What makes some language exact as opposed to its more fuzzy counterparts? Clocks, money, and natural law have a seemingly magical precision that differs from the hand-waving of poetry and prose and the (supposedly) well-intentioned fumbling of the “soft sciences”, but what does that mean? The precision of the former items has created a persistent illusion that one can simply treat the object at hand as something that already passively exists a-priori with language merely pointing out such a thing with varying degrees of precision, a semantics that corresponds to syntax. “Physics envy” does not even begin to describe the problem: the heart of the issue is that by looking at the exactness of physics as a role model, we are looking at its mature form and ignoring what it took to get there, making it look as if it were a simple question of matching fine-grained vocabularies with fine-grained concepts instead of understanding logical and empirical rigor as a process of developing increasingly fine-grained interactions that converge on stable patterns and ultimately identities.
Devoid of such a process, it would be impossible for any linguistic statement to make sense insofar that it would have no relationship to anything else that would give it any meaning at all. A line of code only does something if an interpreter or compiler can run it or if some programmer or mathematician can utilize it by rewriting it in another language or deriving some kind of idea from it. Similarly, any kind of speech act is meaningful insofar as it plays a role in what Wittgenstein called a “language game”--if you say “slab!” whenever you’re commanding someone to bring you a slab, it doesn’t necessarily matter what the word “slab” as a noun means. That utterances “mean” anything in any other sense is, to put it one way, optional.
There is nonetheless a reason one seems to yell “Slab!” and not “Plank!” when requesting a slab, and that’s because even though the latter is possible, setting up these new arbitrary rules every time would be costly and confusing. Insofar that structure exists, different language games can be made more similar and therefore easier to adopt and switch between. Structure enables things to have degrees of similarity insofar that one can now deconstruct one thing and use this deconstruction to derive something else with varying degrees of difficulty (the less difficult, the more similar.) But I digress.
These “games” constitute what Kant calls the synthetic a-priori, the field of intuition in which all abstractions are embedded. It is synthetic because it concerns the whole that defines the parts rather than the parts of any piecemeal basis; a part being what it is because of its function. You might call a removed heart a heart, but no dictionary definition of the heart is based on its material composition or its shape and we only bother to call this artifact a heart because we are looking at what amounts to a metonym for some greater significance it no longer has.
Being a matter of function, the synthetic a-priori cannot be something passively given: things have functionality because something is doing something with them; a function is a role within an enactment, and therefore the synthetic a-priori is what Deleuze calls an active synthesis; a whole that is constituted not out of thin air but as a product of continually fluctuating and evolving pragmatic imperatives. And so just like a heart must pump blood to meaningfully be a heart, any scientific statement must itself ultimately be traced back to a materially grounded question.
How is this the case? For starters, the theory of relativity addresses a chronological form of time, one in which time is evenly divided into linear units. This itself is not simply given: prior to civilization, any sense of time was an attunement, whether by animals or humans, to various solar, lunar, and seasonal cycles. Without any kind of cumulative record keeping or mechanical instruments, the idea of time either being unidirectional or precise simply doesn’t exist as the affordances are not there.
Without repeating the entirety of my chapter about the topology of time, it suffices to say that one could only begin to consider the subtle interactions between space, time, and motion upon having sufficiently precise mechanical clocks and an unequivocal system of time zones that dictated a single “true” time for any one region. Only then could one encounter the problem that eventually occurred: subtle differences and distortions in spacetime made these clocks inevitably fall out of sync with one another, and the theory of relativity addressed why this was happening. But without the synthetic a-priori embodied in heavily standardized mechanical clocks, the very numbers addressed by Einstein’s equations would be without meaning.
This is not in any way a denial of scientific knowledge nor is it in any way a suggestion that language is “arbitrary” or concepts “imaginary”, but simply saying that an abstraction without a process in which it’s embedded is as insignificant as a hammer without a hand. The “exactness” of any language is ultimately the product of a co-evolutionary process of mutual refinement: new affordances open up new games to play while language poses new questions waiting to be answered.
This compounding symbiosis is an act of bootstrapping by which definite concepts can be used to ask questions that extend to the territory of the indefinite. But insofar as the domain is not fully defined, it is impossible here for a linguistic act to simply point to or delimit anything, instead it marks an open neighborhood around that which is already known and as such becomes an interface between the existing language game and that which comes from outside.
Utterances, whether by mouth or otherwise, are then not simply descriptive but aspirational, acting as signposts that hint at and loosely circumscribe potential affordances which must then be terraformed into existence. The “exactness” of money is an example par excellence of such a process: money is only as exact as it is because of a recursive process by which any discrepancy in prices such that one can make money for buying something at a lower price and then ultimately selling it for a higher one without relying on any contingent change in price, that opportunity will be taken; but in order for that opportunity to occur, money must be sufficiently “precise” in order to allow one to find such a reliable discrepancy (for a more detailed exposition, see my polemic against utility theory here.) The opportunity for arbitrage therefore drives the increasingly nuanced exchange of goods while this newfound nimbleness enables new opportunities for arbitrage, inevitably converging on a final state in which the dollar (in some cases, but not all) looks magically exact.
Language is therefore not a passive pointer but an active agent that facilitates the material construction of new concepts by engendering a reflexivity shared by map and territory alike, one that either diverges into entirely new ideas or converges into asymptotically increasing calibration. This is not, however, a stance on the fabled Sapir-Whorf hypothesis: whether language shapes or reflects thought is the wrong question insofar that you cannot separate language from activity or simply isolate the verbal and symbolic components of language and expect to see the whole picture any more than you could see how an arm functions after you cut it off of somebody’s body.
Or perhaps more fittingly, language is a map, and a map only means something based on how it facilitates an exchange between an traveler and a region. The map need not tell you “exactly” what’s there, or even what’s “there” at all; it need only tell you what you can do. A map in this sense may be loosely said to guide action, but more fundamentally it marks affordances. It does not necessarily identify an affordance that exists as some clearly verifiable and distinguishable object, but rather in the manner of a signpost, narratively foreshadowing possibilities that may or may not be realized by reshaping the land in certain ways.
It is in this uncertainty where I can clearly define the difference between syntax, pragmatics, and semantics. Whereas pragmatics refers to the unadulterated function of language with regards to action and syntax refers to the structure of language, semantics appears only as what looks like a lack of correspondence. That is, insofar that a question can be accounted for by a mechanical manipulation of symbols, by deconstructing the formalism into an equivalent anatomy (for programmers, imagine deconstructing a list xs into x:xs, that is, a single list into a head concatenated to the remaining list), is a matter of syntactic entailment. It’s only when there is something opaque to the syntax that one must ask the exogenous question “what could this mean?” In computer science, this is the difference between the internal logic of the code versus how it runs on the computer; the latter is dependent on context that is contingent on things beyond the logic of the code.
Language beyond a certain threshold of complexity therefore always exceeds itself, as Kurt Godel discovered in the realm of math a century ago. Insofar that a question cannot be answered in terms of its own syntax, one must fill the gap by expanding the language game, but this in turn is not the insertion of arbitrary symbols; there may yet be different choices of how to make them relate to the other symbols and those in turn will quite possibly make a difference in terms of how the language and the territory further co-evolve. Figuring out how to fill in those gaps? That's just semantics.