Chapter IV: Theories of the Relations Between Thought and Word and Formalist Logic

[Sidenote: _Relation between the history of Logic and that of the Philosophy of language._]

The history of Logic depends very closely upon the history of the Philosophy of language, or of Æsthetic, understood as the philosophy of language and of expression in general. Every discovery concerning language throws new light upon the function of thought, which, surpassing language, employs it as an instrument, and therefore unites itself with language both negatively and positively. It belongs to the progress of the Philosophy of language, not less than to that of Logic, to have determined in a more exact manner the relations between thought and expression, as also to have dissipated or begun the dissipation of empirical and formalist Logic. This Logic, deluding itself with the belief that it was analysing thought, presents a series of mutilated and empty linguistic forms.

[Sidenote: _Logical formalism. Indian Logic free of it._]

This error, which appeared very early in our western world, has spread during the centuries and yet dominates many minds; so true is this that "Logic" is usually understood to mean just illogic or formalist Logic. We say our western world, because if Greece created and passed on the doctrine of logical forms, which was a mixture of thoughts materialized in words and of words become rigid in thoughts, another Logic is known, which, as it seems, developed outside the influence of Greek thought, and remained immune from the formalist error. This is Indian Logic, which is notably antiverbalist, though very inferior to that of Greece and of Europe in wealth and depth of concepts, and limited almost exclusively to the examination of the empirical concept or reasoning, of naturalistic induction or _expectatio casuum similium._ Indian Logic studies the naturalistic syllogism in _itself,_ as internal thought, distinguishing it from the syllogism _for others,_ that is to say, from the more or less usual, but always extrinsic and accidental forms of communication and dispute. It has not even a suspicion of the extravagant idea (which still vitiates our treatises) of a truth which is merely syllogistic and formalist, and which may be false in fact. It takes no account of the judgment, or rather it considers what is called judgment, and what is really the proposition, as a verbal clothing of knowledge; it does not make the verbal distinctions of subject, copula and predicate; it does not admit classes of categorical and hypothetical, of affirmative and of negative judgments. All these are extraneous to Logic, whose object is the constant: knowledge considered in itself.[1]

[Sidenote: _Aristotelian Logic and formalism._]

It was a subject of enquiry and of disagreement, especially during the second half of last century, whether formalist Logic, the Logic of the schools, could legitimately be called _Aristotelian._ Some, among whom were Trendelenburg and Prantl, absolutely denied this, and wished to restore the genuine thought of Aristotle, opposing it to post-Aristotelian and mediæval Logic. But they themselves were so enmeshed in logical formalism, that they were not capable of determining its peculiar character. The contrast between those two Logics, so far as it struck them, concerned secondary points. If the proper character of formalism consists in the confusion between thought and word, how are we to deny that Aristotle fell into this error, or that at any rate he set his foot upon the perilous way? Certainly he did not proceed to the exaggerations and ineptitudes of later logicians. He was ingenuous, not pedantic. And his books (and in particular the _Analytics)_ are rich in acute and original observations. He was a philosopher, and his successors were very often manual labourers. But Aristotle (probably influenced by the mathematical disciplines) conceived the idea of a theory of _apodeictic,_ which, from simple judgments, through syllogisms and demonstrations, reached completeness in the definition as its last term. The concept was the first term, as the loose concept or name, the last term was the concept defined. He was not ignorant that not everything can thus be demonstrated, that in the case of the supreme principles such a demonstration cannot be given, and it is vain to look for it, and that there is alongside the apodeictic a science of _anapodeictic._ But that did not induce him to abandon the study of verbal forms for a close study of the concepts or of the category, which is the demonstration of itself. In his divisions of judgments he was very discreet; but yet he distinguished them verbally, as universal, particular and indefinite, negative and affirmative. In the syllogism he distinguished only three figures, and affirmed that of those the first is the truly scientific (ἐπιστημὀνικον), because it determines _what is,_ whereas the second does not give a categorical judgment and affirmative knowledge, and the third does not give universal knowledge; but these restrictions did not suffice to correct the false step made in positing the idea of _figures_ and _moods_ of the syllogism. When we examine the various doctrines of Aristotle and compare them with the forms and developments which they assumed later, it can be maintained that no logician was less Aristotelian than Aristotle. But even he was Aristotelian, and the impulse to seek logic in words had been begun in so masterly a manner that for centuries it weighed upon the mind like a fate.

[Sidenote: _Later formalism._]

Why, then, should we rage, like many modern critics, against the later manipulations and amplifications to which Aristotelian Logic was submitted by Peripatetics and Stoics, by commentators and rhetoricians, by doctors of the Church and masters of the University, by Neolatins and Byzantines, by Arabs and Germans? We certainly harbour no tenderness for the _hypothetical_ and _disjunctive_ syllogism, or for the _fourth figure_ of the syllogism, as elaborated from Theophrastus to Galen, or for the _five predicables_ of Porphyry, or for subtleties upon the _conversions_ of judgments, or for the _mnemonic verses_ of Michael Psellus and of Peter Hispanus, or for the geometric symbols of the concepts and syllogisms invented by Christian Weiss in the seventeenth century ("to direct blockheads aright,"[2] as Prantl permits himself to say), or for the calculations upon the moods of the syllogism made by John Hispanianus, which he found to be no less than five hundred and sixty in number, thirty-six of which are conclusive. We also willingly admit that errors have been made in the traditional interpretation of certain doctrines of Aristotle (for example, in the doctrine of the enthymeme).[3] But setting aside these errors, we can say that for those excogitations and distinctions support was already found in the Organon of Aristotle, and that they were derived from principles there laid down. Certainly, with their crude roughness and their evident absurdity, they shock good sense in a way in which the distinctions of Aristotle did not, for these were in some sort of relation with the empirical description of the usual mode of scientific discussions. But the error nestled in themselves; and it was well that it should be intensified, so that it might leap to the eyes of all, just as it is sometimes well that there should be scandals in practical life.

[Sidenote: _Rebellions against Aristotelian Logic. The opposition of the humanists and their motives._]

The rebellions which the school (in the wide sense of the word, from the Peripatetic to the modern) continued to arouse in regard to these doctrines might seem to be of greater interest than this labour of embroidering and carving. But since there has been a time during which every protest, and indeed, every insult levelled against the philosopher of Stagira seemed a sign of original thought, of spiritual freedom and of secure progress, it is well to repeat that an indispensable condition for surpassing the Aristotelian Logic was a new Philosophy of language. Such a condition was altogether wanting in the past and is partly wanting now. It is therefore not surprising that when those rebellions are closely examined, we discover in the midst of secondary and superficial disagreement something quite different from what was expected; not the radical negation, but the substantial acceptance, explicit or understood, of the principles of formalist Logic.

Such is the case with the rebellions of the humanists, Ciceronians and rhetoricians, which took place in the fourteenth and fifteenth centuries, of Lorenzo Valla, of Rudolph Agricola, of Luigi Vives, of Mario Nizolio, of Peter Ramus. The motive power with all of them was abhorrence for the heavy scholastic armour. Culture, leaving the cloisters, spread itself abroad in life; philosophy began to be written in the common tongue, and for this reason men sought forms of exposition that were rapid, easy and clear or eloquent and oratorical. But under these new forms the direction of logical thought remained unchanged. Ramus, for example, who applied to Aristotle the elegant terms of _fatuus impostor, chamæleon somnians et stertens,_ and so forth, ended by claiming that he alone had understood his true thought, and showed by the reforms of it that he proposed (among which was the suggestion that the third figure of the syllogism should pass to the first place) that he, too, was still revolving in the narrow circle of formalism.[4]

[Sidenote: _The opposition of naturalism._]

Even the opposition of naturalism to the Aristotelian Logic did not strike it to the heart, but wished to replace and more often to accompany one form of empiricism with another: the rules of the syllogism with the precepts of induction, the sophistical refutations with the determination of the four idols that preoccupy men's minds. Bacon never dreamed of denying to syllogistic the value of true doctrine. He believed, however, that it had already been sufficiently studied and developed, that it lacked nothing, and even possessed something superfluous, whereas there was still wanting a criterion of invention and of induction, which was of fundamental importance for syllogistic itself. In making the inventory of knowledge (he writes) it is to be observed that we find ourselves almost in the conditions of a man who inherits an estate, in the inventory of which there is noted: "ready money, none" ("numeratae pecuniae, nihil").[5] Hence he raised his voice against the abuse of disputations and of reasoning as to matters of fact; the subtlety of the syllogism is always conquered by that of nature.[6] The syllogism consists of propositions, propositions of words, and words are the counters of concepts; but if the concepts are confused or wrongly abstracted, the syllogistic consequences deduced from them are without any sort of security. Hence the necessity of beginning with induction: "_spes est una in inciuctione vera._"[7] Bacon's position (which was therefore not anti-formalist, but only an addition or complement to formalism) has been renewed, word for word, in all inductive Logics, up to that of the English school of the nineteenth century, and to ours of to-day. Stuart Mill's book expresses the combination of the two empiricisms, syllogistic and inductive, in its very title: "A system of Logic, _ratiocinative_ and _inductive,_ being a connected view of the principles of evidence and the methods of Scientific _investigation._"

[Sidenote: _Labour of simplification in the eighteenth century. Kant._]

In the eighteenth century, while Leibnitz sought an amplification and perfecting of syllogistic in the logical calculus, and some followed him who did not, however, attain to true effectiveness in the history of culture,[8] formalist Logic fell always more and more into discredit, not only as Logica _utens,_ but also as _docens,_ that is to say, as theory.

Hence the moderate tendency, to which Kant adhered, which consists of preserving that Logic, while seeking to correct, and, in particular, to simplify it. For example, Kant undertook to demonstrate the "false subtlety of the four figures of the syllogism," and at the same time rendered traditional Logic yet more formalist by withdrawing from it all examination of the synthesis and the categories, which he referred to his new transcendental Logic. Traditional Logic, which he respected and held to be substantially perfect, constituted (he said) a canon of the intellect and of reason, but only in the _formal_ aspect of their employment, whatever be the content to which it is applied. Its only criterion is the agreement or non-agreement of any knowledge with the general and formal laws of the intellect and of reason; a _conditio sine qua non_ of every truth, but a _conditio_ which is only negative.[9]

[Sidenote: _Refutation of formalist Logic. Hegel; Schleiermacher._]

Hegel, on the contrary, opposed tradition. He understood the character of formalist Logic marvellously well: this "_empirical_ Logic, a bizarre science, which is an _irrational_ knowledge of the _rational,_ and sets the bad example of not following its own doctrines. Indeed it assumes the licence of doing the opposite of what its rules prescribe, when it neglects to deduce the concepts and to demonstrate its affirmations."[10] In so far as it was empirical it was intellectualist, and presented the determinations of reason in an abstract and atomic manner in combining them mechanically. The new concept of the concept, originated by Hegel, creates from itself its own theories and allows the old formalist theories to disappear as dead and dry remains. The forms of thought are henceforth the very forms of the real; the Idea is the unity of concept and representation, because it is the universal itself, big with the individual. Things are realized judgments, and the syllogism is the Idea which identifies itself with its own reality. This at bottom amounts to saying that thought fully dominates reality, because it is not an extrinsic addition or an interposed means, but Reality itself, which makes itself thought, because it is thought. Other philosophers, too, contemporaries and adversaries of Hegel, rejected formalist Logic, and among these was Schleiermacher.[11] He made the logical forms of the _concept_ and of the _judgment_ correspond to the two forms of reality, _being_ and _doing,_ finding corresponding analogies in _space,_ a dividing of being, and in _time,_ a dividing of doing. The concept and the judgment mutually presuppose one another, and give rise to a circle, which is so only when considered temporally; since at the point of indifference, of fusion, of indistinction the two make one.[12] Schleiermacher differed from Hegel (who attains in thought the unity of the real) in being obliged to withdraw the syllogism from the number of the essential forms of thought, because (he says), "if the syllogism were a true form, a being of its own should correspond to it, and this is not found to be the case."[13]

[Sidenote: _Its partial persistence owing to insufficient ideas as to language._]

But if with the Hegelian criticism formalist Logic was surpassed by a truly philosophical Logic, and thereupon lost all its importance, it cannot be said that it was definitely dissolved. In Hegel himself there remain traces of it in certain divisions of the forms of judgment and of syllogism, which he either accepts and corrects or creates anew. Definitive criticism demanded that in any case the error peculiar to this empiricism should be recognized. This error consists in confusing language and thought, taking thought as language, and therefore also language as thought. Hegel could not effect this criticism, for he was logistic as regards the theory of language, conceiving it to be a complex of logical and universal elements.[14] Hence the coincidence between the forms of language and those of thought did not seem to him irrational, provided that both were taken in their true connection. The revival of the Philosophy of language, begun by Vico and carried on by Hamann and by Herder, and then again by Humboldt, remained unknown to him or had no influence upon him. Nor, to tell the truth, has it influenced even later Logic, for had it acquired this knowledge, it would have been freed for ever from formalism or verbalism and have possessed a method and a power of application to the nature of the problems that belong to it. Just a trace of serious discussion (but made rather in the interest of the Philosophy of language than in that of Logic) appears in the polemic between Steinthal and Becker concerning the relations between Logic and Grammar.[15]

[Sidenote: _Formalist Logic in Herbart, in Schopenhauer, in Hamilton._]

For this reason, formalist Logic has continued to exist (with difficulty if you will, but yet to exist) in the nineteenth century. From Kant it had received with the name _formal_ a new baptism and a new legitimization. Among post-Kantians Herbart clung closely to it, though he somewhat simplified it, and hostile as he was to all transcendental Logic, he continued to conceive it as the sole instrument of thought. Schopenhauer held logical forms to be a good parallel to rhetorical forms, and limited himself to proposing some slight remodelling of the former: for example, to consider judgments as always universal (both those called by that name and particular and singular judgments as well), and to explain hypothetical and disjunctive judgments as pronounced upon the comparison of two or more categorical judgments. From the syllogism, which he defined as "a judgment drawn from two other judgments, without the intervention of new conditions," he dropped the fourth figure, but he proclaimed the first three to be "ectypes" of three real and essentially different operations of thought.[16] Kant's teaching was followed in England by Hamilton. Hamilton insisted upon the purely hypothetical character of logical reasonings; he excluded from Logic discussions of possibility and impossibility and of the modalities, and declared that the intrusion into that science of the concepts of perfect or imperfect induction, which refer to material differences and are therefore extralogical,[17] was a fundamental error. In this way he reacted against inductive Logic, which, in his country especially, had prevailed against formalist Logic or had strangely accompanied it. He persuaded himself that he could perfect the latter, by simplifying the doctrine of the judgment, by means of what is called the _quantification of the predicate._[18]

[Sidenote: _More recent theories._]

Later logicians continued to employ these partial and superficial modifications. Trendelenburg, as has been mentioned, believed that he could make progress by referring the thing to its beginning, that is, by turning from Aristotelianism to Aristotle, and owing to the curious influence of a thought of Hegel, he assigned to logic and reality a common foundation which, for him, was not the Idea, but Movement. Lotze reduced the forms of judgments to three only, according to the variations of the copula: categorical, hypothetical and disjunctive judgments; and he made impersonal judgments precede categorical. By this last class he vainly sought to satisfy the desire for a theoretic form which is presupposed in properly logical thought, and it is yet to seek. Lotze always had at bottom an intellectualistic concept of language: poetry and art seemed to him to be directed, not to contemplation and expression, but to emotion and to feelings of pleasure and pain. He could not therefore recognize the primitive theoretic form in art, in intuition, in pure expressiveness. Drobisch, the Herbartian, revealed formalism in all its crudity, beginning with the affirmation that "there are certainly necessary judgments and syllogisms, but no necessary concepts." Sigwart reformed the classification of judgments (of denomination, of property and activity, impersonal, of relation, abstract, narrative and explicative), and retouched that of syllogisms. Wundt, accepting the old tripartition of logical forms, also attempts new sub-divisions, distinguishing judgments for example, according to their subject, into indeterminate, singular and plural; according to their predicate, into narrative, descriptive and explicative; according to their relation, into judgments of identity, superordination, subordination, co-ordination and dependence; and into negative predications and negative oppositions. Brentano's reform does not in general abandon the formalist circle; hence, having assigned the quantity of judgments to their matter, he limits himself to dividing them into affirmative and negative; among immediate inferences he accepts only the inference _ad contradictoriam_; among the laws of the syllogism he denies the law _ex mere negativis,_ maintaining indeed that _ex mere affirmativis nil sequitur;_ he defends, as the law of all syllogisms, that of _quaternio terminorum,_ which used to pass for the sign of the sophism; and he further abolishes the vain distinctions of figures and moods.

[Sidenote: _Mathematical Logic._]

Opposed as radical innovators to these logicians, who work more or less with traditional formulas, are the mathematical logicians, who follow, not philosophy, but certain fictions of the Leibnitzian philosophy. George Bentham, De Morgan, Boole, Jevons, Grassman and now several in England, in France, in Germany and in Italy (Peano), have been and are representative of this tendency. They are innovators only in a manner of speaking, for they are ultra-reactionaries, far more formalist than the formalist Aristotle. They are dissatisfied with the divisions made by him, not because they are toe numerous and arbitrary, but because they are toe few and still bear some traces of rationality They strive to the uttermost to provide a theory of thought, from which all thought is absent This kind of Logic has been well defined by Windelband as "Logic of the green cloth."[19]

[Sidenote: _Inexact idea of language among mathematical logicians and intuitionists._]

These logicians have naturally inherited the other fiction of Leibnitz, namely that of the possibility of a constant and universal language,[20] thus revealing another reason for their aberration, and the usual support of the whole formalist error--ignorance of the alogical nature of language. The nature of language remains obscure from another point of view, even to the modern intuitionists (Bergson). They continue to regard as language, not language in its simplicity, but the intellectualist procedure (classificatory and abstractive) which falsifies the continuous in the discontinuous, breaks up duration, and builds a fictitious world upon the real world. They are therefore ultimately led to attribute the value of a pure expression of reality to music, as though music were not language, and true language (not the intellectualist discourse which they accept in place of it) were not essentially music, that is to say, poetry. For the intellectualists also, a Logic (were they to resolve upon constructing one) would be nothing but formalist.

[Footnote 1: See the recent exposition of the secular Indian Logic, in its most complete form, as found in a treatise of the twelfth century, in II. Jacobi, "Die indische Logik," in the _Nachrichten v. d. Königl. Gesellsch. d. Wissenschaft zu Göttingen,_ Philol.-hist. Klasse, 1901, fasc. iv. pp. 460-484.]

[Footnote 2: _Gesch. d. Logik,_ i. p. 362.]

[Footnote 3: Hamilton, _Fragments philosophiques,_ French tr. pp. 238-242.]

[Footnote 4: Frantl, "Über Petrus Ramus," in the _Sitzungsberichte d. k. bayer. Akad. d. Wissensch.,_ Philol.-hist. Klasse, 1878, ii. pp. 157-169.]

[Footnote 5: _De dign. et augm._ iv. ch. 2-5.]

[Footnote 6: _Ib._ ch. 2.]

[Footnote 7: _Nov. Org._ i., aphorism 14.]

[Footnote 8: It is pertinent to translate here a passage of Hegel, in relation to this Leibnitzian tendency, which is now again becoming fashionable. "The extreme form of this (syllogistic) disconceptualized manner of dealing with the conceptual determinations of the syllogism, is found in Leibnitz, who (_Opp._ t. ii. p. i) places the syllogism under the calculus of combination. By this means he has calculated how many positions of the syllogism are possible, and thus, by taking count of the differences of positive and negative judgments, then of universal, particular, indeterminate and singular judgments, he has arrived at the result that the possible combinations are 2048, of which, after excluding the invalid, there remain 24 valid. Leibnitz boasts much of the utility possessed by the analysis of combination in finding, not only the forms of the syllogism, but also the connections of other concepts. This operation is the same as that of calculating the number of possible combinations of letters that can be made from an alphabet, or of moves in a game of draughts, or of different hands in a game of _hombre,_ and so on. From which it is clear that the determinations of a syllogism are placed on a level with moves in draughts, or hands in _hombre._ The rational is taken as something dead, altogether deprived of the concept, and the peculiar character of the concept and its determinations is left out; that is to say, the character that in so far as they are spiritual facts, they are _relation,_ and that, in virtue of this relation, they suppress their _immediate_ determination. This Leibnitzian application of the calculus of combination to the syllogism and to the connection of other concepts is not to be distinguished in any way from the discredited _art of Lully,_ save for the greater methodicalness in calculation of which it gives proof; it resembles that absurdity in every other respect. Another thought, dear to Leibnitz, was included in the calculus of combination. He had nourished this thought in his youth, and notwithstanding its immaturity and superficiality, he never afterwards abandoned it. This was the thought of a _universal characteristic_ of concepts, of a writing, in which every concept should be represented as proceeding from others or as referring to another; almost as though, in a rational connection, which is essentially dialectic, a content should preserve the same determinations that it has when standing alone.

"The calculus of Ploucquet is doubtless supported by the most cogent mode of submitting the relation of the syllogism to calculation. He abstracts in the judgment from the difference of relation; that is to say, from its singularity, particularity and universality, and fixes the _abstract identity_ of subject and predicate, placing them in a _mathematical relation._ This relation reduces reason to an empty, tautological formation of propositions. In the proposition, 'the rose is red,' the predicate must signify, not red in general, but only the determinate 'red of the rose.' In the proposition, 'all Christians are men,' the predicate must signify only 'those men who are Christians.' From this and from the other proposition, 'Hebrews are not Christians,' follows the conclusion (which did not constitute a good recommendation for this calculus with Mendelssohn): 'hence, Hebrews are not men' (that is to say, they are not those men, who are Christians).

"Ploucquet gives as a consequence of his invention _posse etiant rudes mechanice tot am logicam doceri, uti pueri arithmeticam docentur. ita quidem, ut nulla formidine in ratiociniis suis errandi lorqueri, vel fallaciis circumveniri possint, si in calculo non errant._ This eulogy of the calculus, to the effect that by its means it is possible to supply uneducated people with the whole of Logic, is certainly the worst that can be said of an invention which concerns logical Science'" (_Wiss. d. Logik,_ iii. pp. 142-43).]

[Footnote 9: _Kr. d. rein. Vern.,_ ed. quoted, pp. 101-2.]

[Footnote 10: _Wiss. d. Logik,_ iii. p. 51.]

[Footnote 11: _Dialektik,_ ed. quoted, pp. 74-5.]

[Footnote 12: Work cited, pp. 145, 147-9.]

[Footnote 13: Work cited, pp. 146, 291-2.]

[Footnote 14: _Wiss. d. Logik,_ i. pp. 10-11 and _passim; Encykl._ § 205 and elsewhere.]

[Footnote 15: _Estetica_², p. II, ch. xii.]

[Footnote 16: _Werke,_ ed. cited, ii. pp. 120-135.]

[Footnote 17: Work cited, pp. 159, 165.]

[Footnote 18: See above, pp. 297, dealing with Ploucquet.]

[Footnote 19: In his remarks upon the present state of Logic, contained in his work _Die Philosophie im Beginn des zwanzigsten Jahrhunderts_ (Heidelberg 1904), i. pp. 163-186.]

[Footnote 20: See my remarks in the _Critica,_ iii. pp. 428-433 (concerning the work of Messrs. Couturat and Léau); and cf. same, iv. pp. 379-381.]