Here it is:
But the materialist is not allowed to admit into his spotless machine the slightest speck of spiritualism or miracle.Somehow or other an extraordinary idea has arisen that the disbelievers in miracles consider them coldly and fairly, while believers in miracles accept them only in connection with some dogma. The fact is quite the other way. The believers in miracles accept them rightly or wrongly because they have evidence for them. The disbelievers in miracles deny them rightly or wrongly because they have a doctrine against them.The question of whether miracles ever occur is a question of common sense and of ordinary historical imagination, not of any final physical experiment. One may here surely dismiss that quite brainless piece of pedantry which talks about the need for scientific conditions in connection with alleged spiritual phenomena. If we are asking whether a dead soul can communicate with a living, it is ludicrous to insist that it shall be under conditions in which no two living souls in their senses would seriously communicate with each other. The fact that ghosts prefer darkness no more disproves the existence of ghosts than the fact that lovers prefer darkness disproves the existence of love.It is just as unscientific as it is unphilosophical to be surprised that in an unsympathetic atmosphere certain extraordinary sympathies do not arise. It is as if I said that I could not tell if there was a fog because the air was not clear enough, or as if I insisted on perfect sunlight in order to see a solar eclipse.I conclude that miracles do happen. I am forced to it by a conspiracy of facts the fact that the men who encounter elves or angels are not the mystics and the morbid dreamers, but fishermen, farmers, and all men at once coarse and cautious; the fact that we all know men who testify to spiritualistic incidents, but are not spiritualists; the fact that science itself admits such things more and more every dayThe sceptic always takes one of the two positions: either an ordinary man need not be believed or an extraordinary event must not be believed. For I hope we may dismiss the argument against wonders attempted in the mere recapitulation of frauds of swindling mediums or trick miracles. That is not an argument at all, good or bad. A false ghost disproves the reality of ghosts exactly as much as a forged banknote disproves the existence of the Bank of England--if anything it proves its existence.
It's not always the case that "the disbelievers in miracles deny them ... because they have a doctrine against them." Sometimes they deny miracles because they have found actual evidence of fraud, or have reasonable grounds for suspecting fraud. For instance, James Randi famously exposed the "miracles" of faith healer Peter Popoff as fraudulent by recording secret radio communications sent to him by his wife.
And while it's true that "the believers in miracles accept them ... because they have evidence for them," it's also true that the believers have a doctrine that makes them more inclined to accept evidence that others might reject or doubt.
Overall, however, I'm pleasantly surprised that Chesterton was so open to the phenomena of spiritualism. In this he differs from C.S. Lewis, another famed Christian apologeticist, who dismissed spiritualism as mostly empty blather.
P.S. Late in life, Lewis may have changed his mind a bit. Look at Dave Armstrong's first comment on this page for an excerpt from Lewis's A Grief Observed, in which Lewis recounts a spectral visitation by his late wife. Two reported ADCs from Lewis himself are also mentioned.