Abstract
The paper gives a detailed reconstruction and discussion of Peirce’s doctrine of propositions, so-called Dicisigns, developed in the years around 1900. The special features different from the logical mainstream are highlighted: the functional definition not dependent upon conscious stances nor human language, the semiotic characterization extending propositions and quasi-propositions to cover prelinguistic and prehuman occurrences of signs, the relations of Dicisigns to the conception of facts, of diagrammatical reasoning, of icons and indices, of meanings, of objects, of syntax in Peirce’s logic-as-semiotics.
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Notes
Major contributions include Murphey (1961), Short’s (1984) paper “Some Problems Concerning Peirce’s Conceptions of Concepts and Propositions” which leads up to his treatment of the issue in his Peirce’s Theory of Signs (2008), the two related 1992 papers of Hilpinen (1992, pp. 467–488) and Houser (1992) (ibid. pp. 489–504), as well as and Hilpinen (2007).
It can not be excluded that Peirce knew about the Begriffsschrift but did not care to read it due to the many unfavorable reviews of it at the time; his student Christine Ladd-Franklin mentions it in the 1883 Studies in Logic by Peirce and his students (cf. Anellis 2012). Frege probably learned Peirce’s name from Schröders (disparaging) 1880 review, but neither of the two explicitly faced the other’s ideas nor referred to them.
Peirce’s initial argument here is that symbols are genuine signs in contradistinction to the degenerate sign types of icons and indices. The notion of “degeneracy” comes from the geometry of conic sections where certain sections (the point, the crossing lines, the circle, the parabola) only obtain with particular, non-generic values of the variables, simplifying the equations, as opposed to the generic sections giving ellipses and hyperbolas. Degenerate cases are thus limit phenomena only.From this observation Peirce moves to the special type of symbols which is propositions, the central issue of “Kaina Stoicheia”, able to express facts: “ What we call a “fact” is something having the structure of a proposition, but supposed to be an element of the very universe itself. The purpose of every sign is to express “fact,” and by being joined with other signs, to approach as nearly as possible to determining an interpretant which would be the perfect Truth (...)” (p. 304). Not all Dicisigns, however, are symbols, cf. below.
It should be added that Peirce’s terminology referring to Dicisigns varies, to say the least. Taking his departure in the classic logical trichotomy of Terms, Propositions, Arguments, he invents new terminology in order to indicate his own generalization of that trichotomy to cover all signs. That gives terminological results like “Rhemes, Dicisigns, Arguments”, “Semes, Phemes, Delomes”, or “Sumisigns, Dicisigns, Suadisigns”, just like the parallel version of “Dicent Signs” to “Dicisigns”. Here, we shall generally stick to the “Rhemes, Dicisigns, Arguments” version.
This idea is present already in “On a New List of Categories” (1868) where Peirce outlines the classic distinction term-proposition-argument and defines propositions as follows: “Symbols which also [in addition to determining imputed qualities, FS] independently determine their objects by means of other term or terms, and thus, expressing their own objective validity, become capable of truth and falsehood, that is, are propositions.” (EP I, 8)
In the ten-sign taxonomy of the Syllabus, 1903 (EPII, 296).
As Short also observes, Peirce does in fact—despite Austin’s famous (1961) claim to the contrary—distinguish between a proposition, the tokens representing it (e.g.sentences), the belief of a proposition (the assent to it), and the public claim of a proposition (the assertion of it), cf. below.
Later in the Syllabus, Peirce realizes that Subject terms of propositions must also be classified as Rhemes (in the ten-sign combinatory, e.g., proper names are classified as Rhematic Indexical Legisigns). This seems to imply that they, too, must be considered as unsaturated. Thus, Peirce’s theory differs from both Frege’s and Russell’s in not assuming Arguments/Subjects to be saturated. Saturation, like covalent chemical bonds, are taken to require unsaturatedness in all substances involved in the compound.
Cf. also Shin (2013).
The long argument in the Syllabus (EPII 275-277) has the shape of a deduction taking its premiss in the Dicisign’s truth claim. This is analyzed as a claim that the sign is in actual, indexical connection to its object, and this, in turn, is analyzed as necessitating the Dicisign’s two-part structure. The turning point of the argument is that in order to claim an indexical connection to the object, this connection must, in itself, be depicted in part of the sign. This part of the sign is the Predicate whose first function, then, surprisingly, is to depict the sign itself in its relation to the object. In the Predicate’s picture of the Dicisign itself, then, what we normally woould call the Predicate is involved as a part. Should we paraphrase the result of the argument, we could say that if the Dicisign, for a first glance, says: “Here are some Objects O, and they are characterized by the relational property P”, what it really says on the Syllabus analysis is “Here are some Objects O, and they are really connected to this sign which is why this sign is able to describe them as having the relational property P”. The Syllabus deduction is the object of a detailed analysis in Bellucci (in prep.).
This is how we should understand the claim that “It is, thus, clear that the vital spark of every proposition, the peculiar propositional element of the proposition, is an indexical proposition; an index involving an icon.” (“Kaina Stoikheia”, EPII, 310)—the icon of co-localizing S and P is interpreted as the icon involved by the index connecting S and P in reality. In that way every proposition professes to be like a weathercock.
Peirce continues: “It is impossible to thread our way through the Logical intricacies of Being unless we keep these two things, the Occurrence, and the Real Fact, separte in our Thoughts. John Stuart Mill did not do so; since he argues as if an Occurrence could have a Cause. In truth, both the Cause and its Effect are Facts, and no man will ever understand the subject of causation rightly until he sees that they are so. It is not, for example, the Motion of the Earth, as an Occurrence, that is caused by its momentum and by the gravitational attractions of the Sun and of the other bodies of the Solar System considered as Occurrences; for none of these things are Occurrences. It is the Fact of the motion of the Earth’s centre of gravity of which one component is due to the Fact that it has not ceased to move with a certain velocity in a certain direction, while other components are due to the Facts that the various other bodies, by virtue of their several masses and the gravitating power that resides in every unit of mass, continually communicating, at the distances which they severally are from the Earth’s center of gravity, several component accelerations, to its motion. Mill’s not making the needful distinction between Facts and Occurrences drives him to the declaration that the complete cause of any happening is the aggregate of all its antecedents, a principle which, though it is a necessary result of his views, he utterly ignores from the moment of enunciating it; for the excellent reason that its recognition would eviscerate the conception of Cause of all utility.” (ibid.)
Correlatively, Arguments add to the syntax of Dicisigns the higher-level syntax of deriving one Dicisign from the other in a way so that deriving is represented as lawful and general.
Peirce sometimes speaks as if all Dicisigns refer to actual existence. Such simple Dicisigns form the core of his doctrine, and from this center Dicisigns more remote from actual existence may be defined, such as ordinary universal propositions not involving existence (“All Englishmen are gentlemen”), propositions referring to fictional universes (“Donald Duck wears a sailor’s sweater”), modal propositions, imperatives, interrogatives, requiring each their set of logical rules.
Taking the chain of reasoning as primitive may give as a new idea of biological sign evolution. Instead of assuming simple organisms use very simple signs which then compose to more complex sign during evoution, we can assume that simple organisms use unarticulated, implicit arguments so that semiotic sophistication during evoution rather has the character of the ongoing articulating and making explicit the semiotic machinery, such as the two functions of Dicisigns, (cf. Stjernfelt 2012a); Hoffmeyer and Stjernfelt (in press).
This plasticity is what allows Peirce to experiment with the opposite of his privileging of the Predicate—throwing as much as possible of the Dicisign into the Subject. This can be done by means of converting predicate content into hypostatic abstractions—saying, instead of “Cain killed Abel”, “Cain stood in the relation of killing to Abel”, substituting a 3-place for a 2-place Predicate. Doing so, “killing” may now be taken as an unanalyzed Subject, part of the whole “Subject System” of the Dicisign such constructed, along with Cain and Abel. (Ms. 611, 1908; Murphey pp. 317–318; Letter to Lady Welby Dec. 14 1908; Peirce 1966, pp. 396–397). All such Predicate content abstracted away, what is left is the pure, relational structure of the Predicate, the “continuous predicate”, which Peirce takes to be the realist relational core of Dicisign predication.
Reinterpretability and plasticity of the Universe of Discourse is central in Hintikka’s generalization of the distinction between the algebraists’ logic as a reinterpretable calculus and the Fregeans’ logic as a universal medium. This distinction, Hintikka sees as constitutitve to 20 C philosophy as such. In logic, it may be found the algebraic tradition from Boole through Peirce to Schröder to Löwenheim, to Carnap and model theory (and to himself) versus the more well-known Frege-Peano-Russell-Wittgenstein tradition. More generally, in philosophy, the calculus tradition will be found in figures like Husserl or Cassirer focusing upon the plurality of phenomenological and semiotic means to express the same propositions – while the universal medium tradition will unite Russell, early Wittgenstein and Quine with continental philosophers like Heidegger and Derrida, all agreeing upon the ineffability of truth and impossibility of translation. In Peirce’s doctrine of Dicisigns, the plurality of representations is evident in the fact that the same objects may be addressed using different semiotic tools, highlighting different aspects of them. To Hintikka, these virtues of the calculus tradition also implies that the ineffability of truth of the universal-medium tradition evaporates. If you accept only one language, the question of the relation of this language to its object cannot be posed outside of this langauge—and truth becomes ineffable. If several different, parallel approaches to the same object are possible, you can discuss the properties of one language in another, and you may use the results of one semiotic tool to criticize or complement those of another. Even taking logic itself as the object, Peirce famously did this, developing several different logic formalisms (most notably the Algebra of Logic and the Existential Graphs), unproblematically discussing the pro and cons of these different representation systems. Such pluralism is compatible with a Peircean “extreme” realism.
Peirce gave two different versions of this list. The standard list, resulting from the argumentation for how to combine the three basic trichotomies, occurs in the Syllabus 1903 (EPII, 294-295):
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1.
Qualisign
-
2.
Iconic Sinsign
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3.
Rhematic Indexical Sinsign
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4.
Dicent Sinsign
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5.
Iconic Legisign
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6.
Rhematic Indexical Legisign
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7.
Dicent Indexical Legisign
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8.
Rhematic Symbol—Symbolic Rheme
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9.
Dicent Symbol—Proposition
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10.
Argument
Another version appears in the letter to Lady Welby Oct 12 1904 (8.341):
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1.
Qualisigns
-
2.
Iconic Sinsigns
-
3.
Iconic Legisigns
-
4.
Vestiges, or Rhematic Indexical Sinsigns
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5.
Proper Names, or Rhematic Indexical Legisigns
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6.
Rhematic Symbols
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7.
Dicent Sinsigns (as a portrait with a legend)
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8.
Dicent Indexical Legisigns
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9.
Propositions, or Dicent Symbols
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10.
Arguments.\({\dagger }\)14
The sequence 3 to 8 has been changed. In 1903, the list takes the quali-sin-legisign sequence as fundamental, so that the priority of the three trichotomies is 1-2-3; in 1904 the overall structure follows the rheme-dicisign-argument sequence, so the priority is rather 3-2-1. No argument is given for the change, but the implicit reason must be taken to be that the function of signs in reasoning (given by rheme-dicisign-argument) is decisive. This naturally groups dicisigns together (7-10) while the no less than six rhemes—fragmentary, unsaturated signs—make up the first six types of the list. The 1904 list also has the merit that legisigns are preceded by their sinsign replicas pairwise (2-3, 4-5, 7-8). It is remarkable that none of the two lists choses the most well-known, second trichotomy of icon-index-symbol as its organizing principle. The 1908 version of the triangle depicting the ten combined signs (from the Dec 24 letter to Lady Welby, EPII, 491) is a mirror version of that of the Syllabus, now with arguments in the upper left corner, maybe indicating that the corresponding list should now begin with the most complicated (or complete) sign type, that of the argument, effectively inverting one of the lists given.
-
1.
“Dicisigns are either symbols, when they become genuine propositions, or they are informational indices. Almost all indices are either informational or are elements of informational indices. Thus, when Robinson Crusoe found the footprint generally spoken of as Friday’s, we may suppose that his attention was first attracted to an indentation of the sand. So far it was a mere substitutive index, a mere something apparently a sign of something else. But on examination he found that ”there was the print of toes, heel, and every part of a foot”, in short, an icon converted into an index; and the connection of this with its presence on the shore, could only be interpreted as an index of a corresponding presence of a man. We thus see clearly that a dicisign, or information-bearing sign, is a sign that indicates a Secondness in its object by a corresponding secondness in its own composition. (Ms. 478, pp 46–47, alt. version of Syllabus, 1903)
The most thorough analysis of the weathercock is found in Ms. 7 (“On the Foundations of Mathematics”, ca. 1903): “The reference of a sign to its object is brought into special prominence in a kind of sign whose fitness to be a sign is due to its being in a real reactive relation,—generally, a physical and dynamical relation,—with the object. Such a sign I term an index. As an example, take a weather-cock. This is a sign of the wind because the wind actively moves it. It faces in the very direction from which the wind blows. In so far as it does that, it involves an icon. The wind forces it to be an icon. A photograph which is compelled by optical laws to be an icon of its object which is before the camera is another example. It is in this way that these indices convey information. They are propositions. That is they separately indicate their objects; the weather-cock because it turns with the wind and is known by its interpretant to do so; the photograph for a like reason. If the weathercock sticks and fails to turn, or if the camera lens is bad, the one or the other will be false. But if this is known to be the case, they sink at once to mere icons, at best. It is not essential to an index that it should thus inolve an icon. Only, if it does not, it will convey no information.”
The full quote is interesting in itself: “But it remains to point out that there are usually two Objects, and more than two Interpretants. Namely, we have to distinguish the Immediate Object, which is the Object as the Sign itself represents it, and whose Being is thus dependent upon the Representation of it in the Sign, from the Dynamical Object, which is the Reality which by some means contrives to determine the Sign to its Representation. In regard to the Interpretant we have equally to distinguish, in the first place, the Immediate Interpretant, which is the interpretant as it is revealed in the right understanding of the Sign itself, and is ordinarily called the meaning of the sign; while in the second place, we have to take note of the Dynamical Interpretant which isthe actual effect which the Sign, as a Sign, really determines. Finally there is what I provisionally term the Final Interpretant, which refers to the manner in which the Sign tends to represent itself to be related to its Object. I confess that my own conception of this third interpretant is not yet quite free from mist.” (Prol. to an Apology for Pragmaticism, 1906, CP 4.533)
Here, the Immediate Object is not only defined in terms of “Representation” but also as something whose being is dependent upon the sign. These ways of arguing may easily be mistaken for saying the sign creates a description of the object which is the IO. But “representation” in Peirce generally means denotation rather than signification, and the dependence of the IO on the sign does not exclude its dependence upon the DO—but must be taken to mean that the cutting out or selection of IO from the DO is due to the activity of the sign—rather than taking the IO as being a meaning created by the sign.
Space does not allow us to discuss here Peirce’s embryonic speech act theory according to which propositions are signs fit to be asserted—or to be the objects of assent, interrogatives, imperatives, etc. see (Brock 1981)
It even leads Short into attempting a distinction between the Rheme/Dicisign/Argument trichotomy and the Seme/Pheme/Delome trichotomy (which are synonymous in Peirce).
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Thanks for comments to Barry Smith as well as to the anonymous peer reviews.
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Stjernfelt, F. Dicisigns. Synthese 192, 1019–1054 (2015). https://doi.org/10.1007/s11229-014-0406-5
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DOI: https://doi.org/10.1007/s11229-014-0406-5