The Logic of the Arabians And Its Arabic Text [Al-Risala al-Shamsiyya]

SECOND BOOK: On propositions and rules regarding them

This book is divided into an introduction and three chapters.

INTRODUCTION

Definition of proposition and its primary division

§38. Proposition (literally a decision) is a speech, which allows that he who utters it be told that he is true or false (right or wrong). It is called categorical, if its two extremities (terms) are resolvable into two simple [ideas], as Zayd is informed, or Zayd is not informed, [or from “the Sun is rising” follows “the day is approaching,”] and it is hypothetical, if they are not thus resolvable, [e.g. if the Sun rises day will approach].

§39. The hypothetical [proposition] is either conjunctive (conditional), or disjunctive. It is called conjunctive, if we pronounce in it a proposition (i.e. one of the two propositions of which it consists) to be true or untrue, under the assumption that another (the other) proposition be true. [Example of an affirmative conjunctive] “if this is a man, it is an animal.” [Example of a negative conjunctive], “if this is a man, it cannot be a mineral.”

A hypothetical proposition is called disjunctive if we pronounce in it that two propositions exclude (literally deny or refute) each other, either both in [case of] truth and [in case of] falsity or in one of the two only, or that their mutual exclusion is denied, e.g. “this number is either even or odd.” “That this man is either a writer or a negro, is not admissible.”

First Section: On the categorical (proposition)

First Inquiry: Its parts and kinds

§40. The categorical proposition consists of three parts: the part on which judgment is passed, - which is called subject; the one by which judgment is passed, - which is called predicate; the relation between the two, showing the bearing of the predicate to the subject - which is called judicial relation; and the word which expresses it is called copula, as “is” in the sentence “Zayd is informed.” Such a proposition is called ternary.

In some cases, which are very easily intelligible, the copula is omitted, and the proposition is called binary.

§41. If the relation is of such a description that you can say that the subject is in agreement [with the predicate], the proposition is called affirmative, as man is an animal; and if it is of such a description that you can say that it is not in agreement it is negative, as a man is not a horse.

§42. If the subject of a categorical proposition is a definite individuum, it (the proposition) is called peculiarized or individual (singular). If the subject is a universal, and if the quantity of the singulars (or individua) of which the judgment is true is shown in it, the word expressing the quantity is called wall and the proposition is called fenced or walled-in. It is of four kinds: if it is shown in it that the judgment [applies] to all the singulars, it is [called] an universal [categorical proposition]. This again is either affirmative [or negative: in the affirmative] the wall is “every one,” e.g. every fire is hot. In the negative the wall is “no,” “none,” “not one,” e.g. every fire is hot. In the negative the wall is “no,” “none,” “not one,” e.g. no man is a mineral. If it is shown in it that the judgment [applies] to some things, it is particular, and [again it is] either affirmative, and [in this case] the wall is “some” “one,” e.g. some animals are men, or one animal is a man; or it is negative and the wall is “not all,” “some (are) not,” e.g. not all animals are men, or some animals are not men.

§43. If the quantity of the singulars is not shown in it and if we can neither say that it is a universal nor that it is a particular proposition it is called a physical proposition, e.g. “animal” is the genus and “homo” is the species. But if we can say it is universal or particular [but it is not stated] it is called ambiguous, e.g. man is at a loss, or man is not at a loss. Such a proposition is virtually a particular proposition, for if it predicates that man is at a loss, it predicates that some men are at a loss and vice versa.

Second Inquiry: On the four fenced Propositions.

§44. The expression every C is B, is sometimes employed in reference to the verity, and its meaning is that every possible (imaginable) singular which may exist and is C, is B by reason of its existence; i.e. whatever is the substrate of C is also the substrate of B. [Such a proposition is called verity-proposition القضیه الحقیقه] Sometimes the expression is used in reference to actual existence, and it means that every C in actual existence, be it at the time of the judgment or before or after it, is B in actualexistence, [such a proposition is called actuality-proposition القضیه الخارجیه].

The difference between these two views is evident, for if no square exists in reality, still we are correct in saying every square is a figure in regard to the first view, but not in regard to the second. And if no figure did exist but squares, we would be correct in saying every figure is a square by the second view. From this you can deduce rules regarding the other fenced propositions.

Third Section: On Privatives and Attributes

§45. If a negative particle is part of the subject, e.g. an inanimate being is a mineral; or of the predicate e.g. minerals are without intellect (unintellectual); or of both; the proposition is called privative whether it be affirmative or negative. But if no particle forms part of either extremity then the proposition, if it be affirmative, is called attributive and if it be negative indivisible.

§46. A proposition is affirmative or negative by reason of its affirmative or negative relation (copula) and not by reason of its extremities. If we say “every thing that is not living is without intellect,” it is an affirmative proposition though both extremities are nonentities, and if we say “a moving being is not at rest” it is a negative proposition though both extremities have [positive] existence.

§47. The indivisible negative proposition [e.g. the partner of God is not omnipotent] is more general (contains more) than the affirmative with privative predicate, [e.g. the partner of God is impotent], for the negation may be true though the subject is a nonentity (i.e. though there is no such thing as a partner of God, we can still say if there were one he could not be omnipotent), but the affirmation cannot be true (i.e. if we say the partner of God is impotent, we admit that there is a partner): because affirmation is admissible only in regard to a thing of ascertained (or acknowledged) existence, as for instance in propositions whose subject is an actually existing individuum or in regard to a thing of assumed existence as for instance in propositions whose subject is a verityl. If the subject does exist the indivisible negative and affirmative privative propositions are equivalent. The difference in the expression [between the indivisible negative and the affirmative with a privative predicate] is this: in the ternary, if it is affirmative, the copula stands before the negative particle, and, if it is negative, it stands after the particle, [as there are no binary propositions in English; the following sentence, of the text which refers to a peculiarity of the Arabic language is omitted].

Fourth Inquiry: On Modal Propositions

§48. The relation of the predicates to the subjects, be they affirmative or negative, must have a certain qualification as “necessarily,” “perpetually,” “not-necessarily” “not-perpetually.” Such a qualification is called the materia of the proposition, and the word expressing it, is called the mode of the proposition.

§49. There are thirteen modal propositions into which it is usual to inquire. Some of them are simple, that is to say, their verity is simply an affirmation or negation; and some are compound, that is to say, their verity is composed at the same time of an affirmation and a negation.

§50. There are six simple modal propositions.

1. The absolute necessary [proposition]. It pronounces that the predicate is affirmed or denied of the subject of necessity as long as the essence of the subject exists, as if we say, “every man is of necessity an animal” and “of necessity no man is a stone”.

2. The absolute perpetual [proposition]. It pronounces that the predicate is affirmed or denied of the subject in perpetuity as long as the essence of the subject exists. The preceding affirmative and negative examples apply to this case.

3. The general conditioned [proposition]. It pronounces that the predicate is affirmed or denied of necessity under the condition of [the continuance of] a certain attribute of the subject, as if we say “every writer is of necessity moving the fingers as long as he writes.” “A writer does not keep his fingers at rest as long as he writes.”

4. The general conventional [proposition]. It pronounces that the predicate is affirmed or denied of the subject in perpetuity under the condition of [the continuance of] a certain attribute of the subject. The preceding affirmative and negative examples illustrate this case.

5. The general absolute [proposition]. It pronounces that the predicate is actually affirmed or denied of the subject, as if we say “every man without exception (literally with general absoluteness) is breathing.” “Everyman without exception (literally with general absoluteness) is not breathing.”

6. The general possible [proposition]. It pronounces that there is no absolute necessity that what is contrary to the judgment should not be the case, as “by a general possibility fire may be hot.” “By a general possibility what is warm is not cold.”

§51. The compound modal propositions are seven in number.

1. The special conditioned. It is the same as the general conditioned with the restriction that the relation of the subject to the predicate is not [enounced to be] perpetual in regard to the essence [of the subject].

If it is affirmative, as “every writer of necessity moves his fingers as long as he writes, but not perpetually,” it is composed of the affirmative general conditioned and of the negative general absolute propositions. And if it is negative, as “the fingers of a writer are necessarily not at rest as long as he writes, but not perpetually,” it is composed of the negative general conditioned and of the general affirmative absolute.

2. The special conventional [proposition] is the same as the general conventional with the restriction that [the relation do] not [take place] perpetually in reference to the essence. If it is affirmative it is composed of the affirmative general conventional and of the negative general absolute, and if it is negative it is composed of the negative general conventional and of the affirmative general absolute. The preceding affirmative and negative examples illustrate this case.

3. The not-necessary existencial. It is the same as the general absolute with the restriction that [the relation do] not [take place] of necessity in reference to the essence. If it is affirmative, as “man is actually risible (or it happens that man is risible) but not of necessity (he would be man without that property;)” it is composed of the affirmative general absolute and the negative general possible. And if it is negative, as “man is not actually risible but not necessarily” it is composed of the negative general absolute and the affirmative general possible.

4. The non-perpetual existencial. It is the same as the general absolute with the restriction of non-perpetuity in reference to the essence [of the subject]. Whether it be affirmative or negative it is composed of two general absolute [propositions] one of which is affirmative and the other negative. The preceding affirmative and negative examples explain this case.

5. The temporal. It pronounces that the predicate is affirmed or denied of the subject of necessity during a definite period of the existence of the subject, under the restriction of non-perpetuity in regard to the essence [of the subject]. If it is affirmative, as “an eclipse of the moon takes of necessity place during the time the earth is placed between the sun and themoon but not perpetually,” it is composed of the affirmative absolute temporal and the negative general absolute. And if it is negative, as “of necessity no eclipse of the moon takes place when the earth, moon and sun are at right angles but not perpetually,” it is composed of the negative absolute temporal and the affirmative general absolute.

6. The spread [proposition]. It pronounces that the predicate is affirmed or denied of the subject of necessity and during an indefinite period of the existence of the subject, under the restriction of non-perpetuity in reference to the essence [of the subject]. If it is affirmative, as “every man is of necessity breathing at times but not perpetually,” it is composed of the affirmative absolute spread [proposition] and the negative general absolute. And if it is negative, as “man is of necessity not breathing at times but not perpetually,” it is composed of the negative absolute spread [proposition] and the affirmative general absolute.

7. The particular possible [or contingent proposition]. It pronounces that there is no absolute necessity either for the existence or nonexistence of the thing (or relation). It makes no difference whether it is affirmative, as “by peculiar possibility every man is a writer (i.e.

every man can or may be a writer,)” or negative, as “by peculiar possibility every man is not a writer.” It is composed of two general possible propositions, one of which is affirmative and the other negative.

The general rule is that, if a proposition is restricted by non-perpetuity, it indicates that it is a general absolute proposition, and if it is restricted by non-necessity, that it is a general possible proposition disagreeing in mode but agreeing in quantity.

Second Section: On the different kinds of hypothetical Propositions

§52. The first part (or the first proposition) of a hypothetical is called antecedent and the second consequent.

It (the hypothetical proposition) is either conjunctive or disjunctive. [See §39.]

The conjunctive (conditional) is either cogent (literally adhesive) [or contingent.] In the cogent the consequent is true under the supposition that the antecedent be true on account of the connexion between them, which is the cause thereof, as for instance, if the two propositions be connected by causation [e.g. if the sun rises day approaches, if day approaches the sun rises; if day approaches the world becomes illuminated - the cause of both phenomena being the rising of the sun;] or correlation [e.g. if Zayd is the father of Bakr, Bakr is his son]. In the contingent [the consequent is true if the antecedent is true] by merely accidental agreement of the two parts (or of the two propositions of which the hypothetical consists) in being true, e.g.

if man is endowed with reason, the donkey is endowed with the faculty of braying.

§53. The disjunctive [hypothetical proposition] is divided into the veritable disjunctive proposition [the incompatible and the exclusive]. The veritable disjunctive proposition pronounces that its two parts exclude each other (literally deny or refute each other) both in [case of] truth and [in case of] falsity, [i.e. if the one is true the other must be false and also if the one is false the other must be true,] as “this number is either even or odd.”

The incompatible disjunctive (literally the hypothetical which excludes coexistence) pronounces that the two parts are opposed to each other in truth only, e.g. this thing is either a stone or a tree, [if it is a stone it cannot be a tree, but it may be neither of the two, and therefore if it is not a stone it does not follow that it is a tree]. The exclusive hypothetical (literally the hypothetical which leaves no vacuum) pronounces that the two parts are opposed to each other in falsity only, as “either Zayd is at sea or else he will not be drowned.”

Each of these three kinds [of disjunctives] is either antagonistical [or coincidental].

A disjunctive is called antagonistical if the two parts exclude each other in their nature, as in the above examples; and it is called coincidental, if this exclusion is a mere coincidence as if we say “non-writer” of a black man. But if we say the man is either black or a writer it is a veritable disjunctive proposition; if, he is a not-black or a writer, it is an incompatible proposition; and if, he is either black or a not-writer, it is an exclusive proposition.

§54. Any of these eight [hypothetical] propositions is called negative if that [connexion or exclusion] which is pronounced [to exist] in the affirmative, is denied. If it negatives the cohesion, it is called negative-cogent, if it negatives antagonism it is called negative-antagonistic, and if it denies coincidence it is called negative-coincidental.

§55. The affirmative conjunctive proposition is true (i.e. the inference is correct) of two true and of two false [propositions, e.g. if Zayd is a man he is an animal; if Zayd is a stone he is a mineral]; and of one whose truth and falsity is not known [e.g. if Zayd be writing he is moving his fingers], and of a false antecedent and true consequent, [e.g. if Zayd be a donkey he is an animal,] but not the revers, because from a true [propositiion] does not follow a false one.

The affirmative conjunctive is false (nugatory) of two false parts (propositions) and of a false antecedent and true consequent and vice versa, and if it be cogent also of two true [propositiions], but if it is coincidental, it is impossible that it be false of two true [propositions].

The veritable affirmative disjunctive proposition is true of one true and one false [proposition], e.g. this number is either even or odd; and it is false (nugatory) of two true and of two false [propositions, e.g. four is either even or divisible by two; three is either pair or divisible by two]. The incompatible is true (holds) of two false [propositions, e.g. Zayd may be a tree or a stone]; and it is false (nugatory) of two true ones [e.g. Zayd may be a man or rational]. The exclusive is true of two true [propositions] and of a true one and a false one and it is false (nugatory) of two false ones. The negative is true of what the affirmative is false and it is false of what the affirmative is true.

§56. The universality of a hypothetical proposition consists in this, that (or a hypothetical proposition is called universal if) the consequent be adherent or antagonistic to the antecedent [at all times] and under all circumstances under which the antecedent can be, that is to say, such circumstances under which the antecedentmay be placed by reason of its connexion with things which are compatible with it. The hypothetical proposition is particular if this is the case under some of those circumstances, and it is peculiarized if it is the case under a definite circumstance. The walls (terms indicative) of the affirmative universal are “whenever,” “whatever,” “when,” [e.g. whenever the sun rises it is day], and of the disjunctive “always” [or “at any time,” e.g. at any time either the sun is up or it is not day].

The wall of the negative universal is in both cases, (i.e. in the conjunctive and disjunctive) “certainly not” [e.g. when the sun is up it is certainly not night]. The wall of the affirmative particular is in both cases “it will then be,” [e.g. it will then be day when the sun rises] and of the negative particular in both cases “it will then not be.” An affirmative universal can be rendered negative by the introduction of the negative particle into the wall.

The walls of the ambiguous conjunctive are simply “if” “when” and of the ambiguous disjunctive “either - or.”

§57. The hypothetical [proposition] may be composed [1] of two categorical propositions or [2] of two conjunctive ones or [3] of two disjunctive ones or [4] of a categorical and of a conjunctive one or [5] of a categorical and disjunctive one or [6] of a conjunctive and a disjunctive one. Each of the last three kinds if it be conjunctive is sub-divided into two sorts on account of the natural distinction between their antecedent and consequent.

But the disjunctives are not thus subdivided because their antecedent is distinguished from the consequent by appointment only. There are therefore nine divisions (or kinds) of conjunctive hypotheticals and six of disjunctive hypotheticals. You will be able to form examples yourself.

Third Section: Rules concerning propositions

First Inquiry: On Contradiction

§58. Contradiction is defined as a difference between two propositions in affirming and denying of such a description, that it follows from the difference itself [without medium,] that the one be true and the other false, [e.g. Zayd is a man, Zayd is not a man. But, Zayd is a man, Zayd is irrational, are not included in this definition, because they are contradictory by a medium.]

§59. The contradiction of two peculiar (singular) propositions is not ascertained (established), unless the subject and predicate are identical, [example of the contrary: Zayd stands, Amr does not stand.] The identity of the former (subject) comprizes the unity of the condition, [example of the contrary: a body is visible, if it be white, a body is not visible, if it be black;] and the unity of “part” and “all” (quantity of the proposition,) [example of the contrary: Africans are black, that is to say some of them; the Africans are not black, that is to say not all of them.] The identity of the predicate comprizes unity of time and place, [example of the contrary: Zayd sleeps at night or in bed, Zayd wakes at day time or in the b´az´ar,] unity of relation, [example of the contrary: Zayd is father, i.e. of ’Amr; Zayd is not father, i.e. of Bakr,] unity of possibility and reality, [example of the contrary: wine inebriates in a basin, i.e. it may inebriate; wine does not inebriate in a basin, it does not do so actually.]

If the two propositions be fenced, it is requisite, in addition to the above, that there be a difference in quantity, for two particulars are true, [e.g. some animals are men, some animals are not men,] and two universals are false [e.g. every animal is a man, no animal is a man,] in every matter in which the subject is more general (more extensive) than the predicate. In the “all” it is requisite that there be a difference in the mode; for two possible (contingent) propositions are true and two necessary propositions false in matter of possibility (contingency).

§60. The contradictory of the absolute necessary proposition is the general possible, for if the necessity is of necessity negatived, the two propositions will surely be contradictory. The contradictory of the absolute perpetual proposition is the general absolute; because the contradiction of the negative “at no time” is the affirmation “at some times”, and vice versa.

The contradictory of the general conditioned is the possible temporal, that is to say, the proposition which pronounces that necessity in reference to the attribute [see §50] is not applicable to the converse, e.g. every body affected with pleurisy will cough at times on account of his illness. The contradictory of the general conventional is the absolute temporal, i.e. the proposition which pronounces that the predicate is affirmed or denied of the subject at some times when the subject is under certain circumstances.

The preceding examples illustrate this case.

§61. The contradictory of a compound proposition is the contradiction of its two parts. This will be evident to you after you have comprehended the verities of compound propositions and the contradictories of simple propositions, for after you have ascertained that the non-perpetual existential proposition is composed of two general absolute propositions, one of which is affirmative and the other negative, and that the contradictory of the absolute is the perpetual, you will understand, that its opposite is the opposite perpetual or the agreeing perpetual.

§62. If [the compound proposition] is particular, what we have mentioned will not be sufficient to contradict it, for it would be false, were we to say “some bodies are animals but not always.” And it would be equally wrong, were we to employ the contradictory of either of the two parts [e.g. no body is ever an animal]. The correct way of forming the contradictory is to place the contradictories of the two parts universally into a dilemmatic sentence, that is to say, every one must be the contradictory of one of the two parts, e.g. every single individuum of the genus ‘body’ is ever either an animal or not an animal.

§63. The contradictory of the universal hypothetical is the particular which agrees with it in genus and species, but which is opposed to it in “quale” (quality) and “quantum” (quantity,) and vice versa.

Second Inquiry: On even Conversion (Conversio simplex)

§64. Even conversion is an expression which means that the first part of a proposition be put second and the second part first, and that the truth and quale remain unaltered, (i.e. that the converted proposition remain true, if the original proposition is true, and that it remain affirmative, if the original one is affirmative, and negative if (negative,) (e.g. everyman is an animal -some animals are men; or no man is a stone, no stone is a man.)

§65. There are seven [modal] forms of negative universal propositions, which cannot be converted, viz., the two temporals, the two existentials, the two possibles and the general absolute; because the most peculiar among them, the temporal, does not admit of conversion, and if the most peculiar cannot be converted the more general ones cannot be converted, for if the more general can be converted, surely the more peculiar can also be converted; for an adhaerens of the more general thing, of necessity, also adheres to the more peculiar. We are correct in saying, the moon can by no means be eclipsed, when she, the sun, and earth form a right angle, but not always; and we are wrong in saying, by general possibility some lunar eclipses may happen to [another celestial body and] not to the moon.

In this example we have chosen the most general mode; for every lunar eclipse operates of necessity on the moon.

§66. The [negative] absolute necessary and absolute perpetual, become by conversion [negative] universal perpetual, for if it is of necessity, or always true, that no C is B, it is always true that no B is C, else some B would, by general absoluteness, be C, and this, together with the original proposition, would prove that some B is necessarily not B - in necessary propositions, and that some B is always not B - in perpetual propositions. This is absurd.

§67. The general conditioned and the general conventional become by conversion universal general conventional, for if it is of necessity or perpetually true that no C is B, as long as C exists; no B can ever be C, as long as B exists, else let us suppose that some B is C, whilst it is B, and it follows, if this is taken in connexion with the original proposition, that some B is not B whilst it is B. This is absurd.

The peculiar conditioned and the peculiar conventional are converted into the peculiar non-perpetual conventional. The reason of this process in reference to the general conventional is, that it is an adherent of both kinds of general propositions, (i.e. the general conventional and the general conditioned.) The reason why the converted proposition is peculiar nonperpetual, is, because it is not true that some B is absolutely and generally C, because it is true that no B is always C, and therefore it is converted into “no C is always B,” but the original proposition was that every C is B. We have therefore proved our thesis by reductio ad absurdum.

§§68–70. Paragraphs 68, 69 and 70, and again 72, 73 and 74, and again 84, 85 and 86, are omitted in the translation, because they contain details on modals which are of no interest. The last named four paragraphs are also omitted in most Arabic text books on Logic, and not studied in Mohammedan Schools.

Third Inquiry: On Conversion by Contradiction

§71. This expressionmeans to place the contradictory of the second part of a proposition first, and the first part unaltered second. The quale of the new proposition will be the opposite of the original proposition, but it will be equally true, [e.g. every man is an animal, and no not-animal is a man.]

Fourth Inquiry: On the Cohesion of Hypotheticals

§75. The affirmative universal conjunctive must be convertible into an incompatible proposition, consisting of the antecedent unaltered and of the contradictory of the consequent, and into an exclusive proposition consisting of the contradictory of the antecedent and of the unaltered consequent, and should it not be thus convertible the adhesion and conjunction are unsound.

The veritable disjunctive propositionmust be convertible into four conjunctive propositions. The antecedent of two of them is one of the parts [of the original proposition] unaltered and the consequent is the contradictory of the other part. The antecedent of the other two is the contradictory of one of the two parts and the consequent is the other part unaltered. Every other hypothetical proposition than the veritable must be convertible into another, composed of the contradictories of the two parts.

IV

At first sight, there may certainly appear to be a good deal of justice in Peirce’s specific claims regarding Hegel’s unwillingness to give Secondness its due, and Peirce’s complaints here undoubtedly fit a certain traditional way of reading Hegel as a speculative metaphysician with an extravagantly idealist and a prioristic project. However, in many respects that traditional reading has been challenged in recent years, in ways that show a side to Hegel’s thought in which a greater role for Peircean Secondness can perhaps be found.

The first issue, then, concerns how far Hegel leaves room for what Burbidge called “the brute facts of Secondness”, such as the poke in the back “that Pure Reason fails to account for”. On a traditional view, which Peirce seems to endorse, Hegel’s position is seen as being Spinozistic, ruling out possibility or contingency, and rendering everything necessary. However, as several commentators have argued recently (including Burbidge), this is a mistaken picture of Hegel’s position, for (as Hegel puts it) “Although it follows from discussion so far that contingency is only a one-sided moment of actuality, and must therefore not be confused with it, still as a form of the Idea as a whole it does deserve its due on the world of ob-jects”.[65] Here it is important to remember Hegel distinction between what is actual and what exists or what is “immediately there” (das unmittelbar Daseiende ),[66] where the actual is necessary but the existent is not, and where Hegel is quite happy to accept that (for example) the natural world is not fully “actual” in this sense, though it does of course exist. Thus, while Peirce might have been right to say that Hegel took a greater philosophical interest in actuality than in possibility and contingency, he was far from denying its reality: “It is quite correct to say that the task of science and, more precisely, of philosophy, consists generally in coming to know the necessity hidden under the semblance of contingency; but this must not be understood to mean that contingency pertains only to our subjective views and that it must therefore be set aside totally if we wish to attain the truth. Scientific endeavours which one-sidedly push in this direction will not escape the justified reproach of being an empty game and a strained pedantry”.[67]

Turning now to the second issue, of whether Hegel’s neglect of Secondness can be seen in his corresponding neglect for the role of experience in the acquisition of knowledge, it is again a complex matter to decide whether Peirce is right in what he claims. Central to Peirce’s position is the way in which he sees Hegel as a typical proponent of what in “The Fixation of Belief” Peirce identified as the “a priori method”, and thus as someone who holds that our reason will lead us to a convergence on the truth; according to Peirce, Hegel therefore fails to recognize that unless there is a sufficient role for experience, this method cannot result in any stable consensus, as what is “agreeable to reason”[68] (like what is agreeable to taste) is “always more or less a matter of fashion”,[69] which depends too much on the subjective dispositions of inquirers and not enough on how things are in the world. Peirce thus sees Hegel’s dialectical approach as an attempt to reach truth in this rationalistic fashion, in the hope of showing that each limited category or standpoint can lead to the next until we attain a category or standpoint for which no limitation can be found; but he doubts the feasibility of this enterprise, claiming that not everyone will find the moves Hegel makes or the criticisms he offers “rationally compelling”, so that in the end Hegel cannot claim to reach “absolute knowledge”, as a picture of the world to which we must all consent; rather, he can only appeal to those who already think like him and share his preconceptions:

[Hegel] simply launches his boat into the current of thought and allows himself to be carried wherever the current leads. He himself calls his methoddialectic , meaning that a frank discussion of the difficulties to which any opinion spontaneously gives rise will lead to modification after modification until a tenable position is attained. This is a distinct profession of faith in the method of inclinations.[70]

Thus, rather than guiding his inquiries by the “outward clash” of experience, Peirce claims that Hegel fails to see the significance of Secondness in this respect, because he hopes that by following “that which we find ourselves inclined to believe”[71] (and thus “the method of inclinations”), we can be led to convergence, and so to truth.

Now, one difficulty in assessing Peirce’s criticism here is that he does not tell us precisely what he has in mind: Hegel’sPhenomenology , hisLogic , or theEncyclopaedia system as a whole. As regards thePhenomenology , we have already seen that commentators such as Burbidge would choose to emphasise the role of Secondness in that work, as what moves consciousness on from one standpoint to the next is an awareness of how things around us do not fit how we conceive them to be.[72] In the case of theLogic , Peirce may be correct to say that there is no role for experience as such here, as one category is seen to lead on to another, in accordance with “Hegel’s plan of evolving everything out of the abtractest conception by a dialectical procedure”;[73] but in fact Peirce allows that Hegel might be right to adopt this method here, commenting as we have seen that it is “far from being so absurd as the experientialists think”,[74] his only reservation being its ambitiousness: “[it] overlooks the weakness of individual man, who wants the strength to wield such a weapon as that”.[75] Peirce thus chooses to argue for the necessity of Firstness, Secondness and Thirdness not in this dialectical manner, but by showing (in “A Guess at the Riddle”) how this triad plays a fundamental role in all the “fields of thought”, such as logic, metaphysics, psychology, physiology, biological development, and physics, as well as showing (in the later Harvard lectures) that they have a fundamental role in our phenomenology. It could be argued that by appealing to the sciences in support of his categorial theorizing in this way, Peirce is again showing a greater recognition of Secondness than Hegel, in acknowledging that the empirical nature of these sciences must play a role in warranting our speculations about the categories. But again this implied contrast between Peirce and Hegel is potentially misleading: for Hegel himself uses the second and third books of theEncyclopaedia (thePhilosophy of Nature andPhilosophy of Mind ) in just this way, trying to show how the categories he has developed in theLogic can be used to inform our inquiries into the natural and human worlds, to which they must themselves be compatible: “It is not only that philosophy must accord with the experience nature gives rise to; in its formation and in its development, philosophic science presupposes and is conditioned by empirical physics”.[76] Hegel’sPhilosophy of Nature andPhilosophy of Mind can thus be read not as spurious attempts to use a priori methods to try to establish truths about the natural and human worlds that are in fact really established through the empirical sciences (as Peirce suggests at one point),[77] but rather as attempts to reflect on the categories that our inquiries into these areas employ, in order to “clarify” them[78] and make them more explicit, so that those inquiries can be made more fruitful, in a way that their empirical results will then attest to. Of course, none of this makes Hegel a straightforward empiricist, in confining knowledge to the evidence of the senses or treating that evidence as if it was somehow independent of or prior to our capacity for thought: but Peirce himself was no such empiricist either. Thus, while Peirce’s picture of Hegel as an a priori metaphysician and thus as an opponent of Secondness fits with a certain traditional interpretation,[79] we have seen how it can be argued that this does not do justice to the full story.[80]

In fact, it is perhaps symptomatic of Peirce’s tendency to read Hegel in a rather one-sided way on this issue, that in the Royce review, where he accuses Hegel of making the “capital error” of ignoring “the Outward Clash”, the text from Hegel that he cites in support of this claim does not seem to substantiate it sufficiently. The text Peirce refers to is from the Remark to §7 of theEncyclopeadia Logic , which Peirce renders as follows: “ “We must be in contact with our subject-matter,” says he [i.e. Hegel] in one place, “whether it be by means of our external senses,or, what is better , by our profounder mind and our innermost self-consciousness”“.[81] This is in fact a paraphrase of part of the following:

The principle ofexperience contains the infinitely important determination that, for a content to be accepted and held to be true, man must himselfbe actively involvedwith it , more precisely that he must find any such content to be at one and in unity with thecertainty of his own self . He must himself be involved with it, whether only with his external senses, or with his deeper spirit, with his essential consciousness of self as well. – This is the same principle that is today called faith, immediate knowing, revelation in the [outer] world, and above all in one’sown inner [world].[82]

Aside from the fact that Peirce’s paraphrase is somewhat inaccurate (for example, there is nothing in the original corresponding to the phrase “orwhat is better ”), Peirce’s way of using this remark by Hegel also fails to appreciate its context. For, Hegel’s aim here is not to contrast experience on the one hand with some form of knowledge acquired solely by “our profounder mind and our innermost self-consciousness” on the other, and certainly not to claim that the latter would be “better” than the former. Rather, he is simply registering the fact that some of his contemporaries (and the language he uses strongly suggests he has F. H. Jacobi in mind) have extended “experience” to include not just the evidence of our outer senses concerning the spatio-temporal world around us, but also the evidence of our experience of ourselves as subjects as well as of God. Hegel is thus not saying that knowledge is better had without experience or “the Outward Clash”, but rather noting that his contemporaries have extended this notion of “the Outward Clash” beyond our awareness of the empirical world to our awareness of ourselves and of God, because otherwise we would feel alienated from the latter as much as without experience we would feel alienated from the former. But if this is all that Hegel is saying here, it would seem Peirce is wrong to take the passage in the way he does, as attempting to give priority to our “essential consciousness of self” as a form of non-experiential knowledge, when Hegel’s aim is to show how the concept of experience has come to beextended to knowledge of this kind, rather than being excluded from it (as many more traditional empiricists may have thought). Of course, it may be that Peirce would be critical of this extension;[83] but nonetheless the fact that Hegel here remarks upon it in the way he does in no way suggests that he was opposed to the “infinitely important determination” that “the principle ofexperience contains”, which is what Peirce wants to claim.

The Peircean might argue, however, that Peirce’s characterisation of Hegel’s method as a priori in Peirce’s sense can be shown to be justified, because Hegel’s lacks the commitment torealism that Peirce identifies with the “method of science” and which lies behind its recognition of the importance of experience in our inquiries. In a well-known passage from “The Fixation of Belief”, Peirce makes this connection clear, between the method of science, realism, and what he would later call Secondness:

To satisfy our doubts…it is necessary that a method [of inquiry] should be found by which our beliefs may be caused by nothing human, but by some external permanency – by something upon which our thinking has no effect… Such is the method of science. Its fundamental hypothesis, restated in more familiar language, is this: There are real things, whose characters are entirely independent of our opinions about them; those realities affect our senses according to regular laws, and, though our sensations are as different as our relations to the objects, yet, by taking advantage of the laws of perception, we can ascertain by reasoning how things really are, and any man, if he have sufficient experience and reason enough about it, will be led to the one true conclusion. The new conception here involved is that of reality.[84]

This then brings us to the third issue of dispute between Peirce and Hegel over Secondness: namely, the claim that Hegel is an idealist, who fails to see that experience is needed because our beliefs must be related to “something upon which our thinking has no effect”, whereas the coherentism of the dialectical method neglects to incorporate any such relation, leaving us to move from one standpoint to the next within the circle of thought.

In categorising Hegel as an idealist in this manner, it is plausible to think that Peirce was following the lead of F. E. Abbot, whose work had a major influence in taking Peirce’s thought in a realist direction.[85] In his bookScientific Theism , Abbot portrays all modern philosophy as nominalistic, and thus as idealistic in a mentalistic or subjectivist sense, so that for modern philosophy, nominalism is “its root” and idealism “its flower”;[86] and he sees Hegel as exemplifying this trend:

Hegel, the greatest of the post-Kantian Idealists, says: “Thought, by its own free act, seizes a standpoint where it exists for itself, and generates its own object;” and again: “This ideality of the finite is the chief maxim of philosophy; and for that reason every true philosophy is Idealism.” This is the absolute sacrifice of the objective factor in human experience. Hegel sublimely disregards the distinction between Finite Thought and Infinite Thought: the latter, indeed,creates , while the formerfinds , its object. And, since human philosophy is only finite, it follows thatno true philosophy is Idealism, except the Infinite Philosophy or Self-thinking of God.[87]

It is likely that comments such as these encouraged Peirce to adopt this reading of Hegel.[88]

However, while plausibly read as statements of mentalistic idealism when taken out of context in this way, it is not clear on closer inspection that the remarks Abbot cites here can bear the interpretative weight he places upon them. The first statement might be translated more accurately as follows: “Only what we have here is the free act of thought, that puts itself at the standpoint where it is for itself and where hereby it produces and gives to itself its object”.[89] This comes in the Introduction to theEncyclopaedia Logic , where Hegel is discussing the difference between philosophy and other forms of inquiry. Other inquiries, Hegel suggests, must presuppose their objects (such as space, or numbers), but philosophy need not do so, because philosophy investigates thought and the adequacy of our categories and so produces its own object simply through the process of inquiry itself, as this already employs thought and the categories. Thus, in saying here that (in Abbot’s translation) “Thought…generates its own object”, Hegel is not making the subjective idealist claim, that the world is created by the mind, but rather saying that in theLogic , thinking is not simply taken for granted as an object for philosophy to investigate, as thinking is inherent in the process of investigation itself.

Likewise, Abbot’s second quoted statement is not best read as a declaration of subjective idealism. For, although Hegel does indeed say in theEncyclopaedia Logic that “This ideality of the finite is the most important proposition of philosophy, and for that reason every genuine philosophy isIdealism ”,[90] the context is again important here, as the corresponding passage from theScience of Logic makes clear:

The proposition that the finite is ideal [ideell ] constitutes idealism. The idealism of philosophy consists in nothing else than in recognizing that the finite has no veritable being [wahrhaft Seiendes ]. Every philosophy is essentially an idealism, or at least has idealism for its principle, and the question then is how far this principle is actually carried out. This is as true of philosophy as of religion; for religion equally does not recognize finitude as a veritable being [ein wahrhaftes Sein ], as something ultimate and absolute or as something underived, uncreated, eternal. Consequently the opposition of idealistic and realistic philosophy has no significance. A philosophy which ascribed veritable, ultimate, absolute being to finite existences as such, would not deserve the name of philosophy; the principles of ancient or modern philosophies, water, or matter, or atoms arethoughts , universals, ideal entities, not things as they immediately present themselves to us, that is, in their sensuous individuality – not even the water of Thales. For although this is also empirical water, it is at the same time also thein-itself oressence of all other things, too, and these other things are not self-subsistent or grounded in themselves, but areposited by, arederived from, another , from water, that is they are ideal entities.[91]

When looked at in detail, it is clear that Hegel is not conceiving of idealism here in mentalistic terms: for if he was, he could hardly claim that “[e]very philosophy is essentially an idealism”, as mentalistic idealism is a position held by few philosophers, and not by those classical philosophers directly and indirectly referred to here, such as Thales, Leucippus, Democritus and Empedocles, not to mention Plato and Aristotle – as Hegel clearly recognized.[92] A better reading of the passage is to see Hegel as offering a picture of idealism not as mentalistic, but asholistic .[93] On this account, Hegel claims that finite entities do not have “veritable, ultimate, absolute being” because they are dependent on other entities for their existence in the way that parts are dependent on other parts within a whole; and idealism consists in recognizing this relatedness between things, in a way that ordinary consciousness fails to do.[94] The idealist thus sees the world differently from the realist, not as a plurality of separate entities that are “self-subsistent or grounded in themselves”, but as parts of an interconnected totality in which these entities are dependent on their place within the whole. It turns out, then, that idealism for Hegel is primarily an ontological position, which holds that the things of ordinary experience are ideal in the sense that they have no being in their own right, and so lack the self-sufficiency and self-subsistence required to be fully real. Once again, therefore, Abbot would seem to lack adequate textual support for his account of Hegel’s idealism.

As a result of misreading Hegel in this way, Abbot failed to recognize how much Hegel’s trajectory away from Kantian idealism resembled his own; and in following Abbot here, Peirce did the same. Much like Abbot (and later Peirce), Hegel complains that for Kant “the categories are to be regarded as belonging only tous (or as ‘subjective’)”,[95] giving rise to the spectre of “things-in-themselves” lying beyond the categorial framework we impose on the world; to dispel this spectre, Hegel argues (again like Abbot and Peirce) that we must see the world as conceptually structured in itself: “Now, although the categories (e.g. unity, cause and effect, etc.) pertain to our thinking as such, it does not at all follow from this that they must therefore be merely something of ours, and not also determinations of ob-jects themselves”.[96] Like Abbot (and Peirce), Hegel sees himself as reviving here a vital insight of classical philosophy, which the subjective idealism of modern thought has submerged: “It has most notably been only in modern times…that doubts have been raised and the distinction between the products of our thinking and what things are in themselves has been insisted on. It has been said that the In-itself of things is quite different from what we make of them. This separateness is the standpoint that has been maintained especially by the Critical Philosophy, against the conviction of the whole world previously in which the agreement between the matter [itself] and thought was taken for granted. The central concern of modern philosophy turns on this antithesis. But it is the natural belief of mankind that this antithesis has no truth”.[97] No less than Abbot and Peirce, therefore, Hegel was a realist concerning the relation between mind and world, where that relation is mediated by the conceptual structures inherent in reality, in a way that the nominalist and subjective idealist denies.

If this is so, then once again it can be argued that Peirce’s case is undermined, that Hegel naturally adopted a dialectical method that had no role for Secondness: for, this involves the assumption that Hegel was a coherentist idealist, who rejected the hypothesis that “There are real things, whose characters are entirely independent of our opinions about them”; in seeing Hegel as a realist, we do not have this reason to hold that Hegel to have neglected Secondness in this respect.

V

Thus far, therefore, we have given grounds for supposing that Peirce’s critique of Hegel on Secondness is wide of the mark, in so far as Hegel can be shown not to have held many of the views that Peirce attributes to him, and which Peirce suggests led him to neglect that category in favour of Thirdness. However, I now want to turn to two remaining issues that Peirce identifies as differentiating his view from Hegel’s – the issue of haecceity, and of indexicality – and to show that here there is a genuine difference between these two thinkers; but I want to suggest that on these issues Hegel can perhaps stand his ground in the face of Peirce’s critique, and argue that Peirce’s emphasis on Secondness in these respects is misplaced.

The doctrine of haecceity comes from Duns Scotus, and while its details are notoriously complex, it is evident in a general way why Peirce should associate it with Secondness.[98] For, as we have seen, Peirce distinguishes Secondness from Thirdness in so far as it relates to particularity, whereby the individual is differentiated from other things: “Secondness, strictly speaking, is just when and where it takes place, and has no other being; and therefore, different Secondnesses, strictly speaking, have in themselves no quality in common”.[99] Secondness thus leads inevitably to the classical problem of individuation: how is it that individualscan be unique in this way, where any properties we attribute to them are universal and so can be shared by other individuals?:

A law is in itself nothing but a general formula or symbol. An existing thing is simply a blind reacting thing, to which not merely all generality, but even all representation, is utterly foreign. The general formula may logically determine an other, less broadly general. But it will be of its essential nature general, and its being narrower does not in the least constitute any participation in the reacting character of the thing. Here we have that great problem of theprinciple of individuation which the scholastic doctors after a century of the closest possible analysis were obliged to confess was quite incomprehensible to them.[100]

Scotus’s solution to this problem, which Peirce favours above the others, is to introduce the idea ofhaecceity , as the unique “Thisness” of the thing that makes it an individual, and which cannot be characterised in any way, for to characterise it would make it general again: “An index does not describe the qualities of an object. An object, in so far as it is denoted by an index, havingthisness , and distinguishing itself from other things by its continuous identity and forcefulness, but not by any distinguishing characters, may be called ahecceity ”.[101]

Now, in so far as Peirce associates the doctrine of haecceity with Secondness in this way, I think it is right to see a real difference here with Hegel. This is not because, as some critics have suggested, Hegel does not recognize the status of individualsat all , and so failed to take the problem of individuation seriously;[102] it is just that he was suspicious of answers to that problem which left the solution opaque, in so far as the “Thisness” that supposedly constitutes the individuality of the particular has no determination of any kind, where for Hegel this indeterminacy means that in fact it cannot serve an individuating role, and is rather utterly general. Hegel famously makes this point when he writes as follows concerning sense-certainty, and its claim to grasp the particular thing in its sheer individuality as “This”:

It is as a universal…that weutter what the sensuous [content] is. What we say is: “This”, i.e. theuniversal This; or, “it is”, i.e.Being in general . Of course, we do notenvisage the universal This or Being in general, but weutter the universal, in other words, we do not strictly say what in this sense-certainty wemean to say.[103]

I take this and related passages to suggest that Hegel would reject the Peircean solution to the problem of individuation that he adopts from Scotus, and this his claim that Secondness involves haecceity.

But, the Peircean might ask: what then is Hegel’s solution to the problem of individuation, if it does not involve haecceity in this way? Very briefly, as I understand it, Hegel’s solution is to argue that what constitutes the individuality of a thing is its properties, each of which it may share with other things, but where the particularcombination of these properties makes something an individual: so, while many other individuals also have properties that I possess (being of a certain height, colour, weight etc.), only I have the specificset of properties that determine me as an individual, and so make me who I am. Peirce’s conception of individuality means he would be dissatisfied with this, because he wants individuation to be something more than can be derived from the properties of the individual in this way, and so thinks that things could be different even if they were exactly alike inall qualitative respects:[104] but it is open to the Hegelian to deny this, and to argue that to say that it is the “Thisness” of each that would differentiate them is to make this differentiation wholly mysterious, for if “This” is indeterminate,how can it distinguish one thing from another?

Peirce might go on to claim, however, that where Hegel goes wrong is in failing to see that Peirce’s conception of Secondness here is vital to his view ofindexicality , which picks out the individual as a “bare this”, and not as anything general:

An indexical word, such as a proper noun or demonstrative or selective pronoun, has force to draw the attention of the listener to some hecceity common to the experience of speaker and listener. By a hecceity, I mean, some element of existence which, not merely by the likeness between its different apparitions, but by an inward force of identity, manifesting itself in the continuity of its apparition throughout time and space, is distinct from everything else, and is thus fit (as it can in no other way be) to receive a proper name or be indicated asthis orthat .[105]

Peirce argues therefore that in so far as “the index…designates [the subject of a proposition] without implying any characters at all”,[106] we can refer to the individual as a “this” which appears to us as an individual in the “ouward clash” of experience.

I take it that Hegel’s response to this final issue concerning Secondness reflects the previous one, and is also to be found in his discussion of sense-certainty: namely, that for indexicality to work, a description must be involved in the way the thing is picked out, otherwise what “this” refers to is indeterminate: is it (for example) the door in front of me that I am pushing, the door in the wall, the wall in the building, the building in the city, and so on – what exactly is the “this” to which my indexical refers, outside some further specification of theclass of things to which the “this” belongs?[107] Peirce writes: “We now find that, besides general terms, two other kinds of signs are perfectly indispensable in all reasoning. One of these kinds is theindex , which like a pointing finger, exercises a real physiologicalforce over the attention, like the power of a mesmerizer, and directs it to a particular object of sense”,[108] and gives the example of experiencing as a “Now!” a flash of lightening. But unless the flash is conceptualised in some wayas a particular in distinction from other things (the sky against which it is set, the trees below it, and so on), how can we determine the “particular object of sense” to which the indexical is meant to refer?[109] Of course, in normal contexts, that specification is taken for granted, and so may not be articulated, making it possible to refer to something determinate by just saying “This”: but this background is important and should not be forgotten, as Peirce appears to do when he takes it that two speakers will know that “this” or “now” refers to a flash of lightening “without implying any characters at all”.[110]

However, if the Hegelian is arguing that we are incapable of referring to anything by pointing and just saying “This”, but must also categorise the individual in some general way (“This house”, “This tree” etc.), so that we must use descriptions in picking out individuals, does the Hegelian position have the implications which Peirce fears, and which he thinks Royce accepts: namely, “If the subject of discourse had to be distinguished from other things, if at all, by a general term, that is, by its peculiar characters, it would be quite true that its complete segregation [as an individual from other individuals] would require a full knowledge of its characters and would preclude ignorance”?[111] Peirce’s concern here is that the Hegelian neglects the role of indexicals altogether, and so can only use general descriptions to refer to individuals; but because any such description can never be specific enough to capture the individual (or at least would require a complete knowledge of all other individuals with which to contrast it), this would seem to put the individual out of reach.

Some interpreters of Hegel have indeed taken this to be his view;[112] but others have argued that this is one-sided,[113] in so far as Hegel is not assuming that indexicals haveno reference, but only that they cannot perform this role on their own, independent of a use within a context that helps determine what general kind the indexicals are referring to when we say “This”: so, the proper Hegelian view is that neither the indexical “This”, nor the universal description can pick out the individual on their own, but that both must operate together, where the universal serves to mark out the kind of individual to which we are referring using the indexical.

Now, it might be said that to criticise Peirce as having failed to see this is unfair, as it treats Peirce as if he thought Secondness (and hence individuality and indexicality) could be entirely independent of Thirdness (and hence generality), when (as Peirce emphasises in his Harvard lectures) he agrees with Hegel that each of these categories must involve the others: “Not only does Thirdness suppose and involve the ideas of Secondness and Firstness, but never will it be possible to find any Secondness or Firstness in the phenomenon that is not accompanied by Thirdness”.[114] Peirce might therefore be expected to agree with this Hegelian view of indexicality, and only to object to the way in which Hegel takes it too far, and moves to claim from this that “Firstness andSecondness must somehow beaufgehoben ”.[115]

But, of course, we have precisely tried to show that this concern of Peirce’s is an exaggeration, and that it is possible to read Hegel in a way that shows him to have accorded just the same status to these categories as Peirce himself demanded: namely, as each requiring the others, and none as “refuted” or “refutable”. On this account, then, Hegel’s conception of the Peircean category of Secondness is close to Peirce’s own, so that on many of the issues raised by this category, Peirce and Hegel can find common cause in a way that Peirce failed to recognize, and which therefore may have surprised him.[116]

Notes