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I compared the case to the dipping of an ivory object down into water. There will be at any instant, as the dipping proceeds, a water lin, or locus which is at once occupied by air, water, and ivory. No matter at how early an instant in the dipping process we snap our mental camera, there will have been lines already. Where there has no been no line already there is no line, but only a point.
Some men, like our dear James, are and like Thomas Davidson, the founder of this school, think that this [is] absurd. They think there must be a first line. That is, against the testimony of the sense or imagination they invoke logic. Well, we say to them, put the argument, if there be one into any syllogistic form. They are unable to do so. Very well, we say, if it cannot be put into any of the recognized forms of syllogism, tell us under what new form of reasoning this you can put the argument
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you can put the argument that makes the testimony of fact absurd,—that makes it absurd that Achilles should overtake the tortoise,—for that is the same thing. They are unable to do that. Then we say do you mean to say that the real Achilles will not overtake the real tortoise as a fact? No, they admit that he will. So then, we say, we and all mathematicians, who are the only exact reasoners see no absurdity at all in this. But you have an inscrutable logic which cannot be reduced to any principle, which requires you from true premisses to insist upon what you yourselves admit to be a false conclusion. What is logic for, if not to prevent the passage from true premisses to false conclusions? To this, they have nothing to say, but they go their way still insisting that it is absurd that Achilles should overtake the tortoise. "Absurd" we call after them in a [??]
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should mean contrary to reason, and you are unable to formulate this reason. Why not give up this kind of logic and adopt that of all mathematicians? But it is all in vain. More ineradicable with them than reason itself is that tendency of theirs to consider the general, the law, as an existent thing. I do not see what remains to us, to whom the whole matter is perfectly clear, but to say that they are minds congenitally incapable of a necessary form of thought. Certainly a logic which leads one from true premisses to admittedly false conclusions appears to us to be a poor form of logic; and when that logic is unable to formulate itself we are tempted to call it mental incapacity. Yet they base their whole philosophy up[on] this unhesitatingly. I for my part prefer to cast my lot with the mathematicians, whose logic does not kick up such capers, and is able to give an account of itself.
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"Well," says James, "I hate logic." I reply that I am sorry, but a philosophy ought not to be based upon that sentiment.
But though these gentlemen are unable to formulate their own logic, we have no difficulty at all in formulating it for them. They sometimes think that it is continuity only that they object to. They are mistaken. Continuity is not necessarily involved in what they pronounce absurd. What they find absurd is the endless. The very idea of the future, as endless, is to them absurd, though they may not at once see that it is. In short, though they think in signs like the rest of us, they do not really think in general signs, but only in the such imperfect interpretations of them as can be made into images and slight inhibited efforts.
Logic has three branches. The first which treats of the constitution of signs, what for example it is that