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NOTES

1. J. Van Heijenoort, 'Set-Theoretic Semantics,' in Selected Papers, 1976, p. 48.

2. The logical technique for obtaining such objects is well-known.  First, an object, say an apple, is separated from its color, so becoming an x such that red(x).  Divested in turn of its other attributes--its shape, feel, taste, kind,..., etc.--the apple emerges as an x such that red(x) and round(x) and soft(x) and sweet(x) and (fruit)x ... etc. (Francis Pelletier, Review of E.J. Lowe's Kinds of Being, History and Philosophy of Logic 13, 1992, pp. 125-128.)  The entity which stands in for 'x' is thus no longer an apple, but--like Aristotelian matter or Thomas's materia insigna--an attributeless bearer-of-attributes. 

3. By 'singular term', I mean any nominal referring expression which purports to pick out a particular, the category of particulars being broadly construed so as to include things, processes and events.  Singular terms include proper names ('Scott', 'Vulcan', 'the Palmdale Bulge'), definite descriptions ('the author of Waverley', 'the largest prime number', 'the round square'), and singular possessive phrases ('Euclid's fifth axiom', 'Smith's hangover', 'Yugoslavia's tragedy').

4. According to the Indiscernibility of Identicals, if x and y are identical, every property of x is also a property of y and conversely.  So if (as I maintain) Hesperus and Phosphorus are numerically identical yet differ in some respect, the Indiscernibility of Identicals is false.

5. There is no general agreement concerning what the intension of a singular term might be.  The distinction between intension and extension, however, is often taken to reflect Frege's distinction between the particular a singular term stands for and the conceptual content it expresses.

6. For my 'singular terms'/'term', read Donnellan's 'proper names'/'name'.

7. With the exception of Nathan Salmon.

8. Indeed, when questioned about identity or difference, they would but give forth with a surly "Yea, Yea" or "Nay, Nay".

9. P. Butchvarov, 'Identity,' in Peter A. French et. al. (eds.), Contemporary Studies in the Philosophy of Language, U. of Minnesota Press, Minneapolis, 1979, p. 163 f.

10. 'In an essential way, things are identical in the same way as they are one, since they are identical when their matter is one (in species or in number), or when their substance is one.'

11. Render 'X and Y are one in substance just in case for some Z, X and Y are parts of Z' as:

 (i) for allxy(one(x,y)equivalentfor somez(part(x,z) & part(y,z))
Now (ii) follows from (i) by Universal Instantiation:
 (ii) for ally(one(y,y)equivalentfor somez(part(y,z) & part(y,z))
But (ii) is logically equivalent to (iii).
 (iii) for ally(one(y,y)equivalentfor somez(part(y,z))
Therefore, if X and Y are one in substance just in case for some Z, X and Y are parts of Z, then Y and Y are one in substance just in case for some Z, Y is a part of Z.

12. [...] identity is in any event a oneness, whether this oneness makes reference to a plurality of things, or whether it makes reference to a single thing considered as two, as happens when it is said that the thing is identical to itself.

13. How can 'Hesperus = Phosphorus' and 'Hesperus = Hesperus' differ in meaning, even though Hesperus and Phosphorus are one and the same? These sentences (call them S1 and S2) differ in meaning because there is nothing they both mean.  In other words, both (1) and (2) are false although (3) is true.

(1) means(S1, <H, =, H>) & means(S2, <H, =, H>)
(2) means(S1, <P, =, P>) & means(S2, <P, =, P>)
(3) means(S1, <H, =, P>) & means(S2, <H, =, H>) 
But, it will be objected, H = P. So (1) and (2) follow from (3) by the substitutivity of identicals. 

But the substitutivity of identicals can no more legitimately be invoked to license the slide from (3) to (2) or (1) than it can be legitimately invoked to license the slide from (e.g.) "'4' means 4" to "'4' means 2 + 2".  Frege and Leibniz notwithstanding, the inference from (3) to (2) or (1) is an inference that fails to preserve truth.

14. 'Desideria:  The Voice explained to me that the barbarians, being pagans or else forming part of some heretical sect, did not hesitate to desecrate churches or other places dedicated to religious observance.  According to the Voice, this way of acting on the part of the barbarians could be described as desecratory precisely because the places that they desecrated were sacred.  But what did it really mean--desecratory?  It meant that the barbarians with their devastations did not so much destroy churches as despoil them, once and for all, of their sacred character.  Before the desecration, the church was a place which one entered bareheaded, in a state of reverence, walking slowly and speaking in a low voice; after the desecration it was nothing more than a warehouse, a big shed, in fact a structure possibly intact but devoid of any sacred character.' (A. Moravia, Time of Desecration, Playboy Paperbacks, 1981, p. 110)
 

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