# Are there any empirical categories that do not have vague boundaries?

The Stanford Encyclopedia of Philosophy has an article on vagueness that struck me as odd because it seems to assume that vagueness is a property of only certain kinds of propositions or predicates, while to me it is fairly clear that practically all empirical properties have vague boundaries. The article gives examples of non-vagueness like checkers or mathematics, but those are formalisms where they push the vagueness out of the formalism and into the application. What I mean is that, sure, the rules of checkers have no vagueness, but whether a checker is in a particular square or not is vague. What if it's overlapping the edge? What if it's half in one square and half in the other? The rules of checkers avoid vagueness by simply disallowing such cases.

What kind of physical property does not have boundary conditions where it is not clear how to judge the property? Measurements, no matter how precise, still have imprecision. Even physical classifications like "this is water" are vague. What if it is 3.5% dissolved salts? Is it still water or does it become sea water? If you still call it water, what about 20% salts? Is it still water or is it now a saline solution? At some concentration of salt, it is no longer water, but what concentration that is is vague.

You might argue that although it is vague whether the contents of a vial are water or not, the actual H2O in the vial is precisely (non-vaguely) water. But once again, that's a theoretical thing, not an empirical thing. That is, you can't observe that the H2O in the vial is water; you define that the H2O in the vial is water. As soon as you move to actual empirical judgments vague boundary cases start to rear their heads.

I can't come up with any empirical judgements that aren't subject, at least in principle, to vague boundary conditions. Are there any?

ADDENDUM: One of the answers made me realize that I was not clear enough about my question. I'm not saying that there are no empirically verifiable propositions that are clearly and precisely true or false. The examples given in the answer include "The population of Birkenhead is less than that of New York" and "Elephants can't fly".

I agree that in these cases, there is no vagueness, but there is potential vagueness in the judgments as can be seen by changing the terms to other terms that are chosen to highlight the vagueness. For example: "The population of New York is less today than it was yesterday". Now the truth of the statement depends on whether a tourist is considered part of the population. What about someone who came to New York to a hospice expected to die in a few days. He moved to New York permanently, but will be there less time than the tourist. What about someone who lives half time in New York and half time in New Jersey?

For another example, "A flying squirrel can't fly". This requires deciding whether gliding is flying. If you don't think that's a borderline case, what about an animal that can mostly just glide but can flap to gain altitude but only a half inch and only once a minute or so?

• "Many phenomena appear to be indeterminate: macro-objects (clouds, mountains) appear to have imprecise boundaries" plato.stanford.edu/entries/determinate-determinables/#MetaInde
– user65145
Commented Mar 8, 2023 at 20:37
• there's also the idea of vague terms generating (e.g.?) the sorites paradox. i'm not sure that all terms are vague, but 'existence' might be
– user65145
Commented Mar 8, 2023 at 20:54
• It's worse: everything is meaningless :-) Commented Mar 8, 2023 at 21:03
• if you can give necessary and sufficient conditions for a kind, then whether or not something meets that definition is not, i think, vague. can you think of a counter example and/or show that there are no such definitions about reality?
– user65145
Commented Mar 8, 2023 at 22:43
• The term "empirical categories" is itself vague, as is "vague". We discern (and care) only up to finite level of precision, and if we build in enough allowance for idealization into the "empirical" we can get concepts precise for the purpose (as scientists do in measurements). The SEP point is that in models of reality many concepts can be treated as precise, just as many round objects can be treated as spheres, and only some must stay vague. In this vein, see e.g. Franklin defend mathematical necessities "about reality" in Aristotelian realism, pp. 113ff. Commented Mar 9, 2023 at 0:38

Is anything not vague?

It depends how close you look. A chair is not usually thought of as having vague boundaries. However, if one examines the seat of the chair at the molecular level, the atoms will appear to be a cloud. In other words, the apparently solid boundary of the chair will become vague.

The definition of "vague" will also depend on the human purpose involved. A chair is adequate to support a sitting person; for this purpose, the chair is not vague. However, there are many things, notably human relationships, where the boundaries, if any, are quite vague and expressible only as probabilities.

• tangent, but it's odd to wonder if, supposing everything is infinitely reducible and in every infinite grouping there is at least one vague object, then nothing is not somewhat vague or indeterminate
– user65145
Commented Mar 8, 2023 at 23:26
• "Chair" as a category most definitely has vague boundaries. If you mean the physical object that is a single chair, I'm not sure to how that can be considered a category (except on a molecular level, which you concede is vague). Perhaps you can categorise it in terms of components, but then you have questions like: if you throw water onto a chair and some of it gets absorbed, is that part of the chair? Is a mug glued to a chair part of a chair? What if the back support is glued to a chair? Commented Mar 9, 2023 at 9:54

The issue is not necessarily that it's impossible to create categories with clear boundaries. The issue is that such categories are of limited use, they don't correspond to how humans typically naturally categorise things, and the boundaries are generally arbitrary.

As an example, the well-known Sorites paradox (relating to defining a heap of sand) can be resolved by saying at least 2537 grains of sand makes a heap. This, however, is an arbitrary boundary that would take 2 seemingly identical collections of sand (containing 2537 and 2536 grains respectively) and classify 1 as a heap and the other as not a heap. Most people probably also aren't going to count the number of grains (or really have any idea how many grains there are) before classifying something as a heap or not a heap, yet this level of precision may be required to have this clear boundary.

Categories with clear boundaries on a molecular level might be more useful (but probably only if what you're categorising involves molecular physics or chemistry).

As an example, one could define "pure water" as a category of substances that contain exclusively H2O molecules. Or you could define it as a substance with, say, less than 1 part-per-million of non-H2O molecules.

But it would be roughly impossible to know the exact chemical composition of a significant amount of a real-world substance, down to the last atom (outside of a lab, perhaps). Also, this is again an arbitrary boundary: 1 part-per-million of non-H2O molecules would not be pure water, but 0.99999 parts-per-million would be pure water, even though those 2 substances are essentially indistinguishable. People can, and do, measure the quality of water or other substances based on parts-per-quantity (by taking some sample of it), and might categorise water based on this (to e.g. regulate the quality of water). But the exact boundary is fairly arbitrary.

One could also possibly say "water molecules" is the category of molecules with nothing other than 2 hydrogen atoms and 1 oxygen atom.

Or one could define a category for molecules containing, say, at least 1 oxygen atom.

These seem to have quite clear and useful boundaries.

Disclaimer: my knowledge of molecular physics and chemistry is somewhat limited.

• Nouns are words that clearly represent categories of things, therefore, the primary source of correspondent truth-conditional claims are made with categories. Again, science, and it's precising definitions focuses on categories (An 'atom' is something that is x with properties a,b,c,...) and therefore all theories rely on scientific categories. How are categories not useful? With water, the vagueness of category 'deuterium' seems in no way to make the category useless, and a clean water standards report is replete with categories (ppb's of this...)
– J D
Commented Mar 9, 2023 at 15:39
• @JD FYI, I made some significant edits to my answer. Commented Mar 9, 2023 at 16:43
• Now that's defensible! :D And while you might think I'm being persnickety, I'm just trying to get the most mileage out of essentially good answers.
– J D
Commented Mar 9, 2023 at 16:44
• Also, I'm not sure if you're a word hound, but if you aren't familiar, Lakoff's work on linguistic categorization is worth a read.
– J D
Commented Mar 9, 2023 at 17:18

How about statements such as 'The population of Birkenhead is less than that of New York' or 'Gold is more dense than aluminium' or 'Snakes have no legs', 'Elephants can't fly', 'Shakespeare is a famous dead playwright'? Admittedly there might be scope to tighten the wording (eg 'Elephants cannot fly unaided') but it would seem rather contrived to consider any of those statements as vague.

• Examples like these are why I qualified the question in my last paragraph. I don't doubt that there are empirical propositions that are clearly true or false, but the terms of the propositions always seem subject to vague boundary conditions. The population of New York is not precise. Identifying something empirically as gold is not precise. What about a snake with a mutation? What counts as flying? What counts as famous? Although you can easily come up with many propositions that don't come close to vague boundaries the vague boundaries are always there. Commented Mar 8, 2023 at 21:55
• I agree that many entities ultimately have fuzzy boundaries, but in everyday speech there is no vagueness in a statement such as 'I have never been to Japan' and to claim that there is seems to me to be stretching the point artificially. Commented Mar 8, 2023 at 22:17
• @MarcoOcram A snake with a mutation better be a snake, because all snakes, like all animals, have mutations. The only distinction between snake and non-snake is the magnitude and type of mutation, and there things get fuzzy. Commented Mar 8, 2023 at 22:34
• Your other statements just don't come close to the "vague boundaries" David mentions, but the vague boundaries are still there. You can imagine a person mutated so that the question of whether they have 2 or 3 eyes is ambiguous. For example, if they have a primitive "third eye" that's just able to sense light or darkness, where it's ambiguous whether it counts as an actual eye or not. You can imagine a scenario where there are two official lists of everyone in the "registered population" of a city and the two lists aren't exactly the same. Commented Mar 8, 2023 at 22:36
• I don't think a statement can be considered a category, and it's not clear what the boundary of a statement would be. Representing "Snakes have no legs" in terms of categories would probably be "The category of snakes does not overlap with the category of things that have legs". This may or may not be fair enough, but both of those categories can still have vague boundaries. Commented Mar 9, 2023 at 9:35

Nope.

Water can boil, water can be ice, water can be liquid.

Pure stance of water is normal water, normal it is not fixed 100° of boiling point, physic does not focused on 100% points, but to possibilities of metamorphosis with gap +/- measurement error and other not pure stances like salts in water, pressure, ect. So, you have a water, from direct place, and in normal stace in had similar characteristics of metamorphosis and reaction changes - it is normal, if it hadn't - it is abnormal and physic, chemistry have to say why?

But another question if you talk about living organism - that have more vague. Is one man can live separate from group or not? Why 2 sons from one family have differen characters? But when it is about statistic, it is not about real objects, it is about stance of meta objects. Meta objects have "pure" stance, for example your are a human. Why? Maybe you human at 90%? but doesn't matter, it is pseudo stance, it is doesn't mean nothing - you are a human at 100%. Nothing will happened if you ll call you a unicorn. Maybe.

The problem, that you try to identify "pure" borders(boundary conditions) for the noun and else. Borders it is pseudo category, it is not work this way, borders need only for lab rats, "normal one" - mean not very smart and creative.

• At what point is water considered to be boiling? If there's a single bubble? If you have a lake with one small boiling section, is the lake considered to be boiling? As for boundaries between states of matter (ice and liquid water), it's a bit more complicated than that. Also, it's not clear which categories you're referring to when you say e.g. "water can be liquid". The category of water and liquid both have unclear boundaries when describing complex real-world objects. Commented Mar 9, 2023 at 10:05
• @NotThatGuy i told about possibility, not about "stance at this temperature", possibility with physical and chemical properties of the substance. If you may to get liquid water at P/T ~ correlation +/- it is water, if substance may to reaction like a water - it is water, if it has viscosity like a water, dissolves polar compounds like a water - it is a water. So water has a complex of parameters of changing possibilities(reactions, actions, ect.) If you measure with changing, not with "stance points"(standarts) - you have no problems. Standart of substance may be, but after changing valution. Commented Mar 9, 2023 at 14:25
• @NotThatGuy Is man a man, and woman is a woman or not? Is "dog" is a dog, and not a cat, cow, tortue...? Or you have doubts with it too? Is "house" is a house, why? Where you have no doubts? Commented Mar 9, 2023 at 14:41
• The boundaries between species is blurry. Dogs evolved from wolves, but there's no clear point in time where a wolf gave birth to a dog: it was incremental changes across many generations. Sex and gender are non-binary according to science, so the line between "man" and "woman" isn't that clear. Is a mobile home a house? Is a shack a house? Is a tent a house? I don't have doubts as much as I realise that these categories don't have clear boundaries. Commented Mar 9, 2023 at 16:00
• @NotThatGuy Yes, that is why all is known in changing. Woman can give birth, man can beget inside woman. Baby is changing, nothing sense in man/woman definition if no baby born ability - no changes. A sex - is not about binary, it is about changing, find which changes does give gender concept and you ll definite it exactly. If you don't know about changes then sex=gender(sort, kind), cat=dog, water=black and all have blurry boundaries. Look out of logic, and you will see pure changes. Your house that you call self home. If you are homeless, all houses are only letters "house" without sense. Commented Mar 9, 2023 at 21:21

The counter example in your post disproves your own argument. If we define water to contain h2o compounds, then something being classified as water is now not vague.

– user65145
Commented Mar 8, 2023 at 20:59
• Ah! So, this piece of paper here on my desk is water, since it contains H2O molecules. Commented Mar 8, 2023 at 21:03
• i am confused @DavidGudeman h20 is composed of oxygen and hydrogen. how is that vague? do you need a synthetic statement? do you mean that all perception is vague? that is i suppose more likely
– user65145
Commented Mar 8, 2023 at 22:38
• it contains or holds water (vapour) @causative again, that we can be vague about anything doesn't mean everything is vague
– user65145
Commented Mar 8, 2023 at 23:07
• I wasn’t making an argument that water should be anything that contains H2O. I was making the argument that IF it is, there is no ambiguity, hence disproving his assertion that all categories are ambiguous. @causative
– user62907
Commented Mar 10, 2023 at 8:29

That you can introduce vagueness to a definition ("being in a square") - or even talk about a fact vaguely - does not mean that it is vague. We can define a checker as in a square if and only if it does not overlap, in which case some facts are not vague. Precision may not be how we naturally think and what we act on, but it is possible.

On vagueness in general

if objects fill space, and space is both continuous and gunky (i.e., such that every entity has proper parts), then the shapes and locations of objects will be indefinitely subject to further determination (see Salmieri 2008: 78, n47).[26] And certain interpretations of quantum mechanics (see §5.3 for further discussion) and certain field-theoretic understandings of fundamental particles as having infinitely extensible boundaries (reflecting these particles’ being constituted by long-range interactions) suggest that natural reality is to some extent irreducibly determinable.

https://plato.stanford.edu/entries/determinate-determinables/

Determination is a kind of specification, one in which

(at a given level of specificity) are both similar and incompatible (red and blue are similar in both being colors; nothing can be simultaneously and uniformly both red and blue)

If the reality of something is subject to further determination, then it not maximally determinate, and "vague". So you seem to be asking for an empirical domain that can always be further specified.

• How do you measure if it's overlapping? Look at the edge with a microscope and you'll see spots. Is it overlapping if one atom of the checker is over an isolated spot that you can't see without a microscope? What does "over" mean? Is it judged with a plumb bob or geometrically to the center of the earth? Commented Mar 8, 2023 at 23:18
• let's suppose "yes" then it is overlapping. does that answer your question @DavidGudeman besides which, does that mean that no checkers are in squares? what about those right in the middle?
– user65145
Commented Mar 8, 2023 at 23:29
• i'm not sure how you are inferring absolutely everything is vague (that checker is not overlapping), but i don't know the phrase for what you are actually referring to. you seem to be saying that no means of acquiring empirical knowledge cannot be further specified @DavidGudeman would that mean that all empirical knowledge is vague? if knowledge is defined by how we come to it, then i guess (maybe)
– user65145
Commented Mar 8, 2023 at 23:40
• Please read my addendum to the question. No, I'm not claiming that everything is vague. Commented Mar 8, 2023 at 23:43
• oh right. you should change the question title @DavidGudeman
– user65145
Commented Mar 8, 2023 at 23:43

You're starting to see that there is a problem with categories themselves. Various philosophers have recognized that language categories are inherently fuzzy or prototypical. Philosophers of science, particularly the logical positivists realized that observation statements use language, and language is inherently normative. The normative bias of language categories manifests itself as theory-ladenness and Quine himself turned in the direction of a solution to confirmation holism for an explanation, though retreated a bit. Once a philosopher accepts that theory-ladenness is unavoidable because categories are normative, and then the notion that even radical confirmation holism doesn't prevent underdetermination of meaning, then one has to look elsewhere for meaning besides words themselves. (Shock) Words are a tool, they are not experience.

• i think if some philosophers are doubting that all words are fuzzy, thay have to find not fuzzy(prototypical) words, or we need another non-fuzzy-philosophers and non-prototypical-academic degree. Commented Mar 9, 2023 at 0:28
• Why are you unable to comment to me without this childish pretend condescension? I've been thinking about these topics for over thirty years. I'm not just "starting to see the problem with categories". And this isn't a language issue, it's a concept issue. Commented Mar 9, 2023 at 1:55
• No condescension at all, though I imagine a reading of such might be construed as an indication of narcissism. My answer is nudging you towards post-Logical Positivist/ordinary language philosophy which is 100 years more contemporary than the Fregean obsession with "externalist objective meaning" and "concept and language are wholly distinct". Ever work at Google?
– J D
Commented Mar 9, 2023 at 6:41
• @άνθρωπος Some thinkers are unable of dealing with fuzzy definitions and graded thinking. Black and white thinking is a hallmark of an immature intellect, so any "philosopher" who can't deal with more sophisticated logic is no philosopher at all. Of course, tell them that, and they're likely to be upset and lash out.
– J D
Commented Mar 9, 2023 at 6:46
• @JD It seems quite narcissistic to assume someone interpreting what you said differently from how you meant it is due to them having a character flaw (as opposed to there being any flaw from your side, or due to the inherent subjectivity of language). This is especially ironic on a Q&A about how language is fuzzy. (This is however not to say I support or oppose any particular interpretation here.) Commented Mar 9, 2023 at 11:52