130 ‘Menschliches, Allzumenschliches’, Sämtliche Werke, Vol. II, pp. 546f., §11 and ‘Jenseits von Gut und Böse’, Sämtliche Werke, Vol. V, pp. 29–54, §16–34.
131 ‘Götzen-Dämmerung’, Sämtliche Werke, Vol. VI, pp. 77–8.
132 ‘Nachgelassene Fragmente Sommer 1886 bis Herbst 1887, 5, 22’, Sämtliche Werke, Vol. XII, pp. 193–4.
133 ‘Über Wahrheit und Lüge im aussermoralischen Sinne’, Sämtliche Werke, Vol. I, pp. 873–90. See S. Schroeder, Wittgenstein, Cambridge: Polity Press, 2006, p. 54.
134 ‘ Jenseits von Gut und Böse’, Sämtliche Werke, Vol. V, p. 35, §20.
135 Beiträge zu einer Kritik der Sprache, Leipzig: Meiner, 1923, Vol. I, in Das Philosophische Werk, Vienna: Böhlau, 1999, Vol. I, pp. 364–72.
136 See entry ‘Sprachkritik’ in his Wörterbuch der Philosophie, Leipzig: Meiner 1923–4, Vol. 3.
137 Another expression of this crisis was Karl Kraus, the formidable cultural critic of the late Habsburg Empire. His masterful polemical analysis of language influenced Wittgenstein’s critique of language. Opponents are literally taken at their word. Their style, sometimes even a single ill-judged sentence, is taken to reveal both their fallacies and their character-failings. See A. Janik and S. Toulmin, Wittgenstein’s Vienna, New York: Simon & Schuster, 1973, ch. 3.
138 For example, Beiträge, Vol. III, pp. 616–20.
139 Tractatus 6.54 inherited the image of throwing away the ladder once one has climbed up on it from Schopenhauer and/or Mauthner (Glock, Wittgenstein Dictionary, p. 335). But its position is more sophisticated, if not, in the final reckoning, coherent. Considering also the pronounced difference in method, Wittgenstein is right to distance himself from Mauthner (pace Cloeren, Language and Thought, ch. 17). ‘All philosophy is “critique of language”. (However, not in Mauthner’s sense)’ (4.0031).
140 See Glock, What is Analytic Philosophy, chs. 2, 3, 6, and 9. For comments and help I should like to thank Michael Forster, Peter Hacker, Meret Hauser-Polzer, Susanne Richli, and the participants of the 2013 Mind, Language, World conference at the University of Kent, UK.
CHAPTER 20
NINETEENTH-CENTURY GERMAN LOGIC
GRAHAM PRIEST
Logic, by the way, has not gained much in content since Aristotle’s times and indeed it cannot, due to its nature…In present times there has been no famous logician, and we do not need any new inventions in logic, because it contains merely the form of thinking.
Immanuel Kant. From the introduction to his lectures on logic. (Hartman and Schwarz, 1974: 24–5)
20.1 INTRODUCTION
LET me start by saying how, for the purpose of this chapter, I have chosen to interpret the words of its title: none is innocent. Let us work backwards.1
‘Logic’ is used in many ways, and in different ways even by some of the thinkers we will meet. In a chapter of this length it would be impossible to take on board all these usages. I have chosen to interpret the word in the way that contemporary logicians understand it. That is, logic concerns what follows from what: which premises entail which conclusions, and why. Of course, this cannot be divorced from other important questions, such as: what sorts of things, exactly, are premises and conclusions? What sorts of things constitute them? And how do some of these things which are particularly important in the context of logic, such as negation, work.
Secondly, ‘German’. Defining ‘German’ in terms of the geographical boundaries of modern Germany makes little intellectual sense. What is arguably the modern state of Germany did not, itself, come into existence until 1871. And there were significant thinkers who are clearly in the relevant intellectual community, but who lived outside its contemporary boundaries. (Kant was in Königsberg, which is modern day Kaliningrad, in Russia; Bolzano was in Prague, in the modern Czech Republic.) It seems best, to me, to characterize the intellectual community we are dealing with by its common tongue. So I will take Germans to be people who were native German speakers.
‘The nineteenth century’ might seem the least problematic of the words; but, in fact, it is the most problematic. It is silly to suppose that, intellectually, it came into existence at midnight of 1 January 1801. The nineteenth century started before that; and the eighteenth century ended after that. In exactly the same way, it is absurd to suppose that the nineteenth century ended at exactly 1 January 1901, and that the twentieth century started then. So how best may one understand ‘the nineteenth century’ in this context? To answer this question one needs to situate the century in the history of the development of logic.
20.2 THE HISTORY OF WESTERN LOGIC
Broadly speaking, the history of Western logic falls into three major phases of growth, interspersed by two periods of stasis, and even decline. (The study of logic in the East has its own story to tell.)
The first phase of growth was in Ancient Greece. Aristotle developed the theory of the syllogism, and the Stoic logicians developed a somewhat different theory of logical consequence: a version of what we would now call propositional logic. With the decline of the Western part of the Roman Empire, the study of logic goes into decline in Christendom. Logic is still studied in the Islamic tradition, but mainly by way of writing commentaries, especially on Aristotle, rather than by the development of radically new ideas.
The second major growth phase of logic in the West was in the great medieval universities, such as Oxford and Paris. The high period of this was the development of the logica nova (new logic, term logic) in the fourteenth century. The medieval logicians developed the Aristotelian theory of the syllogism, blended it with Stoic propositional logic, and developed many novel theories of, amongst other things, consequentiae, suppositiones, obligationes, insolubiles (as a first cut: logical consequence, truth conditions, rules of debate, logical paradoxes).
With the rise of Humanism, much of this sophistication fell into oblivion under the general attack on Scholasticism. (In fact, it was only in the second half of the twentieth century that the depth of medieval logic was rediscovered.) There is then a somewhat dull period in logic until the commencement of the third great period of growth, the main bright spot being Leibniz, whose attempt to articulate a characteristica universalis and calculus ratiocinator (a sort of proto-formal language, with rules for calculating in it) arguably provided a premature anticipation of later developments.
The third great period of the development of logic commences in the second half of the nineteenth century, and continues through today (with no sign of coming to an end). This period was inaugurated by logicians applying mathematical techniques to logic—such as those of axiomatization, model theory, abstract algebra—as well as the heightened standards of mathematical rigour being developed in the contemporary mathematics. In the twentieth century, this has produced metamathematics, the foundations of computational theory, the panoply of non-classical logics, and all the standard fare of the contemporary logic curriculum.
Now, the period which is our special concern in this chapter, the nineteenth century, is the site of the rupture into this third great period. It starts with the rump of logic that was left after the decline of medieval logic, and ends with the creation of mathematical logic. German logicians are not the only significant players in this period. However, Germany certainly produced some of the most significant.
Against this background, let us now turn to details.2
20.3 KANT AND LOGIC
Let us start with Immanuel Kant (1724–1804).3 Logic was singularly important for Kant. It provided the tectonic framework for the first of his three great Critiques, Critique of Pure Reason.4 However, Kant is not a significant figure in the history of logic. Indeed, his reading of logic was singularly wrong-headed. He took it, not only that there had been no significant developments since Aristotle, but that there could not be. (See the quotation that opens this chapter.)
He did, however, lecture on logic; and some of his lecture notes were subsequently edited and published by Gottlob Jäsche in 1800.5 The
notes paint a fairly clear picture of the logic of his day (which I will call, henceforth, traditional logic). The main part of this comprises the Doctrine of Elements. There is also a short second part called the Doctrine of Method, which contains a few miscellaneous remarks, mainly about definition. The Doctrine of Elements has three parts: Concepts, Judgments, and Inferences. Inferences contains a discussion of what inferences are valid. Judgments contains a discussion of the parts of inferences, the statements that make up the premises and conclusions; Concepts contains a discussion of the parts of judgments, namely, concepts.
The most striking thing about what Kant has to say about concepts, from a contemporary perspective, is that they are clearly mental, psychological notions. In Judgments, we find, likewise, that judgments, being composed of concepts are psychological acts: they are propositions endorsed as true. (A modern logician is likely to point out that in an inference the premises do not have to be endorsed as true: logic itself need have no concern with the truth or otherwise of the premises.)
According to Kant every judgment has a quality, quantity, relation, and modality. There are three possibilities in each case, which we may tabulate as follows (where the glosses are those of a modern logician, not Kant):
Quantity
Singular The subject of the sentence is a noun phrase
Particular The subject of the sentence is of the form ‘some As’
Universal The subject of the sentence is of the form ‘all As’
Quality
Affirmative The predicate of the sentence is ‘is (are) B(s)’
Negative The predicate of the sentence is ‘is (are) not B(s)’
Infinitive The predicate of the sentence is ‘is (are) non-B(s)’
Relation
Categorical The sentence contains no propositional connective
Hypothetical The sentence is of the form ‘if A then B’
Disjunctive The sentence is of the form ‘A (exclusively) or B’
Modality
Problematic The sentence is stated as possibly true
Assertoric The sentence is stated as actually true
Apodictic The sentence is stated as necessarily true
Oddly, Kant does not observe that only categorical judgments can have a quality or quantity, as such.
Kant’s treatment of modality is also worth noting. Unlike the other categories, which are purely syntactic, modality concerns the attitude one has when one judges a sentence: whether one takes the content to be possible, actual, or necessary. Hence, nothing like modal logic in the contemporary, medieval (or even Aristotelian) sense is possible. In such logics, the modal operator is taken to be part of the content of the sentence, not one concerning the attitude of the person who judges.
In Inferences, we find a fairly standard account of Aristotelian syllogistic, that is, inferences of the form:
All/some/no S is/are M
All/some/no M is/are P
All/some/no S is/are P
—though it is worth noting that this includes syllogisms of the fourth figure (where the middle term, M, occurs as the predicate of the major premise, and the subject of the minor premise). This is not to be found in Aristotle, but is a medieval creation. Kant also claims that the conclusion of any syllogism has apodictic modality (i.e. holds of necessity). This seems to confuse the necessity of the conclusion with the necessity of the connection between premises and conclusion.
After the discussion of the Aristotelian syllogism, we find the simple cataloguing of a few valid propositional inferences, such as modus ponens (A, if A then B; so B) and the disjunctive syllogism (A or B, it is not the case that A; so B).
The section ends, interestingly, with some comments on inductive inference. That topic hardly features in medieval discussions of logic, which concerns itself mainly with deductive inference. By Kant’s time, an awareness of the importance of non-deductive inference has been brought to logic by the ‘scientific revolution’, and its novel conception of scientific methodology.6
20.4 HEGEL AND DIALECTIC
Georg Wilhelm Friedrich Hegel (1770–1831) took over much of Kant’s thought, but changed it in very important ways. Notably, he added a dynamic element that was entirely absent in Kant. From the simplest and most elementary concept, that of being, a sequence of concepts develops in a zig-zag fashion until we reach the concept which is most adequate for characterizing reality, the absolute idea. The concepts are no mere abstracta, however. They are embodied in human and natural history. The conceptual development is therefore embodied in the historical development of the world.
Hegel describes the evolution of concepts in his Science of Logic.7 The matter is covered again more briefly in Part 1 of Hegel’s Encyclopedia of the Philosophical Sciences.8 This is often referred to as the Lesser Logic, as opposed to the Logic (Science of Logic), and is often easier to understand than the Logic—in part because of the Zusätze, culled from Hegel’s lectures, and added by Leopold von Henning.
The part of the Logics which is our major concern here is where Hegel discusses what I am calling logic: the theory of inference. This occurs in Sec. 1, Vol. 2 of the Logic, where the first three chapters are: the Concept, the Judgment, and the Syllogism. Hegel structures the general development of concepts as a sequence of triples—or better, triples of triples. Interestingly, the major exception to this is the chapter on Judgment, which is a quartet of triples, one member of the quartet dealing with each of Kant’s quality, quantity, relation, and modality.9
In these three chapters, Hegel covers much the same ground as Kant covers in his lectures on logic. There are few technical novelties. Where the material mainly differs from Kant, is in that Hegel dresses up the material in terms of the general story of conceptual dynamics he wishes to tell.
The material in question falls under the topic of what Hegel calls Subjective Logic (‘subjective’ because it deals with individual subjects’ reason). He contrasts this with what he calls Objective Logic, which is the dynamical evolution of the concepts. This (according to Hegel) has a certain pattern. Reflection on a concept produces an opposite concept. Thus, the first concept, being, delivers the concept nothing. These two then deliver a concept which is said to aufhebt the pair. This is a term that is virtually impossible to translate into English, since it can mean both to preserve and to get rid of. And Hegel means both of these things at once. The third term in the triad resolves the tension between the first two, so to say, by accepting it. Thus, being and nothing are aufgehoben by becoming. Things in a state of change both are and are not. At any rate, the new term produces its own opposite, and so the cycle starts anew.
Now, this process has absolutely nothing to do with inference, and so with the sense of logic in this chapter. However, it is worth noting that when Hegel’s thought was taken up in the Marxist tradition, this sort of development did come to be thought of as delivering a way of reasoning: dialectical logic. Thus, in Anti-Dühring and Dialektik der Natur10 Friedrich Engels (1820–95) argues that formal (Aristotelian) logic is alright as far as it goes; but to reason properly about things in their dynamics, one requires dialectical logic. He even suggested some laws of dialectical logic, such as the mutual penetration of opposites (things produce their opposites) and the negation of the negation (when the opposite of the opposite arises, it is at a ‘higher level’ than the original). These were never developed into anything like a logic in a sense that a contemporary logician would recognize, however.
Part of the problem was that, even to start to do this, one has to allow for the possibility of contradictory situations. Now, the Principle of Non-Contradiction, which says that such things are impossible, has been high orthodoxy since Aristotle defended the view in Metaphysics Γ. For Aristotle, the Principle was one of metaphysics, not of logic, but it blocks the way of any attempt to reason about situations that are genuinely contradictory.
Unsurprisingly, in virtue of his views about conceptual development, Hegel criticizes and rejects the Princi
ple in the Logic (Vol. 1, Bk. 2, Sect. 1): something can be both P and not-P. He was, in fact one of the few (and certainly the most significant) thinkers post-Aristotle and before the present day, to challenge the Principle. One significant feature of contemporary logic is the development of paraconsistent logics. These are logics which, in a certain sense, do not accept the Principle of Non-Contradiction, and which allow for contradictory states of affairs in a non-trivial fashion.11 Such logics are hardly dialectical logics. They have nothing, as such, to do with zig-zag dialectical developments. However, one might certainly attempt to use the techniques of paraconsistent logic to produce something that is recognizably a dialectical logic—though how one might best do this is moot.12
20.5 NO MAN’S LAND
In the decades that followed Hegel’s death, German philosophy was in something of a state of turmoil: the influence of Hegel waned, or morphed into the materialism of Feuerbach and Marx; under the influence of science, empiricism and naturalism became highly significant, perhaps threatening make philosophy obsolete; this, in turn, prompted a resurgence of Kantianism. Somewhere in this turmoil was the Logische Frage (Question of Logic). The question was, roughly, what to make of logic in a post-Hegelian environment.
The question was put on the table by the person who coined the term in his essay of 1842, ‘On the History of Hegel’s Logic and Dialectical Method. The Logical Question in Hegel’s System’,13 Friedrich Adolph Trendelenberg (1802–72), who followed Hegel in Berlin. In his Logical Investigations14 he argued that Hegel had been right to criticize formal logic for being useless. Logic must always concern itself with content as well as form (a view which, strangely enough, he claimed to find in Aristotle). However, Hegel’s pan-logical metaphysics could not provide what is required in this regard. How, then, to turn this trick? Trendelenberg looked to Leibniz for an answer. (His essay of 1857, ‘On Leibniz’ Outline of a general Characteristic’15 may, in fact, be credited with bringing Leibniz back into the purview of German philosophers.) Though he was critical of many of the details of Leibniz’ characteristica universalis, he argued that what is required for the job at hand is a language which can express our concepts with a precision that natural languages do not do, a Begriffsschrift (concept script).
The Oxford Handbook of German Philosophy in the Nineteenth Century Page 75
