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by Jeremiah McCarthy

Peirce held a form of idealism according to which all real things are signs. I call this “semiotic idealism.”.  The text which gives the best insight into Peirce’s idealism is a fragment published in Volume IV of The New Elements of Mathematics called “Kaina stoicheia” (NEM IV, 235-263)[i].  In this paper I will give a careful examination of the theory of signs in “Kaina stoicheia” and show how the theory supports semiotic idealism.

I. “Kaina stoicheia

As a preliminary I need to examine two peculiarities of the discussion presented in “Kaina stoicheia.”.  First, Peirce asserts on several occasions that signs are not real.

A sign is not a real thing.  It is of such a nature as to exist in replicas.  Look down a printed page, and every the you see is the same word, every e the same letter.  A real thing does not so exist in replica.  The being of a sign is merely being represented.  Now really being and being represented are very different. (NEM IV, 238-239; EP II, 303)
That which is merely represented, however legitimately, cannot be said really to be. (NEM IV 240; EP II, 305)
No sign, however, is a real thing.  It has no real being, but only being represented....[A] symbol, a word, certainly exists only in replica, contrary to the nature of a real thing. (NEM IV, 250; EP II, 313)
It is, of course, quite possible for a symbol to represent itself, at least in the only sense in which a thing that has no real being but only being represented, and which exists in replica, can be said to be identical with a real and therefore individual object.  A map may be a map of itself; that is to say one replica of it may be the object mapped. (NEM IV, 259; EP II, 321)

The passages do not seem to represent Peirce’s usual idea about really being and being represented.  The topic also comes up in the “Lectures on Pragmatism.”.  There Peirce says that “that which is of the nature of a representation is not ipso facto real” (5.96)[ii].  The position of the “Lectures” is that, although “[it] is one thing really to be and another to be represented” (5.97), yet some representations are real.  When one of these will sustain predictions that is proof that the representation “is, or if you like it better, corresponds to, a reality” (5.96).  (Peirce likes “is” better.).  That a true proposition is a reality is the doctrine of “Kaina stoicheia” when the word “real” bears its usual sense with Peirce.  It is customarily defined in some such way as the following: “That is real which is what it is, whatever our thoughts may be concerning that particular thing” (7.339).  But the word “real” will often bear a construction in “Kaina stoicheia” that is, to say the least, highly unusual.  The last passage (EP II, 321) makes the meaning clear enough.  Whatever is real is individual.  If a sign is not an individual, then a sign is not real.  This has no bearing on the reality of signs in the usual sense and it is easy to see that Peirce regards some signs as real, just as in the “Lectures on Pragmatism.” (NEM IV, 250-254; EP II, 313-315 [“Still, I maintain .....agreement between them and the law.” This very long passage begins 15 lines from the bottom of EP 313 and ends on the seventh line of EP 315.)

Besides ignoring the anomaly as not significant, there is another possibility.  It is that the only aberrant passage may be the citation from NEM IV, 259 above.  The word “real” is not consistently used for “individual,” but seems to have its usual meaning in a number of cases: NEM IV, 250, l. 29; 251, ll. 7, 9, 14, 17, 33, 39; EP II, 314, ll. 4, 6, 11, 13, 28, 32, 35).  In one of a series of manuscripts evidently associated with “Kaina stoicheia” (MSS 7-11)[iii] Peirce says, “A sign is not a real thing” but the sort of thing that is embodied in replicas (MS 9, p. 1).  Another manuscript clarifies the denial.

That the sign itself is not a definite real object has been pointed out....It is only represented.  Now either it must be that it is one thing to really be and another to be represented, or else it must be that there is no such thing [as] falsity.  This involves no denial that every real thing may be a representation, or sign, but merely that, if so, there must be something more in reality than mere representation.  Since a sufficiently complete sign may be false, and also since it is not any replica or collection of replicas, it is not real. (MS 7, p. 3)

Accordingly, when Peirce says that a sign is not real he means that it is not, by the very fact that it is a sign, real.  An individual, by the very fact that it is an individual, is real and that is the contrast that Peirce has in mind.  Whichever interpretation is chosen there is no special problem about the unreality of signs in “Kaina stoicheia.”

The discussion of the reality of signs brings out another peculiarity of the text, that it makes all signs non-individual.  In this it differs from later work[iv] in which Peirce recognizes a class of signs called “sinsigns” or “tokens” which are individuals (2.245, 2.255-257, 4.537, 4.544).  The text explicitly makes replicas appertain to all signs (NEM IV, 238-239; EP II, 303).  Since replicas do not themselves exist in replica, a replica is not a sign in the theory of “Kaina stoicheia.”.  According to a later classification a replica is a sinsign (2.246), but one should be careful not to treat them as signs here.  Peirce has occasion to say that indices have replicas (NEM IV,250), but he talks about indices and icons as if they were significant through being in reaction with an object and through possession of a quality in common with an object, respectively (NEM IV, 242-243).  This cannot be strictly true if icons and indices are not individuals.  Only individuals react or embody qualities.  At one point Peirce seems to deny that an index is not an individual (NEM IV, 247, ll. 5-7; EP II, 313, ll. 25-28).  However, it is easy to be careless about observing the distinction between a sign and its replica and this, perhaps combined with an incipient change of doctrine, can account for the ambiguities.  I do not see any evidence of serious confusion.


The discussion of signs in “Kaina stoicheia” is mostly confined to signs of a propositional nature.  The example of a sign with which Peirce begins is a proposition.

A sign is connected with the ‘Truth,’ i.e. the entire Universe of being, or, as some say, The Absolute, in three distinct ways....The sentence ‘Roxana was the queen of Alexander’ is a sign of Roxana and of Alexander...and the real persons Roxana and Alexander are real objects of the sign.  Every sign that is sufficiently complete refers to sundry real objects.  All these objects, even if we are talking of Hamlet's madness, are parts of one and the same Universe of being, the ‘Truth.’.  But so far as the ‘Truth’ is merely the object of a sign, it is merely the Aristotelian Matter of it that is so.  In addition however to denoting objects every sign sufficiently complete signifies characters, or qualities....But, in the third place, every sign is intended to determine a sign of the same object with the same signification or meaning.  Any sign, B, which a sign, A, is fitted so to determine without violation of its, A ’s, purpose, that is, in accordance with the ‘Truth,’ even though it, B, denotes but a part of the objects of the sign, A, and signifies but a part of its, A’s, characters, I call an interpretant of A.  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, the absolute Truth, and as such (at least, we may use this language) would be the very Universe....We may adopt the word [entelechy ] to mean the very fact, that is, the ideal sign which should be quite perfect, and so identical, — in such identity as a sign may have, — with the very matter denoted united with the very form signified by it.  The entelechy of the Universe of being, then, the Universe quâ fact, will be that Universe in its aspect as a sign, the ‘Truth’ of being.  The ‘Truth,’ the fact that is not abstracted but complete, is the ultimate interpretant of every sign. (NEM IV, 238-240; EP II, 303-304)

Form in this passage is Peirce’s category of firstness.  Forms are qualities or characters, things that are such as they are in themselves, that may be embodied, but that have no need of being embodied in order to be.  They are possibilities, ways that something might be.  Matter is Peirce’s category of secondness.  Whatever is material is an individual thing that reacts with other things in its environment.  Consequently, matter is such as it is in relation to a second thing. Whichever of the pair is more affected by being in the relation is said to be “second,” the other correlate is said to be “first.”.  In the relation of killing, for example, the victim is second, the killer first.  In such cases there is an approach to a state of things in which something that is as it is in itself, a first, comes into an accidental relation to a second — accidental because the being of the first in no way depends on its relation to the second.  This extreme case is the relation of a quality or form to the matter that embodies it.[v]

Entelechy “is that which brings things together.  It is the element which is prominent in such ideas as Plan, Cause, and Law.”[vi] .  There are two sorts of connection which do not involve entelechy, the embodiment of form by matter and the reaction of matter with matter.  As an example of the first, consider the regularity with which crows have been black.  If the regularity should be accidental, then there will be no connection between being a crow and being black except that every actual crow has embodied the form.  As an example of the second, consider a stone ornament that falls from a building and strikes a man on the ground.  The man is second, the ornament first insofar as the relation is concerned, but the ornament is not a form.  The relation is a reaction of matter with matter.  Since the ornament happens to fall when the man is in a position to be struck, there is no connection between the reacting elements of the event other than their being the elements in that very event.

In the first case — the embodiment of matter by form — there is nothing which brings together form and matter.  The matter happens to embody a.  certain form.  That is all.  Suppose I add a third element and give it the office of bringing together the other two.  This would have to be something connected with both matter and form, so it is as it is with regard to matter and form, while matter is as it is with regard to form and form is as it is in itself.  The third element, entelechy, is Peirce’s category of thirdness.  Since matter is nothing without form, the third element must bring together form with matter that already embodies some form or other, however it may come to do so.  The third element will have its being in relation to cases in which some form is not yet embodied by matter which already embodies some other form.  It can hardly bring together what are together already.  Accordingly, it will be related to possible cases in which a certain form is embodied and in those cases it will connect some other form with the matter.  This is the description of a law.  If there is a law to the effect that all crows are black, then the regularity with which crows have been black is not accidental.  In every possible case in which a new crow comes to be, the new crow will not break the regularity.

In the second case — -the reaction of matter with matter — the third element that brings the individuals together is as it is in producing the relation between them.  The same considerations hold as before.  The third element has its being in relation to cases in which the reaction has not yet occurred.  It cannot produce a reaction that has already taken place.  Consequently, it will be related to cases in which a man on the ground is in a position to be struck by the ornament.  Here there is the operation of a final cause.  The ornament would fall if it were to strike a man on the ground.  But this is not fundamentally different from the other case.  Both involve laws.  The production of an end-state is merely more obvious in the second case than in the first.[vii]

Such are the analytical concepts in the passage quoted from NEM IV, 238-240.  Now I can proceed to comment on it.  Every sign is connected with an object, which is matter, and characters, which are forms.  A proposition, the kind of sign we are concerned with, is a sign which separately indicates its object (NEM IV, 242; EP II, 307).  The proposition “Roxana was the queen of Alexander” incorporates a pair of signs, “Roxana” and “Alexander,” which pick out the objects of the proposition.  According to the classification in “Kaina stoicheia” the two names are symbols (NEM IV, 243; EP II, 307), but they perform an indexical function in the proposition because each denotes an individual.[viii] The predicate of the proposition, “was queen of,” signifies the characters which are attributed to Roxana and Alexander.  I ignore the temporal index which makes an inessential complication.  Characters are not individuals — not things that react — so the predicate does not have an indexical function.  It calls to mind an icon of the character which it signifies.

Dealing with the denoting function of proper names presents two problems.  First, proper names do not denote unless the interpreter is already acquainted with their objects.  The names cannot supply this acquaintance themselves (NEM IV, 243; EP II,307; MS 313, pp. 2-3; 2.357, 2.360, 3.419).  The trouble here has to do with the right sort of acquaintance and how to get it.  I may be acquainted with Alexander in some sense if somebody tells me the story of some episode in his life.  However, it is not so clear that I can denote Alexander on the basis of this acquaintance any more than I can denote a character in a novel on the basis of reading it.  What kind of acquaintance do I need?.  Second, the denotative function of a sign supposedly brings its interpreter “the experience of the very object denoted” (NEM IV, 243; EP II, 307).  The problem with this is that it seems to be false.  Some objects, Alexander among them, seem not to be objects that can be experienced.  What does “experience of the very object denoted” amount to?. 

The fundamental point about the denoting function of proper names is that for a proper name to denote, it must be possible to break out of the system of proper names and get connected with the object of the name by means of indexicals.  Otherwise there will be no distinguishing proper names of fictitious and real objects.  So an interpreter who cannot connect the name “Alexander” with its object by means of indices should not count as being able to denote Alexander even if he has some competence in using the name because he has been told a story about Alexander.

The ability to denote Alexander depends on the interpreter’s being able to locate Alexander in space and time.  For example, the name may be introduced as belonging to the man who was king of Macedonia in 334 B.C.  If the interpreter does not know where the kingdom of Macedonia was or is unfamiliar with the time scale used, the name will not denote.  That is, the attempt to introduce the object of the name and to associate it with the name will fail.  But if the interpreter knows how to locate Macedonia — if he can point it out on a map and knows how it is related to his own location or if he can give a direction for finding it — then he can denote Macedonia.  If the interpreter is acquainted with the origin of the time scale and the units of time it uses, he can locate the king of Macedonia referred to in relation to himself and to other objects known to him.  So when a system of indexical signs is in place that allows the interpreter to locate an object referred to, he will be able to use the name to distinguish its object from others.  That seems to be the main element in denotative competence.  When an interpreter is presented with a name that is disconnected from any indices of its object, he has no way of telling whether subsequent uses of that name or other names or indexicals refer to the same object.  Indeed, he has no way of telling whether the name refers to any real object at all.  If being able to denote with a name is for the most part an ability to distinguish the object of the name from other things, it is perhaps worth noting that denotative competence can develop or have different degrees according to how well the user of the name can make distinctions between its object and other things.

For me to make good on my assertion that the relations made use of to denote involve indices I need to say a little about different kinds of relations.  Indices involve existential relations.  An existential relation is a relation between things that is nullified if either of its correlates ceases to exist (3.419).  Relations of similarity and rational relations are different.  Relations of similarity can obtain between imaginary objects or an imagined object and a real one.  As for rational relations, the connection between a law and what it governs is unaffected when any or all of the objects it governs do not exist.  The non-existence of these does not affect the fact that if an object of a certain description were to exist, something else would happen.

The spatial relations that Macedonia has to other places are all existential.  The relation of being north of Athens is destroyed if either correlate, Macedonia or Athens, ceases to exist.  For this relation to be useful in referring to Macedonia an interpreter in Athens needs to know which way is north.  This depends on knowing or finding an index of the North Pole such as Polaris or the end of a compass needle or some landmark.  If either the location on the planet to be denoted or the device used to denote ceases to exist, the relation is nullified.  The landmark, the end of the compass needle, or even the interpreter’s body oriented in the right direction can all serve as indices of Macedonia if the interpreter knows how many units distant Macedonia is.  The measure of distance is another index.  The landmark, compass needle, or interpreter and Macedonia will not be a certain number of units distant if either ceases to exist. 

The temporal relations of Alexander to other objects are existential as well.  The non-existence of either of the correlates of such a relation destroys the relation.  For temporal relations to be useful in referring to something, the interpreter needs to be acquainted with the origin of a time scale, that is, he needs to know how many units of the scale separate him from the origin.  The number of units separating an event from the origin is an index of the event.  It serves to locate the event in relation to the origin and so in relation to an interpreter who knows his own relation to the origin.  If the event to be located, the interpreter, or the event that constitutes the origin ceases to exist, then the relation of being a certain number of units from the origin or from the interpreter ceases to exist.  So these relations are existential and are involved in the use of indexicals.  Dates depend on the use of indices of time although in the context of “Kaina stoicheia” dates are not themselves indices.  They are symbols which have the peculiarity that their replicas are produced as effects of their objects through a comparison of the event dated with the origin of the time scale by means of the unit.  Thus the dating of an event or the interpretation of a date is an effect of the event, much as if the date were an index.  Dated events in which Alexander was a participant allow him to be located in time and inform the interpreter of Alexander’s relation to other objects and to himself.

On the basis of the discussion of indices it seems correct to say that an interpreter is acquainted with an object when the object is in a familiar relation to something with which he is familiar.  It is important to keep in mind that the relation needs to be an active relation to the objects to be denoted.  Anybody who is shown a map of something real or who is given a list of dates of real events is thereby put into an existential relation to the objects of the signs, but nothing need get denoted.  Denotation is a purposive activity.  The signs will not serve the purpose of their utterer if the interpreter cannot put them to any denotational use.  His relation to the objects will then be passive.  He cannot locate them with respect to one another or to himself in space or time.  The interpreter has an active relation to the objects only through his ability to use indices to become acquainted with them. 

Proper names, dates, and definite descriptions are symbols.  They are significant merely because they will be interpreted to denote their objects.  But unlike general terms, the capacity of them to be interpreted depends on the ability of the interpreter to connect the symbols with indices of the objects they denote. General terms depend on common knowledge of objects like the object with which the general term is connected in a proposition by an utterer.  But they do not depend for their significance on the interpreter’s prior acquaintance with any particular object that a term may be connected with in a proposition (cf. 2.261).

The remaining problem is what to make of Peirce’s statement that the denoting function of a sign brings the interpreter “the experience of the very object denoted” (NEM IV, 243; EP II, 307).  This seems to be true for indexicals used to point out something in the immediate environment of the interpreter.  It is also true of signs that direct the interpreter how to find their object.  But Alexander is not in the immediate environment of anyone and, indeed, is nowhere to be found.  However, if experience is to be understood as associations that depend on existential relations (3.419), then it seems that, perhaps, there is such a thing as experience of Alexander.  That is, there are associations that depend on existential relations for which Alexander is responsible.  To take an obvious case, it is a fact that the Greek equivalent of “Alexander” is inscribed on certain statues.  That is an association between an inscription and a object of a certain appearance.  The association affords information about Alexander.  Similarly for associations between replicas of the name and replicated descriptions in ancient texts.  The latter may seem to represent a very thin notion of experience, but the associations are existential relations produced by Alexander.  So the denotational function of the name gives the interpreter experience of its object in the only sense in which anybody can have experience of an unobservable entity.  It permits him to recognize observable effects of Alexander.

The name “Alexander,” as a symbol, is a kind of law, viz., the law that an interpreter will associate a replica of a certain description with Alexander.  An utterer takes advantage of his knowledge of the law so that he produces a replica of the name if it is likely that the interpreter will associate the name with Alexander.  The symbol, acting on an utterer as final cause, must be able to get replicas of some sort produced and so the utterer needs to know the probable effect of a certain description of replica on the interpreter.  The replicas of a name need not agree in appearance but only in the characteristic that any of them would be taken by some interpreter as an occasion for making the association.  Of course a replica must have some other characters which suggest to the interpreter the symbol that the replica belongs to.  Otherwise no association will take place.  “We may call these things embodying the same sign replicas of it.  They need not be alike as things.  Man, homo, anthropos are the same sign.”[ix]

The signifying function of a sign brings its interpreter “face to face with the very character signified” (NEM IV, 242; EP II, 307).  A symbol can no more supply acquaintance with characters it signifies than with the objects it denotes.  But the interpreter of the predicate “is queen of” will have had experience of objects with which replicas of the predicate are associated.  Accordingly, the interpreter will begin to associate replicas of a certain description with an icon of the relation, not in every respect, but with regard to certain prescinded characters which are the characters signified by the predicate.  The predicate is a law which takes an interpreter from a replica to the characters signified via an association between the replica and an icon with respect to those characters.  An utterer takes advantage of his knowledge of the law so that he produces a replica of the predicate if it is likely that the interpreter will associate it with the characters of being female and spouse of something that is a monarch.  For a predicate to convey anything to an interpreter it must represent something that the interpreter can be acquainted with.  But he need not be acquainted with the object to which the predicate is referred by an utterer, in the respect in which the predicate is referred to it.  It is requisite for signification, then, that a predicate should relate an interpreter to forms which may be embodied by an object.  The predicate will bring the interpreter face to face with the signified characters if he cares to follow out the connections with his experience that the replica will suggest.

The third way in which a sign is connected with the universe has to do with its interpretant.  With denotation and signification the correlates of the sign were brought under a category — matter and form respectively — in order to explain those sign functions.  If we keep the parallel which denotation and signification suggest, then the connection of a sign with an interpretant should be explained by the category of entelechy.  The purpose of a proposition is the expression of truth, so truth, as the entelechy of signs, should provide the relation of sign to interpretant.  A sign determines an interpretant for the sake of truth.  In other words, one sign is an interpretant of another if the relation between them will contribute to the expression of truth. 

Assertion is a kind of replication that produces assent by an interpreter to the asserted proposition.  Assertion, then, communicates a proposition.  An interpreter will have had experience of assertions and will have formed an association between assertion and the truth of the proposition asserted.  Once the association is established the interpreter will not assent to an asserted proposition regardless of its assumed truth, but he will assent to it in the absence of any reason not to.  An utterer who asserts a proposition takes advantage of the interpreter’s association to communicate truth.  That is, the utterer asserts a proposition if his assertion will tend to communicate truth.  For his part, the interpreter assents to the proposition if his assent will tend to communicate truth.  The transmission of the sign occurs through the operation of an end — the communication of truth — which is shared by utterer and interpreter.  I do not mean to imply, by the way, that the end is entirely voluntary for the interpreter.  It is much more so for the utterer.[x] . The interpreter is assumed to have a disposition to believe what he is told.  Legal and social penalties are attached to lying, but for these to exist there must be a prior disposition to believe.  Knowledge of the penalties strengthens the disposition (NEM IV, 249).  The sign transmitted satisfies the requirement that signs are related as sign to interpretant if the relation contributes to truth.  The sign and its interpretant are so related here that they contribute to the expression of truth, so the interpreter’s sign is the interpretant of the utterer’s sign although the signs happen to be identical, the same proposition.  This is, perhaps, the simplest and most common sort of communication having truth as its final cause.

For a more complicated case suppose the utterer says, “Alexander had three wives.”.  If the interpreter did not know this, then something is communicated to him.  Suppose he had a vague notion that Alexander was not married.  On hearing the utterer he thinks, “Then he was married.”.  This is an interpretant of the sign.  To connect it with the sign the interpreter assumes a common purpose with the utterer, to express truth, and he takes the interpretant as being so related to the sign that it is true if the sign is.  The purpose of relating one sign to another as interpretant is to express truth or communicate it from the interpreter’s self that assents to the premiss to the interpreter’s self that assents to the conclusion.  Without the common purpose of the utterer and interpreter the latter would have no way of connecting an interpretant with a sign.  The activity of interpretation would lack a final cause and the interpreter would have no criterion for deciding when one sign is so related to another as to contribute to the expression of truth.  In a case where sign and interpretant are different we can see that assent to the interpretant is much more a voluntary matter than in the previous case.

The example of interpretation I just gave is deductive and the interpretant is true.  But that the interpretant should be true is not required by the model of interpretation that emerges from “Kaina stoicheia.”.  A sign need only determine an interpretant without violation of the sign’s purpose (NEM IV, 239; EP II, 304).  Suppose that someone interprets a sign in order to determine a true interpretant.  If the method of interpretation really contributes to the expression of truth in the way the interpreter thinks, then there is no violation of the purpose of sign interpretation.  The procedure which non-deductive inference follows is not guaranteed to make the conclusion of every sound inference true.  The method does assure the interpreter that a true interpretant will be found eventually (2.780-781, 5.167-173).  Accordingly, there is no difficulty in regarding the conclusions of non-deductive inferences as interpretants.  The purpose of every sound inference is the expression of truth and every sound inference contributes to that purpose whether or not its conclusion is true.

So far I have discussed signs that are obviously purposive, signs that are replicated by an utterer in order to convey some truth to an interpreter.  In his account of the relation of sign to interpretant in “Kaina stoicheia” Peirce must have had intentionally replicated signs uppermost in his mind.  But not all signs are like this.  A weathercock is made and set up on purpose, but it does not indicate the direction of the wind on purpose.  The cock faces the direction of the wind whether or not anybody is likely to interpret it as a sign.  Smoke is a sign of fire, but the fire does not produce smoke according to the law that if the smoke is likely to be taken as a replica of an index of fire, then the fire produces smoke.  A great many signs are of this nature.  In every case, although the replication of the sign is not purposive, yet the interpretation of the sign will be found to be purposive.

Consider how smoke is a sign of fire.  In “Kaina stoicheia” all signs are general.  To say that smoke is a sign of fire is to say that the complex of characters which the word “smoke” signifies is a sign of fire.  The complex is an index because nothing can instantiate it, i.e. be a replica of it, without being in a cause and effect relation to a fire which is in the vicinity of the replica.  An interpreter will be able to do nothing with a replica of the index unless he knows how a replica of it is related to the objects of the index.  He needs to know that the index requires that every instance of itself should be an effect of a fire nearby.  Given this knowledge, the interpreter can conclude that there is a fire near the smoke.  The conclusion is an interpretant of the index.  The replica was not produced intentionally, but the determination of the interpretant is purposive.  The interpreter will assure himself that a certain proposition is an interpretant of the index by establishing that the interpretant is so related to the index that it contributes to the expression of truth (cf. 5.473).  Conformity to this rule in the determination of the interpretant is conformity to truth as the final cause of sign interpretation.

Now consider how the replica of a symbolic proposition is related to it.  A symbol, like an index, is general.  But it is significant merely because its replica presents an occasion for it to be interpreted.  A symbolic proposition is an association of signs.  However, its predicate, being general, is not more especially associated with its own subject than with many others.  To associate signs depends on being able to associate replicas which, as singulars, can be put together (NEM IV, 246-247; EP II, 310).  For a symbolic proposition to be anything at all it has to be a tendency for an utterer to associate a replica of its predicate with a replica of its subject.  The proposition “Alexander was married” is a law according to which the utterer replicates the predicate “was married” as a sign that applies to what the subject denotes, if he replicates the name “Alexander.”

Of course the law of association does not limit the utterer to saying nothing about Alexander except that he was married.  In sign interpretation the conduct of utterer and interpreter is governed by a common end, the expression of truth.  Therefore, if replicating according to the symbol “Alexander was married” will communicate truth, then the utterer replicates the symbol.  But it will not always be to the point to replicate it even though it is true.  If the utterer replicates that symbol or any symbol when it will not contribute to truth, then he violates the assumption on which interpretation operates.  Accordingly, the norms of interpretation do not permit an utterer to talk at random or require him to say everything he knows as fast as he can.

So far I have considered the replication of symbols mostly from the utterer’s side.  Looking at it from the interpreter’s side suggests the question, “How does the interpreter tell what the utterer means to do with a symbolic proposition?”.  The syntax of the replica provides the clue and the question of the syntax of a proposition shows that according to the theory of “Kaina stoicheia” it is quite hopeless to treat propositional symbols as if they incorporated descriptions of their replicas.  The commonest replicas that an interpreter has to deal with are probably assertions of symbols.  The symbol must associate its subject and its predicate somehow if it is to be a proposition and can only do so by being a rule for connecting replicas of its subject and its predicate.  The connection of the parts of the replica is taken by an interpreter to be an index, or rather a replica of an index, of a connection between the subject and the predicate that belongs to it.  The form of the replica incorporates, or is understood to incorporate, an icon of the connection which it denotes.  The syntactic form of an assertion is a propositional index having as its object a union of form and matter and incorporating into itself an icon of that union (NEM IV, 248; EP II,310-311; 2.309-314, esp. 2.312).

If the topic of replication could be left here it would be reasonably simple.  The symbolic proposition would operate to produce replicas of a certain syntactic form which provides the interpreter with the clue he needs to interpret the predicate replicated as belonging to the replicated subject.  But the topic of syntax and of the identity of symbolic propositions is not so straightforward.

I grant that the normal use of a proposition is to affirm it; and its chief logical properties relate to what would result in reference to that affirmation.  It is, therefore, convenient in logic to express propositions in the indicative mood.  But the proposition in the sentence, ‘Socrates est sapiens,’ strictly expressed, is ‘Socratem sapientem esse.’.  The defense of this position is that in this way we distinguish between a proposition and the assertion of it; and without such distinction it is impossible to get a distinct notion of the nature of the proposition.  One and the same proposition may be affirmed, denied, judged, doubted, inwardly inquired into, put as a question, wished, asked for, effectively demanded, taught, or merely expressed, and it does not thereby become a different proposition. (NEM IV, 248; EP II, 311-312)

The cases that concern interpretation as a process aiming at truth include affirmation, denial, judgment (affirmation to oneself), and inward inquiry (feigned judgment for the sake of discovering interpretants).  These do not present much of a problem for my account of the proposition except for the last case.  Here the symbol will be mentioned and preceded by a sign like “suppose that.”.  How can this be a replica of the symbolic proposition?.  The “that” clause seems to be an index incorporating an icon of a replica of the proposition.  The prefixed sign is a sign that the symbol referred to is to be taken to have a suppositious connection between subject and predicate.  The whole replica — but not the incorporated icon of a replica — is a replica of the symbolic proposition because it was produced for the sake of interpretation according to a law which governs the production of replicas.  A symbol having a suppositious relation between subject and predicate is a law according to which a replica is formed which contains a sign of that relation.

Doubting a symbol may be understood to work on the same plan as feigned judgment, with a special sign employed to qualify the relation of subject to predicate in a symbol otherwise referred to.  Other cases use syntactic or other variations to the same end.  “Is Socrates wise?” (symbol put as a question), “Would that Socrates were wise” (wished for), “Socrates is wise, isn’t he?” (asked for), “Be wise, Socrates!” (effectively commanded if there can be uptake on the part of Socrates), “Socrates’ being wise” (merely expressed).  To teach a symbol the denotative function must be effective or be made effective for an interpreter so that he can gain an active relation to its object which he can use to verify that the form is united with the object as the symbol represents them to be united.  In this case the symbol will be elaborated into a maxim of conduct.

The notion of symbolic proposition that emerges from all this is very highly generalized.  An association between a subject and a predicate makes a proposition and nothing more is needed.  To understand the Peircean symbolic proposition as it appears in “Kaina stoicheia” we need to generalize the notion of an association between subject and predicate so that the law of association can take various forms without changing the identity of the symbol.  This is analogous to generalizing the idea of replica so that various sorts of replicas can be replicas of the same symbol.  For a symbolic proposition we need only some law of association which operates to produce replicas if these are likely to produce interpretants.  The syntax of the replica, either by itself or together with some other sign, represents to the interpreter what kind of sign or action it is the purpose of the symbol to produce.[xi]

There is one more problem about symbolic propositions in “Kaina stoicheia” for there is some evidence that Peirce thought that there are no false symbols.  “The formula, if a symbol at all, is a symbol of its object.  Its truth, therefore, consists in the formula being a symbol” (NEM IV, 254).  But then Peirce writes the phrase “sufficiently complete and true symbol” almost with the next stroke of the pen, as if the word “true” were not superfluous.  A symbol sufficiently complete ought to be true if there are no false symbols.  The definition of “symbol” does not rule out false symbols, either.  “A symbol is defined as a sign which is fit to serve as such simply because it will be so interpreted” (NEM IV, 243).  Then are there or are there not any false symbols?

The definition of “symbol” has to be the controlling factor in deciding the question which, therefore, amounts to asking whether a false symbol answers to the definition.  It is perfectly evident that a false symbol such as “The Titanic is unsinkable” can get an interpretant of itself produced since the latter was quite successful in that direction.  If it were not so nobody would have false beliefs.  Nor can we say that the proposition is not a symbol because, having been found to be false, it will not produce an interpretant.  As much might be said of a true symbol which is not presently believed or is believed to be false.  It is most natural to hold that a formula’s being a symbol consists, not in its truth, but in the fact that it behaves in the way that the definition of “symbol” would lead us to expect.  Whatever acts like a symbol under conditions that might be realized, consistent with the norms of interpretation, is a symbol.

Although falsehood does not prevent a sign from being a symbol, the conditions governing the “will” in the definition of “symbol” are of two different kinds.  It would be a mistake to overlook the distinction.  Interpretation is normative.  It proceeds on the assumption that its aim is truth and it is carried out in such a way as to contribute to that aim.  The conditions on the “will” have to do with the purpose of interpretation.  A condition on any symbol is that it will determine an interpretant that has some relevance to the end.  That end is incompletely or imperfectly realized while there is truth that remains uncognized.  In the course of working out the purpose of sign interpretation a more and more comprehensive cognition will be produced.  If a symbol is false, the achievement of the purpose requires that it be found to be false.  When it is found to be false it will not be interpreted.  Some conditions under which a symbol will determine an interpretant — conditions under which it contributes to the end — are transitory.  If a symbol is true, the achievement of the purpose of interpretation requires that it should be found to be true.  A symbol that will be found to be true will not be deprived of its capacity to determine an interpretant.  So there are conditions that are not transitory, but permanent, under which a symbol will determine an interpretant.  Such a symbol contributes to the end by being a part of it, an element of “the perfect Truth,” “the ideal sign which should be quite perfect,” the “entelechy of the Universe of being” (NEM IV, 239-240).


In order to relate the discussion of semiotic to idealism I will first consider how Peirce defines “law.”.  A law is “a formula to which real events truly conform.  By ‘conform,’ I mean that, taking the formula as a general principle, if experience shows that the formula applies to a given event, then the result will be confirmed by experience” (NEM IV, 251-252).  The word “formula” is a neutral or perhaps somewhat nominalistic way of referring to a law since a formula is evidently a representation of some sort.  In fact it is an assertory symbolic proposition (NEM IV, 252).  As always, the question is whether the formula is a mere representation or not.  In aid of showing how a symbol can be a final cause of events and hence not a mere representation, Peirce gives definitions [of] “cause” and of each of the four causes.

The conception of cause in general is defined in three clauses.  A cause and a causatum are both facts.  A cause is

a fact which could, within the range of possibility, have its being without the being of the causatum;.  but, secondly, it could not be a real fact while a third complementary fact, expressed or understood, was realized, without the being of the causatum; and thirdly, although the actually realized causatum might perhaps be realized by other causes or by accident, yet the existence of the entire possible causatum could not be realized without the cause in question. (NEM IV, 252)

The mode of possibility is logical possibility.  The “entire possible causatum” is the total of logically possible cases which realize the causatum.

An internal cause is one that is a part of the causatum so that the causatum cannot be without it.  (This requires some emendation of the definition of “cause” which, as it stands, does not hold for internal causes.  Peirce says “the scope of the word will be somewhat widened in the sequel” (NEM IV, 252) and I suppose he had this generalization, at least, in mind.).  An external cause is not internal.  An individuating or physical cause is an individual thing or fact while the other factor mentioned in the definition is a general principle.  A defining or psychical cause is a general principle, while the other factor mentioned in the definition is an individual (NEM IV, 252-253).  With this apparatus Peirce can obtain definitions of the four Aristotelian causes.  A material cause is an internal individuating cause.  An efficient cause is an external individuating cause.  A formal cause is an internal defining cause.  A final cause is an external defining cause (NEM IV, 253).  I suspect that the fundamental distinction for Peirce is between individuating and defining causes (see 1.211-212).

As an example of a law Peirce uses “Every stone on earth has a real downward component of acceleration.”.  This formula, which is also an assertory symbolic proposition, is a final cause.  (1) It is possible for the formula to be true without the being of the causatum.  It might be that any stone on earth would have a real downward component of acceleration though there were no stones on earth.  (2) If another factor is present — in this case a stone on earth — the causatum will be realized.  Nothing is a stone on earth consistently with the truth of the formula and the non-occurrence of the causatum.  (3) Although an existing stone on earth might have a downward component of acceleration through some other cause or by accident, yet the possession of such a component in every logically possible case of a stone on earth involves the truth of the formula (NEM IV, 253-254).  In other words the symbolic proposition is not an accidental regularity but an entelechy.  It is the final cause of the events that conform to it, so as a representation it hardly merits the qualification “mere.”

I have articulated the idea of symbolic proposition on the basis of evidence and hints from “Kaina stoicheia” and elsewhere.  If my elaboration is right, then a true symbol is not only a law for associating replicas, it is also a final cause of events which it may be employed to represent.  I will assume that anyone who is skeptical about the theory of cognition this implies will admit at least that a symbol is an active general principle, not an individual inscription or something of that nature.  But the skeptic who is not so very nominalistic might still say, “If it makes you happy to call the law of gravitation as applied to stones on earth a ‘symbol,’ then do so.  However, you originally defined a symbol as a sign which is a sign merely because it will be so interpreted.  In the case of symbolic propositions you developed the idea and made out that a symbolic proposition is a law for associating replicas, if the association will tend to get the symbol interpreted.  Now what does the law of gravitation have to do with replicating symbols to produce interpretants?.  Do not deceive yourself by using the word ‘symbol’ for a law that governs the facts as well as for a law that governs the discourse about the facts.  What could be more different from a law that works the planets in their orbits than a law that works a mere association of signs?”

The objection is well taken.  Peirce’s argument shows that the formula has to be regarded as a final cause of events that conform to it, but it does not make it clear whether the same formula also counts as a cause of the association of signs in semiosis.  To show that it does it is necessary to show that it is logically impossible for the principle of semiosis to operate but not the law of the facts.

If the symbol “Every stone on earth has a real downward component of acceleration” is operative as a principle of semiosis, then it will be a final cause of sign association and will satisfy the three clauses in the definition of “cause.”.  (1) The principle may be a law of association of signs without producing any association.  If a condition satisfying the antecedent is not cognized by an interpreter, he will not make the association governed by the symbol.  (2) If a third factor, the cognition of a fact satisfying the antecedent, is given, then the interpreter will replicate a sign corresponding to the consequent — will produce the causatum — if that contributes to the truth.  (3) Some of the representational effects must be able to occur through the operation of some other law or by accident.  Stones might accelerate toward certain objects only, say diamonds as big as the Ritz, one of which happens to be located at the center of the earth.  Or there might be no such law but through some coincidence a stone might have a real downward component of acceleration.  Descriptions of the stones would be true in these cases but they would not be effects of the law.  If they were counted as such, the law would be nothing more than a common character of a class of events, a uniformity which will not support predictions.  But the occurrence of the representational effect — the replication of a proposition representing that a certain stone has a real downward component of acceleration — in every case in which it is possible to replicate according to the law, involves the reality of the law.  The last clause shows that the law of the facts and the principle of semiosis are one and the same.  There is no logically possible case in which the principle of semiosis operates to produce a discrepancy between it and the law of the facts.  Therefore, the semiotic principle is just the law of the facts, cognized.

Universally quantified conditionals represent laws.  But every symbolic proposition is an entelechy and a law in some way, so it remains to show how singular and particular propositions can represent perfections of being.  I have interpreted singular propositions as rules for replicating subjects with predicates that belong to them and this involves something like a law.  When an utterer states that Alexander was married he expresses a certain entelechy.  In replicating the symbol the utterer conforms to a rule which makes every character of a married man a character of Alexander.  The utterer attributes a type, M, to the object.  The type is understood to signify a complex of characters (or forms) F1,..., Fn each of which applies to whatever the type applies to.  The type can be analyzed according to the apparatus for defining causes as the formal cause of the possession of the characters of marriage by Alexander.  The difference between the analysis of final cause and formal cause lies in the fact that a final cause is external and a formal cause is internal.  The causatum could not logically be without the cause when a cause is internal.  The causatum is the possession by Alexander of all the characters of a married man.  The cause, as a type, is a complex of forms to which objects may be expected to approximate with regard to their embodied forms.  For that reason a type is not an accidental conjunction of characters, but an active general principle, just as a law is.  The realization of the entire possible causatum of the type “married” would mean that in every logically possible case in which certain social and legal relations of dependence exist between a man and a woman, the couple will attempt to found and maintain a family.  That is the definition of marriage. 

Particular propositions are to be treated in essentially the same way as singular propositions.  The fact that the subject is indesignate or vague makes no difference in the embodiment of an entelechy by the object of a proposition.

As to the relation between facts and symbols, Peirce defines a fact as “such abstracted element of an event as is expressible in a proposition” (NEM IV, 252; see also 6.67).  A more accurate statement would strike out the words “expressible in.”.  Every fact is a symbol and the event from which the fact is abstracted, “the universe in its totality” (NEM IV, 252), may also be regarded as a fact, “the fact that is not abstracted but complete” (NEM IV, 240), and presumably as a symbol.  A true symbol is an objective or external sign.  Here I need to introduce the objective/subjective distinction which Peirce says he never uses, but which turns up very early as the external/internal distinction.[xii]   Peirce uses the terms “objective “ and “subjective” at least once to formulate the question of nominalism and realism and it seems that he always should have done so to distinguish realism from conceptualism (see 1.27).  Whatever is objective or external is as it is independently of what any particular person or group thinks about it or about anything else.  What is subjective is not objective.  What is subjective is real if it is as it is independently of what any particular person or group thinks about it.  Otherwise it is fictitious.  Something may be real and not objective.

To illustrate, consider the proposition that Don Giovanni seduced a thousand and three women in Spain.  The proposition represents the Don as a seducer of a certain number of women because that is how Da Ponte represented him in the libretto of the opera.  The object of the proposition, Don Giovanni, is not independent of how Da Ponte represented him.  Therefore, the Don is a fiction.  The fictive representation is real because it is independent of what Da Ponte or any other particular person or group thinks about it.  However, it is subjective.  It is not independent of how Da Ponte represented the Don.  But the fact that Da Ponte represented him in the libretto as a seducer is objective.  It is independent of what anyone thinks about the way Don Giovanni is represented in the libretto or about anything else.[xiii]

Now I want to apply these distinctions to an understanding of truth, reality, and the final opinion.  If a symbol such as “Alexander was married” or “Every stone on earth has a real downward component of acceleration” is a cognition then, of course, it is an object of the final opinion.  The analysis of symbolic propositions shows what any object of a final opinion must be.  According to the set of distinctions just presented every object of a final opinion is an objective or external reality.  It is independent of what any particular utterer or interpreter thinks about it or about anything else.  But — an important point — what utterers and interpreters think who think in accordance with the norms of semiosis is not independent of the objective reality which is the final cause of semiotic activity.  The object of the ideally complete opinion at which semiosis aims is the truth.  “The ‘Truth,’ the fact that is not abstracted but complete, is the ultimate interpretant of every sign” (NEM IV, 240).

The ideally complete sign is also “the very Universe” (NEM IV, 239).  “The ideal sign [would] be quite prefect and so identical, — in such identity as a sign may have, — with.  the very matter denoted united with the form signified by it” (NEM IV, 240).  In other words an ideal sign would be purged of subjective elements that would make it false.  The objective sign would be identical or, according to the qualification, a replica of an objective sign would get produced, which replicated sign would be identical with the matter it denotes united with the form it signifies.  The union of matter and form would be governed by entelechy.  It is worth noting that the perfection of cognition is a state of things that can be approached but not realized without contradiction (6.173).  For if it were complete, the purpose of semiosis would be attained and that which was cognized in the cognition would not be a symbol.  The being of a symbol consists in the fact that it will determine an interpretant.  With the purpose of interpretation realized no sign could determine an interpretant in accordance with the aim of truth.  Accordingly, every cognitive representation is a cognition of a state of things which is governed by entelechy and which is imperfectly realized, i.e., one in which the operation of entelechy is not exhausted.  If every cognition involves the objective employment of entelechy, then anyone who agrees with the account of semiosis will have no objection to the metaphysical validity of the category.  And if every cognition, however complex, represents a state of things in which entelechy is imperfectly realized, then we may consider the universe in general under the governance of entelechy: something the being of which consists in the governance of events, but which requires for its complete being that more events should come to pass than ever can have come to pass.  This most general application of the category of entelechy, viewed as the factor which produces regularity from disorder, is what Peirce calls “Reason” (1.165).

Greenlee, commenting on Peirce’s identification of reality with the object of the final opinion, thought Peirce could not have meant that “the [final] opinion is the physical reality.”[xiv].  But if the word “physical” is not taken too narrowly, I can see no reason to deny that every objective symbol is part of the “physical reality” and that the latter is nothing but an objective symbol.  Perhaps the defender of Greenlee will say that physical reality is the dynamic aspect of things which falls under the category of matter.  What reacts is objective, but certainly it is not a symbol.  A reply might begin by pointing out that every sufficiently complete symbol incorporates a dynamic aspect, its object, which falls under the category of matter.  If Greenlee’s defender wants to maintain that matter alone is the physical reality, that is foreclosed as an intelligible position by the discussion of the categories.  All matter embodies form.  The idea that any objective reality should be deprived of the governance of entelechy is foreclosed by the discussion of sign interpretation.  For no matter how surd a fact we have to deal with, it must be cognizable.  That is, it must be subject to the law that if an interpreter gains an active relation to the object, then he can verify that the forms represented to be embodied by the object are embodied by it.  Any objective reality which can be known in accordance with the norms of interpretation will be found on analysis to involve entelechy and will be a symbol.  An idealism that makes the world to be a symbol is an idealism which admits that elements not of the nature of entelechy are essential to the semiotic character of the world just because they are essential constituents of any symbolic proposition.[xv]

Jeremiah McCarthy


[i] Numbers preceded by “NEM” refer to volume and page of Charles S. Peirce, The New Elements of Mathematics, 4 vols., ed. Carolyn Eisle (The Hague, Mouton Publishers: 1976; Atlantic Highlands, N.J., The Humanities Press, 1976).

[ii] Decimal numbers refer to volume and paragraph in Charles Sanders Peirce, Collected Papers of Charles Sanders Peirce, 8 vols., ed. Charles Hartshorne, Paul Weiss, and Arthur W. Burks (Cambridge: The Belknap Press of Harvard University Press, 1965-67).

[iii] Manuscript numbers refer to items listed in Richard S. Robin, Annotated Catalogue of the Papers of Charles S. Peirce (n.p.: The University of Massachusetts Press, 1967).

[iv] Max H. Fisch, Kenneth Laine Ketner, and Christian J. W. Kloesel, “New Tools of Peirce Scholarship, With Particular Reference to Semiotic,” Studies in Peirce’s Semiotic, Peirce Studies, no. 1 (Lubbock: Institute for Studies in Pragmaticism, 1979), p. 17, date “Kaina stoicheia” (MS 517) 1904.  This is too late.  Only two trichotomies of signs appear in the text.  By the latter part of 1903 Peirce had distinguished three trichotomies (2.243-253) and by some time in 1904, six (8.333-339).  The use of only two trichotomies is characteristic of “The Lectures on Pragmatism” (5.73-76, early 1903) and earlier work (e.g. 1.558-559, 2.92, 2.95).  The evidence suggests that the date of 1904 is two or three years late.  If the manuscript were written in 1904 it would present a serious anomaly in the development of the theory of signs.

[v] Adapted from 1.527.  See also NEM IV, 292-300.  As for these conceptions being Aristotelian matter and form, that may be.  But Peirce reverses the priority of matter to form.  Aristotle says, “A matter is potential because it may attain to form; it is when it is actual that it is in its form” (Meta., 1, 1050a15-16).  For Peirce form is potential being and matter without form is a nonentity (1.527).

[vi] NEM IV, 294-296.  This comes from the paper “Sketch of Dichotomic Mathematics” which has clear affinities with “Kaina stoicheia.”.  The former is dated 1904 by Fisch et al., “New Tools,” p. 17 and once again I am skeptical.

[vii] The conception of final cause here is very close to that devised by Charles Taylor and advocated, slightly modified, by Larry Wright, Teleological Explanations: An Etiological Analysis of Goals and Functions (Berkeley: University of California Press, 1976), pp. 31-39.  The assimilation of laws to causes involved in this conception has been criticized as a reductio of it by Andrew Woodfield, Teleology (Cambridge: Cambridge University Press, 1976), pp. 83-84.  I fail to see what is wrong with generalizing the concept of final cause to include laws.  An unfamiliar idea is not thereby absurd.

[viii] Names are apparently classified as indexical legisigns later (see 2.259, 2.261, 2.265).

[ix] MS 9, p. 1.  In related MS 4, pp. 2-3 (first fragment), pp. 2-3 (second fragment) Peirce says that if replicas can be transformed into each other, then they replicate the same symbol, not merely equivalent symbols.  This suggests that translation of a word into another language gives a replica of the same symbol replicated by the original.  In New Elements, IV, p. 248 it is evident that the same proposition can take very different grammatical forms as replicas.  In Charles S. Hardwick, ed., Semiotic and Significs: The Correspondence Between Charles S. Peirce and Victoria Lady Welby (Bloomington: Indiana University Press, 1977), p. 32 (letter of 10/12/04), we have, “The difference between a legisign and a qualisign, neither of which is an individual thing, is that a legisign has a definite identity, though usually admitting a great variety of appearances.  Thus &, and, and the sound are all one word.”.  But in some of the Syllabus material Peirce treats the word “man” as if it “prescribes the qualities of its replica in themselves” (2.292) as consisting of three sounds or representamens of sounds.  Peirce calls what I have taken as the symbol, the “meaning” of the word.  When this is connected with a prescription for making replicas of some certain description we have a word.  It is not easy to say how closely the description of a replica is tied to a symbol, but I think that 2.292 makes the connection tighter than it usually is.  For my purposes not much turns on this question.

[x] The interpreter is assumed to have a disposition to believe what he is told.  Legal and social penalties are attached to lying, but for these to exist there must be a prior disposition to believe.  Knowledge of the penalties strengthens the disposition (NEM IV, 249).

[xi] For an interpretation which makes symbols much less generalized than mine see T. L. Short, “Life Among the Legisigns,” Transactions of the Charles S. Peirce Society, XVIII (1982), 294, 303-305.

[xii] For the alleged non-use of the distinction see Hardwick, Semiotic, p. 69 (letter of 12/14/08).  On “external” and “internal” see 7.339, 8.13.  Hardwick, Semiotic, pp. 116-117 (letter of 3/14/09) makes the connection between “external” and “objective.”

[xiii] The definition of “external” at 6.327.  may conflict with my use of the word “objective” here.  This is not certain, however, and I do not find any other indications of conflict.  The necessary alterations would make the distinctions I want to draw less elegant, but would change nothing substantive.

[xiv] Douglas Greenlee, “Peirce’s Concept of Sign: Further Reflections,” Transactions of the Charles S. Peirce Society, XII (1976), 140-141.

[xv] This is a revised version of a paper that appeared under the same title in Transactions of the Charles S. Peirce Society, XX (1984), 394-433.

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