Category Archives: Logic

Very Unique

My unique (but not very unique) microwave

Everyone has their pet peeves, and peeves about language abound. My pet peeve is with people who object that “very unique” is illogical. For example, this pithy statement:

Uniqueness is a binary condition. Something is unique or it is not. There are no degrees of uniqueness. Something cannot be partly unique, mostly unique, very unique, etc.

Well-known language authorities are a bit less succinct. Bryan Garner writes:

unique. Strictly speaking, “unique” means “being one of a kind,” not “unusual.” Hence the phrases *”very unique,” *”quite unique,” *”how unique,” and the like are slovenly. … Unless the thing is the only one of its kind, rarity does not make it unique. For instance, if a thing is one in a million, logically there would be two things in two million. Rare indeed but not unique.

(I note for the record that there is nothing logical about his “for instance”. Without the assumption of uniform distribution, the inference fails. “One in a million” does not equal “one in every million.” Slovenly indeed!)

Or Fowler’s Modern English Usage:

…uniqueness is a matter of yes or no only; no unique thing is more or less unique than another unique thing, as it may be rarer or less rare; the adverbs that u. can tolerate are e.g. quite, almost, nearly, really, surely, perhaps, absolutely, or in some respects; & it is nonsense to call anything more, most, very, somewhat, rather, or comparatively u.

(Why is “quite unique” tolerable but “very unique” beyond the pale? No explanation.)

Have these pundits any training in formal logic? I doubt it.

Before I begin, a disclaimer. If you feel ‘very unique’ is redundant, or poor style for some other reason—well that’s a matter of taste. My beef is with the first quote’s “cannot” and Fowler’s “nonsense”, with their belief that logic is on their side. It isn’t.

Let me start my discussion with the preeminently logical field of math, which does use ‘unique’ absolutely. The classic example:

Two is the unique even prime.

No one ever writes “Two is the very unique even prime.” But note: uniqueness is not a property of two by itself. Rather we have a description (“even prime”—what logicians call a predicate), of which the number two is the sole instance.

When you omit the predicate, ‘unique’ loses its absolute character. Take the sentence “The Taj Mahal is unique”. True. But so is the building at, say, 235 Orchard Street, New York City: it’s the only building at that address. Everything is one of a kind, in the sense that it is the only thing equal to itself! My microwave is unique, as it is the only Sharp Model R-2A48 microwave with serial number 239404.

I imagine when you read the last sentence, you said, “Really? That’s how you justify the caption at the top of this post?” I concede: “My microwave is the unique microwave with serial number 239404” is a world away from “My microwave is unique.” We have two sharply distinguished uses for ‘unique’. One follows the mathematician’s pattern: “x is the unique item satisfying the predicate P(x)”. The predicate is explicitly stated; the definite article ‘the’ is mandatory. The other use, with ‘the’ forbidden, means little more than ‘unusual’.

Bryan Garner is wrong: ‘unique’ doesn’t mean just “being one of a kind”. The use with mandatory ‘the’ doesn’t even imply unusual, but it does possess the “only one of its kind” feature. What about the non-‘the’ use?

To say something is unique is to suggest it is the sole instance of some implicit and not-very-specific description. The less specific the description, the more unique the item. This usage of ‘unique’ admits degrees because one of its essential aspects—the specificity of the predicate—admits degrees. It is not binary, not “a matter of yes or no only”.

The Taj Mahal is the only Wonder of the World in India. (According to some lists.) The Taj Mahal is more unique than the building at 235 Orchard Street NYC, since a broader description singles it out. But make the description still broader by striking out “in India”, and it loses its unique status.

If the ‘very unique’ haters had thought things through, they would have inveighed against ever using ‘unique’ sans a defining characteristic. They would have rejected “The Taj Mahal is unique” as an illegitimate usage. They would hold that ‘unique’ carries no implication of rarity.

There is a related word restricted in this very manner: sole. You cannot grammatically say

The Taj Mahal is sole.

Nor are people tempted to qualify ‘sole’ with ‘very’. They don’t say

The Taj Mahal is the very sole Wonder of World in India.

grammatical though it is.

The Merriam-Webster article Is It Wrong to Say ‘Very Unique’? remarks

The grammarian Joseph Wright, for example, in his A Philosophical Grammar of the English Language from 1838 (and like others before and since), gave a list of adjectives “which admit of no variation of state”—in other words, that cannot be modified. His list includes words like square, dead, entire, false, and obvious. And yet, evidence of actual usage shows that almost square, nearly dead, whole entire, mostly false, and plainly obvious are all commonly used and standard.

Let me single out ‘square’ from this list. I have run across books arguing that something is either square or it isn’t. ‘More square’ is illogical!—or so they claim. Shallow thinking, I claim! Yes, this holds in Euclidean geometry; but in our physical world, nothing is perfectly square. Either ban ‘square’ for physical objects, or allow comparative use.

Shallow thinking likewise vitiates the arguments against ‘very unique’. Either say OK to it, or use ‘unique’ only as mathematicians do.

 

 

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Topics in Nonstandard Arithmetic 10: Truth (Part 4)

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Previous “Truth” post

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Nonstandard Models of Arithmetic 26

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MW: Continuing the recap… Continue reading

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Nonstandard Models of Arithmetic 25

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Previous Enayat post

MW: It’s been ages since John Baez and I discussed Enayat’s paper—not since October 2020! John has since moved on to fresh woods and pastures new. I’ve been reading novels. But I feel I owe it to our millions of readers to finish the tale, so here goes.

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Topics in Nonstandard Arithmetic 9: Tricks with Quantifiers

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Every specialty has its tricks of the trade. They become second nature to practitioners, so they often don’t make it into the textbooks. Quantifiers rule in logic; here are some of the games we can play with them. I’ll start with tricks that apply in logic generally, then turn to those specific to Peano arithmetic.

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Topics in Nonstandard Arithmetic 8: Extensions and Substructures

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Substructures and extensions loom large in math: subgroups, subrings, extension fields, submanifolds, subspaces of topological spaces… So too in the model theory of PA.

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Nonstandard Models of Arithmetic 24

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MW: Indicators: we don’t need to discuss these, to prove the Paris-Harrington theorem. But I think they offer valuable insight.

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Nonstandard Models of Arithmetic 23

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MW: OK! So, we’re trying to show that M, the downward closure of B in N, is a structure for L(PA).  In other words, M is closed under successor, plus, and times. I’m going to say, M is a supercut of N. The term cut means an initial segment closed under successor (although some authors use it just to mean initial segment).

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Non-standard Models of Arithmetic 22

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MW: So we have our setup: BMN, with N a model of PA, B a set of “diagonal indiscernibles” (whatever those are) in N, and M the downward closure of B in N. So B is cofinal in M, and M is an initial segment of N. I think we’re not going to go over the proof line by line; instead, we’ll zero in on interesting aspects. Where do you want to start?

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Topics in Nonstandard Arithmetic 7: Truth (Part 3)

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Last time we looked at Tarski’s inductive definition of truth formalized inside ZF set theory. Continue reading

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