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Regarding properties of objects, say, length or mass, I'm confident that "to have" will usually work but am unsure about "to be" or "to be of". Consider the following examples:

(a) The vectors must have the same length. (b) The vectors must be the same length. (c) The vectors must be of the same length.

and

(d) The aggregate must have a density greater than 1800 kg/m³. (e) The aggregate must be a density greater than 1800 kg/m³. (f) The aggregate must be of a density greater than 1800 kg/m³.

(a) and (d) sound best to me, but I'm unclear whether the others are acceptable alternatives. I looked at Ngrams for the three formulations using length, weight, mass, and density with inconsistent results.

  • be mass > have mass > be of mass
  • be density ≈ have density > be of density
  • have weight > be weight > be of weight (though be of was more common before 1940)
  • have length > be length, be of length
Dave Tamblyn
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    Be density and be mass sound wrong. Of is good with both of them. Vectors are abstract, hence their properties can be; but density and mass (and many other properties) are physical, not abstract, so they can be had by physical objects. – John Lawler Mar 12 '23 at 20:10
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    Does this answer your question? Meaning and usage of "be of" – Peter Shor Mar 12 '23 at 20:31
  • (b) The vectors must be the same length. New (g) The aggregate density must be greater than 1800 kg/m³. Presumably 'aggregate' here is synonymous with 'gravel'. – Weather Vane Mar 12 '23 at 20:44
  • ... or (h) The density of the aggregate must be greater than 1800 kg/m³. – Weather Vane Mar 12 '23 at 20:54
  • I agree that "to be" works well when the sentences are restructured as suggested: the (property) of the (object) is ... But I was asking how the property relates to the object. That is, the object {is, is of, has} property ... The 2x4 {is, is of, has} length 8 feet. – Dave Tamblyn Mar 12 '23 at 21:33
  • @PeterShor, Sorry, but that thread is of little comfort or use. I see that the answer in the other thread got +30 rating, but isn't it a cop-out to say everything is idiomatic? – Dave Tamblyn Mar 12 '23 at 21:45
  • @JohnLawler, the distinction between abstract and physical objects is intriguing but not convincing. Is it that abstract nouns possess some purity that physical objects lack? A vector in general is abstract, but (4,3,2,1) is a specific vector of length four. So, (4, 3, 2, 1) {is, is of, has} length four? – Dave Tamblyn Mar 12 '23 at 23:34
  • No, it's merely that abstract attributes don't exist and therefore have no physical properties. Things that do exist are subject to physical laws and language is designed to deal with those (at least in a 1-G field at STP for humans). Abstract concepts are just names in systems of nodes (more abstractions) and follow their own logic, but anything semantic is metaphoric. – John Lawler Mar 13 '23 at 03:23

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