“Fruits are tasty.” Do you believe that, or not?
Well… it’s pretty clearly neither true nor false, so maybe it’s meaningless, as logical positivism recommended? It does seem to have some tenuous meaning… The problem is not so much that it’s meaningless as that it’s extremely indefinite. Which things count as “fruits”? Do you mean to include eggplants—technically berries—as fruits? Does “tasty” mean “tastes good” or “has some taste, not none?” (Is anything absolutely tasteless?) Tastes good according to whose liking? Does “are” imply “every single one,” or “generally speaking, but with some exceptions”?
This is an extreme case, but all ordinary statements about eggplant-sized phenomena are also indefinite to some degree. What even counts as an eggplant? How about the various species of technically-eggplants that look and taste nothing like what you think of as one?1 Is a diced eggplant cooked with ground beef and tomato sauce still an eggplant? At exactly what point does a rotting eggplant cease to be an eggplant, and turn into “mush,” a different sort of thing? Are the inedible green sepals that are usually attached to the purple part of an eggplant in a supermarket—the “end cap,” we might say—also part of the eggplant? Where does an unpicked eggplant begin, and the eggplant bush it grows from end?
These are not questions with definite answers. Nor are they matters we are uncertain about; it is not that there are objectively correct answers that we haven’t yet scientifically determined. They are matters of definition—or, more accurately, of indefiniteness.
This is awkward for rationalist epistemologies. What does it mean to believe that eggplants are fruits if you can’t even say what an eggplant or a fruit is? What would it mean for the belief to be true or false?
Earlier I asked “What sort of world would rationalism be true of?” It would be made of ontologically definite objects, categories, properties, and relationships. This is explicit in some rationalisms, notably logicism. It’s implicit in others. For example, most versions of probabilism quietly pass over the issue, but can’t work without ontologically definite beliefs, preferences, actions, and outcomes.
Ontologically definite objects are ones that something could be true or false about, without any wishy-washiness.
- There is a truth about which ontologically definite object something is, so either two are the same one, or different ones.
- There is a truth about whether some bit of matter is part of a definite object, or not.
- A definite object either is, or is not, a member of a definite category.
- An ontologically definite object has definite properties. They could be absolute (“is red”) or parameterized (“is 72% red”). What they can’t be is vague (“well, reddish I suppose”).
- Definite objects either do, or do not, stand in definite relationships with each other. The cat is on the mat, or it’s not.
Rationalism’s impulse, encountering an indefinite statement, is to try to rephrase it in ontologically definite terms. It seeks a fully-specified technical definition for what each word means, splitting it into many different well-defined categories if necessary. Are eggplants fruits? Yes and no. Wearing your chef’s hat, no, they would make a lousy dessert; wearing your botanist’s hat, yes, they are the seed-bearing structure of an angiosperm.
Rationalism’s diagnosis, again, is that natural language is defective. We’ll have to replace it with something precise: formal logic, for instance.2
Formal logic fixed the problem with “is,” but ∀x eggplant(x) ⇒ fruit(x) does not help with the ambiguity of “fruit.” More generally, formal logic dealt with syntactic ambiguity, but did not directly address the semantic ambiguity hidden inside predicates. (“Predicates” are words in a logical formula that represent categories, properties, and relationships, such as “eggplant,” “purple,” and “bigger.”)
Nevertheless, logic helps. A first step is to make explicit which meaning of “fruit” is used in the belief:
|∀x eggplant(x) ⇒ fruitbotanical(x)||True|
|∀x eggplant(x) ⇒ fruitculinary(x)||False|
|∀x eggplant(x) ⇒ ¬ fruitculinary(x)||True|
The symbol ¬ means “not,” so you believe that every eggplant is a fruit in the botanical sense, and that every eggplant is not a fruit in the culinary one.
The second step is to give “necessary and sufficient conditions” in logic to define the terms. We want to say something like:
fruitbotanical(x) ≝ seed_bearing(x) ∧ structure(x) ∧ (∃y angiosperm(y) ∧ part_of(x,y))
That is: “a thing x is defined to be a botanical fruit if, and only if, it is a seed-bearing structure and there is some angiosperm y that x is part of.”
We have had more than a century of experience with this, and it has not gone well.3 Several patterns of difficulty emerge from serious attempts:
You typically discover a never-ending variety of weird exceptions, complications, and borderline cases. Is a glass bottle of poppy seeds “seed-bearing”? What is not a “structure”? Is a seedless banana a fruit?4 Is an eggplant still “part of an angiosperm” after it has been picked? (Does an entire object count as part of itself?) And what about the problems already encountered with cooked eggplants, rotting ones, and so forth?
The attempt often bogs down in taxonomizing an unbounded proliferation of “different senses,” which—as you repeatedly split them to deal with special cases—come to seem increasingly contrived, convoluted, and ad hoc. Dictionaries I consulted gave dozens of different definitions of “fruit,” with complicated relationships among them, all of them problematic in some way. “The developed ovary of a seed plant with its contents and accessory parts”: how developed does it have to be to count as a fruit? Which parts count as “accessories”? And “fruit” is quite well-behaved, as words go. The Oxford English Dictionary distinguishes 645 senses of “run.”
You find yourself trying to make one nebulous category (“fruit”) precise in terms of several others (such as “part”), which also turn out to be nebulous. Then you need to define those. You might think that eventually this process would terminate, that you would have covered the space of categories, that it would ground out in something solid; but in practice this never happens. The set of terms proliferates exponentially, and apparently endlessly. It is not bounded by the size of a dictionary, due to the repeated fragmentation of “senses.”
The definition itself expands into an enormous formula that seems so unwieldy as to be uninterpretable and unusable in practice.
Later I will suggest reasons these particular patterns of trouble arise.
The lesson is not so much that it is definitely impossible ever to make perfectly accurate definitions (although that seems to be true). It’s that we do not in fact have perfect definitions, yet this is rarely a problem in the routine practice of science and engineering. We would need perfect clarity only if we needed absolute truth, but we don’t.
Genes are interesting to geneticists, but what counts as one is notoriously impossible to define.5 A software engineer may explain a system as “more-or-less a model-view-controller architecture.” “More-or-less” might mean that there isn’t a completely strict separation between the view and the controller. What counts as an MVC architecture is not precisely defined, but the category is central in current web development practice anyway.
Increasing precision is often useful, or even critical, in technical practice. Indeed, sharpening terms is a form of ontological remodeling, an operation central to meta-rationality. It’s just that it’s rarely possible to drive the process to completion in order to locate something capable of being absolutely true or false.
The imprecision of natural language has at least two different aspects. There’s ambiguity: one word with several meanings. That’s not the culprit here: we subscripted different senses of “fruit,” but it didn’t solve the problem. You can subdivide senses as finely as you like, and still not gain perfect precision. This other issue is that individual senses remain resistant to definition.
Replacing natural language with a precise mathematical formalism—logic—doesn’t solve this second problem. The issue is not with language, it is with the categories that terms refer to. The difficulty is not that we can’t get a statement to refer to the right category. It is that there is no sharp dividing line in the world that reliably does the work we want.
The problem is in the territory, not in the map. It’s an ontological issue, not a representational one. We want terms to “carve nature at its joints,” but the eggplant-sized world has no joints.6 There is no natural, intrinsic, absolute distinction between eggplants and non-eggplants; nor can any specialized or technical subdivision of the category fully fix that. We’ll explore reasons in several of the following chapters. We’ll also look at some other failed rationalist attempts to solve the problem.
Language is not the problem, but it is the solution. How much trouble does the imprecision of language cause, in practice? Rarely enough to notice—so how come? We have many true beliefs about eggplant-sized phenomena, and we successfully express them in language—how?
These are aspects of reasonableness that we’ll explore in Part Two. The function of language is not to express absolute truths. Usually, it is to get practical work done in a particular context. Statements are interpreted in specific situations, relative to specific purposes. Rather than trying to specify the exact boundaries of all the variants of a category for all time, we deal with particular cases as they come up. We use resources available in the context to make good-enough distinctions for action. In Part Three, we’ll see how rationality relies on reasonableness to do that job.
Categorization serves practical purposes, so the underlying issue is not “is this absolutely and objectively an eggplant” but “can I make a decent moussaka from it?” Whether something counts as an eggplant (if it’s been in the refrigerator rather a long time) may depend on how badly you want moussaka. This is a main reason attempts at objective definition fail.7
This also explains the explosion of definitional “senses”: they are attempts to specify in advance, in full generality, what will count as a member of the category in different contexts and for different purposes. Contexts and purposes are unenumerable, so this is impossible. In fact, we’ll see later that almost any word can mean almost anything, in some unusual context. This implies that analyzing words as having some enumerable set of “senses” can’t work.
- 1. There are three or so species of eggplant—authorities disagree on how many—and the category is polyphyletic. (That is, different eggplant species are less closely related to each other than they are to non-eggplants.) Solanum aethiopicum, the Ethiopian eggplant, probably the same species as the Scarlet eggplant, looks very much like an heirloom tomato. Solanum macrocarpon, the African eggplant or gboma, is commonly eaten but intensely bitter, and dangerously toxic if you over-indulge. For more fascinating facts, read Doganlar et al., “A Comparative Genetic Linkage Map of Eggplant (Solanum melongena) and Its Implications for Genome Evolution in the Solanaceae,” GENETICS 161:4 (2002) pp. 1697-1711.
- 2. Formal logic is unattractive in many ways, so we might prefer an alternative. From the 1960s through the 1980s, artificial intelligence researchers attempted to devise better “knowledge representation languages.” By 1990 it became apparent that all were either equivalent to logic—mere “notational variants”—or so technically flawed as to be unusable. There doesn’t seem to be anything that can do the job better.
- 3. The problem of intractable indefiniteness, and its solution, have been discovered repeatedly in many different fields, among them the philosophy of science, linguistics, cognitive psychology, and artificial intelligence. Terry Winograd’s “Moving the semantic fulcrum” cites and summarizes the literature as of 1985. He discusses particularly John Searle’s “Literal Meaning,” which works through some entertainingly ridiculous examples. (Erkenntnis 13 (1978) pp. 207-224.) Searle attempts to find something in the vicinity of “the cat is on the mat” that could be absolutely true, and fails. His conclusion, and Winograd’s, is that meanings are unavoidably context-dependent. We’ll explore that same answer in Part Two of The Eggplant. A fine recent discussion is Michael Huemer’s “The Failure of Analysis and the Nature of Concepts,” pp. 51–76 in Chris Daly, ed., The Palgrave Handbook of Philosophical Methods, 2015. I don’t fully agree with his conclusions, but he explains several problems clearly.
- 4. “The term ‘seedless fruit’ is biologically somewhat contradictory, since fruits are usually defined botanically as mature ovaries containing seeds.”—Wikipedia.
- 5. See, for instance, Portin and Wilkins, “The Evolving Definition of the Term ‘Gene’,” GENETICS 205:4 (2017) pp. 1353-1364. James Watson’s The Double Helix says that he intended the paper announcing the discovery of the structure of DNA to begin “Genes are interesting to geneticists.”
- 6. In philosophy, categories in the world that are absolute, intrinsic, or objective are called “natural kinds.” Pretty much the only available examples of natural kinds of eggplant-sized objects were biological species. Philosophers have reluctantly more-or-less accepted the recent factual discovery that species are necessarily nebulous, and that this makes the “natural kind” concept obsolete. See the Stanford Encyclopedia of Philosophy article “Natural Kinds.” Plato was first to use the phrase “cut nature at the joints.” It’s closely related to his Theory of Forms, which I consider the worst of philosophical disasters.
- 7. Whether something is an eggplant is not subjective either, of course. The planet Pluto is not an eggplant, despite some superficial similarities.