Genotypes determine phenotypes in contexts. Therefore, genotypes are functions, from contexts to phenotypes. So if you want to study genotypes, adopt the obvious research strategy: describe the possible phenotypes, and the potentially relevant contextual factors; then try to describe each genotype as a function G such that for each coherent cluster c of contextual factors, some phenotype P is such that G(c) = P. For practical purposes, you may want to decompose G, say as follows: G1(c1) = G2, and G2(c2) = P; where c1 and c2 are choices, perhaps overlapping, from c.
Something went wrong there. If you find yourself concluding that genotypes are functions—to be characterized in terms of phenotypes and contexts—and that embryology is a form of applied mathematics, get your assumptions checked. But when reading the first paragraph, you probably felt wool being pulled over your eyes somewhere around ‘Therefore’. Hold onto that suspicion.
Meanings determine extensions in contexts. Therefore, meanings are functions, from contexts to extensions. Human Languages determine meanings given articulations in contexts. So each Human Language is a function from articulations and contexts to meanings, and hence a function from articulations and contexts to extensions. So if you want to study Human Languages, adopt the obvious research strategy: describe the possible articulations, extensions, and potentially relevant contextual factors; then try to describe each Human Language as a function H defined for a certain class of articulations such that for each articulation a in the class, and each coherent cluster c of contextual factors, there is an extension E such that H(a, c) = E. For practical purposes, you may want to decompose H, perhaps as follows: H1(a, c1) = H2; H2(c2) = E. Then you can say that H1 is the “syntactic component,” which maps articulations and certain aspects of context onto the “semantic component” H2, which maps certain aspects of context onto extensions. {Or maybe H2 can take certain aspects of a as a second input: H1(a, c1) = H2, and H2(a, c2) = E.} Warning! In specifying H1 and H2, you may have to invoke notions of syntactic structure; and you may find that the notions needed to specify H1 are remarkably like those needed to specify H2, as if Human Languages are procedures that generate structured expressions whose meanings are correspondingly structured. But don’t get distracted. Meanings are functions—sets of context-extension pairs—that can be represented in structure-dependent ways.
By way of saying why I think this line of thought goes wrong at the first step, and then compounds the error, let me go back to the parody of reasoning in the first paragraph. Idealizing a lot, one might say that genotypes determine phenotypes in contexts. But then ‘context’ covers a lot. Think of all that initial transcription via flavors of RNA, protein folding, replication and cytodifferentiation, the exquisitely detailed effects of hormones, timing, and genetic “switches.” Then there are more intuitively “environmental” factors, like the availability of nutrients and oxygen. By the time things as complicated as Lepidoptera larvae have emerged, factors like ambient temperature may also have had an effect on phenotypic traits like future wing color. Traits that emerge very late and “outside the shell”—e.g., secondary sexual characteristics or acquisition of a Human Language—involve further complexities. To wax Rumsfeldian, there are enough known unknowns to keep armies of scientists occupied for some time. The unknown unknowns may include deeper sources of the chasm between animals and the “instructions” specified by animal DNA. (Plants, other eukaryotes, and bacteria can speak for themselves.)
Anyone who cooks can appreciate the basic point. There may be a thin and boring sense in which cake recipes determine cakes in suitable contexts. But even given a system that gets a recipe “executed,” one way or another, a lot depends on ancillary factors: quality of ingredients; altitude and temperature; yada, yada; and crucially, how various indeterminacies in the recipe are resolved by the executive chef, who may manifest as a committee.
No recipe fit for print can be fully explicit about everything one needs to do make a viable German Chocolate cake, much less a good one. Consider a possible dialog.
Cook’s Illustrated: stir well.
Ill-prepared Cook: for how long, with what kind of implement, with what force?
Cook’s Illustrated: heat oven to 350.
Ill-prepared Cook: oven?
Luckily for us, biology knows how to stir, find the oven, and get animals to come out. (Even better, some animals end up knowing how to make cakes.) But it’s not helpful to describe cake recipes as functions from contexts to cakes, not even if one intends ‘function’ intensionally. Recipes are neither procedures that map contexts to products nor sets of context-product pairs. Given a cake, there may be a thin and boring sense in which some very complex procedure that was “grounded” in a recipe led to the cake. But describing everything except the recipe as the “context” would be a joke, and perhaps in some contexts a good one, if not for the danger of the joke being taken seriously. Likewise, though with far more of a vengeance, for any thought that genotypes are functions from contexts to phenotypes. So why is it so tempting to say that meanings determine extensions in contexts, and then infer that meanings are functions that map contexts to extensions?
Here’s a suggestion. While expressions of a Human Language don’t have meanings that determine extensions, or even functions from contexts to extensions, it sometimes does little harm to adopt the idealization that they do have such meanings. And for certain purposes, this idealization is useful, in ways illustrated by good textbooks. But if Human Languages did have meanings that determine functions from contexts to extensions, that would call for explanation. And if we had such an explanandum to explain, we might well explore the reductive strategy of identifying meanings with (functions from contexts to) extensions—or perhaps functions from possible worlds to (functions from contexts to) extensions, or from contexts to functions from possible worlds to extensions, or maybe from contexts to functions from worlds (possible or not) to extensions at those worlds. Moreover, smart people have explored the reductive strategy in various ways; and in the course of exploration, they have discovered many things and generated many debates. Many of these discoveries and debates have been interesting. And in daily work, driven by the discoveries and debates, it’s easy to forget that the initial idealization—that meanings determine functions from contexts to extension—isn’t remotely plausible, unless ‘context’ covers so much that one may as well say that cake recipes determine cakes in contexts.
That leaves the question of what meanings are. But maybe they are instructions for how to make concepts, which may or may not have extensions. One can say this without characterizing meanings in terms of concepts made (cp. cake-recipes and cakes made). One can also say that Human Languages are procedures that generate expressions, which link instructions for how to articulate to instructions for how make concepts, without characterizing the procedures in terms of generated expressions. One might even say that Universal Grammar (UG) is a biologically implemented “metaprocedure” that children use to acquire Human Languages, given suitable contexts, without characterizing UG in terms of contexts and acquirable Human Languages. What something can be used to do depends on what it is, not the other way around. That's a very old point that should not be forgot.
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