As useful as it is to the poet, the punster, and the demagogue, the ambiguity of ordinary language is intolerable to the philosopher. Disambiguate we must. One type of ambiguity is well illustrated by the Old Testament verse, Timor domini initium sapientiae, "The fear of the Lord is the beginning of wisdom." 'Of' functions differently in 'fear of the Lord' and 'beginning of wisdom.'
Clearly, in 'fear of the Lord' the Lord is the object, not the subject of fear: the Lord is the one feared, not the one who fears. In 'beginning of wisdom,' however, wisdom is the subject of beginning, that which begins; it is not the object of beginning — whatever that would mean. Thus we could write, "The fear of the Lord is wisdom's beginning," but not, "The Lord's fear is wisdom's beginning."
The foregoing is an example of subject/object ambiguity. Here is an example of what I will call objective/appositive ambiguity: 'As a young man, I was enamored of the city of Boston.' The thought here is that the city, Boston, was an object of my love. Clearly, 'of' is being used in two totally different ways in the sample sentence.
I wonder if all uses of 'of' can be crammed into the following little schema:
A. Subjective Uses of 'Of.' 'The presidency of Bill Clinton was rocked by scandal.' 'The redness of her face betrayed her embarrasment.' 'She cited the lateness of the hour as her reason for leaving.' The presidency of Bill Clinton is Bill Clinton's presidency. And similarly in the other two examples.
Here 'of' expresses possession or belonging. The sharpness of the knife is the knife's sharpness. The wife of Tom is Tom's wife. The uncle of the monkey is the monkey's uncle. The ace of spades is the ace belonging to the spade suit. A jack of all trades is all trades' jack. Of course, if you want to be understood in English you cannot say, 'Marvin is all trades' jack.' But that's irrelevant.
The set of natural numbers is the natural numbers' set. The set of all sets is all sets' set.
'Several are the senses of "of."' The 'of' which is used — as opposed to mentioned — functions subjectively inasmuch as the thought could be put as follows: '"Of"'s senses are several.'
The square root of -1 is -1's square root.
B. Objective Uses of 'Of.' 'When I first met Mary, thoughts of her occupied my mind from morning until night.' Obviously, her thoughts could not occupy my mind; 'thoughts of her' can only mean my thoughts about her. Note that 'Mary's thoughts' could be construed in three ways: Mary's thoughts; thoughts about Mary; Mary's thoughts about herself.
Pictures of Lily are pictures that depict (are about) Lily.
'What was once called the Department of War is now called the Department of Defense.' It would not be idiomatic to refer to the Department of Defense as the department about defense, but this is presumably the thought: the DOD is the department concerned with defense.
'The study of logic will profit only those of a certain cast of mind.' This sentence features first the objective, then the subjective use of 'of.' The thought is: The study which takes logic as its object will profit only those whose mind's cast is such-and-such.
'The Sage of the Superstitions is a man of leisure.' This sentence features first the subjective, then the objective use of 'of.' The thought is: The Superstition Mountains' sage is about (is devoted to) leisure.
'Of all Ponzi schemes, that of Bernie Madoff was the most successful.' The first 'of' is objective, the second subjective. The thought is: Concerning (with respect to) all Ponzi schemes, Bernie Madoff's scheme was the most successful.
C. Dual Uses of 'Of.' 'Thoughts of Mary filled Mary's mind.' In this example, Mary is both the subject and the object of her thoughts, assuming that 'Mary' refers to the same person in all occurrences. So in 'thoughts of Mary,' 'of' functions both subjectively and objectively.
D. Appositive Uses of 'Of.' 'The train they call The City of New Orleans will go five hundred miles before the day is done.' 'Former NYC mayor Ed Koch referred to the city of Boston as Podunk.' Clearly, 'city of Boston' is not a genitive construction, logically speaking. We could just as well write, 'the city, Boston.' So I call the 'of' in 'city of Boston' the 'of' of apposition. If the grammarians don't call it that, then they ought to.
The House of the Rising Sun is not the rising sun's house — the sun, rising or setting, 'don't need no stinkin' house' — or the house devoted to the study of the rising sun, but the house, The Rising Sun.
The kingdom of Heaven is the kingdom, Heaven.
ADDENDUM: A little more thought reveals that my quick little schema is inadequate. Where would these examples fit: 'He drank a glass of wine.' 'She purchased ten gallons of gasoline.' 'Boots of Spanish leather are all I'm wishin' to be ownin'." (Bob Dylan) 'He is a man of the cloth.'
'Glass of wine' expresses a relation between a container and what it contains, and that does not seem to fit any of the four heads above. And note that 'a gallon of gasoline' is unlike 'a glass of wine.' A gallon is a unit of measure whereas a glass, though it could be a unit of measure, is a receptacle. A gallon is not a receptacle. 'Hand me that gallon' makes no sense. 'Hand me that gallon can' does.
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