A defense of Charles Sanders Peirce and William James against the charge that their asymptotic approaches to truth and hope are juvenile.

Why We Won’t Ever Arrive at Truth

On the surface, Nick Gall’s two excellent and stimulating Erraticus essays on hope are a feature story surveying the big names of meliorism—a middle-way approach between pessimism and optimism—but he drops numerous hints that he sees some formulations as superior to others. (I also found the essays inspiring, significant praise I consider higher than just being right.)

Gall calls Charles Sanders Peirce and William James’ version of meliorism “juvenile,” “tender-minded,” and “naive.” Briefly, he categorizes Peirce and James’ versions of meliorism as asymptotic. Asymptotic refers to a mathematical function that gets closer and closer without end to a particular value, represented as a straight line—the asymptote. 

Throughout most of his first essay, he offers an even-handed survey of prominent versions of meliorism. But towards the end of the first and throughout the second, it is clear that he considers Charles Peirce and William James’ meliorisms inferior to John Dewey and Richard Rorty’s, yet Gall doesn’t clearly make this argument in his essays.

Perhaps because his essays purport to be a survey of the various forms of meliorism, Gall doesn’t devote much space to arguing that Peirce and James’ asymptotic meliorism (hereafter asymptoticism) is a critical weakness. For Gall, the “juvenile” feature of asymptoticism is: hope for eventual arrival at truth/perfection/salvation. For example, Gall says:

  1. Peirce and James offer a “naive hope in eventual perfection.”
  2. Peirce and James espouse a “juvenile desire to finally arrive at perfection.”

These statements seem to conflict with his correct description of an asymptotic curve as one that “draws ever closer to an axis without ever touching it.” In other words, the curve is never arriving, yet ever approaching. Here I will defend Peirce and James by highlighting the distinction between eventual arrival and ever approaching. 

I primarily aim to defend Peirce and James against Gall’s charge that they are juvenile asymptotic forms of meliorism. My conclusion is that Peirce and James are not predicting or prophesying an eventual arrival at anything, and for James, the ideal form is not even monistic, contrary to what Gall claims. The claims listed above are not accurate and Gall must clarify the offensive character in question.

Read “Truth as Pragmatism’s Only Hope

Asymptoticism in Peirce: Eventually or Never Arriving?

Since Gall identifies Peirce and James’ asymptoticism as the damning quality, let’s first consider asymptotic curves. Properly so called, an asymptotic curve never arrives at the asymptote. In other words, there is no finite solution where the two lines intersect, and infinity isn’t a solution. Consider the following function: y = 1/x

A graph image of an asymptote.

The axes here are also the asymptotes (y = 0 and x = 0) because the distance between them and the curve continues to decrease but the curve has no end. Again, (∞, 0) is not a point on the curve. If it were, it would be the last point on the curve, but there is no last point. In other words: it doesn’t make sense to say that the curve intersects with the asymptote at infinity.

Now let us reflect on whether Peirce and James are looking forward to an eventual arrival at truth, perfection, and salvation, or whether they are saying this is even possible. My first conclusion is that Peirce’s asymptoticism is not a prophecy or a prediction—Peirce is describing the logical form of the method of science. 

As I’ve said, Gall makes conflicting statements on asymptoticism. On at least two occasions, he refers to eventual arrival at truth/salvation. On the other hand, he also correctly describes asymptotic curves that ever approach and never arrive. Although Peirce himself never uses the word “asymptote,” he was very knowledgeable of mathematical limits and so was certainly familiar with functions that endlessly tend towards a particular value.

But in his essay “How To Make Our Ideas Clear,” Peirce says: 

[Truth/reality] is independent . . . of what you or I or any finite number of men may think about it . . . . [The progress of science] might even conceivably cause an arbitrary proposition to be universally accepted as long as the human race should last . . . and if, after the extinction of our race, another should arise with faculties and disposition for investigation, that true opinion must be the one which they would ultimately come to.

Yet, that successor race need not come to that ultimate opinion either; belief may not be settled by our species and no minds in the course of the universe may ever believe these truths. Likewise, referring to infinite inquirers is obviously not intended as a possible eventuality. Peirce is describing the logical form of scientific inquiry and not an eventual apotheosis. Therefore, Peirce isn’t offering a prediction or prophecy that one day minds will eventually arrive if we stick to the method. Peirce is saying that scientific inquiry aims at a singular truth, so progress would look like a convergence of our beliefs, guided by their empirical effects.

Similarly, Gall quotes the following passage from Peirce:

Thus, the tendency to habit would be started; and from this with the other principles of evolution all the regularities of the universe would be evolved. At any time, however, an element of pure chance survives and will remain until the world becomes an absolutely perfect, rational, and symmetrical system, in which mind is at last crystallized in the infinitely distant future.

An infinitely distant future isn’t a point on the timeline. As I said, there is no last point at infinity. When Peirce talks about a “finite number of men” versus infinite inquirers and a “infinitely distant” future, he is talking about the logical form of the method and not about a possible eventuality.

For an example of how logical form need not line up with empirical results, we can effortlessly conceive of perfect forms that could never occur in nature. The mathematician’s conception of a circle is more perfect than any circles in nature ever could be.

Similarly, physicists talk of the Planck length (P) as the theoretical minimum unit of physical change (named after Max Planck). Thus, we can think of the Planck length as the bottom-level pixels of the physical universe. But this theoretical minimum doesn’t stop me from conceiving of a distance of half of P (P/2) or a distance much smaller like 1/P. Similarly, completeness, unity, and crystalized perfection are the logical form, but that need not correspond to anything in this world, just like half a Plank length.

The keyword here is that Peirce refers to the opinion that they would come to, were it possible—Peirce is describing the logical form of scientific inquiry.

Scientific inquiry presumes there is truth and falsity and that it is possible to improve our opinions such that they contain less falsity and more truth. The logical limit of this would be to hold no falsity and all the truths. Again, this is not a prediction in this, the next, or any universe containing minded inquirers. So, Peirce’s account of inquiry certainly isn’t a prophecy of an eventual arrival at truth or even a prediction that some distant inquirers will arrive there. The ultimate goal might not even be possible, but we pursue it and make objective progress.

Read “What Do I Hope from Pragmatism?

Asymptoticism in James: We’re ‘Constituted to Believe’

I’m similarly skeptical that James prophesies an eventual arrival at complete truth/salvation, that the process is ever approaching this goal, or if his account should be considered asymptoticism at all. James can be seen to be making a move analogous to Peirce’s logical form. Like Peirce, James is not predicting or prophesying, and instead of discussing the “logic” of scientific inquiry, James describes us as a scientist: we have these habits to believe in God and salvation and this generally works out well for us. 

Gall says it very well: “[James’ meliorism] is not primarily directed at how the world will change in the future . . . James’ focus is on how we should feel about the future of the world—for what should we hope, given our beliefs about such a future.” The only thing I would add to this is that James is not so much focusing on how we should feel, but on how we do feel.

For example, James says, “It would contradict the very spirit of life to say that our minds must be indifferent and neutral in questions like that of the world’s salvation.” We care for the world’s salvation by nature—this is our shared spirit of life. An ethicist might make an argument of the form: if you assume my x, y, z premises are true and you are a rational-minded person, then you should do this or that.

James describes us as a scientist would: look around, we observe x, y, and z, and this theory accounts for what we observe.

For another example of this constitutional spirit of life referred to above, consider the following passage from James’ canonical Pragmatism (1907):

What we were discussing was the idea of a world growing not integrally but piecemeal by the contributions of its several parts. Take the hypothesis seriously and as a live one. Suppose that the world's author put the case to you before creation, saying: "I am going to make a world not certain to be saved, a world the perfection of which shall be conditional merely, the condition being that each several agent does its own 'level best.' I offer you the chance of taking part in such a world. Its safety, you see, is unwarranted. It is a real adventure, with real danger, yet it may win through. It is a social scheme of co-operative work genuinely to be done. Will you join the procession? Will you trust yourself and trust the other agents enough to face the risk?".... Would you say that, rather than be part and parcel of so fundamentally pluralistic and irrational a universe, you preferred to relapse into the slumber of nonentity from which you had been momentarily aroused by the tempter's voice?” . . . . Of course if you are normally constituted, you would do nothing of the sort. There is a healthy-minded buoyancy in most of us which such a universe would exactly fit. We would therefore accept the offer . . . and loyalty to our old nurse Nature would forbid us to say no.

Here James refers to the “normally constituted . . . [with their] healthy-minded buoyancy” to pursue salvation. So, analogous to Peirce who is concerned with the logical form, James is also not prophesizing a possible eventuality, but is describing the orientation of our natural habits and instincts. James says we are constituted to believe—our nature forbids us to say no. He isn’t saying we are chasing idols and phantasms—we are impelled by our nature to believe.

This is what we do.

Finally, Gall doesn’t offer a strong case for asymptoticism in James, and from my discussion above, the case for asymptoticism in James is scant.

Read “Rortian Liberalism and the Problem of Truth

James Retains His Pluralism

Gall’s case for James’ purported asymptoticism is largely based on Gall’s contention that James’ meliorism is actually monistic. I believe Gall misidentifies James’ meliorism here.

In his first essay, Gall cites James in “The Moral Philosopher And The Moral Life” for his formulation of tragic pluralism. James says we can’t all be right about everything; the method of science abides by the evidence, which means countless falsities over time are butchered. James notes, however, “Some part of the ideal must be butchered . . . It is a tragic situation.” In the long run, most beliefs ever held are almost entirely wrong.

But Gall charges James with betraying the tragic pluralism he himself propounds: “James’ meliorism is designed to spark the letting loose of hope by offering confidence in the possibility that we may one day transcend tragic pluralism—reaching the goal of eternally perfect unity (monism).”

I don’t think this is what James is saying; he actually retains his pluralism.

As James says in the passage above, our healthy-minded nature drives us to cooperate and strive to secure the path to truth and salvation—but for James, this is a fundamentally pluralistic and irrational universe” (ital. mine). He says the world “[grows] piecemeal by the contributions of its several parts” (ital. mine), not “integrally”. So, James actually prefers a probable piecemeal pluralistic perfection. 

For a final example of James’ express pluralism, consider the following from Pragmatism, which Gall also quotes: “[The confused pragmatist letter writer] speaks of what he calls the rational unity of things, when all the while he really means their possible empirical unification. He supposes at the same time that the pragmatist, because he criticizes rationalism’s abstract One, is cut off from the consolation of believing in the saving possibilities of the concrete many” (some ital. mine). Here again, James is very explicit about the “saving possibilities of the concrete many.”

In summary, Gall’s claim for James’ monistic asymptoticism is inadequate.

Read “The Pragmatic Truth of Existentialism

This Is What We Do

Peirce and James are not dangling the eventual arrival at perfection in front of our faces, and they are not saying that we are on track to arrive at truth/salvation someday. Not only is this perfection not eventual, but they are also not even saying it is possible we will arrive at a rational unity/truth one day. I think both would say there is objective progress, but if there are ideals involved, they are descriptive and not prescriptive.

James notes there is piecemeal amelioration among the “saving possibilities of the concrete many” and Peirce would say there are certainly examples of theories converging on particular truths, but a complete and crystalized Truth is not forthcoming. For Peirce, the most we can say is that the logical form of investigation has its sights set on truth. This doesn’t guarantee it is even possible. Likewise, James says it is our nature and serves us well to have faith, hope, and belief. He thereby upholds faith, hope, and belief, but isn’t claiming that a final salvation is actually in the cards.

In other words, the logician Peirce and his close friend James are describing how things already are and not how they should be. For Peirce, scientific investigation is oriented around this ever-ameliorating approach to an ideal—this is what we do and this orientation is presumed by the form of inquiry. James says that faith and pursuing salvation are what normal healthy humans do. But neither prophesies that minds will eventually arrive at truth and salvation, just as an asymptotic curve never arrives at the asymptote.

Ian Cran

Ian is a writer with a background in philosophy. He lives in Seattle. He recently published a printed zine on a doctrine he calls pragmagism. The web version can be found at the Journal of Sophistry. A few other scattered writings can be found on Twitter, Medium, and Substack.

3 thoughts on “Why We Won’t Ever Arrive at Truth

  • I suppose it is the truth/adequacy of an entire theory of the world that you are mostly discussing here–what Putnam called a “God’s eye” picture of the universe– and not such paltry “truths” as whether snow is white, Strauss wrote Arabella or it is indeed January 3, 2023 as I write this comment. But I would be interested in hearing whether the subjects of your piece believed that it is possible to dissociate a concept of truth from such big ticket items as “perfection” of an adequate scientific theory of the universe and “salvation” (whatever that might be precisely), whether that too was considered asymptotic by any or all of those philosophers.

    I’m no expert on pragmatism, but I would think that pragmatists would have use of a more workable, everyday concept of the term, and I’d be curious to hear whether you think James, Peirce and Rorty were also at odds on how that everyday notion should be unpacked.


    Walter Horn

    • Hi Walter, Yes, I think James would say there are smaller more serviceable salvations and he is intentionally vague about what he means by “salvation” to allow for these. Likewise with Peirce: he would say we may have arrived at particular truths, but we can never be certain. James had a much more down-to-earth conception of more ordinary truth that did not require metaphysical certainty.


  • There is no absolute truth to which we can ever attain. All we can manage is to develop out sciences and get closer to what us REALLY happening and on this basis try to apply its limited truth to the physical world that we know the best.


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