Agnosticism simply means that a man shall not say he knows or believes that for which he has no grounds for professing to know or believe.
T. H. Huxley (1825-1895) English biologist [Thomas Henry Huxley]
(Attributed)
Huxley claimed in later years to have developed this formulation, along with the word "Agnostic," at the 1869 meeting of the Metaphysical Society. The truth regarding the word itself, at least, appears a bit more complex and unresolved than that. I have not been able find when this precise definition of Agnosticism was first published.
Huxley expanded on the definition in a series of essays in 1889. See here and here.
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We have not the slightest objection to believe anything you like, if you will give us good grounds for belief; but, if you cannot, we must respectfully refuse, even if that refusal should wreck morality and insure our own damnation several times over. We are quite content to leave that to the decision of the future. The course of the past has impressed us with the firm conviction that no good ever comes of falsehood, and we feel warranted in refusing even to experiment in that direction.