Towards Understanding Pragmatism as the Logic of Explanation[1]

 

2009 SAAP Paper Submission

 

Abstract:  It is generally lamented that C.S. Peirce never completed his several ambitious book projects.  However, this sentiment is often accompanied by a neglect of Peirce’s 150-page monograph of 1901, “The Logic of Drawing History from Ancient Documents, especially Testimonies.”  This monograph presents an intriguing transition in Peirce’s thought, as it offers an extensive account of his mature logic of inquiry, and yet was written before Peirce joined the debates surrounding pragmatism.  In particular, Peirce fully distinguishes abduction and induction in this monograph, and as in 1903 he declares pragmatism to be the logic of abduction, we may find some insight into Peirce’s efforts to distinguish himself from other “pragmatists” in this earlier work.  This paper will endeavor to begin such an inquiry by providing some background to this monograph in Peirce’s criticism of Humean historiography and then briefly exploring one dimension of abduction’s function – that of providing explanations.   

 

Paper:

 

 

I:  Abduction before Pragmatism

            In the fall of 1901 Peirce completed a monograph of 150 typed pages entitled “The Logic of Drawing History from Ancient Documents, especially Testimonies.”[2]  Peirce begins with a critique assessing testimonies by the “method of balancing likelihoods” he considers common to David Hume and the German higher critics, especially the historian of philosophy Eduard Zeller.[3]  From here Peirce moves to a detailed exposition of his mature logic of science, including an account of the role of “economy” in evaluating hypotheses worth holding.  Finally, this monograph concludes with three extensive examples of Peirce’s method in action on three topics of ancient history:  the tradition regarding the transmission of Aristotle’s texts, the dating of Plato’s dialogues, and the biography of Pythagoras. 

            In addition to its intrinsic interest, this monograph also rests at a transition in Peirce’s philosophical career.  Specifically, William James’ announcement of “pragmatism” in his 1898 address “Philosophical Conceptions and Practical Results” led to a burgeoning philosophical movement, accompanied by vigorous debate.  Although James explicitly attributes the principle at the heart of pragmatism to Peirce, especially 1878’s “How to Make Our Ideas Clear,” there is evidence that Peirce was not aware of this until two years later.[4]  This evidence is a letter Peirce wrote to James on November 10th, 1900 concerning the origin of the term “pragmatism” for an entry on it in James Baldwin’s Dictionary of Philosophy and Psychology (1902).[5]  Peirce asks whether he or James invented the term, and when it first appeared in print, to which James replies that Peirce originated the term and that James used it in 1898.  In addition, James remarks that he sent Peirce two copies of his 1898 address, but had not received acknowledgement of receipt.[6]  Peirce does not use the term “pragmatism” in his 1901 monograph; however, in light of his 1903 claim that pragmatism is the logic of abduction (i.e., hypothesis), the sustained account of abduction in 1901 offers substantial insight into Peirce’s pragmatism, in part precisely because Peirce is not engaged in distinguishing his pragmatism from that of others claiming the mantle.  

For this paper, we will begin with the background to Peirce’s 1901 monograph; specifically, its precursor in an unpublished essay entitled “The Laws of Nature” concerning Hume’s critique of miracles.  From here we will briefly recount Peirce’s conception of abduction as an explanation involving at least virtual prediction, and conclude by suggesting that the maxims of economy in adopting hypotheses offered in 1901, and elsewhere, are potential corollaries or clarifications of Peirce’s pragmatism. 

 

II:  Contra Humean Historiography

            Peirce’s 1901 monograph appears to originate in his correspondence with Samuel P. Langley, at that time the Secretary for the Smithsonian Institute.  In response to Peirce’s behest for an opportunity to publish his work on logic, Langley requested an essay on the topic of the change in conception of a “law of nature,” especially since the time of David Hume.  More specifically, Langley desired an evaluation of Hume’s argument against miracles in 1748’s An Enquiry concerning Human Understanding.  However, Peirce and Langley fundamentally disagreed as to the nature of the topic, and the Smithsonian ultimately published an essay on “The Laws of Nature” written by Langley alone.[7]  As Peirce opens his unpublished monograph with reference to “Hume’s Theory” of balancing likelihoods in assessing testimonies, and that he considers this the implicit methodology of the German higher critics, a closer look at Peirce’s evaluation of Hume’s argument is appropriate.  We will begin with a brief summary of Hume’s well-known argument, distinguished by reference to Hume’s other uses of the terminology involved, before turning to Peirce’s critique.

            Although the publication of Hume’s first Enquiry included an open disavowal of his first work, A Treatise on Human Nature, therein he offers a set of distinctions relevant to the issue of the laws of nature and miracles.[8]  Specifically, Hume asserts that there are (at least) three meanings of the term “nature”:  the first is in opposition to the miraculous, the second is in opposition to the rare and unusual, which Hume claims is the common meaning, and the third is in opposition to the artificial.[9]  Thus, the existence of shoes is “natural” in the first and second sense, while “unnatural” in the third sense.  On the other hand, miracles seem “unnatural” in all three senses – the first by definition, the second by their rarity, and in the third by analogy between human and divine action.  Admittedly, the third case is controversial, but overall this set of distinctions shows Hume’s prejudice against miracles. 

            Hume asserts that “[t]here must, therefore, be a uniform experience against every miraculous event, otherwise the event would not merit the appellation.  And as a uniform experience amounts to a proof, there is here a direct and full proof, from the nature of the fact, against the existence of any miracle…”[10]  A miracle is then, by Hume’s definition, that which has never been experienced, and so naturally no testimony has been sufficient to properly establish belief in a miracle.

            In effect, Hume’s argument against “miracles” amounts to what Peirce typically calls a “pooh-pooh” argument.  A “pooh-pooh” argument is a limited form of induction that consists in denying improbabilities.  This may seem hardly like an argument or reasoning at all, but Peirce includes it as a crude or rudimentary form of induction because it possesses the self-corrective tendency characteristic of induction.[11]  As Peirce articulates it in 1903, “The first order of induction, which I will call Rudimentary Induction, or the Pooh-pooh argument, proceeds from the premiss that the reasoner has no evidence of the existence of any fact of a given description and concludes that there never was, is not, and never will be any such thing.”[12]  This form of argument is self-corrective because the shock of experience may provide evidence for a fact previously dismissed.  In fact, Peirce admits that pooh-pooh induction is indispensable for two related reasons.  The first, somewhat broader, reason is that a pooh-pooh argument rests upon ignorance, which is our relationship to most possible objects of knowledge:  “It goes upon the roughest kind of information, upon merely negative information; but that is the only information we can have concerning the great majority of subjects.”[13]  A bit more narrowly, this crudely inductive argument also serves to prevent occurrences of doubt by dismissing possible, though unlikely, events, such as being robbed at gunpoint:  “For here the unexpected, when it comes, comes with a bang. But then, on the other hand, until the fatal day arrives, this argument causes us to anticipate just what does happen and prevents us from anticipating a thousand things that do not happen.”[14]  In other words, a person with a diminished “pooh-pooh sense” would suffer from paranoia, in a broad sense.

            For all its indispensability for finite beings such as us, pooh-pooh arguments are also fundamentally compromised by this finitude.  That is, an individual’s assessment of what is likely rests largely upon the idiosyncrasies of their experience.  This supports taking the “method of balancing likelihoods” of Hume and German higher criticism as a form of pooh-pooh argument, because Peirce’s main criticism of this method is that it rests too greatly upon subjective likelihoods; that is, Hume and Zeller pooh-pooh that which seems unlikely to a European gentleman of the eighteenth or nineteenth century.  Quoting Peirce: 

To such a pitch is this [higher criticism] carried that, although we can have no knowledge of ancient history independent of Greek (and Latin) authors, yet the critics do not hesitate utterly to reject narratives attested sometimes by as many as a dozen ancient authorities -- all the testimony there is, at any rate -- because the events narrated do not seem to persons living in modern Germany to be likely.[15]

 

Thus, the methodology adopted by Hume and the higher critics is actually a defective form of a rudimentary inductive argument.  That is, rather than inferring the unlikelihood or impossibility of an event or class of events from an absence of evidence, they first dismiss any evidence contrary to their preconceived sense of probability.[16]   As stated in 1901, Peirce’s finds his methodology of evaluating testimony superior because it demands accounting for all of the evidence, even evidence for events that are highly improbable.  In other words, Peirce demands an explanation for the evidence that we do see, even that which is ridiculous or known to be false.

 

III:  Abduction as Explanation

 

            For Peirce, an explanation is an abduction, which resolves an unexpected event into the consequence of a general principle.  That is, the event in question would not be unexpected, or at very least predicable, if the hypothesis had been known before hand.  In Peirce’s words, “Accepting the conclusion that an explanation is needed when facts contrary to what we should expect emerge, it follows that the explanation must be such a proposition as would lead to the prediction of the observed facts, either as necessary consequences or at least as very probable under the circumstances.”[17]  In order to understand Peirce’s maxims for assessing testimony and his criticism of Hume, we need to explore his account of explanation. 

            As we have seen, by Peirce’s definition the need for an explanation begins with a surprising event.  In fact, all knowledge begins with a surprising event, which reveals to us that we had an expectation that in this case was not met.[18]  Of course, this claim is consistent with Peirce’s arguments in “Some Consequences of Four Incapacities” and elsewhere that an ego develops through an awareness of ignorance and error, as well as the doubt-belief model of inquiry from “The Fixation of Belief.”  Peirce now answers the questions “How surprising?” and “What is surprising?”  The answer to the first question is, perhaps surprisingly, “Not particularly surprising at all.”  The irritation of doubt, the shock of surprise, does not have to be strong to call forth an explanation.  As Peirce asserts, “Let me not, however, be understood to make the strength of an emotion of surprise the measure of a logical need for explanation.  The emotion is merely the instinctive indication of the logical situation.  It is evolution (φυσισ) that has provided us with the emotion.  The situation is what we have to study.”[19]  This qualification relates to the notion of “feigned hesitancy” in the later Peirce, which occupies a middle ground between the “noble metal” of genuine doubt and the paper doubt of Descartes that Peirce savages in 1868.  More colloquially, puzzlement, even if self-generated, may inspire inquiry as much as an acute shock.  For example, Peirce consistently claims that the tri-dimensionality of space requires an explanation, although it is a commonly experienced fact – no one wakes up and boggles at the fact that space is three-dimensional yet again today.

            For Peirce, the experientially (emotionally) unsurprising fact of space requires explanation precisely because it is a regularity.  Peirce regularly denies Paul Carus’ position that irregularity is that which demands explanation.  The point here is that Carus, and those who agree with him, confuse a violation of regularity – an unmet expectation – with an irregularity.  Let me clarify.  Take a set of die throws, each with a different outcome.  Here there is no call for an explanation beyond an appeal to chance; one could say that the outcome of a die toss is regularly irregular.  Conversely, if a set of tosses has the same outcome, an explanation is needed proportional to the size of the set.  For example, three sixes in a row needs no explanation, nor perhaps 10 – but if someone rolls 50 sixes in a row, an immediate explanation is that the die is rigged.  That is, this regularity contradicts the expected “regularity” of random outcomes.  Of course, 50 sixes in a row could be the product of chance, but this is prohibitively unlikely.  In general, Peirce is very sensitive to the limitations of regularity in our experience:

I am, for reasons similar to this, as well as for others, confident that mere irregularity, where no definite regularity is expected, creates no surprise nor excites any curiosity.  Why should it, when irregularity is the overwhelmingly preponderant rule of experience, and regularity only the strange exception?  In what a state of amazement should I pass my life, if I were to wonder why there was no regularity connecting days upon which I receive an even number of letters by mail and nights on which I notice an even number of shooting stars!  But who would seek explanations for irregularities like that?[20]

 

Returning to Peirce’s example of the dimensionality of space, most writers on the nature of space never explain why three dimensions rather than some other number, because they do not expect any dimensionality besides three.  On the other hand, Peirce’s investigations into geometry and physics led him to expect another dimensionality, and thus he desires an explanation for why a regularity of three dimensions rather than a regularity of, say, four.[21]  This ground for explanation is crucial to Peirce’s method of assessing testimonies.  For example, even if it is false that Pythagoras had a golden thigh, a historian should explain why this tradition (regularity) rather than another.

            To clarify further his theory of explanation, Peirce compares it to that of John Venn’s Empirical Logic, which largely follows the account of John Stuart Mill.  The first point is Peirce’s broad agreement with Venn that isolated facts demand explanation.  However, every fact is more or less isolated from other facts, and hence the demand for explanation is more or less.[22]  Nonetheless, Peirce considers the call for explanation to be more specific than Venn’s characterization.  That is, it is not a fact’s isolation, but rather its connection to other facts that render it unlikely, which needs explanation.

But I [Peirce] suspect that when Mr. Venn speaks of isolation, he is thinking of there being other facts from which the given fact is separated; and that it is not isolation that he means, but separation.  Now separation is itself a kind of connection; so that if that be his meaning, the state of things which calls for explanation is a connection which is not satisfactory to the mind…If he [Venn] were to say, "unsatisfactory in being contrary to what ought to be expected," he would come to my [Peirce’s] position, precisely.[23]

 

Beyond this general call for explanation, Venn follows Mill in asserting that there are two, or perhaps three, kinds of explanations.  Peirce agrees that there are in fact two kinds, with the third being a minor modification of the second.  More properly for Peirce, there are two kinds of rationalization, one being regularization and the other being explanation proper.[24]  Regularization is a meager form of explanation that postulates that an event is in fact something that happens.  Peirce uses Venn’s example of an “explanation” as to why a wilting flower is robust in the morning – “Because it/they always do.”  More formally, regularization is a syllogism following the general pattern of an abduction:

[Rule]               Plants of a certain class usually revive in the morning;

            [Result]            This plant belongs to that class;

            [Case]              .·.  This plant might be expected to revive in the morning.[25]

 

This also parallels Peirce’s typically example of hypostatic abstraction, the much-maligned explanation of opium putting someone to sleep because it possesses a “dormitive virtue.”[26]  Peirce asserts that these regularizations are minimally explanatory because at least they postulate that an effect associated with one object will likely be seen the in presence of similar objects.  In other words, “[n]ow it is true that the effect of the regularization is that the fact observed is less isolated than before; but the purpose of the regularization is, I think, much more accurately said to be to show that it might have been expected, had the facts been fully known.”[27] 

            On Peirce’s terms, then, regularization differs from explanation proper primarily in degree.  That is, we desire an explanation for a fact brought into relation with a number of other facts, the combination of which renders the first fact unlikely.  Using Venn’s example, why is it difficult to walk on ice?  For Peirce, considering this fact in isolation calls for no explanation – it is difficult to walk on ice because my experience is as such.  In the case of indirect experience, “[t]ell a man who never saw ice that frozen water is very hard to walk on, and he may ask whether the feet stick to it, or put other questions in order to figure to himself what you mean; but as long as the fact is apprehended by him as a simple one, he will no more ask why it should be so than a common man asks why lead should be heavy.”[28]  Instead, taking the fact that it is difficult to walk on ice in conjunction with the set of facts that motion is easy on ice – ice skating, sledding, etc. – is the basis for asking for an explanation.  Once more, “[a]n isolated fact is precisely what a demand for an explanation proper never refers to; it always applies to some fact connected with other facts which seem to render it improbable.”[29]  Regarding the above example of regularization, being told effectively that a certain (kind of) plant is robust in the morning and wilts over the course of the day because that is what is does is sufficient for certain purposes.  On the other hand, asking why this plant has a certain behavior, in contrast to other kinds, requires a deeper sort of explanation.

            Obviously, Peirce’s emphasis on expectation intimately ties explanation to prediction.  Indeed, Peirce claims that all proper explanations/ hypotheses involve at least virtual predictions.  For example, “[b]ut evidently, science has, not so much to describe experience, as to generalize it.  To generalize it is to comprehend it.  Moreover, generalization refuses to limit itself to the past, but involves virtual prediction.”[30]  Peirce’s definition of virtual in Baldwin’s Dictionary of Philosophy and Psychology is pertinent here:  “A virtual X (where X is a common noun) is something, not an X, which has the efficiency (virtus) of an X.”[31]  Thus, a virtual prediction is not actually a prediction, a before-saying, but does have the (dis)confirmatory force of a prediction.  It is clear from Peirce’s own examples that virtual prediction primarily involves the unification of known evidence into a conceptual whole, something along the lines of a retroactive interpretation.  This is consonant with the final clause of Peirce’s definition of a virtual prediction:

By the term "virtual prediction," I mean an experiential consequence deduced from the hypothesis, and selected from among possible consequences independently of whether it is known, or believed, to be true, or not; so that at the time it is selected as a test of the hypothesis, we are either ignorant of whether it will support or refute the hypothesis, or, at least, do not select a test which we should not have selected if we had been so ignorant.[32]

 

            This definition points again to the flaw in Humean historiography – it selects a test prejudiced against the evidence it has before it.  In other words, it prefers to dismiss evidence rather than make an honest effort to explain it.  This is likely unfair to Hume himself, and perhaps to other writers whom Peirce castigates, but does suggest the difficulties inherent in making plausibility the only level of evaluation, as error, imposture and foolishness are always plausible explanations for something that strains our credulity.[33]

           

IV:  Demi-cadence on Economy

 

If we are to take Peirce’s claim that pragmatism is the logic of abduction – and hence of explanation and hypothesizing – seriously, then we may need to pay more attention to the maxims of economical research he offers.[34]  Of course, several scholars have explored Peirce’s prescient account of economy in scientific research, but the link between economy and the clarification of concepts is far from obvious.  Let us conclude by noting only the first rule offered in 1901 concerning the evaluation of hypotheses, and perhaps of pragmatically clarified concepts:  “Now the first rule which we should set up is that our hypothesis ought to explain all the related facts. It is not sufficient to say that testimony is not true, it is our business to explain how it came to be such as it is.”[35]   


 

[1] Explanation:  1382, from L. explanationem noun of action from explanare "to make plain or clear, explain," lit. "make level, flatten," from ex- "out" + planus "flat" (see plane (1)). Originally explane, spelling altered by infl. of plain. The verb explain is first attested 1513.

[2] Partially published in CP 7.164-7.255 and EP 2: 75-114; see MSS 690 and 691 for the full versions (one handwritten, one typed). 

[3] Peirce focuses his disdain on Zeller, who wrote a very popular history of Greek philosophy (Philosophie der Griechen [1844-1852]).  This is likely because of Peirce’s explicit omission of biblical criticism done in a similar fashion:  “But the German critics (I [Peirce] speak only of those who treat of the history of philosophy, for I have never looked into the Biblical criticisms) are as illogical as Hume and in much the same way” (CP 6.513 “Answers to Questions Concerning the My Belief in God [c. 1906]).

[4] Note that “How to Make Our Ideas Clear” does not contain the term “pragmatism” in any form (in spite of the headings added by the editors of the Collected Papers).  Moreover, Peirce declined to include his sense of “pragmatism” in the Century Dictionary, despite writing the entry for “pragmatic” – see CP 5.13 [c. 1906].  As an intriguing aside, Peirce’s subdefinition of “pragmatic method” is as follows:  “the treatment of historical phenomena [by historians] with special reference to their causes, antecedent conditions, and results” (Century Dictionary, 4667 [1889-1914]).

[5] The entry for “Pragmatic and Pragmatism” in Baldwin’s Dictionary asserts that the concept, if not the name, originated in 1878, while James’ 1898 statement of pragmatism “…pushed this method to such extremes as must tend to give us pause” (CP 5.3 [1902]).

[6] CP 8.253 and 8.253 n. 8 [1900].  Peirce’s questions may sound odd in light of his later self-presentations as the founder of pragmatism; nonetheless, the issue of who invented the term is different from whether Peirce used the term to describe his position.

[7] From a letter from Peirce to Langley:  “Certainly nothing can be farther from my desire to quarrel with you any task you may set me, but the difficulty of bringing subjects so remote from one another, and so complex, as Hume’s argument and the Laws of Nature into one piece was extreme.  Hume’s argument has nothing to do with the Laws of Nature.  That is the difficulty” (VUC 286 [1901], author’s italics). 

[8] From Hume’s “Advertisement” to his first Enquiry:  “Yet several writers, who have honoured the Author’s Philosophy with answers, have taken care to direct all their batteries against that juvenile work, which the Author never acknowledged…Henceforth, the Author desires, that the following Pieces may alone be regarded as containing his philosophical sentiments and principles”  (Enquiry 83 [1748/1777]).

[9] See Treatise 3.1.2.7-10 [1739-1740]

[10] Enquiry 10.1.12 [1748/1777]; Peirce notes that this definition of a miracle is the only one relevant to Hume’s argument – see VUC 313 [1901]

[11] Peirce’s later articulations of “pooh-pooh” induction most closely match the second genus of induction described in the 1901 monograph.

[12] CP 7.111 [1903]; see also CP 2.269 [1910]:  “A Pooh-pooh Argument is a method which consists in denying that a general kind of event ever will occur on the ground that it never has occurred. Its justification is that if it be persistently applied on every occasion, it must ultimately be corrected in case it should be wrong, and thus will ultimately reach the true conclusion.”

[13] CP 7.111 [1903]

[14] CP 2.757 fn1 [c. 1902]

[15] CP 6.536 “Hume on Miracles” [1901]

[16]  In “marvelous” although not “miraculous” cases, Hume is much more accepting of testimony:  “Now moral evidence is nothing but a conclusion concerning the actions of men, derived from the consideration of their motives, temper, and situation.  Thus when we see certain characters or figures described upon paper, we infer that the person, who produced them, would affirm such facts, the death of Caesar, the success of Augustus, the cruelty of Nero; and remembering many other concurrent testimonies we conclude, that those facts were once really existent, and that so many men, without any interest, would never conspire to deceive us; especially since they must, in the attempt, expose themselves to the derision of their contemporaries, when these facts were asserted to be recent and universally known”  (Treatise 2.3.1.15 [1739-1740]).

[17] CP 7.202 [1901]

[18] See CP 7.188 [1901]:  “No man can recall the time when he had not yet begun a theory of the universe, when any particular course of things was so little expected that nothing could surprise him, even though it startled him.  The first surprise would naturally be the first thing that would offer sufficient handle for memory to draw it forth from the general background…The first new feature of this first surprise is, for example, that it is a surprise; and the only way of accounting for that is that there had been before an expectation.  Thus it is that all knowledge begins by the discovery that there has been an erroneous expectation of which we had before hardly been conscious.”

[19] CP 7.190 [1901]

[20] CP 7.189 [1901]

[21] See CP 7.197 [1901]

[22] See CP 7.198 [1901]

[23] CP 7.198 [1901].  Peirce notes that the discrepancy between his position and that of Venn’s may arise from the differences of their respective empiricisms.  Venn seems to follow the British empiricist school, in which logical thought begins with percepts, or even with impressions of sense.  In contrast, for Peirce logical thought begins with perceptual facts, which are judgments regarding percepts, and thus already in a relation with other facts.  “But I [Peirce] maintain that logical criticism cannot go behind perceptual facts, which are the first judgments which we make concerning percepts.  A perceptual fact is therefore an abstract affair.  Each such fact covers only certain features of the percept.  I look at an object and think that it seems white.  That is my judgment of the object perceived, or my judgment concerning the percept, but not the percept itself; and it is idle to attempt to criticize by any logic that part of the performance of the intellect which draws that judgment from the percept, for the excellent reason that it is involuntary and cannot be prevented or corrected” (CP 7.198 [1901]; original emphasis).

[24] CP 7.199 [1901]

[25] CP 7.199 [1901]; compare CP 2.623 [1878]

[26] For example:  “Even in this burlesque instance [Moliere’s Le Malade Imaginaire of 1673], this operation of hypostatic abstraction is not quite utterly futile. For it does say that there is some peculiarity in the opium to which the sleep must be due; and this is not suggested in merely saying that opium puts people to sleep”  (CP 5.534 [c. 1905]).

[27] CP 7.199 [1901]

[28] CP 7.200 [1901]; this suggests the role of collateral experience in interpretation.

[29] CP 7.200 [1901]

[30] CP 8.155 “Review of Pearson’s Grammar of Science” [1901]; emphasis added

[31] CP 6.372 [1902]

[32] CP 2.96 [c. 1902]

[33] CP 8.223 [c. 1901]:  “By plausibility, I mean the degree to which a theory ought to recommend itself to our belief independently of any kind of evidence other than our instinct urging us to regard it favorably.”

[34] One article devoted solely to this question, although without referring to the 1901 monograph, is W.M. Brown’s “The Economy of Peirce's Abduction,” Transactions of the Charles S. Peirce Society, 19:4 (1983:Fall) pp. 397-411.  Other examples abound.

[35] CP 7.225 [1901].  The remaining rules are 2) assume that principal testimonies are true, 3) accept only strictly objective and great probabilities, 4) divide hypotheses into testable parts, 5) enlarge the field of facts to judge between two hypotheses, 6) prefer hypotheses substantially tested in the testing of another hypothesis (CP 7.226-7.230 [1901]).