…in my article of Jan. 1901, I enumerated as the three logically sound criteria of objectivity; first, that that which one can destroy at will, with scarce an effort, like a daydream or a house of cards, cannot have any very independent being; secondly, that matters to which everybody will assent, when the question is fairly brought before him, can hardly be mere madness; and thirdly and best, that if there be a notion upon which can be based predictions in endless succession, all capable of being verified or refuted, this series of predictions cannot go on turning out successfully with never a failure in all its endless protraction unless there be enough objective truth in the notion to account for this success. All these three criteria emphatically declare for the objectivity of nature’s approximate conformity to law; and approximate conformity is amply enough to prove the objectivity of some habits inhering in the physical universe.
The article Peirce refers to is "Pearson's Grammar of Science" (published in EP 2 and CP 8). The passage reads: "We have just three means at our command for detecting any unreality, that is, lack of insistency, in a notion. First, many ideas yield at once to a direct effort of the will. We call them fancies. Secondly, we can call in other witnesses, including ourselves under new conditions. Sometimes dialectic disputation will dispel an error. At any rate, it may be voted down so overwhelmingly as to convince even the person whom it affects. Thirdly, the last resort is prediction and experimentation."