Abstract
This essay focuses on Charles S. Peirce’s grammar of representation and its relevance for a logical conception of scientific inquiry. Closely relying on Peirce’s writings, one of his important trichotomies of signs will be discussed in particular: that distinguishing between substitutive signs, or “semes”, informational signs, or “phemes”, and persuasive signs, or “delomes”. According to Peirce, these three categories of signs result from an extension of the traditional division between “terms”, “propositions”, and “arguments” to all signs (not just symbols), understood as the foundational elements with and on which the scientific mind operates. It is shown that such an extended view of logic, conceived as a “semiotic”, or general doctrine of signs, is consistent with Peirce’s metaphysical views on truth and reality. Logic-as-semiotic, and its three corresponding branches of stecheotic, critic, and methodeutic, is thus conceived as a requisite normative trivium for the practice of scientific inquiry, whose purpose is to represent reality truthfully. In the end, we aim to remind that Peirce’s semiotic epistemology must necessarily be contextualized within the frame of his comprehensive philosophy of the scientific “settlement of opinion”.
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Notes
References to Peirce (1931–1935) are given by CP, in decimal notation, followed by volume and paragraph number; references to Peirce (1982–2009) are given by W, followed by volume and page number; references to Peirce (1998) are given by EP2, followed by page number; references to Peirce’s unpublished Mss. (Houghton Library, Harvard University) are given by R, followed by Ms. number as established by Robin (1967) and page number as penned by Peirce.
In the actual reading of the lecture, Peirce declared that “every man is fully satisfied that there is such a thing as truth, or he would not ask any question. That truth consists in a conformity to something independent of his thinking it to be so, or of any man’s opinion on that subject” (EP2: 240 [1903]).
In a 1909 unpublished manuscript, Peirce assured in the same vein that “no thinking about it will at all modify the Real object, since this is precisely what is meant by calling it Real. It is sometimes an object shaped by thinking,—of which the very last sentence affords an example; but so far as it is Real, it is not modified by thinking about it” (R 634: 9 [1909]). In the specific case of fiction, however, the object happens to be “modified” by the representation. For instance, Conan Doyle could have imputed blindness to Holmes, therefore affecting “him” as an object of thought.
This amounts to saying that a character may be “prescinded” from an object while an object may not be “prescinded” from a character.
Hence, “to say that every proposition is either true or false is to say that whatever the predicate, X, of a proposition may be, its subject S is either X or not X” (EP2: 168 [1903]), and “it is propositions alone that are either true or false” (EP2: 224 [1903]). Likewise, “any proposition you please, once you have determined its identity, is either true or false” (EP2: 351 [1905]).
A fact may thus be construed as an abstract state of things, itself a constituent element of reality, that “can be wholly represented in a simple proposition” (EP2: 378 [1906]).
In an 1895 unpublished essay, Peirce thus maintained that “the real world cannot be distinguished from a fictitious world by any description. Now reality is altogether dynamic, not qualitative. It consists in forcefulness. Nothing but a dynamic sign [i.e. an index] can distinguish it from fiction” (CP 2.337 [ca. 1895]). Ten years later, in his 1906 Monist paper, Prolegomena to an Apology for Pragmaticism, he reminded in the same vein that indices “furnish positive assurance of the reality and the nearness of their Objects” (CP 4.531 [1906]).
Peirce thus argued that “the expressed subject of an ordinary proposition approaches most nearly to the nature of an index when it is a proper name which, although its connection with its object is purely intentional, yet has no reason (or, at least, none is thought of in using it) except the mere desirability of giving the familiar object a designation” (CP 2.357 [1902]).
In other words, “when the subject is not a proper name, or other designation of an individual within the experience (proximate or remote) of both speaker and auditor, the place of such designation is taken by a virtual precept stating how the hearer is to proceed in order to find an object to which the proposition is intended to refer” (CP 2.357 [1902]). Peirce gave the following example of such a “precept by following which a singular could be found” (EP2: 168 [1903]): “Some woman is adored by every Catholic. This means that a well-disposed person with sufficient means could find an index whose object should be a woman such that allowing an ill-disposed person to select an index whose object should be a Catholic, that Catholic would adore that woman. Thus the subject of a proposition if not an index is a precept prescribing the conditions under which an index is to be had”. Peirce made it also clear that a proposition could “describe, or otherwise indicate, the kind of collateral observation by which [its] Object is to be found. Thus, a proposition whose subject is distributively universal […], such as ‘Any man will die,’ allows the interpreter, after collateral observation has disclosed what single universe is meant, to take any individual of that universe as the Object of the proposition, giving, in the above example, the equivalent ‘If you take any individual you please of the universe of existent things, and if that individual is a man, it will die” (EP2: 408 [1907]). Thus, it may be “necessary to give a general direction as to the manner in which an object intended may be found. Especially it is necessary to be able to say that any object whatever will answer the purpose, in which case the subject is said to be universal, and to be able to say that a suitable object occurs, in which case the subject is said to be particular” (CP 4.59 [1893]).
In his unpublished New Elements, probably written in early 1904, Peirce thus remarked that “in addition […] to denoting objects, every sign sufficiently complete signifies characters” (EP2: 304 [1904]). Such a “complete” sign is a proposition.
In that particular example, the predicate itself acts as an index existentially connected with the said case.
In his 1885 paper On the Algebra of Logic, published in the American Journal of Mathematics, Peirce thus contended that “the index asserts nothing; it only says ‘There!’ It takes hold of our eyes, as it were, and forcibly directs them to a particular object, and there it stops” (W5: 163 [1885]). Its purpose is to bring its interpreter to have a collateral experience with its object, or to give determinate instructions to live one.
Note in passing that a symbolic predicate is a so-called legisign, or general sign: a legisign “is not a single object, but a general type which, it has been agreed, shall be significant. Every legisign signifies through an instance of its application, which may be termed a Replica of it” (EP2: 291 [1903]). Accordingly, I agree with Short (2007, p. 210) that “the essential feature of legisigns and their replicas […] is that the purpose they have to signify constitutes their significance”. We shall then complete what has been said above: proper names and designations are legisigns as well, albeit indexical instead of symbolic. As a matter of fact, Peirce often used the definite designation “the” as an example of a prototypical legisign: “there is but one word in the English language which is used as a definite article, and this word is no more printed that it is pronounced. In a literal sense, it cannot be printed or pronounced; it can only govern and determine what is printed or pronounced. Its being consists in its so governing existents, while it does not itself exist. I term such a sign a Type” (R 295: 24–26 [ca. 1906]). In other words, indexical legisigns are “types” as well, but types whose actual instances are meant to be construed as referring to something individual and real which they are existentially connected with.
Peirce also noted that depending on the kind of concept symbolically signified, an object may actually be conceived as a set of partial objects. Some propositions may thus involve polyadic predicates destined to be saturated by multiple subjects that could each function indexically. For instance, “John” and “Peter” in “John kills Peter”, and “John”, “the book”, and “Peter” in “John gives the book to Peter” are such “partial objects” (EP2: 492 [1909]). Said Peirce in his 1907 rejected letter to the editors of the Nation and the Atlantic Monthly: “The object of a sign, though singular, may nevertheless be multiple, and may even be infinitely so. […] What, for example, is the object of ‘runs’? Answer: it is something, a runner. What is the object of ‘kills’? Answer: it is a pair of indesignate individuals, the one a killer, the other killed by him. So ‘gives’ has for its object a triplet of related indesignate singulars, a giver, a gift, a recipient of that gift from that giver” (EP2: 408 [1907]). Incidentally, Peirce showed also that a predicate in a position of subject really remains a predicate: “the sentence ‘every man loves a woman’ is equivalent to ‘whatever is a man loves something that is a woman’” (EP2: 17 [1895]). Several passages testify to that doctrine. For instance, in the same draft chapter of his unfinished Grand Logic cited above, Peirce observed that “we find in grammatical forms of syntax, a part of the sentence particularly appropriate to the index, another particularly appropriate to the symbol. The former is the grammatical subject, the latter the grammatical predicate. In the logical analysis of the sentence [however], we disregard the forms and consider the sense. Isolating the indices as well as we can, of which there will generally be a number, we term them the logical subjects, though more or less of the symbolic element will adhere to them unless we make our analysis more recondite than it is commonly worth while to do; while the purely symbolic parts, or the parts whose indicative character needs no particular notice, will be called the logical predicate” (CP 4.58 [1893]).
Anything existentially connected with something else necessarily reacts with that second thing: “nothing can be contiguous but acts of reaction. For to be contiguous means to be near in space at one time; and nothing can crowd a place for itself but an act of reaction” (CP 4.157 [ca. 1897]). Likewise, “any real connection whatsoever between individual things involves a reaction between them” (EP2: 153 [1903]).
It follows that iconic predicates cannot generally signify any kind of characters, or concepts, like symbolic predicates can. An icon merely signifies a quality, or complexus of qualities, as it immediately is and this, even if no mind ever interpreted it as a sign: “an icon is significant with absolute directness of a character which it embodies” (EP2: 320 [1904]). Symbolic predicates, on their side, may generally signify the character or concept they do (by virtue of a habit of interpretation), even though their proper interpretation may ultimately result in pure icons (i.e. composite mental photographs of images of all the past experiences which actual instantiations of this or that concept have implied). More essentially, contrary to mere icons, they are susceptible of signifying any possible consequences which the possession of the character signified would imply for its object, provided conditional events are actually fulfilled. For instance, stamping a stone as “hard” implies that it would resist an attempt to leave a mark, if scratched (e.g. EP2: 254 [1903], EP2: 401 [1907]). Something’s reality is not indeed reducible to its mere existence, i.e. its capacity to actually react with (and affect) me and the other things in its universe: it also comprises all the predictable possible and conditional facts that its very existence does not necessarily actualize hic et nunc but which would occur if conditions were fulfilled, and provided that object really is governed by the law which its related predicate is purported to signify.
In both cases, subject and predicate must actually be “physically collocated” (Stjernfelt 2015): a proposition or quasi-proposition forces us to regard its (quasi-)predicate as a sign of the same object to which its collocated (quasi-)subject is itself connected, therefore conveying some information about that object. Said Peirce in his unpublished Basis of Pragmaticism essay: “a proposition has a subject (or set of subjects) and a predicate. The subject is a sign; the predicate is a sign; and the proposition is a sign that the predicate is a sign of that of which the subject is a sign. If it be so, it is true” (EP2: 379 [1906]).
Put differently, “the fact that the [photograph] is known to be the effect of the radiations from the object renders it an Index and highly informative” (EP2: 297 [1903]). Peirce thus argued that “we have an important division of indices into those which give information and those which merely serve to identify individuals” (R 491: 4 [ca. 1903]).
Other passages in Peirce’s writings attest to that understanding, although he used “proposition” in its broader sense: “a man’s portrait with a man’s name written under it is strictly a proposition, although its syntax is not that of speech” (EP2: 282 [1903]), or “a portrait with the name of the original below it is a proposition. It asserts that if anybody looks at it, he can form a reasonably correct idea of how the original looked” (CP: 5.569 [1906]), etc.
In the 1907 rejected letter to the editors of the Nation and the Atlantic Monthly, already cited, Peirce appealed to the semiotic distinction raised by John of Salisbury “between that which a term nominat,—its logical breadth,—and that which it significat,—its logical depth. In the case of a proposition, it is the distinction between that which its subject denotes and that which its predicate asserts. In the case of an argument, it is the distinction between the state of things in which its premisses are true and the state of things which is defined by the truth of its conclusion” (CP 5.471 [1907]).
In his unpublished Sketch of Logical Critics, Peirce defined “reasoning” in the following terms: “By ‘Reasoning’ shall here be meant any change in thought that results in an appeal for some measure and kind of assent to the truth of a proposition called the ‘Conclusion’ of the reasoning, as being rendered ‘Reasonable’ by an already existing cognition (usually complex) whose propositional formulation shall be termed the ‘Copulate Premiss’ of the reasoning” (EP2: 454 [1911]).
Of course, “the first step of inference usually consists in bringing together certain propositions which we believe to be true, but which, supposing the inference to be a new one, we have hitherto not considered together, or not as united in the same way. This step is called colligation” (EP2: 22 [1895]). A mere proposition cannot, by itself, signify any one of the possible consequent propositions which it might imply: its meaning is undetermined. But such determination of an intended conclusion is precisely that which two premisses are purposed to do.
It shall here be mentioned that Peirce invariably pointed out the irrelevance of psychology for the business of logic, the reason being that the latter is precisely concerned with signs and not with “judgments as they are in the mind” (R 637: 30 [1909]). More precisely, in his unpublished Basis of Pragmaticism essay, Peirce had argued that “Logic includes a study of reasoning […] and reasoning may be regarded […] as a psychical process. If we are to admit that, however, we must say that logic is not an all round study of reasoning, but only of the conditions of reasoning being bad or good, and if good to what degree, and in what application. […] The psychological process of reasoning is wholly aside from the purpose of logic” (EP2: 386 [1906]). As a result, Peirce had reminded a few years earlier that “the logicality of a given argument […] does not depend on how we think that argument, but upon what the truth is” (EP2: 257 [1903], our emphasis).
See Bellucci (2004; 2018) for a historical account of this extension of the scope of logic.
I believe it unfortunate that Peirce had used “rheme” (from ancient Greek ῥῆμα, rhêma, or “verb”) to refer to pure indices. Defined as that which remains when a proposition is severed from its subject (e.g. EP2: 221 [1903], EP2: 308 [1904]), a rheme shall thus only be conceived as a predicate (or its equivalent). To our knowledge, there is only one instance in Peirce’s writings acknowledging the “onomatic” nature of subjects (from ancient Greek ὄνομᾰ, ónoma, or “name”): in the 1903 Syllabus, it is stated indeed that “any term fit to be the subject of a proposition may be termed an Onome” (EP2: 286 [1903]). On this ground, following Bricteux (2014, p. 28), I think that Peirce should have maybe called his “indexical rheme” an “indexical onome” instead, and could have simply distinguished between rhematic and onomatic semes, which is the direction taken here.
Summing it up, an iconic seme is anything that is fit to serve as a substitute for anything that it is like (EP2: 273 [1903]), an indexical seme is anything that is fit to serve as a substitute of anything that it is existentially connected with (EP2: 163 [1903]), and a symbolic seme is anything that is fit to serve as a substitute of anything that supposedly constitutes an instance of the very character, or concept, that the symbol is purposed to signify.
An alternative term for pheme was the well-known “dicisign”, or “dicent sign” (e.g. EP2: 275 [1903], EP2: 292 [1903], and EP2: 478 [1906]): a sign “that says” something.
The fact that an interrogation or command expresses remains the same, whether it be interrogated or commanded: “an assertion has its modality, or measure of assurance, and a question generally involves as part of it an assertion of emphatically low modality” (CP 4.57 [1893]).
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Gaspard, J. “A familiar logical triplet”: on Peirce’s grammar of representation and its relation to scientific inquiry. Synthese 199, 5669–5686 (2021). https://doi.org/10.1007/s11229-021-03041-7
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DOI: https://doi.org/10.1007/s11229-021-03041-7