In book four chapter ten of The Essay Concerning Human Understanding John Locke makes some good arguments for the existence of God. He also describes the position of the cogito metaphysically, as it were, rather reminiscent of Descartes. To exist is to be aware of existing. Reason leads to God, and that brings me to a point Locke didn't make about the existence of objects and other people.
Locke could have written that mathematics that one did not invent oneself are proof of the existence of reason in some sentient being. One could not believe that Euclid, Pythagoras or Einstein's abstract works weren't at least evidence of reasoning going on in some self-aware being and not a natural occurrence by non-sentient mass.
In book four chapter eleven I believe Locke finds sensations and sense data distinct from ideas. Ideas arise from sense data, and sense data from external objects; well, objective sources and non-self sources may be plainer than objects for terminology.
Referent objects may be the entire mass-energy of the Universe. Even great office buildings of more than one-hundred stories are simply arrangements of atoms that humans experience as solid because of human physical structure. If people were made of neutrinos they would find the solid building less substantial than vapor. Like the office building, the language and proofs of much of Locke's essays are embedded in the field-criterion Universe of being an element in-the-field given unto self-aware being. That is they work to a relative, circumstantial scale.
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