Charles Pierce (1839-1914) was the founder of American pragmatism. He is considered by some to be the greatest American philosopher. He largely originated the mathematical theory of relations (the “relatives” of the title here). Along with Frege, he is regarded as a co-founder of mathematical logic. Along with Saussure, he is considered a co-founder of semiotics.

Pierce had a keen interest in the philosophy of science, and particularly in the idea of evolution. But unlike most philosophers of science, he was also interested in Kant and Hegel. Moreover, he had a very unusual familiarity with medieval logic. Like Leibniz, he only published a tiny fraction of what he wrote.

Pierce thought it was very important to defend a realist position, and to criticize the nominalism that he saw as pervasive in the modern world. John Boler’s Charles Pierce and Scholastic Realism: A Study of Pierce’s Relation to John Duns Scotus (1963) focuses on this angle. He documents Pierce’s engagement with a narrow but important slice of the work of Scotus, centered on issues of realism and nominalism. A reading of Boler’s work will help to get a little deeper into Pierce’s thought. This will be a lengthy one-off.

Boler is aware of the hazards of writing about “isms”. He notes, however, that since Pierce himself dwells extensively on such terms, they will be unavoidable in understanding his thought.

“In its technical form in Pierce, pragmatism holds that the meaning of a statement consists in the truth of a conditional proposition stating what would happen as a result of certain tests. Two points are of special import here: that apparently simple conceptions like hardness are at bottom conditional in form; and that such conceptions relate not so much to what does happen in any one test, but to what would happen in response to a certain type of test” (Boler, pp. 12-13, citations omitted).

The reference to tests recalls Pierce’s interest in science, but what is essential here is the broader point that every assertion should be understood as shorthand for the assertion of one or more conditionals, even when its surface grammar is unconditional or categorical.

In a move that is ancestral to Brandom’s inferentialism and emphasis on the constitutive role of counterfactual robustness and subjunctive constructions, Pierce explains ordinary properties of things as condensed or hypostasized representations of if-then conditionals. This proto-inferentialism is central to Pierce’s conception of what reality is.

The other key aspect of reality for Pierce is clarified by focusing on the notion of constraint that such conditionals imply. This could be seen as ancestral to Brandom’s work on modality. It is reflected in the concern with what would happen if this or that.

“We find, says Pierce, that our opinions are constrained; there is, therefore, something that ‘influences our thoughts and is not created by them’: this is ‘the real’, the thing ‘independent of how we think it’. But problems arise if we hold that the real is that which influences our sensations, which in turn influence our thoughts…. Such problems disappear, according to Pierce, if reality is taken not as the source or stimulus of the knowledge process, but as its goal or completion” (pp. 14-15).

In the mid-20th century, the dominant philosophy of science was logical empiricism, which explicitly advocated a rigidly foundationalist view of reality as the source of knowledge. Since then things have turned again, and there is more diversity of opinion.

In this notion of reality as the goal of knowledge and not its source, there is an important partial convergence with Aristotle’s insistence in the Metaphysics on the primacy of the “final” cause. Aristotle’s own view of this was largely covered up by the Latin creationist adaptations of his work that took their bearings from Avicenna. The convergence of Pierce with Aristotle is only partial, because Pierce focuses on the temporal working out of processes of evolution, in contrast to Aristotle’s omnitemporal that for the sake of which.

There is a similar partial convergence and difference between Pierce and Aristotle with respect to the meaning of the primacy of actuality. In Pierce, actuality is understood in the modern way, in terms of present facts, though he understands evolution in terms of progress toward the better. (Aristotle and Hegel more emphasize a normative meaning of actuality, which may be at odds with present facts.)

“If on the face of it Pierce’s conception of reality seems a little odd, we might consider an oversimplified application in scientific inquiry. It may be, for example, that Copernicus got the idea for his hypothesis when he was looking at things from a moving platform. But the ‘objectivity’ of his theory is not validated by tracing it to some such suggestion; it is validated by checking the results of, among other things, his predictions. In general, a scientific hypothesis is not accepted because of where it came from but because of where it leads” (p. 15).

This also illustrates Pierce’s non-foundationalism.

“Pierce eventually comes to define reality as what will be thought in the ultimate opinion of the community” (ibid).

The “opinion of the community” is here subject to a kind of historical teleology of progress. This is the optimistic view that better ideas will prevail, given enough time. Brandom has argued that Hegel’s account of mutual recognition — which was not well-known in Pierce’s time — is a substantial improvement over Pierce’s ideal of eventual community consensus.

“Nominalists sometimes contend that a general is just a ‘word’, a fiction created by the mind as a convenience for talking about the world. Pierce is ready to grant that a general is of the nature of a word, but he points out that on his definition of reality this does not in any way prevent a general from being real” (p. 16).

Pierce seems to prefer the term “general” to the more common “universal” in logic. Either way, it means not something that applies to all things, but something that applies to many things.

Boler quotes Pierce, “[The great realists] showed that the general is not capable of full actualization in the world of action and reaction but is of the nature of what is thought, but that our thinking only apprehends and does not create thought, and that thought may and does as much govern outward things as it does our thinking” (ibid, brackets in original).

“How did pragmatism manage to get involved in this sort of thing? The clue to that lies with Pierce’s notion of the ‘would be’, which makes of the pragmatist a realist of an extreme sort. A character — hardness, say — does not consist in the actual responses to actual tests; as we shall see, Pierce criticizes his own early formulations of the pragmatic maxim for suggestion that it does. Hardness is something general, involving a relation of a type of test to a type of response. What is more, Pierce is not just denying that the would-be is the same as a totality of actualities; the very fact that a character is a would-be indicates that it has a different mode of being from that of actual events. The theory also involves the notion of really active (general) principles, which govern actual events” (p. 17).

What makes Pierce’s realism “extreme” is his emphasis on the real character not only of higher-order things, but also of higher-order relations. Pierce thinks of reality as not only saying something about what is, but also about what would be, under a broad range of alternate possibilities. Pragmatism in his eyes looks not only at present facts, but at what would be. Pierce argues that scientific laws already fit this model, but he wants to extend it to ordinary life as well.

“The reader who is scandalized that pragmatism should be mixed up with metaphysical questions might look at [citations to Pierce’s Collected Papers], where pragmatism is said to be ‘closely associated with Hegelian absolute idealism’ and with scholastic realism” (p. 17n).

[quote from Pierce:] “In calling himself a Scotist, the writer does not mean that he is going back to the general views of 600 years back; he merely means that the point of metaphysics upon which Scotus chiefly insisted and which has passed out of mind, is a very important point, inseparably bound up with the most important point to be insisted upon today” (p. 19).

That is to say, Pierce’s interest in Scotus is focused on the issue of realism and nominalism.

[Pierce again:] “But though the question of realism and nominalism has its roots in the technicalities of logic, its branches reach out about our life” (quoted, ibid).

Pierce says modern philosophy has been swept by a “tidal wave of nominalism” (quoted, p. 20).

Boler writes that in the Renaissance, “In the struggle for control of the universities, the humanists sided with the followers of Ockham in an attempt to overthrow the Dunces [Scotists], who were then in power. As a political favor, but with little concern for or understanding of the real issues involved, the humanists championed nominalism…. But if nominalism was misbegotten, realism on its own side was badly defended. The narrow, rationalistic anti-empiricism of the Dunces made the position unpalatable to those occupied with the growth of the new sciences…. Pierce will have to correct misinterpretations of the earlier controversy” (ibid).

[Pierce:] “The nominalist Weltanschauung [worldview] has become incorporated into what I will venture to call the very flesh and blood of the average modern mind” (quoted, p. 20n).

[Pierce:] “[I]t is proper to look beyond the letter [of scholastic formulations] to the spirit of it” (quoted, ibid).

Boler says “The most common and striking argument that the scholastic realists advanced for their position was the necessity of justifying scientific knowledge. Science, as Aristotle had said, deals with generals; and if science is true of the real world, the objects of scientific conceptions must somehow be real” (ibid).

Indeed Aristotle holds that knowledge in the strong sense applies only to universals. Of individuals we have only acquaintance and practical judgment.

[Pierce:] “Still it remains true that I do know that the stone will drop, as a fact, as soon as I let go of my hold. If I truly know anything, that which I know must be real” (quoted, p. 22).

[Boler:] “Pierce then explains that he can make such a prediction because he knows what kind of thing he is dealing with…. What interests him, however, is how this uniformity is different from that, say, of a run of sixes with honest dice” (ibid).

The run of sixes is only a repeated fact. Facts alone tell us nothing of what would be if the facts were different. In Aristotelian terms, most facts are called accidental. What is in a factual sense not only does not tell us what ought to be, it does not tell us what would be, independent of current particulars.

“After all, one need only see that every proposition contains a predicate in order to realize that our thinking is characterized by the use of generals; but that does not yet touch the issues dividing the nominalist and realist” (p. 24).

The very possibility of thought as distinct from opinion depends on judgments about the applicability of universals. This extends also to any kind of art or craft or practical know-how.

“Although the cook must handle particular apples, her indifference to individual apples indicates that what she wants is an apple and not a this” (p. 25).

If we were completely without universals, there could be no meaningful saying. Everything would only be this — and thus indistinguishable from anything else. We would be reduced to a completely inarticulate pointing.

“Pierce does not think that you can find generals in the sense that an archaeologist finds vases” (ibid).

No universal and no reality is simply there to be found, or immediately given. Reality as a distinguishing criterion is bound up with being able to say something about what would be under alternative conditions.

“As a matter of fact, Pierce feels that the realist position has been misunderstood because of a nominalistic prejudice that whatever is real must have the same mode of reality as all other real things” (ibid).

For a consistent nominalist, there would only be brute fact.

“Pierce insists that no great realist of the thirteenth or fourteenth century ever held that a general was ‘what we in English call a thing’. This is why he denies that the controversy in the middle ages had ‘anything to do with Platonic ideas’ ” (p. 26).

I like to rehabilitate the word “thing”. To be real, or to be a thing, is to be polymorphic, to be a subject of what would-be, and to have a less-than-numerical unity. In contrast, to be an object in the Scotist sense is to have numerical unity.

A strictly numerical unity or identity is always artificial. No idea is an object. People are like ideas, and not like objects.

He quotes Pierce again, “Let the artificers of such false inductions dare to set up predictions upon them, and the first blast of nature’s verity will bring them down, houses of cards that they are” (p. 27).

Insofar as words in a language express differences in the world, they are in fact not arbitrary in the way that proper names are. “Nominalism” treats words in general as mere names.

Boler continues, “Now, what is the difference between the group of things called Harry and the group of things called gold?” (ibid). “Now we take some of the things called Harry (the cat, an old rubber stopper, and a bar of soap), and we find that they all float in water. The next thing called Harry that we select may float in water, but we would bet on it about as we would on a run of sixes with dice” (p. 28).

Names are truly arbitrary, as the list of things called Harry illustrates. But the property of floating in water is not indifferent. We can use it as a “test” to distinguish things, which is just to say that it is a counterfactual, a would-be, and thus a meaningful basis of classification.

“If this regularity is due to the scientist’s giving the same name to similar objects, the question at best misses the point. What Pierce finds important is precisely the original similarity…. The problem still remains why the same term was applied to certain things” (p. 29).

“Pierce says of Ockham: ‘He allows that things without the mind are similar, but this similarity consists merely in the fact that the mind can abstract one notion from the contemplation of them. A resemblance, therefore, consists solely in the property of the mind by which it naturally imposes one mental sign upon the resembling things’ ” (pp. 29-30).

The situation resembles that of Aristotle’s critique of the sophist Protagoras, who claimed that “Man is the measure of all things”.

On the dropping of the stone, Pierce says the nominalist “may admit that there is in the events themselves an agreement consisting in the uniformity with which all stones dropped from the hand fall to the ground, but if he admits that there is anything at all, except the mere fact that they happen to do so, that should in any sense determine the different stones to fall every time they are dropped, he ceases to be a good nominalist and becomes a medieval realist” (p. 30).

Pierce again: “The man who takes the [nominalist] position ought to admit no general law as really operative…. He ought to abstain from all prediction” (ibid, ellipses and brackets in original).

And again, “My argument to show that law is reality and not figment — is in nature independently of any connivance of ours — is that predictions are verified” (ibid).

Yet again, “for if there was any reason for it, and they really dropped, there was a real reason, that is, a real general” (p. 31).

Back to Boler, “He does not think that the nominalist wants to deny scientific prediction, but he objects strenuously that nominalism does not explain it” (p. 32).

I previously presented Bertrand Russell’s critique of the modern notion of (efficient) cause in a positive light, because it was a critique of that notion of cause. But by Pierce’s lights, Russell would be a nominalist who fails to produce real explanations.

“While the realist bases his stand on the objective reality of our general conceptions, the nominalist bases his arguments on the independent reality of things…. Pierce feels that the good reasons for this view are distorted by its overemphasis, but that these can be preserved if the real is taken as the normal term or goal of our mental processes: that is, if we hold that our mental activity leads into the real world rather than away from it…. That is to say, whether he can refer the theory to Kant or not, Pierce continues to defend the idea that reality must be that which draws our opinions and not that which triggers them” (pp. 34-35).

While the nominalist may appeal to what Aristotle calls independent things, it now seems to me that she is not entitled to this. “Independent”, “reality”, and “things” all depend on the general and the would-be.

I really like this idea that reality is something we move toward, rather than something we proceed from.

“However much we may have to go into the technicalities of logic and grammar, we should not forget Pierce’s insistence that the nominalist-realist controversy is about real things…. The medieval realist was interested in an objective ground for general conceptions, while the modern nominalist wants to stress that the ‘thing’ exists apart from the mind…. [A] realist need not hold that all conceptions involve a real (that is, objective) generality, or that any universal is a ‘thing’…. [A] proper definition of reality is essential to any adequate solution of the problem” (p. 36).

“Broadly speaking, the scholastics held that only individual things (what they called ‘supposits’) exist. But these supposits have an intelligible structure (what the scholastics called a ‘nature’), which is not simply identical with the supposit as an individual. When a carpenter makes a bed, it is possible for him to have given the same structure to another thing. When someone looks at the bed, he sees that it could have been made with other materials — or better, he realizes that there could be other beds. It does not seem unreasonable to say, then, that it is the same structure, or nature, that is (1) in the mind of the maker, (2) in the bed, and (3) in the mind of the viewer” (p. 39).

“Notice, however, that while any and every bed will have a certain structure, the structure is not identical with any individual bed or group of beds; the structure is a sort of plan, whereas this or that bed is an execution or instance of the plan. In the world of supposits, however, we do not find plans existing alongside the instances of those plans” (ibid).

Structures and plans are higher-order things, not reducible to immediate particulars.

“First intention is thought about the real world; second intention is thought about first intention. Notice that first and second intentional concepts are equally mental. The objects of first intentional concepts, however, are real things, while the objects of second intentions are the first intentional concepts themselves. Thus although first intentional concepts are, in a sense, entia rationis [beings of reason], they have real things for their objects. Second intention can be defined, then, as having for its objects only entia rationis” (p. 43).

Here again we see the Avicennan notion of first and second intentions. This formulation makes it particularly clear that “second” intentions are second-order intentions — that is, intentions with regard to other intentions. Avicenna may have been the first to explicitly talk about second-order things.

“It should be clear even from the way Scotus states the problem that he does not intend to treat nature as another ‘thing’ (like Socrates, Plato, and the line)…. Scotus maintains that Socrates and Plato are ‘numerically distinct’, and consequently if they have the same nature, that nature must have a ‘less than numerical unity’ ” (p. 47).

I hold that anything real must have “less than numerical unity”, and I think this is an implicit assumption in Plato and Aristotle. Oddly enough, it is the neoplatonic enthusiasm for the One that led to more explicit examination of all the ways in which everything else is not a pure Unity.

“If it were maintained that this lesser unity is a contribution of the mind, and that the only real difference was the numerical one, it would follow that our scientific conceptions would not give us information about the real world…. I think that Pierce is making the same point when he says that the nominalist makes the real world to be an unknowable thing-in-itself” (p. 48).

Knowledge involves the ability to meaningfully generalize about the real world. It is exact, “numerical” identity that is artificial. Numerical identity is a valid concept in mathematics, but that is about the extent of it. Any kind of substance or essence or reality has a “thickness” that is mutually exclusive with the razor-thin, absolutist character of numerical identity.

“By a nature’s lesser unity Scotus does not mean something having the viscosity of taffy; the nature is not spread out in a physicalistic sense. As a matter of fact, he emphasizes that the so-called common nature is real in one object and not in two. The word ‘common’, then, may be misleading. Actually, Socrates has a Common Nature even if he is the only only man existing, for he is still a man and not manness itself. The Common Nature lacks a numerical unity precisely because it can be real without being determined to exist in any one thing. Although individuated in any existent thing — in Socrates, the nature is his in the sense of being this nature rather than that — the nature itself is indeterminate with respect to this thing and that” (p. 50).

“Such abstractions, however, should not be confused with second intention; for Scotus, this would be confusing metaphysics with logic…. However much an abstraction of this sort is a construction of the mind, it is a construction done with an eye on the real object. In second intention, ‘predicate’ would refer to ‘being a man’ without reference to any object beyond that predicate itself. In short, metaphysics is like logic in that its objects are abstractions of a second order; but it is like physics because its objects are real” (p. 61).

The common nature is thus sharply distinguished from a second intention. Avicennan intentions all have a psychological aspect, which Husserl criticized in Brentano’s revival of intentionality.

“As we shall see, Pierce gives a special status to some things ordinarily called individuals — notably the human person. Ultimately, such individuals are for Pierce living laws and thus essentially general” (p. 64).

What are commonly called individuals have a kind of streaming continuity that is neither numerical nor absolute. It is not the identity of individuals that makes them precious, but rather their differentiated and “less than numerically identical” essence.

“New developments in logic, Pierce feels, make the whole question of universals easier to express and to solve. Abstractions like humanity turn out to be simple forms — the limiting cases — in a general process whereby relations are treated as things (hypostasized) in order to serve as the terms for higher order relations. Pragmatism shows that scientific formulas take the form of such relations. When successful prediction indicates that these formulas are not fictions, they are called laws. Laws are manifested in things as real powers, or, in pragmatic terms, as real ‘would-be’s’ ” (pp. 65-66).

What common sense regards as individual terms or things turn out to be hypostasized (or as I like to say, shorthand for) relations. This makes excellent sense.

The “new developments” Pierce refers to are the explicit formulation of higher-order concepts.

Boler quotes Pierce, “[Logic] is the science of the necessary laws of thought, or, still better, (thought always taking place by means of signs), it is a general semiotic, treating not merely of truth, but also of the general conditions of signs being signs (which Duns Scotus called grammatica speculativa), also of the laws of the evolution of thought … which I content myself with inaccurately calling objective logic, because that conveys the correct idea that it is like Hegel’s logic” (p. 68).

“Pierce considers the basic logical elements to be the term, proposition, and argument. Of these, the argument is not only the most important but the most fundamental form. It is not, strictly speaking, composed of propositions in turn composed of terms; on the contrary, insofar as propositions can stand alone, they are implicit arguments, while terms are implicit propositions” (p. 69).

I am delighted to read this. Higher-order things come first, and that is why we cannot be foundationalist.

“In the proposition ‘Socrates is a man’, the predicate is ‘is a man’, a form that Pierce calls a rhema or a rheme. The logical subject of a proposition is what is placed in the blank space of a rhema to make a proposition. Of course the logical and grammatical subjects will not always coincide; in the example ‘Anthony gave a ring to Cleopatra‘, the underlined words are the logical subjects — a reasonable enough position which leads Pierce to frequent attacks upon the status of the common noun according to grammarians. Pierce brings grammar into line with logic by taking the basic grammatical forms as subject and verb, the subject being a demonstrative or something that can take its place, adjectives and common nouns being parts of the verb” (ibid).

Pierce thinks in terms of n-ary relations. Nouns are part of the verb. The demonstrative subject he recommends would be a generic “this”, a “free” variable having in itself no description or properties. This would bring grammar into line with the syntax of expressions in predicate logics, where propositions begin with “For all x”, or “There exists x”, and all the differentiation is grouped under the predicate.

“In speaking of the rhema, Pierce says it is obtained by erasing the logical subject(s) of a proposition, which shows perhaps as well as anything why the term is a derived form rather than a building block for propositions. That the proposition itself is an implicit argument requires a more complicated explanation — one involving Pierce’s contention that the copula is illative” (pp. 69-70).

In traditional logic, where a proposition has the surface grammar “A is B”, the “is” was called the copula. When Pierce says the copula is really illative, he means that what is logically meant by the surface grammar “A is B” is the conditional “If A(x), then B(x)”.

“First of all, Pierce denies that the copula is ‘is’, holding instead that ‘is’ is a part of the predicate. Still, he insists that a proposition cannot adequately be treated in terms of subject and predicate alone: for ‘composition is itself a triadic relationship, between two (or more) components and the composite whole’. Second, Pierce denies that the link between subject and predicate is identity, for he considers identity to be in reality only another general predicate. And finally, he affirms that the link, that is, the copula, is a form called consequence” (p. 70).

“Is” is part of the predicate. Identity is only another general predicate. Logic is built by elaboration of the notions of composition and consequence. The claim that composition is “triadic” goes along with this, and may turn out to help explain what Pierce means by “thirdness”.

“Pierce holds that the relation of premise(s) to conclusion is the same as that of antecedent to consequent. Consequence, then, is the prototype of argument; it is the ‘one primary and fundamental logical relation, that of illation, expressed by ergo [therefore]’. Note particularly that the consequence is the relation of consequent to antecedent, not just a consequent and an antecedent. An argument is somehow more than just its premises and conclusion, just as a proposition is more than its terms. Pierce tells us that a proposition is an assertion or predication of a predicate of a subject. Consequence, in which the copula is explicit, is the basic (what might be called the ‘normal’ predicational and inferential form” (ibid).

The idea that logical consequence is a relation has been generally accepted by later logicians. Consequence relation is now a standard term in advanced studies of logic. It specifies what follows from what in a given logic.

On the other hand, Pierce’s insight that there is or should be exactly one fundamental logical relation in a logic — consequence, or whatever we may call it — was not reflected in what came to be standard 20th-century presentations of logic. There has been a great deal of advanced work in several fields that could be seen as carrying forward the kind of unification that Pierce envisioned. But it has mostly used function-like constructs as basic, rather than relational ones. And it is still not mainstream.

“For Pierce, then, predication is essentially a form of consequence. We might note in passing two rather important effects of this doctrine. First, even the perceptual judgment is but a limiting case of hypothetical inference. Second, categorical propositions in their basic (or normal) form are, without exception, conditionals. The latter point in particular has a bearing on Pierce’s pragmatism” (p. 71).

These are all claims that I have made in the context of thinking mathematically about Aristotelian logic, without being aware of the precedent in Pierce. (See Aristotelian Propositions; Searching for a Middle Term; Syllogism; Predication.)

“We must now determine what Pierce means by calling the rheme a ‘relative’, for it is in terms of relatives that he will ultimately explain the generality of the predicate. A relative, he says, ‘is the equivalent of a word or phrase which either as it is [a complete relative] or else when the verb “is” is attached [a nominal relative] becomes a sentence with some number of proper names left blank’…. Pierce reserved ‘relation’ to indicate a relationship said to be true of one of the objects (usually the noun-subject), the others not being considered” (p. 73, brackets in original).

In more standard terminology, Pierce’s “relative” is an n-ary relation, like the fundamental construct used in a relational database. He avoids the term “relation” here because the Latin relatio was used to translate Aristotle’s category of pros ti or “toward what”, which resembles the way he does use “relation”.

“In treating the order and independence of relatives, Pierce finds that a triad cannot be reduced to dyads nor a dyad to monads. He does discover, however, that all relatives higher than triads can be reduced to triads” (ibid).

The same is true in algebra and physics — all the fundamental characteristics of higher-order equations can be understood in terms of the behaviors of second-order equations. And the classic laws of physics are mainly second-order differential equations. Second-order things are “triadic” in Pierce’s sense.

“If categorical propositions are virtual hypotheticals, it might be that all monadic predicates are virtual relations…. A more plausible suggestion is that monadic predicates are simply limiting cases of higher relatives. A nonrelative character, then, is a limiting case of a relative character” (p. 74).

The nonrelative is the limit case or “degenerate” case of the relative. Everything “is” a relation, in the sense that everything can be characterized in a relational way, without presupposing fixed terms. Pierce argues that the laws of physics do not presuppose fixed terms either; that reality is best expressed in terms of higher-order relations, which we can also more simply call higher-order things. Things are convenient hypostatizations of bundles of relations.

But the other essential side of this is that all meaningful differences discernible by common sense (at least all the good ones) are liftable into the higher-order context. A higher-order context means more difference and more distinctions. In no way does it connote an obliteration of difference or canceling of distinctions. It induces a kind of fluidity, as Hegel already observed. But in Pierce’s metaphor of debtor’s court, we still feel the reality of the sheriff’s hand on our shoulder.

“We can now return to the problem of relating monadic predicates to higher relatives. Pierce’s solution is reflected in three points he makes about collections. First, the older logic had reached its limit in treating things that are similar to one another as a collection; the logic of relatives provides the notion of a system that can be constituted by any combination of its members. Cause and effect, symptom and disease, the triadic relation of a sign to its object and interpreter, and, most important, a scientific law or mathematical formula — all constitute systems whose members are not necessarily similar to one another. The contribution of the logic of relatives, according to Pierce, is to treat a class or collection as a degenerate form of system” (p. 76).

A class or collection is a degenerate form of such a system, a sort of fossilized result.

“Generality, on [a common] account, revolves around the similarity of the members of a collection, which can be subjects or subjects or subject-sets” (pp. 76-77).

This similarity is none other than the resemblance of which the medieval logicians and theologians spoke.

“The lesson to be learned from the logic of relatives, Pierce insists, is that this scheme must be turned around…. The power of the new logic … is that it allows us to move not just from a sample to a collection, but from a fragment of a system to a whole system” (p. 77).

“We can approach the same idea from a slightly different angle by examining Pierce’s second point about collections: the distinction between discrete and continuous collections…. The most important kind of nondiscrete collection is that of possible objects” (ibid).

For me at least, this use of continuity is new and interesting.

Boler quotes Pierce, “The possible is necessarily general; and no amount of general specification can reduce a general class of possibilities to an individual case. It is only actuality, the force of existence, which bursts the fluidity of the general and produces a discrete unit” (p. 78).

As a “force of existence”, Pierce’s actuality is clearly not the actuality of that for the sake of which, to which I have given so much attention in Aristotle.

Boler continues, “Pierce eventually comes to hold that every predicate specifies a continuous collection of possible objects…. The quality spectrum that corresponds to monadic predicates is a simple form of the more complex continuity of a process. The events in a process are related not by being similar to one another, but by being ordered to, or successively realizing the end of, the process” (ibid).

Here we do have explicit mention of an end.

“There remains a third point about collections…. Pierce points out that a collection is not the same as its members. Even the collection whose sole member is Julius Caesar is not identical with Julius Caesar…. Pierce comes to define a collection as a fictitious entity made up of less fictitious entities” (pp. 78-79).

I think this has to do with the idea that nouns are “names” for collections.

“Pierce contends that the common noun is an accident of Indo-European grammar, being in reality only a part of the verb or predicate; the same is true of adjectives. But if ‘man’ is an unessential grammatical form, ‘humanity’ and ‘mankind’ are not. For the latter are not parts of the predicate at all: they are the predicate made into a subject by a process called ‘subjectification’ or, more often, ‘hypostatic abstraction’ ” (p. 79).

“Humanity” is more essential than “man”, because it more clearly refers to an essence, rather than to a concrete collection. “Subjectification” here does not refer to anything psychological. It is used in the quasi-Aristotelian sense that — in the same way as “hypostatization” — abstracts something as “standing under” something else.

“Some have held that abstraction is a mere grammatical change with no logical significance, but Pierce thinks this is a serious mistake” (ibid). “Pierce considers abstraction one of the most powerful tools of the human understanding. It is through abstraction that the mathematician is able to treat operations as themselves the subject of further operations. Equally important is the fact that the language of science abounds in abstractions: velocity, density, weight, and the like. Biological and chemical classification likewise require that the scientist deal with collections and their relations; and scientific laws and formulas are themselves the essential characters of collections” (p. 80).

Operations become the subject of further operations. And this is how we get to the idea of a subject as a thing standing under.

“Pierce’s insistence on the importance of subjectification is one reason why he rightly calls himself a Scotist…. Scotus considers abstraction proper to be the process whereby the mind operates on the Common Nature as known, giving it a numerical unity it did not of itself possess. Only the predicables, the second intentional notions like genus and species, are universals in the strict sense; but second order abstractions like humanity and whiteness are also universals (in a sense) because they are ‘fit to be predicated’: that is, they have a unity allowing them to be predicated of many individuals” (ibid).

The mind operates on the common nature, giving it a numerical unity it did not of itself possess. For Scotus this is an advancement of knowledge. But claiming for things a unity that they do not have is reductionism.

“For both Scotus and Pierce, abstractions can be treated in terms of either their logical behavior or their real reference. A biologist, for example, may use abstractions in speaking of a collection of animals or the differentiating character of sentient things, but he is not doing logic. Conversely, a logician may talk of the collection of fairies as an ’empty’ collection, but it is not a logical inquiry that establishes that there are no fairies; actually the logician is not interested in fairies but in collections…. In general, although any predicate can be made a subject by a logico-grammatical process, that process does not of itself determine that a collection or a character is real” (p. 81).

At a formal level this is clearly true. Subjects in this quasi-grammatical sense are abstractions from higher-order predicates.

“Consequently, it is important to distinguish in Pierce, as we did in Scotus, between second intention and abstraction. Second intention is ‘thought about thought as symbol’, and thus requires an act of abstraction: our thinking about things is itself made a thing to be thought about. Both logic and grammar make use of the process: ‘subject’, ‘predicate’, ‘noun’, ‘verb’, and the like are all second intentional terms” (pp. 81-82).

“As we reach the higher level relations of hypostasized relations, we sometimes lack names for the relations and use instead scientific formulas or laws. Even where we have the names at hand, the explicitly relational form of the law can be substituted. Such would seem to be the reasoning behind Pierce’s contention that what the scholastics called a nature was in fact a law of nature: the nature of a diamond, for example, consisting in a higher order character, a relation of relations, or law” (p. 83).

Here I think of the various passages in which Aristotle points out some commonly recognizable phenomenon that has no name.

“When Pierce says that some abstractions are real, he does not mean that they have the same mode of being as existing physical objects” (ibid).

Abstraction in itself is not subjective in the psychological sense. It designates a formal operation of giving a shorthand designation (a name) to something that previously had none. But then if we are not careful with our new shorthand, we may use it in an overgeneralized way that effectively is subjective in the psychological sense.

“The mental depends for its reality on someone’s thinking it, but then it has characters as a mental reality despite what anyone thinks about it” (p. 84).

I’m not fond of the term “mental”, but if we think of it merely as a named variable that gets its meaning from its use in various contexts, what he is saying is true. (What I call meaning (Fregean Sinn or “sense”) is not the same thing as reference (Fregean Bedeutung). Abstraction works on the technicalities of reference, which in turn depend on anaphora, or back-reference in speech to things that have not been explicitly named.)

“The fact that someone has made an abstraction is as real as the fact that someone dreamed. And just as this is not the issue when it is said that a dream is unreal, so it is also not the issue when it is said that an abstraction is real. The reality in question is the reference of the abstraction” (ibid).

If I give something a name, you may doubt its appropriateness (whether it is a good name), but regardless, it remains a fact that — for better or worse — I gave it that name.

“Real abstractions are distinguished first of all from second intentions, for the latter refer only to to entia rationis. A real abstraction, though itself an entia rationis, refers to something that does not depend on what someone thinks or thinks about it. Second, real abstractions are to be distinguished from abstractions which purport to refer to the real…. Notice that only experimental inquiry will establish the latter distinction…. The question of real collections and characters is something beyond this” (ibid).

Second intentions in this way of speaking are psychological or what I think of as spontaneous, in that they are formed at a material, preconscious level in the imagination, whereas abstractions are the result of formal or symbolic operations.

“As we saw, Pierce uses ‘relation’ to indicate a relationship said to be true of one of the objects related, usually the noun-subject, the others not being considered. In much the same way, ‘power’ seems to indicate a lawlike relationship which is said to be true of the noun-subject or, in this case, what is usually called the cause” (p. 90).

“What a power explains is the special regularity involved. When we say, for example, that a charged battery has a power which an uncharged battery does not, we imply that it is not a mere chance similarity that a motor attached to the battery will start. We feel that there is some reason why a motor attached to one battery will start while, attached to the other, it will not. As a matter of fact, we feel that there is something about the charged battery even when it is not attached to the motor which makes it different from the uncharged battery” (pp. 90-91).

Pierce here explicitly gives a positive sense to the scholastic way of explaining things by powers.

“[T]he nominalist has not yet explained why all pieces of opium cause people to go to sleep. Pierce may seem to say this, but I think his real reply is that the logic of relatives shows that to admit a real connection between taking opium and going to sleep is to admit a real general: a system whose members are the taking-opium event and the going-to-sleep event” (p. 91).

Boler says elsewhere that scholastic powers are used to explain the same kinds of regularity or non-arbitrariness that are explained by the higher-order relations that are expressed in scientific “laws”.

“The pragmatic maxim transforms ‘x is hard’ into ‘If x were scratched by carborundum, it would not leave a mark’; the hardness is the hypostatization of the relation between test and response” (ibid).

“The would-be, which Pierce insists upon in his later writings, is but the pragmatic equivalent of ‘power’ in the sense we have just discussed. In short, pragmatism is not just a matter of changing abstract terms into concrete ones; it is the very logic of abduction” (pp. 91-92).

“Abduction” is another of Pierce’s neologisms, formed by analogy with “induction” and “deduction”. It is what is involved in creative thought.

“At this point some remarks should be made about the noetic of abduction. From the above discussion, it seems obvious that there is some analogy between abductive inference and ‘seeing connections’. Indeed, Pierce calls abduction insight, instinct, and perhaps even intuition. But his own attacks on intuitive cognition suggest that something slightly more complicated is at work here” (p. 92).

The status of intuition is an area in which Pierce and Scotus are far apart. For Scotus, intuition is something objectively grounded in perspectiva, that gives us superior knowledge. Pierce on the other hand has Kantian scruples that make this kind of claim illegitimate.

“The fact that, out of an infinity of possibilities, the scientist can achieve his purposes with relatively few guesses suggests to Pierce that we have an instinct for the truth and that the mind and nature must be pretty much of whole cloth.”

Talking about these things is difficult, because the key terms are all said in many ways. Kant and Pierce reject claims of intellectual intuition as privileged access to immediate truth. Nonetheless Pierce says we have an instinct for the truth. The difference is that it is neither privileged nor immediate.

The non-separation of mind and nature and the “relatively few guesses” are consequences of the new realist understanding he is developing. The non-separation shows we are far from the dualism of Descartes. As Pierce himself recognizes, there is a degree of affinity between his work and that of Hegel. But this non-separation also represents a major difference from Scotus, who is motivated by an Augustinian concern to relate mind to a supernatural order and to separate it from nature. The very concept of “mind” as separable from nature in this way has an Augustinian heritage.

“[R]eality must be viewed as the goal of our mental activity and not its source” (ibid).

Similarly, knowledge and understanding are something we aim at, not what we start from. There is fertile ground for a Socratic ethic here. Knowledge is something we earnestly seek at every moment, not something we claim to already have. Aristotle’s unique orientation toward the primacy of the final cause was lost in his assimilation to the creationist paradigm through the introduction of an Avicennan abstract efficient cause as “cause of existence”, and only began to be recovered by Hegel. In making reality a goal and not a starting point, Pierce aligns himself explicitly with the broad outlines of Hegel, and implicitly with Aristotle’s unique insistence on the primacy of the final cause.

“Where William James praised pragmatism for its nominalism in reducing the meaning of a conception to particular experimental actions, Pierce says again and again that pragmatism involves realism” (p. 96).

The empiricist concept of “action” here attributed to James — a secular descendant of the Avicennan efficient cause adopted by the theologians to make a creationist Aristotle — is too narrow, too immediate, and too blunt an instrument to serve as a basic building block for the point of view Pierce is developing.

This affects the very nature of pragmatism. The Greek pragma (thing we are practically concerned with) and praxis (“action” or practice) come from the same root. The narrow concept of action as an impulse — which Galileo took from the first creationist commentator on Aristotle, John Philoponus (490-570 CE), who worked in the Alexandrian neoplatonic school of Ammonius — became attached on the side of nature to the Avicennan abstract efficient cause as cause of existence that had been promoted by the Latin theologians. In the resulting view, God as efficient cause works by creation, and nature as efficient cause works by a kind of impulse that led to the later billiard-ball model of mechanism.

With this division once achieved, it became possible for early modern writers concerned with nature to focus exclusively on the “natural” billiard-ball model. All action in the created world comes to be thought on the model of Philoponan impulse. One consequence of this is that action comes to be thought of as something immediate.

What Pierce objects to in James’ “particular experimental actions” can be understood as involving this kind of immediacy, which Pierce has already moved beyond, in what he himself recognizes as a convergence with Hegel. Hegel treats immediate action as an appearance, and against this develops his own much more ramified notion of practice, which he sometimes calls by its Greek name of praxis. Hegelian and Piercean practice replaces the narrow concept of immediate action with something understood in a deeply contextual way that is closer to what I have been calling Aristotelian “activity” or “act”.

Whereas James the charming and accessible behavioral psychologist thinks of reality as consisting in shallowly specifiable, immediate “actions” and “events” that directly cause one another, Pierce the obscure but brilliant semi-Hegelian logician thinks of it in terms of a vast and intricate evolving structure of if-then conditionals that condition one another, in ways that are analyzable in terms of his new theory of higher-order relations.

“The logical form of the conditional proposition is what Pierce calls a consequence…. The ‘conception of the effects’ referred to in the pragmatic maxim cannot be a statement of an event but must be a conditional statement. For Pierce, then, pragmatism shows that hardness consists not in actions or events, but in relations of actions and events” (p. 98).

“The stress upon the would-be, characteristic of his later writings on pragmatism, carries the relation of consequence one step further. If the hardness of a diamond consists in the conditional fact that it would give a certain response to a test, then hardness is not just this present and actual relation which holds between this test and this response, but a general relation that holds for all possible tests and responses of this type…. When I say that it would so react, there is no particular event I could now specify: in speaking of a possibility I am not speaking of a collection of discrete acts” (pp. 98-99).

Pierce’s “would-be” takes us into the realm of Aristotelian potentiality.

“Pierce concludes that the pragmatist must admit a theory of real possibility…. Pierce simply says that the conditional proposition of the pragmatic reformulation has a peculiar and essentially modal structure” (p. 100).

Real possibility is one dimension of Aristotelian potentiality. Pierce’s argument that everything is not reducible to events and actions parallels Aristotle’s critique of the Megarians (who reduced everything to a thinly factual actuality) in book Theta of the Metaphysics.

“Pragmatism shows that the meaning of a conception like hardness ultimately involves the notion of would-be, habit, or power. A power or habit is a nonrelational expression for a law” (pp. 101-102).

“One source of confusion lies in what I think is the mistaken notion that pragmatism must be a reductionist theory. A reductionist pragmatism, as I understand it, contends that only actual events are real — powers and laws, abstractions of all sorts, are only shorthand expressions for actual events…. That is to say, the pragmatic maxim is a formula by which all statements that are not event-statements are reduced to a series of statements containing only event-statements” (p. 106).

The latter-day reductionist repeats the error of the Megarians, who claimed that everything real is actual, while taking actuality in its non-Aristotelian sense of mere present factuality.

“It seems to me that Pierce’s pragmatism was never intended to be like this at all” (ibid).

“The gain is not that we have rid the world of powers and of laws, but that we have found a way of expressing our meanings so that we can tell a real law from a fiction” (pp. 106-107).

With this emphasis on expressing our meanings, we can see a Piercean background to Brandom’s “expressivist” view of logic.

“When I say that the way Pierce talks of laws and powers as explanations, I do not at all mean that I find what he says about causes and explanations to be pretty clear” (p. 108).

This talk of explanations suggests that Pierce ends up rediscovering something close to Aristotle’s own notion of cause as a “reason why”.

“[I]n denying that events are causes, Pierce is not denying that ‘individuals’, in the sense that Socrates is an individual, can be causes…. Pierce not only holds that Socrates is not an event, but he goes on to say that Socrates is not strictly an individual. For the realist, Pierce says, ‘things’ do not need reasons: they are reasons” (p. 109).

“[F]or Pierce it is the consequence and not the consequent which is at issue…. Pierce’s conclusion is that the pragmatist must therefore hold that some possibilities are real” (p. 111).

“He says, for example, that the idea that a law admits of no exception is nominalistic: there cannot be exceptions to a law that consists only in what happens” (p. 112).

“Pierce admits to the nominalist that a would-be can ‘only be learned through observation of what happens to be’, but he insists that a would-be cannot consist simply in what happens to be actual” (p. 113).

“Burks’s remark that ‘action is based on actualities, not on potentialities’ is only partly true for Pierce” (pp. 114-115).

“By insisting upon the conditional analysis of our conceptions, Pierce has incorporated into his system a special theory of real potentiality” (p. 116).

Pierce still has a less than fully Aristotelian notion of potentiality, limited to its “real possibility” aspect. But this is already a huge advance over the idea that immediate actions and events define reality.

“[C]ertain instances of predictive knowledge ‘oblige’ the pragmatist to ‘subscribe to a doctrine of Real Modality’ ” (p. 117).

Modal logic, which develops notions like possibility, necessity, and other kinds of constraint or conditioning, was very much out of favor in Pierce’s day, when monomorphic views of facts were overwhelmingly dominant. Since the later 20th century, modal logic been considerably developed, and Brandom has related it to more broadly philosophical concerns. Boler recognizes that Aristotle and the scholastics did work with modal logic.

“For Pierce, however, the predicate, if true, indicates a real relation to which the notion of form does not do justice. Form cannot ‘reach outside itself’. It is adequate for the static generality of similar things, but for the dynamic generality a principle of law or entelechy is needed” (p. 120).

Form in the sense of the species discussed in medieval perspectiva does have this static and self-enclosed character. Scotus introduced new ideas of formal distinction and “formal being”. In the present state of my understanding of Scotus, it seems that Scotus takes his bearings on the nature of form from the perspectiva tradition. But Albert the Great and Thomas Aquinas among others speak of form at least sometimes in a more expansive way, giving it some of the role that entelechy has in Aristotle.

For my own self, I find it hard to think of form as anything other than relational. The most elementary notion of form in Plato and Aristotle is probably that of geometrical figure. I have always seen geometrical figure in relational terms, rather than as a self-enclosed whole.

The Greek word in book V of Euclid’s Geometry for the ratio or relation of two magnitudes is none other than logos, which was translated to Latin as ratio. If we were to extract an implicit concept of form from Euclid’s use of figures, it would consist of many ratios or relations, rather than a single notion of shape as it appears in optics.

“We have already seen the prototype for this reasoning in Pierce’s theory of the illative copula. A consequence is more than an antecedent and a consequent, and a proposition is more than a subject and a predicate” (ibid).

Pierce’s “illative copula” is what is now called logical consequence, or a consequence relation. Each of the plethora of logics we have today can be conceptually characterized in terms of a differently detailed specification of the consequence relation.

“The relation of similarity is not adequate to handle the notion of process, even when similarity is treated in terms of a spectrum of possible variations. For the events in a process are related to one another not in being similar but by successively realizing a potency in time” (p. 127).

Here it sounds as though similarity is being viewed in the same way that sees geometrical figure as a unary “shape”, rather than a complex of relations. But in the recent series on Boulnois’s Being and Representation, it seemed that the usual scholastic way of talking about resemblance followed the perspectiva tradition’s decentered approach, seeing resemblance as a multifarious play of relations, rather than a putatively simple relation between two unanalyzed unitary shapes.

Next we come to the anti-psychologism in logic that Pierce seems to share with his contemporaries Husserl and Frege. (Pierce and Husserl are known to have actually corresponded.)

“Pierce is interested in dissociating ‘idea’ and ‘thought’ from the psychological connotation that someone has an idea or that a thought is in someone’s mind. The thought-like character of a real law does not result from someone’s thinking it, but from the element of final causation that is involved in its operation” (p. 130).

Here we get to a few more connections with Aristotle. Even if Pierce’s recovery of the notion of final cause is stunted by his overemphasis on temporal development toward a future, it seems that he does follow Aristotle and Hegel in recognizing that first things come last in the order of knowledge.

[Pierce:] “The thought thinking and the immediate thought object are the very same thing regarded from different points of view” (quoted, p. 131).

Like Hegel, Pierce endorses Aristotle’s thesis of the inseparability of the thought that thinks from what it thinks.

“For Pierce, however, the predominance of continuity tends to eliminate the concept of substance, and the supposit (Socrates, for example) comes to be treated as a process. What we call ‘things’ are not strictly individuals but generals. Socrates is not just a member of a collection, partaking in generality through his similarity to other men; he is a fragment of a system. A dynamic process himself, the human person is continuous with that system which is humanity and which is, in turn, continuous with the whole evolution of Reason” (p. 141).

Substance in the later tradition came to be highly reified. The more fluid view of substance that Pierce emphasizes is another thing he shares with Hegel, and indeed with Aristotle. Pierce is reportedly a major influence on Whitehead, both on logic and on Whitehead’s central notion of process.

“What emerges from the discussion is a world of process, characterized by continuity and set in motion by the rule of Reason through final (and not efficient) causality” (p. 144).

“Continuity” seems to be Pierce’s preferred term for the more fluid view of substance. This is the climax of Boler’s book. To me it sounds more Aristotelian than Scotist, because Scotus is one of the great historic promoters of Avicennan efficient causality. What follows, while it makes a number of additional points about Pierce’s relational perspective, is mainly a summary.

“The objective generality of a predicate is a matter of its reference to many subjects. This becomes critical when the predicate is itself made a subject of further operations. This process, which Pierce calls hypostatic abstraction, can be accomplished in terms of either extension or comprehension. In an extensional treatment we utilize the notion of a collection: something constituted of members all of which have some character, however trifling. In the comprehensional analysis the character itself becomes the subject of discourse. Here Pierce’s relational treatment of predicates comes to the fore.”

Pierce’s “hypostatic” abstraction is a new and valuable characterization of what abstraction actually is. I suspect it is in some way ancestral to the computable notion of abstraction developed by Church in the 1930s, where abstraction consists in giving some unnamed thing a name.

“A collection is made up of similar members. But the logic of relatives allows the development of the more interesting notion of a system. In a system the members are not necessarily similar to one another; the mode of connection is something more complex, such as giver-of-to, cause-of, quotient of, and so forth. Any relational character delimits a system whose members are the subjects of the proposition having that predicate. Thus a relative predicate can be general in three ways: (1) as itself a sign; (2) as delimiting a system (or set); and (3) as true of many (sets of) subjects.”

There is a one-to-one mapping between predicates in the sense of predicate logics, and what are here called relational characters.

“Induction is suited only to collections; it infers that the character of a whole class is the same as that of the sample upon which it operates. The character that each member has may be quite complex, of course, but it must be the same in each member. The move from fragment to system — which is pretty much what is ordinarily called seeing connections — is a different mode of inference, namely, abduction. The operation of hypostatic abstraction involves abductive inference. To make a predicate a subject is, in the logic of relatives, to treat a relation as a thing; thus it requires, if only trivially, that the relation be recognized as significant to begin with. Pierce points out that the resultant ‘thing’ is a creation of the mind, an ens rationis” (p. 146).

We treat a relation as a thing by giving it a name that allows us to refer to it. Naming an unnamed thing is a creative act of the same general sort as seeing a connection.

“An abstraction, like a dream, is a fact in someone’s mental biography. When the realist contends that some generals are real, however, he is concerned with the reality of that to which such an abstraction refers. Abstractions of second intention refer only to the mind’s way of representing objects, and not to the things represented. Real abstractions are also ‘second order’ conceptions, but the objects to which they refer (namely, the thirdness of things) are, or purport to be, real aspects of things, which can be called ‘realities’ ” (p. 147).

I won’t attempt to explain “thirdness” here, but we have already seen a few hints. It is related to composition and consequence.

“The nominalist contention, according to Pierce, is that wherever generality is found, it is a function of the symbol as symbol — that is, of a second intention — and does not reflect a generality independent of the mind. Pierce hails as the nominalist’s true contribution the correlation of a general with the activity of a symbol; that is, Pierce argues that the general is of the nature of a word or an idea. But for Pierce the important question of whether a general is real still remains unanswered. At this point the issue begins to exceed the limits of logic, for it becomes necessary to distinguish within first intentional abstractions those that are objective and those that are subjective. On Pierce’s account, such a distinction cannot be made by the logician, for it turns upon the matter of successful prediction” (ibid).

“The special contribution of Pierce’s pragmatism now becomes relevant. The pragmatic formulation makes the rational purport of any conception consist in the truth of a conditional proposition relating to the future. This means that (1) every predicate involves (virtually) a relative character, which brings into prominence the generality of the character itself as a system, in contrast to the more commonly recognized generality of the collection of similar (sets of) subjects; and (2) every predicate becomes a virtual prediction. Of course, pragmatism does not verify predictions; it simply puts our conceptions into a form that will allow for the scientific inquiry which alone can separate law from fiction. The fact of scientific prediction, however, shows that in some cases something more than an accidental succession of events or a simple uniformity is involved. Ultimately, prediction shows there is something real now that accounts for a future actuality; and since the only actuality involved is the future event, the present reality must be a possibility” (ibid).

Pierce’s consistent emphasis on the relations he invented under the name of “relatives” could be an early alternative to the set-theoretic foundations of mathematics that were being developed around the same time, though I don’t know that Pierce ever presented it as such.

“It should be clear by now that Pierce’s pragmatism involves not only the belief that generals are real, but a special conception of the nature of real generals. This brings us to the last phase of Pierce’s realism, where he criticizes the attempt to account for real generality by form alone. The schoolmen, as Pierce sees them, realized the importance of habits or dispositions, but unfortunately they treated them as forms. Lacking the logic of relatives and pragmatism, they were unable to do justice to the relational structure of real generals. The result was a static doctrine of substantial forms that could not account for the important elements of continuity and process” (p. 148).

Neither the scholastics nor Pierce understood form in a relational way.

“Scholastic realism was a step beyond nominalism, for it could account for the generality of qualitative possibility, the generality of monadic predicates. But the notion of potentiality, of would-be instead of might-be, could only be grasped in the dynamic conception of law. That is, the unity of a process is found not in the similarity of the events in the process, but in the more complex conception of a system that orders those events. The distinction here is that of firstness and thirdness…. Also involved is the idea that a relative is a system that not only delimits a collection of similar (sets of) subjects, but relates the subjects of each set. This activity of relating Pierce calls ‘mediation’, and he considers it definitive of thirdness” (ibid).

According to Boler, Pierce uses the Hegelian term “mediation”, and “considers it definitive of thirdness”. In Pierce’s day, the old overemphasis on the thesis-antithesis-synthesis triad in elementary accounts of Hegel was very much dominant. This may have influenced Pierce’s odd choice of “thirdness” for one of his key concepts. The connection with Hegelian mediation is far more illuminating.

“[T]he argument that a would-be is not the same as any collection of actualities, is again applied in the broader field of the reality of some thirdness. Pierce has so described secondness that nothing is included in it except the bare reaction-event; as a result, he has no difficulty in showing that thirdness is not contained in secondness” (p. 149).

As throughout Boler’s book, actuality is used only in the thin sense of a present state of affairs. But the important and valuable point is how the would-be decisively moves beyond this.

“If the individual as such is a bare event, it is difficult to avoid Pierce’s conclusion that there must be some real generality in the objective make-up of the world. As to the ordinary notion of a person or ‘thing’ as an individual, Pierce more or less denies it. The person or thing is a ‘cluster’ of potentialities, and therefore a habit or law itself. The important problem of Socrates’ relation to humanity is now not so much a question of the relation of an individual to a type, but of a fragment to a system” (ibid).

We even get a partial recovery of Aristotelian potentiality.

“Because of the emphasis I have placed on it, the nature of the Scotistic element in Pierce’s realism deserves a separate, if brief, summary. The distinction of two problems of realism is Scotistic, or at least scholastic. And within the logical analysis, Pierce’s treatment of abstractions as ‘second order’ conceptions is definitely Scotistic. From this issue the discussion of ‘real’ abstractions arises, and Pierce himself has acknowledged his indebtedness to Scotus for the use of the term ‘real’ ” (pp. 149-150).

This suggests that there is in Scotus somewhere a relatively explicit discussion of what would now be called second-order things. Unfortunately, though the book includes many citations to the works of Scotus, there is none for this one.

“Once the question of logical predicability is handled, Scotus turns his attention to the Common Nature. It is not a supposit, for the evidence indicates that it consists in a less-than-numerical identity. While it is real, the Common Nature is not a separate substance; indeed, the mode of its unity suggests a different mode of being. The Common Nature is to be found, in a certain sense, in individual things, but it cannot be identical with the individuality of such things. Ultimately, Scotus decides that the Common Nature is not a res [thing] but a realitas [reality]: something essentially conceivable but real before the operation of the intellect. These realities — or formalities, since they are ‘formally distinct’ from one another — are neither physical things nor logical concepts. They are real, but in what has been called a ‘metaphysical mode’ ” (p. 150).

“Scotus’ arguments for the real lesser unity are supplemented in Pierce by the arguments from the fact of prediction. Pragmatism and the logic of relatives influence the conception of the structure of these realities: what Scotus held to be formlike nature Pierce conceives of as a law of nature. But Pierce’s laws have a different mode of being from individuals and they retain a strong resemblance to Scotus’ metaphysical mode — in fact, Pierce also calls them realities” (ibid).

“There are differences in the two theories, of course…. The main difference lies with Pierce’s self-acknowledged denial that the nature is contracted in individuals…. The important point, however, is that in the very fact that Pierce denies the Scotistic doctrine of contraction he reveals the extent of Scotus’ influence: the framework of Scotus’ solution to the problem of universals, without the notion of contraction, provides the basic points of reference for the structure of Pierce’s own theory” (ibid).

I think there are quite a few more differences, but at least from this account, it seems as though the realist arguments of Scotus are largely if not wholly independent of his voluntarism.