We must locate this passage into a double context :
See Robert Purrington, The First Professional Scientist : Robert Hooke and the Royal Society of London (2009), Ch.8 : And All Was Light : Hooke and Newton on Light and Color, page 135-on.
For the general context, we have to take into account the diffusion of Descartes' Physics and philosophy around the middle of the 17th Century.
Newton made extensive study of Descartes' theories (regarding : motion of bodies, celestial physics and light) : see Isaac Newton, Philosophical Writings (editor Andew Janiak, 2004).
All Newtonian's theory was in contrast with Descartes' ones.
Abou the rivalry with Hooke, [see Purrington, passim and pages 141-42], we have to consider the
delivering [by Newton of] a long manuscript on light and color to the [Royal] Society. The paper, consisting of an “Hypothesis” and a “Discourse,” was read by Oldenburg in five parts between 9 December and 10 February 1675/6 [footnote : Newton to Oldenburg, 7 December 1675; Corresp. I, 362–386].
Newton began by saying that he would not make any hypothesis about the aether and its role in the propagation of light, not thinking it necessary «to concern my selfe whether the properties of Light, discoverred by me, be explained by this or Mr Hook’s or any other Hypothesis capable of explaining them . . . » [footnote : «An Hypothesis explaining the Properties of Light discoursed of in my severall Papers.» Corresp. I, 362–386.] Further on he discussed Hooke’s discovery of diffraction, noting others who had observed it as well, but certainly giving Hooke credit.
Hooke was, however, unimpressed, and after hearing the first part of the “Discourse” on 9 and 16 December, noted «that the main of it was contained in his Micrographia, which Mr. Newton had only carried farther in some particulars.» [footnote : Birch, 3, 269. Hooke made very much the same comment on Newton’s theory of planetary motion. Everything we know of Hooke suggests that he really believed these assertions.]
The result of this new exchange, indirect though it may have been, with Oldenburg as intermediary, was to rekindle the old animosity of four years before.
The rift between Hooke and Oldenburg was growing at this time, and Hooke felt that the Secretary was trying to exacerbate the ill will between himself and Newton. Ironically, this alienation prompted Hooke to write a very conciliatory letter to Newton [footnote : Hooke to Newton, 20 January 1675/6. Corresp. I, pp. 412–3], hoping to heal the rupture that he felt the Secretary had fomented. He wrote Newton on the day the latter’s heated reply was read to the Society, 20 January, and the Diary suggests that he wrote him immediately after the meeting, hoping to heal the rupture.
In Newton’s more than cordial reply to this letter [footnote : Corresp., I, 416–7], he mentioned
having called at Hooke’s lodgings only to find him out. And it was in this letter that
Newton penned the famous line:
«If I have seen further it is by standing on ye shoulders of Giants,»
making it clear that Hooke was one of those giants. This almost friendly exchange of letters between brought a sort of peace and established a basis for Hooke’s correspondence with Newton after Oldenburg’s death in 1677.
In conclusion, I think that we have to read it in a "multiple way" : Newton's theories and discoveries was made possible also by a careful study of the works of previous "Giants", like Descartes and Hooke, all of them surpassed by the ability of Newton to "see further".
From the on-line transcription of David Brewster, Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton, vol. 1 (Edinburgh: 1855), in The Newton Project we can recover a longer quotation from the letter :
you defer too much to my ability in searching into this subject. What Descartes did was a good step. You have added much several ways, and especially in considering the colours of thin plates [emphasis added].
If I have seen farther, it is by standing on the shoulders of giants.
But I make no question you have divers very considerable experiments beside those you have published, and some, it's very probable, the same with some of those in my late papers. Two at least there are, which I know you have often observed, — the dilatation of the coloured rings by the obliquation of the eye, and the apparition of a black spot at the contact of two convex glasses, and at the top of a water-bubble; and it's probable there may be more, besides others which I have not made, so that I have reason to defer as much or more in this respect to you, as you would to me.
How much of this is flattery? How much is gratitude? Who knows...