, not listed in this first book of definitions. If so, they may be distinguished. If not, then toes and ears are lately discovered synonyms and we must resign ourselves to wearing socks on our ears and supporting eyeglasses with our toes. Clearly, the question of whether toes and ears have distinct proper functions requires further consideration.

(4) Every line of Krauss's monograph is pregnant with implications. Here, we see a practical consequence for possible world semantics. If one models functions in a form of dynamic logic (say, PDL), then the fact that a single artifact may be used to attain mutually exclusive ends is inconsistent with Kripke semantics. Although she does not say as much, we view Krauss's mountain example (and also "A door is to open. A door is to shut.") as an implicit advocacy of monotone neighborhood semantics instead of Kripke semantics and thus a rejection of Kripke's axiom K.

(5) Here, we may draw a sharp contrast between the evolutionist and the creationist. For the creationist, there was a first cat with the purpose of having kittens, but which did not fulfill this purpose for a previous cat. In other words, the definition has a base case -- it is recursive, not corecursive.

For the evolutionist, the definition is subtly different than standard corecursive definitions, since certain not-quite-cats were (presumably) for having kittens. The first cat fulfilled this purpose for a previous not-quite-cat, and the first not-quite-cat fulfilled a similar purpose for some previous not-quite-a-not-quite-cat and so on. Even the first organism could have fulfilled the function of some previous building blocks and so on all the way to the big bang (and beyond, if our universe is oscillating).

Thus, the debate between evolution and creation is essentially nothing more than an argument over fixed point constructions. We see, then, that the creationist's God is not merely the prime mover. He is the base case for the universal construction.

Jesse F. Hughes
Last modified: Tue Feb 8 13:35:08 CET 2005