“All argument is against it; but all belief is for it.”

Sec. 284
The Gay Science (1882)

Commonly attributed to Spencer, information provided in The Quote Verifier: Who Said What, Where, and When (2006) by Ralph Keyes and The Survival of a Fitting Quotation. (2005) by Michael StGeorge http://anonpress.org/spencer/, indicates the attribution may have originated with the book [w:The_Big_Book_(Alcoholics_Anonymous)|Alcoholics Anonymous]]. It was used exactly as written above in the personal stories section of the first edition in 1939 and in 'Appendix II: Spiritual Experience' of all subsequent editions.
: "Contempt prior to examination" was a phrase used by William Paley, the 18th-century English Christian apologist. In A View of the Evidences of Christianity (1794), he wrote:
::The infidelity of the Gentile world, and that more especially of men of rank and learning in it, is resolved into a principle which, in my judgment, will account for the inefficacy of any argument, or any evidence whatever, viz. contempt prior to examination.
:Paley's characterization of non-believers was later modified and used by other religious authors who uniformly attributed their words to Paley. In Anglo-Israel or, The British Nation: The lost Tribes of Israel (1879), Rev. William H. Poole may have been the first to render the quotation in its more familiar and enduring form:
::There is a principle which is a bar against all information, which is proof against all argument, and which cannot fail to keep a man in everlasting ignorance. This principle is, contempt prior to examination.
:Various authors following Rev. Poole would offer new iterations of the quotation into the early decades of the 20th century. Most of these credited William Paley, but by the early 1930s the first obscure publications to falsely attribute this quote to Spencer emerged. Its usage for decades since as a maxim in Alcoholics Anonymous and the twelve-step recovery community has popularized its erroneous association with Herbert Spencer.
Misattributed

Source: Towing Jehovah (1994), Chapter 8, “Famine” (p. 213)

Hilbert-Courant (1984) by Constance Reid, p. 143

Light (1919), Ch. XX The Cult
Context: My spirit is no longer what it was. Vaguely I seek, everywhere. I must see things with all their consequences, and right to their source. Against all the chains of facts I must have long arguments to bring; and the world's chaos requires an interpretation equally terrible.

Source: Complexity and Postmodernism (1998), p. 86

A Neglected Argument for the Reality of God (1908)
Context: An "Argument" is any process of thought reasonably tending to produce a definite belief. An "Argumentation" is an Argument proceeding upon definitely formulated premisses.
If God Really be, and be benign, then, in view of the generally conceded truth that religion, were it but proved, would be a good outweighing all others, we should naturally expect that there would be some Argument for His Reality that should be obvious to all minds, high and low alike, that should earnestly strive to find the truth of the matter; and further, that this Argument should present its conclusion, not as a proposition of metaphysical theology, but in a form directly applicable to the conduct of life, and full of nutrition for man's highest growth. What I shall refer to as the N. A. — the Neglected Argument — seems to me best to fulfil this condition, and I should not wonder if the majority of those whose own reflections have harvested belief in God must bless the radiance of the N. A. for that wealth. Its persuasiveness is no less than extraordinary; while it is not unknown to anybody. Nevertheless, of all those theologians (within my little range of reading) who, with commendable assiduity, scrape together all the sound reasons they can find or concoct to prove the first proposition of theology, few mention this one, and they most briefly. They probably share those current notions of logic which recognise no other Arguments than Argumentations.

Source: A Neglected Argument for the Reality of God (1908), V