Skepticism about Logic in Germany at the Turn of the Nineteenth
Century
Michael N. Forster
I have known Professor Hans-Friedrich Fulda for almost thirty years now, since coming
to Germany as a visiting student in 1984 to work with him on my doctoral dissertation
about Hegel and skepticism. He was a very intellectually inspiring and generous host
during my visit, and I have continued to learn from him ever since. This article is largely
concerned with two of his central topics: Hegel’s relation to skepticism and Hegel’s
Logic. I dedicate it to him with great respect and gratitude on the happy occasion of his
eightieth birthday.
I would like in this article to attempt to do two main things. First, I want to try to give
an account of what seems to me an extraordinarily important and almost completely
neglected strand in the history of nineteenth-century philosophy: the emergence around
the turn of the century of an awareness that traditional logic lacked any sound
epistemological defenses and was vulnerable to skepticism, and the development in the
train of that awareness of projects to reform logic radically in order both to exploit and to
cure the epistemological vulnerability in question. Pursuing this strand will require us to
explore connections between some philosophers who are not usually thought of as
influencing each other or as having much in common at all, in particular C.G. Bardili,
Friedrich Schlegel, Hegel, and eventually Frege. Strange bedfellows indeed! But as I
1
hope to show, bedfellows nonetheless. Second, I want to try to show that when this strand
of the history of philosophy is properly understood, a certain general conception of the
nature of skepticism and its relation to philosophy that was developed by some of the
same thinkers (specifically, Schlegel and Hegel), and that might be thought to face a
stubborn counterexample in the case of logic, can be seen not in fact to do so.
*
Skepticism played a large role in the motivation of Kant’s critical philosophy, and an
even larger role in the thought of some of his epigones, such as the self-proclaimed
skeptic, G.E. Schulze. But one area in which they did not think that any serious skeptical
challenges arose was general, or formal, logic. Thus, in the Critique of Pure Reason
(1781/7) Kant wrote that the traditional principles of formal logic are “certain entirely a
priori” (A54/B78), that formal logic “contains the absolutely necessary rules of thought
without which there can be no employment whatever of the understanding” (A52/B76),
and that it constitutes “a closed and completed body of doctrine” essentially unchanged
since Aristotle (Bviii). Likewise, Schulze in his book Aenesidemus (1792) included
formal logic among the principles that he took to be immune to skeptical attack, writing
that “the touchstone of all that is true is general logic, and every reasoning about matters
of fact can lay claim to correctness only to the extent that it conforms to the laws of
logic.”1
1
G.E. Schulze, Aenesidemus, oder über die Fundamente der von dem Herrn. Prof.
Reinhold in Jena gelieferten Elementarphilosophie, nebst einer Verteidigung gegen die
2
One of the most striking and interesting things that happened in the next generation of
German philosophy, it seems to me, is that this orthodox view that traditional logic was
certain in a way that made it immune to skeptical attack came to be rejected, with
dramatic consequences for how the content of the discipline was conceived.
Three thinkers were especially important in this process. One of them was the today
largely (and perhaps not altogether undeservedly) forgotten C.G. Bardili, a former teacher
of Hegel’s at the Tübingen “Stift,” who in 1800 published a lengthy treatise titled Outline
of the First Logic Purified of the Errors of Previous Logic in General and of the Kantian
in Particular. Bardili’s project was then championed by Reinhold in his Contributions
towards an Easier Overview of the Condition of Philosophy at the Beginning of the
Nineteenth Century (1801-3), who among other things in 1801 published there as part of
his campaign on its behalf a second, shorter piece by Bardili titled On Bardili’s First,
Kant’s Transcendental, and the hitherto General Logic. A second important thinker in
the process was Friedrich Schlegel, especially in the Lectures on Transcendental
Philosophy that he delivered in Jena in 1800-1. A third important thinker in the process
was Hegel, especially in his 1801 essay The Difference Between Fichte’s and Schelling’s
Systems of Philosophy and his 1802 essay The Relation of Skepticism to Philosophy.
(Hegel knew the relevant work of both Bardili and Schlegel: besides having been
Bardili’s pupil at Tübingen, he discusses Bardili’s Outline and Reinhold’s championing
of it extensively in the Difference essay; and he had personally attended Schlegel’s
Lectures on Transcendental Philosophy in Jena.)
Anmaßungen der Vernunftkritik (published anonymously and without specification of
place of publication, 1792), p. 45.
3
*
Schlegel and Hegel developed their ideas about skepticism concerning logic in the
context of a broader set of ideas about skepticism and its relevance for philosophy that
they developed during the years 1800-2. So it may be helpful to begin with some
discussion of that broader context. Since I have already discussed this in detail in two
other articles – “Schlegel and Hegel on Skepticism and Philosophy” and “Does Every
Genuine Philosophy Have a Skeptical Side?” –2 I shall be brief about it here, merely
outlining some of its most important aspects.
The general picture that emerges in this connection is that Schlegel first developed a
number of original and interesting ideas on the subject, and that Hegel then adopted and
refined them in various ways.
In fact, a similar picture of influence also applies to the positive philosophical positions
that they espouse: Schlegel in the Lectures on Transcendental Philosophy developed an
early version of Absolute Idealism, i.e. a metaphysical monism whose single principle
was spiritual/mental in nature; explicitly conceived this principle as a synthesis of
Spinoza’s principle of substance with Fichte’s principle of consciousness; called it Geist;
insisted that philosophy must expound it as a whole; and envisaged doing this in a
circularly-structured encyclopedia of the sciences. Hegel then more famously went on to
develop just such a positive philosophical position himself.
Michael N. Forster, “Schlegel and Hegel on Skepticism and Philosophy,” in Die
Begründung der Philosophie im Deutschen Idealismus, ed. E. Ficara (Würzburg:
Königshausen und Neumann, 2011); “Does Every Genuine Philosophy Have a Skeptical
Side,” forthcoming.
2
4
But what is more relevant for our present purposes is the fact that the same sort of
picture of influence applies to Schlegel’s and Hegel’s views about skepticism and
philosophy as well. Schlegel in the Lectures on Transcendental Philosophy developed at
least three key ideas in this area which Hegel subsequently took over and refined. First,
and fundamentally, he argued that philosophy begins with skepticism and always retains
skepticism as an essential aspect of itself: “Philosophy begins with skepticism”;
“Skepticism is eternal too, like philosophy . . . [namely] to the extent that it belongs to
philosophy.”3 His more specific idea here was that skepticism performs the vital function
for philosophy of destroying the illusion that finite things exist independently of the
Infinite, or Absolute: “The finite does not exist at all, it only exists in relation to the
whole”; “The illusion of the finite must be destroyed; in order to do that all knowledge
must be subjected to a revolutionary condition”; “Philosophy perforce proceeds
polemically . . . Philosophy begins by raising itself to the concept of the whole and
abstracting from the individual. This is necessary. Philosophy must represent the whole;
but it can only do this indirectly. It drives the human mind away from the finite, it
challenges the latter”; “Consciousness begins with error, namely with the finite. Now if
there is only one science . . . then the task arises of destroying error – and philosophy
constitutes this. Philosophy would therefore be . . . destruction of the finite.”4 Now,
Hegel repeated this whole position quite precisely a year or so later in The Relation of
Skepticism to Philosophy. For Hegel too: “Skepticism itself is most intimately one with
3
KFSA, 12:4, 10; cf. 18, 42. (KFSA = Kritische Friedrich Schlegel Ausgabe, ed. E.
Behler et al. [Munich: Schöningh, 1958–].)
4
KFSA, 12:11, 77, 93, 97. Cf. F.C. Beiser, German Idealism (Cambridge, Mass.:
Harvard University Press, 2002), pp. 456-7, who, though, seems not to notice that this is
the function of skepticism in philosophy for Schlegel.
5
every true philosophy”; “Skepticism . . . can be found implicit in every genuine
philosophical system, for it is the free side of every philosophy.”5 Moreover, for Hegel
too skepticism’s function in philosophy was to destroy the illusions of the finite: “A true
philosophy necessarily has a negative side as well, which is turned against everything
limited . . . , against this whole territory of finitude . . . ; and is infinitely more skeptical
than [modern] skepticism.”6
Second, Schlegel considered viable, and endorsed as an appropriate beginning for
philosophy, an unusually radical form of skepticism. In particular, he regarded the laws
of logic, including the law of contradiction, as vulnerable to skepticism. (This point is
naturally of central importance for our purposes, so we shall return to it in more detail
later.) Relatedly, he also rejected the conception that what seems to be empirically given
furnishes certain knowledge of the truth, namely on the grounds that it is always already
theoretically infused, consequently involves a mixture of truth and falsehood, and
therefore requires theoretical purification: “The phenomenon is merely crude intuition, in
which truth and error are still combined. But facts must be results, they must be
discerned, the truth decided upon. All results of philosophy are contained in the one
[proposition]: that theory and empiricism are one, that they cannot be absolutely
separated.”7 Hegel’s position just a year or so later in The Relation of Skepticism to
Philosophy and other texts was strikingly similar: He too had an unusually radical
conception of the form that skepticism should take. Indeed, the main purpose of the essay
just mentioned was to argue against tame forms of skepticism, such as that propounded
5
Werke, 2:227, 229. (Werke = G.W.F. Hegel, Werke, ed. E. Moldenhauer and K.M.
Michel [Frankfurt am Main: Suhrkamp, 1970].)
6
Werke, 2:227-8.
7
KFSA, 12:98.
6
by his contemporary G.E. Schulze, in favor of a much more radical form of it.8
Accordingly, like Schlegel, Hegel at this period held that a genuine skepticism attacks
logical laws.9 (Once again, this point is naturally of central importance to us, and we shall
return to it in more detail later.) Similarly, in close agreement with Schlegel’s rejection of
a reliance on what seems empirically given, Hegel in The Relation of Skepticism to
Philosophy conducted a concerted skeptical attack on modern philosophy’s reliance on
so-called “facts of consciousness,” observing that the best forms of skepticism, such as
Plato’s Parmenides and the ancient Pyrrhonists’ Ten Tropes, attacked these first and
foremost. Hegel indeed developed Schlegel’s radicalism somewhat further in this
connection, not only thus arguing in the same spirit as Schlegel that the claim of
seemingly immediate experience to be a sure guide to truth was skeptically questionable,
but also suggesting that the very self-ascription of experiences, or of mental states more
generally, was vulnerable to skeptical attack.
Third, Schlegel implies that ancient forms of skepticism are superior to modern ones.
As might perhaps be expected given Schlegel’s longstanding fascination with Plato since
the late 1780s and its persistence into the period of the 1800-1 lectures, his paradigm of a
genuine skepticism was the skeptical side of Plato’s thought. Thus in the lectures he says
that “Plato represented skepticism very completely/perfectly [vollkommen]”;10 that
In this connection, Hegel points out, among other things, that Schulze’s interpretation of
the dispute between the Pyrrhonists and the Academic skeptics in antiquity inverts its real
character: according to Schulze the Pyrrhonists complained that the Academic skeptics
were too radical, whereas Hegel notes, quite rightly, that the Pyrrhonists’ actual
complaint was that they were not radical enough (see Werke, 2:230-3).
9
Werke, 2:141.
10
KFSA, 12:42.
8
7
philosophy must be dialectical and therefore Socratic;11 and that several of Plato’s
writings, especially the Phaedo, are “suited to produce a yearning for the Infinite.”12
Concerning the Phaedo, Schlegel was presumably thinking mainly of Socrates’
autobiographical account at 96a ff. of how in his youth he had found both natural
scientific and commonsense explanations to be undermined by a certain sort of broadly
skeptical criticism through paradoxes that had led him to lose all faith in them, and this
had then motivated him to develop surer explanations in terms of the theory of forms
instead. But Schlegel was probably also in part thinking of Socrates’ account at 89c ff. of
the need to resist the common “misology” of supposing that equally convincing
arguments can be supplied on both sides of any issue and that accordingly everything is
in flux (namely, by not losing, but sustaining, faith in rational argument). Schlegel does
not in the transcription of the 1800-1 lectures that survives discuss other ancient forms of
skepticism. But in a remark from 1803-7 he wrote: “Skepticism is the center of
philosophy as such – and in this respect Greek philosophy is of great value. For the tone
of Greek philosophy as a whole is skepticism.”13 And accordingly, the Cologne lectures
on philosophy from 1804-6, besides underscoring Plato’s credentials as a representative
of genuine skepticism, also contain an extensive and respectful discussion of ancient
Academic and Pyrrhonian skepticism, whose characteristic method was one of
establishing “equipollence [isostheneia],” or an balance of arguments on both sides of
each issue.14 So presumably this broader conception of where in ancient thought valuable
forms of skepticism are to be found was already part of Schlegel’s position in the 1800-1
11
KFSA, 23:103, cf. 97.
KFSA, 12:8.
13
KFSA, 18:562, cf. 187-9.
14
KFSA, 13:347-54; cf. 12:124-30, 181-2, 229-30.
12
8
lectures (its absence from the transcription being merely due to the transcription’s
incompleteness).15 In sharp contrast to this very positive assessment of ancient
skepticism, Schlegel in the 1800-1 lectures argued that modern forms of skepticism are
quite inadequate: he characterizes Maimon, Reinhold, and Platner as all skeptics of a sort,
and states that Maimon is the most important of them, but then he goes on to observe
damningly, “But this skepticism stands in opposition to idealism” (i.e. instead of being
one with it, as it ought to be).16 Now a year or so later Hegel went on in The Relation of
Skepticism to Philosophy to champion a position that was strikingly similar to Schlegel’s
in all these respects. Thus, Hegel too argued that ancient forms of skepticism are greatly
superior to modern ones. Hegel too identified Plato as the paradigmatic representative of
a genuine skepticism. Moreover, while Hegel focused on Plato’s Parmenides rather than
Plato’s Phaedo, he had in mind just the same function that Schlegel primarily associated
with the latter work, namely a skeptical discrediting of commonsense and natural
scientific cognition through paradoxes in preparation for an ascent to knowledge of the
Infinite, or Absolute: “What more perfect and self-supporting document and system of
genuine skepticism could we find than the Parmenides in the Platonic philosophy, which
encompasses the whole domain of that knowledge [of everything limited, of so-called
facts of consciousness, and of the doctrines of the natural sciences] through concepts of
15
Concerning the incompleteness of the transcription generally, see Friedrich Schlegel:
Neue philosophische Schriften, ed. J. Körner (Frankfurt am Main: Schulte-Bulmke,
1935), p. 49.
16
KFSA, 12:95. Where Maimon is concerned, Schlegel’s more specific complaint is that
he rests content with a form of skepticism that precludes a philosophical knowledge of
the whole in the following way: “He accepts from Kant the separation of experience and
reason. He teaches: there is a knowledge of reason, but it is not applicable, both in the
theoretical domain and in the practical.” In the case of Platner, Schlegel’s complaint is
somewhat similar: Platner “considers his skepticism to be philosophy itself. But in this
way philosophy is brought to a halt [fixirt] and its progressive tendency impeded.”
9
the Understanding and destroys it? . . . This skepticism does not constitute a special thing
of a system, but it is itself the negative side of the cognition of the Absolute, and
immediately presupposes Reason as the positive side.”17 Again, Hegel too included a
broader range of ancient forms of skepticism as genuine skepticism as well, especially
Academic and Pyrrhonian skepticism, with their “equipollence” method (much of his
essay is devoted to a detailed and nuanced discussion of these ancient forms of
skepticism, especially Pyrrhonism).18 Finally, Hegel too in sharp contrast rejected
modern forms of skepticism as greatly inferior, moreover mainly, like Schlegel, on the
ground that they cling to finite cognition and obstruct a knowledge of the Infinite, or
Absolute, instead of destroying the former and proceeding thence to the latter.
Hegel went on to develop all three of these ideas about skepticism and philosophy that
he had taken over from Schlegel more elaborately than Schlegel had done, and with some
new nuances that tend to enhance their interest. I have argued at length in other work that
in one form or another all three ideas are correct and important, so I shall not repeat my
general case for that here. Instead, I would like now to focus on the theme of skepticism
concerning logic specifically.
One reason for doing so is that logic might appear to be an especially challenging area
for the three ideas in question. For it might initially seem that logic does not begin with or
respond to skepticism; that it is not vulnerable to skepticism; and that in particular ancient
skepticism had no good resources against it. The historical account that follows will in
17
Werke, 2:228.
Like Schlegel’s choice of the Phaedo with its depiction of “misology,” Hegel’s choice
of the Parmenides was probably in part motivated by the fact that this dialogue too could
plausibly be read as representing the equipollence method (e.g. since it in effect argues
first that “The One is not” by reducing “The One is” to absurdity but then that “The One
is” by reducing “The One is not” to absurdity).
18
10
part be concerned to show that these potential objections can be answered (especially the
first of them: the claim that logic does not begin with or respond to skepticism).
*
As I mentioned, Schlegel in the Lectures on Transcendental Philosophy represents the
laws of logic, including even the law of contradiction, as vulnerable skepticism: “Logic
as the organon of truth offers us the law of contradiction . . . But the source of truth lies
for us far higher than in these laws [of logic]; for skepticism also lays claim to these
laws.”19 Moreover, other works of Schlegel’s from around the same period show that his
own skepticism about logical laws generally, and the law of contradiction in particular,
went as far as denying their validity. For example, he explains the confusion that often
occurs in texts, including and indeed especially superior texts, in terms of the confused
nature of reality; and accordingly, he depicts the fundamental nature of reality as chaos.20
(A few years later, Schlegel’s Cologne lectures on philosophy from 1804-6 would adopt a
similarly skeptical position about the validity of the logical laws of contradiction and
identity, as well as about syllogistic reasoning.21)
Hegel’s position at around the same period is strikingly similar. Thus already in a
review of Bouterwek from 1801 he criticizes Bouterwek for purporting to assume only as
much as a skeptic would allow but then going on to assume the validity of logical laws,
“whereas the consistent skeptic on the contrary denies the concept of a [logical] law
19
KFSA, 12:3.
For discussion of this, see my German Philosophy of Language from Schlegel to Hegel
and Beyond (Oxford: Oxford University Press, 2011), esp. pp. 61-2.
21
See esp. KFSA, 12:316-21; cf. 13:259-60, 280.
20
11
altogether.”22 Moreover, in the Difference essay Hegel challenges the law of identity with
his own novel principle of “the identity of identity and non-identity.”23And both there and
in The Relation of Skepticism to Philosophy he even calls into question the law of
contradiction. For example, in the latter work he says that the higher standpoint of
“Reason” violates it: “The so-called ‘law of contradiction’ is . . . so far from possessing
even formal truth for Reason, that on the contrary every proposition of Reason must . . .
contain a violation of it. For Reason, to say that a proposition is merely formal means:
affirmed alone, without likewise claiming its contradictory opposite, it is just for this
reason false. Hence to recognize that the law of contradiction is formal means to
simultaneously know it to be false.”24
Bardili’s contribution to this whole line of thought was significantly different, but no
less interesting in its own way. His main work, Outline of the First Logic Purified of the
Errors of Previous Logic in General and of the Kantian in Particular,25 is arguably not
his most significant piece in this connection.26 Much more interesting is the shorter essay
that Bardili published soon afterwards in Reinhold’s Contributions, titled On Bardili’s
First, Kant’s Transcendental, and the hitherto General Logic. There he argues that Kant
22
Werke, 2:141.
Werke, 2:96.
24
Werke, 2:230. Cf. the first of Hegel’s Habilitationsthesen from 1801: “Contradiction is
the rule of truth, not of falsehood [Contradictio est regula veri, non contradictio falsi].”
25
C.G. Bardili, Grundriß der Ersten Logik gereinigt von den Irrthümmern bisheriger
Logiken überhaupt, der Kantischen insbesondere (Stuttgart: Löflund, 1800).
26
Despite its subversive and revolutionary bluster, the work does not discuss the
epistemology of traditional logic extensively, consider traditional logic’s vulnerability to
skepticism, or even revise traditional logic’s content very dramatically (in particular, as
Hegel in effect complained in the Difference essay, the work retains a conventional
commitment to the law of identity – rather than, for example, developing Hegel’s novel
principle of “the identity of identity and non-identity” – as well as a conventional
commitment to the law of contradiction).
23
12
has left logical laws “merely rhapsodically . . . gathered together” –27 i.e. picked up
uncritically from tradition. He notes the oddity of the fact that Kant combines a demand
for the investigation of the grounds of possibility of other kinds of knowledge with an
entirely uncritical acceptance of logical laws: “The Kantian school has itself demanded
an appropriate metaphysics for everything that is supposed to be scientific in each kind of
human knowledge, in which the connection of this piece of knowledge with its a priori
grounds should be developed. Is only logic alone to do without such a metaphysics, and
yet be, and be called, a science, indeed quite pure science?”28 And perhaps most
interestingly of all, he points out that it seems to be an assumption underlying Kant’s
complacency about logical principles that they have not been subjected to any serious
skeptical attack, and he questions the historical accuracy of that assumption: He says that
“Kant thought he had recognized that the dogmatists and skeptics had remained standing
with their quarrels only on the territory of metaphysics; and that on the territory of logic
on the contrary an eternal peace has always prevailed.” But he asks rhetorically “whether
it is really true that skepticism has only called into question the objective in human
cognition, or has not on the contrary also more than once dared to attack the validity of
the laws of our understanding themselves.”29
Ueber Bardilis erste – Kants transcendentale – und die bisherige allgemeine – Logik,
in K.L. Reinhold, Beyträge zur leichtern Uebersicht des Zustandes der Philosophie beym
Anfange des 19. Jahrhunderts (Hamburg: Perthes, 1801-3), 2:83.
28
Ibid., p. 85.
29
Ibid., pp. 88-9.
27
13
*
This sudden wave of awareness of traditional logic’s lack of adequate epistemological
defenses and of its consequent vulnerability to skepticism seems to me philosophically
deep and interesting.
As I have argued in detail elsewhere,30 Kant’s conception of the certainty of traditional
logic rested on a claim that conformity to it and conviction in it were constitutive of the
very nature of thought, so that to violate traditional logic would be to cease to think – a
claim that ultimately went back to Aristotle’s defense of the law of contradiction along
similar lines in Metaphysics, book gamma. But neither Aristotle’s original case nor
Kant’s more dogmatic repetition of its conclusion stands up to critical scrutiny: people
certainly quite often seem to believe contradictions, even explicit ones (e.g. Heraclitus,
Plato, and Engels); the Aristotelian argument against the possibility of doing so breaks
down at key points, and is by no means improved on by Kant, who as was just mentioned
merely repeats its conclusion dogmatically; and even if such a case did work, the reply
would still be available, “If not thinking, why not schmthinking?” (i.e. something similar
to and as good as, or perhaps even better than, thinking).
The philosophers from the beginning of the nineteenth century whom we are
discussing here do not quite make this case against the Aristotelian-Kantian position, but
they do have something very much like it in mind. Thus, as we saw, Bardili accuses Kant
30
See my Kant and Skepticism (Princeton, NJ: Princeton University Press, 2008), ch. 12.
Cf. my Wittgenstein on the Arbitrariness of Grammar (Princeton, NJ: Princeton
University Press, 2004), ch. 5.
14
of having failed to provide any adequate epistemological defense of formal logic.
Moreover, Schlegel’s insistence in Georg Forster (1797) and elsewhere that it is proper
to ascribe inconsistencies to certain thinkers reveals that he rejects the AristotelianKantian position that it is impossible to think in violation of the laws of formal logic.31
The same is true of Hegel’s insistence on ascribing inconsistencies to previous thinkers in
works such as the Phenomenology of Spirit and the Lectures on the History of
Philosophy. Moreover, Hegel also makes his rejection of the Aristotelian-Kantian
position clear by means of more explicit statements on the subject, such as his remark at
Encyclopedia, # 119 that “it is ridiculous to say that contradiction is unthinkable.”32 In
addition, the mature Hegel’s position at Encyclopedia, # 82 and elsewhere that while
traditional logic may indeed characterize the “Understanding” it fails to characterize
“Reason” strongly suggests a version of the “thinking vs. schmthinking” point that I
recently mentioned.
More positively, as Schlegel, Hegel, and Bardili all imply, the prospects of developing
forceful skeptical arguments against traditional logical principles look good. It may be
helpful in this connection to distinguish between two broad types of skepticism in which
they are interested: paradox-skepticism (i.e. roughly, the discovery of counterexamples to
logical principles) and equipollence-skepticism (i.e. the discovery that equally plausible
arguments can be given for and against logical principles).
Concerning, first, paradox-skepticism: Schlegel and Hegel both believe that there are
good reasons for rejecting such central principles of traditional logic as the law of
For some further discussion of this, see my German Philosophy of Language from
Schlegel to Hegel and Beyond, pp. 60-3.
32
Cf. Science of Logic, in Werke, 6:563.
31
15
contradiction, the law of identity, the law of bivalence or excluded middle, and syllogistic
inference. For example, Schlegel clearly at least believes that there are good reasons for
affirming contradictions in defiance of the law of contradiction. For this is the force of his
diagnosis of contradictions in texts as the result of contradictions in reality, and of his
characterization of reality as fundamentally chaos. And Hegel rejects traditional logical
principles in an even more thoroughgoing and systematic way (as we shall see in some
detail shortly).
What initially moved Schlegel and Hegel to take this position? It seems to me that it
was largely a perception that ancient philosophers had already made cogent cases for
paradoxes. Thus, as I have mentioned in passing, when Schlegel in his 1800-1 lectures
approves of Plato’s Phaedo as a form of skepticism, he evidently has in mind mainly the
series of paradoxes to which Socrates at 96a ff. in the dialogue attributes his
abandonment of both natural scientific and commonsense explanations in his youth.33
Similarly, in the Cologne lectures on philosophy from 1804-6, where Schlegel argues that
the laws of identity and contradiction have only a relative validity, he indicates that he
approves of Heraclitus’s denial of them in light of his doctrine of flux.34 Likewise, as has
already been mentioned, Hegel in The Relation of Skepticism to Philosophy celebrates
Plato’s Parmenides as a demonstration that even our most fundamental everyday
concepts all turn out to be self-contradictory.
33
These paradoxes concern how adding one to one can yield two, given that it seems that
neither the first one nor the second one nor both of them can become two; how dividing
one can cause it to become two, given that in the previous case the cause of this effect
was the opposite cause of addition; how of two people one can be taller by a head while
the other is shorter by a head; etc. It seems to me very likely that these paradoxes derive
from the Eleatic Zeno and his case against pluralism. Cf. Plato’s depiction in the
Parmenides of a young Socrates learning about Zeno’s arguments from Parmenides.
34
KFSA, 12:316-19.
16
But Schlegel and Hegel also went on to develop more independent arguments of their
own against traditional logical principles. For example, as part of his criticism of the laws
of identity and contradiction in the Cologne lectures, Schlegel insists in his own voice
that life does in fact contain contradictions.35 And he also develops a criticism of
syllogistic reasoning, arguing that it is (1) trivial because reducible to a principle of the
transitivity of identity, (2) not needed in order to infer correctly, and (3) merely local in
its original motivation (namely, a need to combat Sophism among the Greeks).36
Hegel’s independent arguments were more elaborate and sophisticated. For example,
concerning the law of contradiction: Already in The Relation of Skepticism to Philosophy
he endorses Spinoza’s characterization of the one substance as causa sui but he also
insists that this characterization is self-contradictory (his reasons are partly the obvious
one that the very concept of a “cause” implies independence from the effect, but mainly
that while Spinoza’s characterization implies that the one substance’s essence includes its
existence, the very concepts of “essence” and “existence” – at least as usually conceived
– imply a separation between the two).37 Then in his mature Logic he famously argues
that even such fundamental concepts as pure being turn out to be implicitly selfcontradictory (in this particular case because if being is genuinely pure, really abstracts
from all characterization, then it is indistinguishable from nothing). And he endorses
Kant’s discovery of contradictions in the Antinomies, but argues that there are many
more of these than the four Kant identified, and insists, contrary to Kant, that the
35
KFSA, 12:321.
KFSA, 12:315-16. This criticism of syllogistic reasoning is closely related to
Schlegel’s famous claim in Athenaeum Fragments, no. 82 that asserting is more
important than proving.
37
Werke, 2:229-30.
36
17
contradictions in each case afflict reality just as much as thought.38 Finally, in his mature
philosophy more broadly Hegel also argues that such pervasive phenomena as motion
and change involve self-contradiction.39
Again, concerning the law of identity, a = a, already in the Difference essay, and then
throughout the rest of his career, he questions this law on the grounds that it involves a
merely abstract concept of identity and is at best trivial, whereas the more proper concept
of identity essentially involves difference, or non-identity. His argument here is basically
that such uninformative identity statements as those with which the law is concerned are
merely secondary and parasitic on informative ones like “Cicero = Tully,” “The Morning
Star = The Evening Star,” or “The gene = the DNA molecule,” and that in the latter cases
the thought of the identity of the two items in question always involves a transition from
the thought of them as different from each other. 40
Again, concerning the law of excluded middle, in his mature Logic Hegel sketches a
case against this law that turns on a claim that instances of neither-nor do occur. Hegel’s
own examples of this are not especially convincing. But convincing examples are not
hard to find. For instance: “Is Hegel a religious thinker or not? One can’t really say yes or
no”; “Is this a river or not. Neither, it’s in between.”41
Finally, already from an early period Hegel also in a way rejects syllogistic (and other
forms of deductive) reasoning as a failure in its entirety. This is already the force of his
See Encyclopedia, in Werke, 8, # 48.
For a sophisticated recent discussion and defense of Hegel’s position concerning
motion and change, see G. Priest, In Contradiction (2nd ed., Oxford: Clarendon Press,
2006), chs. 11-12.
40
See esp. Science of Logic, at Werke, 6:38-45. For a fuller explanation and qualified
defense of Hegel’s position on this subject, see my Hegel’s Idea of a Phenomenology of
Spirit (Chicago: University of Chicago Press, 1998), pp. 200-4.
41
See Science of Logic, at Werke, 6:73-4; Encyclopedia, at Werke, 8, # 119.
38
39
18
repudiation in the Difference essay of Reinhold’s “tendency to give and establish by
grounds [Begründungs- und Ergründungstendenz],” an approach which Hegel says “geht
los,” i.e. both begins and comes undone, before and outside philosophy.42 Hegel retains
this position throughout his career; for example, he later reiterates it at Encyclopedia, #
12 and 50. His most fundamental case for rejecting syllogistic (and other forms of
deductive) reasoning lies in his doctrine that “the true is the whole” (as he famously puts
it in the preface of the Phenomenology of Spirit). For this doctrine implies that there
could never as a matter of principle be any discrete premises that were true or any
discrete truths to infer to from them as conclusions.43
Turning now to equipollence-skepticism: Bardili and Hegel (namely, in his remarks on
Bouterwek) both imply that skeptics have already developed serious attacks on logic,
presumably meaning by this the ancient skeptics with their equipollence method. Such an
implication is historically correct. One of the most impressive examples of this sort of
attack is recorded by Cicero in the Academica, where the Academic skeptic is represented
as (among other things) calling into question the law of bivalence, or excluded middle, by
means of a version of the Liar Paradox: “Clearly it is a fundamental principle of dialectic
[i.e. logic] that every statement . . . is either true or false. What then? Is this a true
proposition or a false one – ‘If you say that you are lying and say it truly, you lie’?”44 The
word “lie [mentior, cf. Gk. pseudesthai]” here just means “speak falsely,” and the
Werke, 2:25: “It can be demanded of propositions that they give a justification of
themselves. The justification of these propositions, as presuppositions, is supposed not
yet to be philosophy itself. And thus the giving and establishing by grounds begins/comes
undone before and outside philosophy [und so geht das Ergründen und Begründen vor
und außer der Philosophie los].”
43
For more discussion of this, see my Hegel’s Idea of a Phenomenology of Spirit, pp.
158-9.
44
Cicero, Academica (Cambridge, Mass.: Harvard University Press, 1979), II.95-8.
42
19
paradoxical proposition involved could be recast more simply in the form: “This
statement is false.” The Academic skeptic’s basic point is that both the assertion that such
a proposition is true and the assertion that it is false lead to contradiction, which
constitutes a ground for classifying it as neither true nor false, contrary to the law of
bivalence, or excluded middle. If the standard method of “equipollence” is applied, this
consideration can then be set over against whatever reasons we have for believing the law
of bivalence, or excluded middle, in order to generate equipollence and hence a
suspension of judgment concerning it.
Another noteworthy example of an ancient skeptical attack on logic in the manner of
the equipollence method is the attack in Sextus Empiricus’s Outlines of Pyrrhonism on
(quasi-)syllogisms of the form “Socrates is a man. All men are animals. Therefore
Socrates is an animal.”45 Here the Pyrrhonian skeptic objects that such reasoning is
viciously circular, since in order to know the premise that all men are animals one would
already need to know the conclusion that Socrates is an animal.46 In accordance with
usual Pyrrhonian procedure, the purpose of this objection is not to refute such reasoning
outright, but instead to counterbalance whatever reasons we have for believing in its
reliability, in order to generate equipollence and hence suspension of judgment
concerning it.
I say “(quasi-)syllogism because the discoverer of the syllogism, Aristotle, in the Prior
Analytics only envisages premises with universal (“all”) or particular (“some”) subjects,
not premises with individual subjects (e.g. “Socrates”). However, most of the subsequent
logical tradition, including Hegel, would certainly classify arguments of the above form
as syllogisms as well.
46
Sextus Empiricus, Outlines of Pyrrhonism (Cambridge, Mass.: Harvard University
Press, 1976), II.195-6.
45
20
A third noteworthy ancient skeptical attack on logic in the spirit of the equipollence
method can be found in the trilemma that constitutes the heart of the Pyrrhonian Five
Tropes of Agrippa: all assertions are futile because they must either be founded on an
infinite regress of justifications or on a regress of justifications that at some point
involves vicious circularity or on a dogmatic hypothesis that is vulnerable to being
confronted with an opposite dogmatic hypothesis that is no less justified. This trilemma
seems to show that logical inference is futile as a means to achieving its purpose, namely
establishing truth. The trilemma itself involves a form of equipollence in the last of its
three legs. But it could also be employed in an equipollence manner in its entirety,
namely by being set over against whatever reasons there are in favor of thinking logical
inference suitable for its purpose of establishing truth in order to generate equipollence
and hence suspension of judgment on the issue.
Hegel was well aware of, and sympathetic towards, all of these ancient skeptical
arguments against logic. Thus, he discusses the Liar Paradox and its undermining of the
law of bivalence sympathetically in the Lectures on the History of Philosophy.47 He
himself reproduces Sextus Empiricus’s argument against (quasi-)syllogisms of the form
“Socrates is a man. All men are animals. Therefore Socrates is an animal” in the Science
of Logic.48 And he already shows a thorough knowledge of and sympathy with the
Agrippan trilemma in The Relation of Skepticism to Philosophy, afterwards sustaining or
Werke, 18:529. Hegel actually cites Cicero’s Academica in this connection.
Werke, 6:383, cf. 456. O.F. Gruppe (whom we shall consider further a little later in this
paper) later likewise reproduced this argument in his Wendepunkt der Philosophie im
neunzehnten Jahrhundert (1834), probably under Hegel’s influence (he had attended
Hegel’s lectures in Berlin). It was then also discussed by C. Prantl in his Geschichte der
Logik im Abendlande (Leipzig: Hirzel, 1855-70) and by H. Lotze in the Logic of his
System der Philosophie (1874/81).
47
48
21
indeed strengthening his sympathy with it.49 Moreover, he applies it against traditional
logic specifically at various points in the Science of Logic.50
Hegel will also have recognized that equipollence-skepticism had good prospects in
the area of traditional logic for another reason: Clearly, to the extent that Hegel’s own
paradox-arguments against central principles of traditional logic were plausible, an
equipollence skeptic might be able to draw on them in order to counterbalance whatever
reasons favored those principles.
More recent attacks on aspects of traditional logic have potentially added further grist
to equipollence-skepticism’s mill here. For example, additional arguments have been
developed against the law of bivalence, or excluded middle, based on considerations in
mathematics (intuitionism), set theory (Russell’s Paradox), and quantum mechanics –
arguments which an equipollence skeptic might again be able to exploit in order to
counterbalance whatever reasons support the law. And even the law of contradiction has
come under plausible attack. In particular, Graham Priest has recently made a
sophisticated case against this law in his book In Contradiction. Priest too draws on the
Liar Paradox, but he argues that the only satisfactory solution to it requires abandoning,
not the law of bivalence, but the law of contradiction. His argument rests in part on the
availability of variants of the paradox that cannot be defused by dropping the law of
bivalence in the way described above, e.g. “This statement is not true” (even a truthvalueless statement is “not true”). This creates pressure towards the more radical solution
For more on Hegel’s attitude to the Agrippan trilemma, see my Hegel and Skepticism
(Cambridge, Mass.: Harvard University Press, 1989) and Hegel’s Idea of a
Phenomenology of Spirit, pp. 152-3.
50
See Science of Logic in Werke, 6:347 (dogmatic hypothesis vulnerable to an opposite
dogmatic hypothesis), 362-3 (infinite regress), 383 (vicious circularity).
49
22
of allowing exceptions to the law of contradiction. Priest also argues plausibly that there
are further considerations speaking against the law of contradiction that arise from set
theory (Russell’s Paradox); the phenomena of motion and change (as Hegel already saw);
and conflicts within such normative domains as law and morality. In addition, Priest
shows that an array of familiar arguments against violating the law of contradiction, such
as the argument that this inevitably entails “explosion,” or the truth of anything whatever,
can be plausibly defused. It is easy to imagine how an equipollence skeptic about logic
could exploit Priest’s forcefully argued case in order to call the law of contradiction into
question in his habitual manner – drawing on this negative case as a counterweight to
whatever reasons seem to support the law.51
*
However, Bardili and Hegel’s positions on logic were not only negative; they also had a
positive side.
51
Concerning the distinction I have drawn above between paradox-skepticism and
equipollence-skepticism, it may be worth noting that Hegel himself seems to believe that
paradox-skepticism is in a certain way more fundamental than equipollence-skepticism.
For his early discussions of Kant and skepticism in his Habilitationsthesen (1801) and of
the skepticism of Plato’s Parmenides and its relation to Pyrrhonian equipollenceskepticism in The Relation of Skepticism to Philosophy (1802) already imply – and his
later discussions of Kant’s Antinomies and skepticism in the mature Logic of the Science
of Logic and the Encyclopedia more clearly show – that he in effect turns Kant’s
treatment of the mathematical antinomies into a general model here, conceiving
equipollence problems in general as arising out of self-contradictions in basic concepts
just as they do according to Kant’s diagnosis of the two mathematical antinomies
specifically (Kant explains the equal balance of opposed arguments that arises in these
two cases in terms of an alleged self-contradiction in the subject concept “the world”
shared by the thesis and the antithesis).
23
If one takes Bardili’s own account in On Bardili’s First, Kant’s Transcendental, and
the hitherto General Logic of how he had been motivated to develop a quite new logic in
his Outlines at face value, then he did so largely in response to his perception that logic
had not hitherto been provided with any adequate epistemological defenses, in particular
not by Kant, and that it was consequently vulnerable to skeptical attack. This situation
both liberated him to attempt to develop a new logic and positively motivated him to do
so in order to provide one that would possess the adequate epistemological defenses that
traditional logic lacked. Bardili’s main strategy for providing such defenses was to reject
Kant’s conception of logic as merely formal, and to reconceive logic as instead
ontological, just as much concerned with the world as with the mind.
I want to suggest that Hegel’s highly original mature Logic was similarly motivated by
his perception of traditional logic’s lack of adequate epistemological defenses and of its
consequent vulnerability to skeptical attack, which similarly both liberated him to reform
logic and positively induced him to do so in order to render it epistemologically secure.
Moreover, I want to suggest that Hegel’s project was heavily influenced by Bardili’s
here.
This last point can easily be obscured by the fact that Hegel’s only detailed discussion
of Bardili’s project, in the Difference essay of 1801, was early, negative, and immediately
followed by several years during which Hegel, far from following Bardili’s conception of
logic as the very core of philosophy and as ontological, instead developed a merely
introductory, critical logic (the core of philosophy in his own Jena system was instead
metaphysics, followed by the philosophies of nature and spirit). However, there are cases
in the history of philosophy in which a thinker encounters ideas in a predecessor, reacts
24
negatively to them at first, develops a contrary position, but then eventually finds them
bubbling up again years later, causing him to revise that contrary position in fundamental
ways which bring it close to the ideas in question.52 And I would suggest that this is
exactly what happened to Hegel – that his abandonment of his early introductory, critical
logic in favor of his mature logic, with its fundamental role in his philosophy and its
ontological character, in about 1806 was a sort of delayed echo of Bardili’s project.
A broader inventary of some of the common ground that Bardili and Hegel share in
their projects should suffice to make that suggestion plausible: (1) Both of them take
skepticism about logic seriously and think that the epistemological defenses of logic that
have hitherto been provided, in particular by Kant, have been entirely inadequate. (2)
Both of them in large part for this reason undertake a fundamental reform of logic. (3)
Both of them in their reform of logic emphatically reject Kant’s conception of it as
merely formal. (4) Both of them instead opt for a conception of it as ontological, i.e. just
as much concerned with the world as with the mind. (5) Both of them make the new
logics they thus develop fundamental to the whole of philosophy.53 (6) Both of them see
being [Sein] as fundamental to all thought. (7) Both of them conceive Urteilung not just
in the usual sense of “judgment” but also in the etymological sense of an “original
division” as central to logic. (8) Both of them incorporate into logic a critique of the
modal categories of actuality, possibility, necessity that tends to reduce these to the single
52
For example, as I have argued elsewhere, something like this happened to Wittgenstein
when he encountered ideas from Herder and Hamann in the work of Fritz Mauthner early
in his career, largely rejected them at first, but then went on to revise his early philosophy
in their spirit and to adopt them himself in his later philosophy. See my German
Philosophy of Language from Schlegel to Hegel and Beyond, p. 269.
53
Bardili actually aspires to reduce philosophy to logic, whereas the mature Hegel
similarly but somewhat more modestly makes logic foundational for the whole of
philosophy.
25
category of necessity. (9) Both of them include as part of logic material on organic and
animal life, and on human practical life.54
*
How exactly do Bardili and Hegel suppose that their new logics attain an epistemological
security (especially in the face of skeptical attacks) that traditional logic lacked? A full
answer to this question is beyond the scope of this paper. But I would at least like to try
to sketch the main lines of an answer.
A key move that Bardili and Hegel both make here is to reject Kant’s conception that
logic is purely formal, purely concerned with principles that constitute the very nature of
thought. Besides the sorts of problems concerning the intrinsic implausibility of this
Kantian conception that Hegel raised, it also immediately provoked the following sort of
skeptical worry: if this were the status of logic, then it seems that one could only be sure
that reality conformed to logic to the extent that reality was thinkable, not that it did so
tout court. Both Bardili and Hegel therefore reconceive logic as instead concerned just as
much with the constitutive principles of reality as with those of thinking. This was in
some ways a return to Aristotle’s original conception of the nature of logic. For example,
54
There are certainly also some significant differences. For example, Bardili makes the
law of identity central to his new logic, whereas Hegel criticizes it (already countering it
in the Difference essay with his distinctive principle of “the identity of identity and nonidentity”); Bardili remains faithful to the law of contradiction, and indeed even to the
traditional Aristotelian-Kantian conception that to violate it would be to cease to think,
whereas Hegel calls these into question; and Bardili does not use a dialectical method to
develop his logic in a continuous chain as Hegel does.
26
in the Metaphysics Aristotle had conceived the law of contradiction not only as a law of
thought but also as a law of being qua being.
Beyond making this move, Bardili’s reform of logic was rather modest. In particular,
he preserved the law of identity, indeed making it central to his own logic, he took over
traditional logic’s commitment to the law of contradiction, and he even accepted the
traditional conception that to contradict oneself would be to cease to think.
By contrast, Hegel was evidently more impressed by the availability of skeptical
arguments against the laws of contradiction, identity, and excluded middle, as well as
against syllogistic (and other forms of deductive) inference, and consequently developed
much more ambitious reforms of logic in response. His general strategy here was, I think,
basically to accept certain skeptical arguments against such logical principles, but instead
of simply violating and rejecting the principles, to demote both the principles themselves
and to a lesser degree also their violations to the status of an inadequate standpoint, and
to transcend that whole standpoint in a certain way. This, I suggest, is part of what he
means to convey when he says the following just before beginning with the main body of
the Logic in the Encyclopedia: “Incidentally, when skepticism is still today considered an
irresistible enemy of all positive knowledge in general and hence also of philosophy,
insofar as philosophy is concerned with positive cognition, it should be noted against this
that it is actually only finite, abstract thought that needs to fear skepticism and cannot
resist it, whereas philosophy on the contrary contains the skeptical moment within itself,
namely as the dialectical. But philosophy does not then remain with the merely negative
result of dialectic, as happens with skepticism. Skepticism fails to understand its result in
holding onto it as mere, i.e. abstract, negation. By dialectic’s having the negative as its
27
result, this, precisely as result, is also the positive, for it contains what it results from as
sublated [aufgehoben] within itself and does not exist without it. But this is the basic
nature of the third form of the logical, namely the speculative or the positively rational.”55
Let me therefore now try to illustrate this general strategy by discussing some specific
cases.
Consider first Hegel’s attitude to the law of contradiction. Already in the Difference
essay from 1801 he makes many statements that look at first sight like outright
endorsements of contradictions and rejections of the law of contradiction.56 However, his
considered position in the work seems rather to be that while the positing of
contradictions is indeed a virtue in the lowly standpoint of mere “reflection,” permitting it
a level of insight that it could not otherwise attain, it is not involved at the higher
standpoint of “speculation”: “Insofar as speculation is viewed from the standpoint of
mere reflection, the absolute identity appears in syntheses of opposites, i.e. in
antinomies”; “The unification of opposed concepts in antinomy – for the faculty of
conceptualizing, the contradiction – is . . . the true revelation of the inconceivable in
concepts, the revelation that is possible through reflection.”57 His later discussion of the
law of contradiction in the Science of Logic retains the same twofold character: on the
one hand, seeming to endorse contradictions and rejections of the law of contradiction,
but on the other hand, intimating that this endorsement is only relative to the level of the
Encyclopedia, in Werke, 8, # 81, Zusatz 2.
See e.g. Werke, 2:28-9, 36-41, 115.
57
Werke, 2:41, 128-9 .
55
56
28
finite standpoint and that there is a higher standpoint at which contradictions are
somehow resolved.58
How exactly are we supposed to understand this position? At least concerning Hegel’s
mature version of it, I suggest the following interpretation. From a conventional
viewpoint, there are two ways in which someone might be said to “impute
contradictions,” one of which is in principle unproblematic, but the other of which
involves a violation of the law of contradiction and is therefore problematic: on the one
hand, it is in principle unproblematic to impute contradictions to thoughts or concepts; on
the other hand, it violates the law of contradiction and is problematic to impute them to
reality. Now at Encyclopedia, # 48 Hegel famously criticizes Kant for taking the sorts of
contradictions that he discovered in the antinomies to be merely contradictions in thought
rather than in reality; Hegel says that this shows altogether too much tenderness for
reality. This can easily make it sound as though Hegel himself believes that there are
contradictions in reality. However, matters are not so simple. For, officially, he intends to
overcome the very distinction between thought and reality. Moreover, he intends to do so
in such a way that it is thought rather than reality that predominates in the resulting
synthesis of the two (this is why he uses mentalistic rather than ontological vocabulary to
name the resulting synthesis: “Idea,” “Concept,” “Spirit,” etc., rather than “Being,”
“Substance,” etc.). As he himself puts the point at Encyclopedia, # 215: “In the negative
unity of the Idea, the infinite overlaps and includes the finite, thought overlaps being,
subjectivity overlaps objectivity. The unity of the Idea is thought, infinity, and
subjectivity, and is in consequence to be essentially distinguished from the Idea as
58
Werke, 6:74-80.
29
substance.” So he is not in the end quite saying that reality is contradictory after all.
Rather, he is saying that insofar as one is still wedded to the concept of reality in
contradistinction from thought, one does better to ascribe contradictions not only to
thought but also to reality, but that such a concept of reality is in the end inadequate. To
be sure, he is also saying that when one transcends such inadequate concepts as those of
reality and thought conceived in contradistinction to each other to the higher standpoint
that synthesizes them, the “Idea,” one will still have to impute contradictions to it. But is
this really a violation of the law of contradiction and hence problematic? The situation is
ambiguous, but tends to justify a negative answer: This is neither an unequivocally
“innocent” imputation of contradictions to thoughts or concepts nor an unequivocally
“guilty” imputation of them to reality. Rather, it is something in between those two
things, but closer to the former than to the latter. It seems to me that one can at least say
this much about Hegel’s considered position on the law of contradiction with some
confidence. Whether or not such a synthesis of thought and reality as he aspires to here is
really available, or even intelligible, is, it seems to me, a further and difficult question.
Concerning next the law of identity, Hegel’s considered position is again more subtle
than it may initially appear. He holds that the law of identity, a = a, in some sense
succumbs to paradox, in particular because of its essential involvement of difference, or
non-identity. But he also implies that the law is trivial and uninteresting rather than
downright false. How can he hold this puzzling combination of views? As in the previous
case, essentially because he holds that both the law and even its skeptical violation are
ultimately transcended by a higher standpoint. A preliminary point to note here is that
besides (1) invoking the essential involvement of difference, or non-identity, against the
30
law of identity, Hegel also has two additional criticisms of the law: (2) He objects that the
proper use of the notion of identity occurs not in the sorts of uninformative identity
statements with which the law is concerned, but instead in informative identity
statements, such as “Cicero = Tully,” “The Morning Star = The Evening Star,” or “The
gene = the DNA molecule.” (3) He also objects that uninformative identity statements
like those involved in the law employ a merely “abstract” concept of identity. These three
criticisms are all intimately connected, namely in the following way: Given that it is
informative identity statements that are the proper ones, and that these essentially involve
a transition from thinking of difference, or non-identity, to thinking of identity, this
shows that such a transition is internal to any proper concept of identity itself. That
explains Hegel’s skeptical observation that identity essentially involves difference, or
non-identity, as well as his paradoxical-sounding thesis that the proper concept of identity
is the concept of an “identity of identity and non-identity.” It also explains his claim that
the concept of identity that appears in the law of identity, a = a – like the concept of nonidentity that appears in its skeptical violation – is merely a partial abstraction from that
proper concept of identity. Of course, making sense of Hegel’s critical stance towards the
law of identity in this way in terms of an ascent to the paradoxical-sounding thesis that
the proper concept of identity is that of an “identity of identity and non-identity” might
seem to incur the unacceptably high cost of still leaving him committed to a selfcontradiction in this paradoxical-sounding thesis itself. But does it really? Arguably not,
for as Hegel conceives matters, while informative identity statements do involve a
transition from the thought of difference, or non-identity, to the thought of identity, such
a fundamental change in the conception of the object(s) in question ensures that although
31
the words designating the object(s) stay the same throughout the transition, the concepts
they express change in step with the transition.59 Strictly speaking, therefore, no selfcontradiction occurs.60
Concerning next the law of excluded middle, Hegel again in a way commits himself to
a skeptical intuition that attacks the law – in this case by insisting that intermediate cases
of neither-nor do occur – but also takes the law to be trivial and inadequate rather than
just plain false. He believes that this combination of positions is available to him because
there is ultimately a higher standpoint than either that of the law or even that of its
skeptical violation, namely the standpoint of “the identity of identity and non-identity.” In
his view, it is ultimately this higher standpoint that generates the intuition of intermediate
cases that constitutes the skeptical violation involved. For, as he conceives it, this higher
standpoint implies that nothing is ever either simply a certain way or simply not a certain
way (as well as that it is always both a certain way and not that way).61
Finally, concerning syllogistic (and other forms of deductive) inference, Hegel’s most
fundamental skeptical criticism of such inference, in terms of the holistic nature of truth,
leads him to consign it to the inferior standpoint of the mere “Understanding.” At the
superior level of “Reason” attained by his own Logic, by contrast, he substitutes for it a
novel dialectical method of inference, i.e. a method which does not like syllogistic
inference depend on the possibility of truth-preservation between discrete premises and
59
For this specific point, cf. O.F. Gruppe, Gegenwart und Zukunft der Philosophie in
Deutschland (Berlin: Georg Reimer, 1855), pp. 194-5. Gruppe makes the point in his
own voice, but he had attended Hegel’s lectures and is no doubt reflecting the spirit of
Hegel’s position.
60
For this whole position on the law of identity, see Science of Logic, at Werke, 6:38-45.
For some further discussion of it, see my Hegel’s Idea of a Phenomenology of Spirit, pp.
200-4.
61
See Science of Logic, at Werke, 6:73-4; Encyclopedia, at Werke, 8, # 119.
32
conclusions, and which therefore avoids conflicting with the holistic nature of truth, but
which instead works (roughly) by identifying self-contradictions in lower concepts and
then resolving them in higher concepts. In addition, at this superior level he reinterprets
the traditional forms of syllogism radically as in effect merely metaphors for the structure
of the Absolute.62
Such, in short, are Bardili’s and Hegel’s attempts to achieve a radical reform of logic
that would afford it epistemological defenses capable of withstanding skepticism.
Whether their attempts succeed in the end one may reasonably doubt. But however that
may be, it seems to me important to recognize that they both made such attempts, and
that in doing so they were largely motivated by a plausible perception that traditional
logic lacked adequate epistemological defenses and was consequently vulnerable to
skeptical attack, a perception which both liberated them to undertake such a reform and
provided them with a positive incentive to do so.
62
Hegel first developed dialectic as a method during the early Jena period, initially
assigning it a merely introductory, critical function in the early Logic but then, beginning
around 1806, giving it a more genuinely philosophical, constructive function in the
mature Logic that already lies behind the Phenomenology of Spirit (1807). Hegel’s
recasting of syllogisms as merely a sort of metaphor for the Absolute already began as
early as the Logica et Metaphysica of 1801/2, and then continued in the mature Logic.
The earliness of these developments is to a great extent explicable in terms of the fact
that, as we have seen, Hegel already developed the skepticism about syllogistic (and
other forms of deductive) inference that largely motivated them by the time of the
Difference essay of 1801.
33
*
Hans Sluga has written that “between Leibniz and Frege no attempt was made at a
fundamental reform of logic.”63 However, as we have seen in the preceding, this is not
true. Whatever one may think of their success or failure, Bardili and Hegel had both
attempted just such a reform early in the nineteenth century.
Moreover, their general project of pointing out the epistemological vulnerability of
traditional logic, skeptically criticizing it, radically reforming it, and reconstructing
philosophy based on its reformed version as a new foundation was subsequently
continued by the sometime student and then critic of Hegel, the influential O.F. Gruppe,
in his Wendepunkt der Philosophie im neunzehnten Jahrhundert (1834) and Gegenwart
und Zukunft der Philosophie in Deutschland (1855).64
This whole situation encourages me to advance a rather surprising hypothesis: namely,
that the recognition by Schlegel, Bardili, and Hegel around the turn of the nineteenth
century that traditional logic lacked adequate epistemological defenses and was
vulnerable to skepticism, together with the resulting project developed by Bardili and
Hegel of reforming logic both in exploitation of this situation and in order to cure it,
63
H. Sluga, Gottlob Frege (London: Routledge and Kegan Paul, 1980), p. 11.
Cf. ibid., pp. 22, 25. Concerning Gruppe’s influence, note in particular that he receives
respectful treatment in Trendelenburg’s Logische Untersuchungen. I shall say a little
more about the latter in what follows.
64
34
formed an essential part of the intellectual background for Frege’s revolutionary reform
of logic later in the century.65
Let me put the core of my case for this hypothesis in the form of a rhetorical question.
Recall that, as Kant in effect pointed out, between the time of the ancient Greeks (Kant
only specifies Aristotle, but he should have included the Stoics as well) and Kant himself
just before the turn of the nineteenth century the content, and (Kant should have added)
the epistemological justification, of logic had remained virtually unchanged for over two
thousand years. As we have seen, following those two thousand plus years of
monotonous continuity, there suddenly emerged at the beginning of the nineteenth
century, centered mainly on the university of the small German town of Jena, a group of
thinkers who attacked the traditional psychologistic epistemological rationale for logic,
argued that traditional logic was vulnerable to skepticism, set out to reform logic
radically in order to exploit that situation and render logic more epistemologically secure
(among other things), in the process rejected Kant’s conception of logic as concerned
only with the form of thought, and instead championed an account of logic that ascribed
it ontological significance. Just a few decades later in the same century at that very same
university in the very same small German town of Jena another thinker emerged, Frege,
who likewise questioned logic’s traditional psychologistic epistemological rationale,66
65
As far as I know, this hypothesis is a novel one. For example, W. and M. Kneale in
their monumental history of logic and in particular of its modern culmination in Frege,
The Development of Logic (Oxford: Clarendon Press, 1978), do not even mention
Schlegel, Bardili, or Hegel.
66
See especially the preface to G. Frege, Grundgesetze der Arithmetik (1893)
(Hildesheim: Georg Olms, 1962), pp. xiv ff., where Frege explicitly attacks what he sees
as Erdmann’s empirical-psychologistic epistemological grounding of logical laws, but
also implicitly (and much more importantly) Kant’s transcendental-psychologistic
grounding of them as constitutive of the very nature of thought.
35
worried about skeptical threats to logic (in his case, more specifically, threats of
relativism, subjective idealism, and solipsism),67 set out to reform logic radically in order
to render it more epistemologically secure (among other things), in the process rejected
Kant’s conception of logic as concerned only with the form of thought,68 and instead
championed a conception of it as having ontological significance.69 So my rhetorical
question is simply this: Does it really seem likely that the occurrence of these two
strikingly similar episodes in the history of thought within just a few decades of each
other in the same university in the same small German university town after thousands of
years that had contained nothing even remotely like them was merely accidental?
I do not mean to suggest here that the influence of the group of thinkers in question
from around the turn of the nineteenth century was the only or even the main one at work
on Frege, nor that the motives for rethinking traditional logic that it furnished were his
only or even his main motives. For example, Kant and Leibniz were clearly more salient
influences on him (as Sluga, Lothar Kreiser, and others have shown), and Trendelenburg
and Lotze may well have been so too (as Sluga, Gottfried Gabriel, and others have
argued). Also, his own explicit explanations of his revolution in logic almost always
account for it in terms of the quite different motive of making logic more serviceable for
mathematics. However, I do want to suggest that the influence and the motives that I
have just identified were among those at work on him, and indeed that his project
probably would not have emerged without them.
67
See ibid., pp. xvi, xix.
See ibid., pp. xiv ff.
69
See ibid., pp. xiv-xvii.
68
36
In order to support this hypothesis, it is helpful to consider Frege’s relation to Hegel in
particular. Michael Dummett has proposed that Frege should be seen as part of a realist
reaction against Hegelian idealism.70 But Hans Sluga has rejected this interpretation on
the grounds that Hegelian idealism had ceased to be a real power in Germany by 1830,
after which the greatest cultural influence was instead in the hands of scientific
naturalism; and that accordingly Frege should be seen as reacting against the latter rather
than the former.71 However, it seems to me that Sluga presents us with a false alternative
here, that while Frege was indeed surrounded by and an opponent of scientific
naturalism, he was also, as Dummett thought, surrounded by and an opponent of
Hegelian idealism. Several considerations support such a view. Perhaps most
importantly, Trendelenburg, whose work Frege evidently knew, had made his reputation
largely by expounding in detail, sharply criticizing, and to a considerable extent also
quietly borrowing from Hegel’s Logic in his own work Logische Untersuchungen (1840;
3rd revised edition 1870).72 Perhaps a little less importantly, Frege’s teacher Lotze, who
M. Dummett, “Frege, Gottlob,” in Encyclopedia of Philosophy, ed. P. Edwards (New
York and London: Macmillan, 1967), 4:225. Cf. M. Dummett, Frege: Philosophy of
Language (London: Duckworth, 1973), p. 684.
71
Sluga, Gottlob Frege, esp. pp. 8-9.
72
A. Trendelenburg, Logische Untersuchungen (repr. of 3rd ed., Hildesheim: Georg
Olms, 1964). Sluga points out that Frege knew and cited other work by Trendelenburg,
but he remains agnostic on the question of whether Frege knew the Logische
Untersuchungen. However, I find it very hard to believe that he did not. The following
are my main reasons: (1) The work’s public prominence at the time and its obvious
relevance for Frege’s own project make it quite unlikely that Frege would have ignored
it. (2) In the work Trendelenburg either champions or at least clearly articulates a whole
series of positions and issues that would later become strikingly central to Frege’s logic.
In particular, Trendelenburg champions (a) a thesis of the primacy of judgments over
concepts, (b) a thesis that all concepts are general in nature, (c) a thesis that individuals
can only be expressed or known through general concepts, and (d) a thesis that logic is
not merely concerned with forms of thought but also has ontological significance. And in
addition, he (e) clearly describes Kant’s thesis that modality is merely epistemic in nature
70
37
may have strongly influenced his logic (as Sluga, Gottfried Gabriel, and others have
argued), was on the metaphysical-religious side of his philosophy basically a sort of
Hegelian idealist (e.g. he championed a form of monism and argued that the single
principle in question was Geist), namely one who had taken on board a strong strand of
scientific naturalism and fallibilism.73 In addition, a colleague of Frege’s at the University
of Jena, C. Fortlage, who worked on logic and probably influenced Frege’s unusual
logical notation, was heavily influenced by Hegel.74 Moreover, as we are about to see,
Frege’s preface to The Basic Laws of Arithmetic (1793) strongly suggests that Frege was
well aware of, and consciously competing with, Hegelian idealism.
Some philosophers name their most important and influential opponents explicitly and
discuss them extensively – whether in a spirit of generosity, impartiality, or contempt.
Others go beyond expressing contempt and refuse even to mention them. I want to
and (f) touches on the issue of multiple generality in sentences and of the logic of such
sentences (for this key issue, see 2:337; it comes up in connection with a discussion of Sir
William Hamilton’s logic). (3) Frege’s colleague and fellow teacher of logic at the
University of Jena, R. Eucken, had been a student of Trendelenburg’s. This makes it even
less likely that Frege would have ignored Trendelenburg’s central work on logic, and it
makes it almost certain that even if he had not actually read it he would at least have been
familiar with its main positions from oral communications. (4) When Frege late in life
came to publish a collection of essays on the philosophy of logic, he chose the title
Logische Untersuchungen (1918-23). It seems unlikely that this was intended only, or
even mainly, as a nod of respect to Husserl’s intervening work of the same name, since
Frege was very critical of Husserl’s positions, but much more likely that it was largely
intended as a nod of respect to Trendelenburg’s work.
73
I say that this is perhaps less important for the following reasons: (1) The extent of
Lotze’s influence on Frege’s logic is unclear and disputed (for example, Kreiser is
skeptical about Sluga’s and Gabriel’s emphasis on it, noting rightly that Frege is only
known to have attended Lotze’s lectures on philosophy of religion and that it is not
known whether he attended any of Lotze’s lectures on logic or read his books on the
subject). (2) While, as I have mentioned above, Lotze was influenced by Hegel on the
metaphysical-religious side of his position, he shows relatively little evidence of having
been influenced by him in his logic.
74
See L. Kreiser, Gottlob Frege: Leben – Werk – Zeit (Hamburg: Felix Meiner, 2001),
pp. 158 ff.
38
suggest that something like the latter is the case with Frege in relation to Hegel. More
specifically, I want to suggest that in Frege’s famous and extensive critique of Benno
Erdmann’s Logik (1792) in the preface to The Basic Laws of Arithmetic for psychologism
and idealism, Erdmann is largely a sort of stand-in for Hegel, whom Frege will not even
deign to mention.
A first clue that something like this may be going on in the preface can already be seen
by comparing Frege’s scathing attack on Erdmann there with what Erdmann actually says
in his Logik. For it turns out that, far from holding the positions about the nature of logic
that Frege attributes to him and criticizes, Erdmann in fact holds positions that are
strikingly similar to Frege’s own.75 I therefore suggest that Erdmann is largely
functioning in the introduction as a sort of substitute for a broader movement and another
person (rather as in Aristophanes’ play Clouds Socrates stands in for Sophism and
especially Protagoras), and I suggest that the movement in question is idealism and the
person its leading representative Hegel.76
75
Some examples: (1) pace what Frege says about him, Erdmann in fact like Frege
himself denies that logic is part of psychology; (2) pace what Frege says about him,
Erdmann in fact like Frege himself in particular denies that logic is descriptive of how
people think; (3) pace what Frege says about him, Erdmann in fact like Frege himself
insists that logic is instead concerned with how people should think; (4) pace what Frege
says about him, Erdmann in fact like Frege himself sharply opposes Kant’s conception of
logic as purely formal, abstracting from all content; (5) pace what Frege says about him,
Erdmann in fact like Frege himself insists that logic instead only abstracts from the
specificity [Besonderheit] of content; and (6) pace what Frege says about him, Erdmann
in fact like Frege himself avoids any implication of idealism. Indeed, almost the only
grains of truth in Frege’s characterization of Erdmann’s position lie in Erdmann’s
concession to psychology of a certain preparatory role in logic and Erdmann’s omission
of the sort of Platonism that Frege champions. See B. Erdmann, Logik (Halle: Niemeyer,
1892), esp. pp. 1-34.
76
Kreiser apparently entertains a generically similar suspicion about the preface, but he
instead casts Husserl in something like the role I am assigning to Hegel (Gottlob Frege,
39
Frege’s overall reaction in the preface to this Erdmann-Hegel (as I shall call the fusion
of figures involved) is a striking combination of grudging agreement and sharp dismissal.
The following are some of Frege’s main allusions to Hegelian positions there, and his
stances towards them: (1) Frege opens his discussion of Erdmann-Hegel by saying that
one obstacle that stands in the way of the acceptance of his own position by logicians lies
in “the corrupting intrusion of psychology into logic. Decisive for the treatment of this
science must be the conception of logical laws [der verderbliche Einbruch der
Psychologie in die Logik. Entscheidend für die Behandlung dieser Wissenschaft muss die
Auffassung der logischen Gesetze sein].”77 Now the German here is admittedly not quite
“Wissenschaft der Logik,” but rather “Logik . . . dieser Wissenschaft.” Nonetheless, it
surely very much calls to mind the title of Hegel’s main work on logic: the Science of
Logic [Wissenschaft der Logik] (1812-16). (2) In discussing the difference between
Erdmann-Hegel’s (alleged) conception of logic as psychological laws that might vary and
his own conception of logic as laws of truth that hold regardless of how people happen to
think, Frege then chooses to use the example of the law of identity: “Every object is
identical with itself.”78 Since (as we have seen) Hegel had famously in effect rejected this
law, championing in its stead a principle of “ the identity of identity and non-identity,”
Frege seems to have chosen this example with Hegel in mind. (For how many other
people have wanted to give up the law of identity in the way that Frege is considering?)
In addition, Frege in the course of his discussion implicitly agrees with Hegel, as against
Kant, that it is possible to think in violation of this law, so that the Kantian conception
pp. 242 ff.). For reasons that should in part become clear from my positive case below, I
find that interpretation less plausible.
77
Grundgesetze der Arithmetik, p. xiv.
78
Ibid., p. xvii.
40
that logical laws are secure because they are constitutive of the very nature of thought is
mistaken.79 On the other hand, Frege also more explicitly disagrees with ErdmannHegel’s (alleged) view that whatever validity this and the other laws of logic have instead
depends on people’s de facto psychological conformity to them. Rather, he holds that
they are “laws of truth” in accordance with which people should think insofar as their
goal is to achieve truth. So Frege is partly agreeing with Hegel here and partly
disagreeing with him. (3) Frege then goes on to draw a distinction between what is
objective [objectiv] and what is actual [wirklich], and to insist that not everything
objective is actual (in particular, he insists that numbers are objective, though not actual,
i.e. not capable of acting on the senses).80 This distinction and insistence are immediately
recognizable as a distinction and insistence of Hegel’s (Hegel expounds them most
clearly and famously in the Encyclopedia, # 6). On the other hand, Frege puts them to a
non-Hegelian use of his own here, employing them to support a doctrine that there exists
a realm of “the objective non-actual” (including numbers) which he takes to be especially
important.81 This is of course his own Platonist “third realm” (as he would later call it) –
whose very existence, and whose superiority to the “actual,” Hegel would have denied.
So here once again we find Frege combining partial acceptance of Hegel with partial
rejection of him. (4) Frege next goes on to consider the word “representation
[Vorstellung]” and to accuse Erdmann-Hegel of an equivocation on the word: something
within the mental life of the individual vs. something that is independent of all
79
Cf. ibid., pp. xv-xvi.
Ibid., p. xviii.
81
Ibid.
80
41
individuals and in the same way.82 Frege’s linguistic point here actually works much
better if one substitutes the word Idee for the word Vorstellung. And that the former word
is indeed in his mind can be seen from the fact that he immediately goes on in this
connection to discuss Erdmann-Hegel’s “Idealismus.”83 The significance of this is that
the word Idee is a central term of art in Hegel’s philosophy; “die Idee” is indeed the
highest category of Hegel’s Logic. So Frege’s accusation of equivocation turns out to be
a criticism of a central feature of Hegel’s Logic. That this reading of what is going on in
the passage is correct is confirmed by the fact that Trendelenburg in a passage of his
Logische Untersuchungen that must surely have inspired Frege’s discussion here had
distinguished between precisely the two senses of the word Idee in question, had
explained their role in Idealismus, and in particular had alleged that Hegel had conflated
them in his version of Idealismus.84 So here again Frege is partly agreeing with Hegel,
but partly disagreeing with him: he is agreeing with him to the extent of recognizing that
he already has something like Frege’s own objective conception of representations/ideas
(or “senses”/“thoughts,” as Frege more usually calls them); but he is disagreeing with
him to the extent of accusing him of failing to distinguish representations/ideas in this
objective sense from mere individual psychological items. (5) Frege then goes on to
accuse Erdmann-Hegel of having been seduced by that equivocation into idealism (or
even solipsism): “Thus everything drifts into idealism and from that point with perfect
consistency into solipsism [So mündet denn Alles in den Idealismus und bei grösster
82
Ibid., pp. xviii ff.
Ibid., p. xix.
84
Trendelenburg, Logische Untersuchungen, 2:507-15.
83
42
Folgerichtigkeit in den Solipsismus ein].”85 This is again easily recognizable as a
characterization of, and complaint against, Hegel, who was of course the most famous
“idealist” of them all. (6) Finally, Frege goes on to argue for the aptness of the verb
“ergreifen [to grasp]” in its metaphorical dimension for characterizing the relation of our
cognition to its objects because of its etymologically-derived implication of the
independence of the objects cognized from our cognition of them, in opposition to
Erdmann-Hegel’s (allegedly) psychologistic conception of the subject-matter of logic as
only subjective representations.86 This point again recalls Hegel, who had famously made
“begreifen [to grasp/understand]” and its cognate “der Begriff [the Concept]” central to
his own Logic, and who had similarly discussed the word’s metaphorical nature in that
role and in particular its etymological origins in the notion of grasping.87 Indeed, it seems
clear on closer inspection that Frege in this discussion is thinking just as much of
begreifen/Begriff as of ergreifen. For immediately after discussing the latter he in the next
paragraph explicitly turns his attention to Begriffe.88 (Here again, as previously in case
(4), it seems that Frege’s refusal to deign to discuss Hegel explicitly even extends to a
refusal to deign to use his vocabulary: just as Erdmann is made to stand in for Hegel, so
Vorstellung is made to stand in for Idee and ergreifen for begreifen/Begriff.) Frege is
therefore here once again in effect both agreeing and disagreeing with Hegel: agreeing
with him on the aptness of the term ergreifen/begreifen for characterizing the subjectmatter of logic, due to its fortunate etymologically-derived implication of the subjectGrundgesetze der Arithmetik, p. xix. Frege goes on to elaborate on this complaint over
the course of several pages.
86
Ibid., p. xxiv.
87
See esp. Lectures on Aesthetics, at Werke, 13:518-19. Cf. Encyclopedia, at Werke, 8, #
160.
88
Grundgesetze der Arithmetik, p. xxiv.
85
43
matter’s independence from thinkers, but disagreeing with what he considers to be
Hegel’s contradiction of such independence in his official idealism (Frege’s linguistic
point is thus largely intended as an ad hominem criticism of Hegel). In sum, Frege’s
preface to The Basic Laws of Arithmetic contains an extensive, albeit masked, critique of
Hegel’s conception of logic – a critique characterized by grudging agreement with certain
aspects of it but sharp rejection of others.
This evidence from the preface of The Basic Laws of Arithmetic that Frege seriously
engaged with Hegel’s Logic (whether he knew it directly or only through other people),
and moreover that he did so in ways that were not only negative but also in part positive,
strongly supports the thrust of my earlier rhetorical question: namely, that the critical and
reforming project concerning traditional logic that Schlegel, Bardili, and Hegel developed
early in the nineteenth century was an important influence on Frege’s own critical and
reforming project concerning the discipline several decades later. For the preface to The
Basic Laws of Arithmetic shows that Frege was familiar with that earlier project in its
culminating and most important form, namely Hegel’s, and that he not only disagreed
with it in certain ways (e.g. by insisting on an unequivocal Platonism), but also agreed
with it in others.
Among the agreements that are especially important for recognizing the continuity
between the two projects are the following: First, Frege agrees with Hegel and his group,
against Aristotle and Kant, that it is quite possible to think in violation of traditional
logical principles, so that Aristotle and Kant’s claim that it is impossible to do so fails to
provide logic with the epistemological security that they thought it provided. Second, like
Hegel and his group, Frege is consequently worried about a certain sort of skepticism
44
concerning logic that threatens (in Frege’s case, more specifically, relativism, idealism,
or solipsism concerning logic). Third, like Hegel and his group, Frege is both liberated by
this state of affairs to undertake a radical reform of logic and motivated to do so in order
to render logic more epistemologically secure (albeit that the specific reform of its
content that he envisages is for the most part quite different from theirs).89 Fourth, like
Hegel and his group, Frege, having rejected the psychologistic epistemology of logic that
had predominated from Aristotle to Kant, is accordingly in particular motivated to ascribe
to logic not only psychological but also ontological significance (in Frege’s terminology,
significance not only as “laws of thought” but also as “laws of truth,” i.e. as something
like the most general laws of nature).90
I say “for the most part” because I would not rule out the possibility of certain very
general continuities with, and debts to, Hegel in this area. For example, Hegel had argued
that the apparent subject-predicate form of all propositions in certain cases masks a
deeper real structure (see his famous discussion of the “speculative proposition” in the
preface of the Phenomenology of Spirit; and also Encyclopedia, # 166, 180). Is it too farfetched to suggest that Frege’s theory that propositions of the form “Some . . .” and “All .
. .” only appear to be subject-predicate in form, and that this appearance masks their real
structure as quantifications over variables, owes a debt to Hegel’s generically similar
position?
90
It is worth noting that besides like Frege insisting that logic has not only psychological
but also ontological significance, Hegel also like Frege accordingly emphasizes that logic
is concerned with truth (see e.g. Science of Logic, at Werke, 6:264-9). As can be seen
from Frege’s critique of Erdmann-Hegel in The Basic Laws of Arithmetic, especially
from his remarks there about Vorstellung and ergreifen, he probably recognized that he
shared this common ground with Hegel’s project to a certain extent. However, he had
probably received it from that project largely in indirect ways. One likely intermediary
here is his teacher, the neo-Hegelian Lotze. See e.g. H. Lotze, Grundzüge der Logik und
Encyklopädie der Philosophie (published posthumously in 1885) = Outlines of Logic and
of Encyclopaedia of Philosophy (Boston: Ginn and Company, 1887), pp. 5-6: “The forms
and laws of thought, with which we are to become acquainted, have neither a ‘merely
formal’ nor a ‘perfectly real’ significance. They are neither mere results of the
organization of our subjective spirit, without respect to the nature of the objects to be
known, nor are they direct copies of the nature and reciprocal relations of these objects.
They are rather ‘formal’ and ‘real’ at the same time. That is to say, they are those
subjective modes of the connection of our thoughts which are necessary to us, if we are
89
45
Finally, there is one potential objection to this general line of interpretation of Frege’s
reform of logic that should be addressed. Someone who reads the development of Frege’s
own views about the nature of logic roughly in the manner of Sluga or Hilary Putnam
might object that the position that Frege champions in The Basic Laws of Arithmetic
(1893) is only a late position, but that at the time of the Begriffsschrift (1879) he himself
held a Kantian conception of the nature of logic as laws of thought –91 so that nothing can
be inferred from the later work about his original motives for his reform of logic in the
earlier work. However, such a reading of Frege’s own development seems to me
mistaken. It is true that in the Begriffsschrift he describes logical laws as “laws of thought
[Gesetze des Denkens].”92 But then, he does so later in The Basic Laws of Arithmetic as
well, where he in effect carefully distinguishes between a Kantian way of interpreting this
expression (which he repudiates) and a way of interpreting it that is conformable with a
conception of logical laws as very general laws concerning reality (which he accepts). 93
So his mere use of this expression in the earlier work establishes nothing. Moreover, on
closer inspection the Begriffsschrift is pretty clearly already committed to the latter of the
two conceptions of logical laws just mentioned, for it characterizes logical laws as
“abstracting from the specific constitution of things [von der besonderen Beschaffenheit
by thinking to know the objective truth.” Another likely intermediary between Hegel and
Frege here is Trendelenburg, who discusses both Hegel’s and Aristotle’s ontological
conceptions of logic in his Logische Untersuchungen.
91
See Sluga, Gottlob Frege, p. 108; H. Putnam, “Rethinking Mathematical Necessity,” in
Words and Life (Cambridge, Mass.: Harvard University Press, 1996).
92
G. Frege, Begriffsschrift und andere Aufsätze (Darmstadt: Wissenschaftliche
Buchgesellschaft, 1964), p. x. Three years later Frege similarly describes them as “forms
of thought [Denkformen]” (ibid., p. 114).
93
Grundgesetze der Arithmetik, pp. xv-xvi.
46
der Dinge absehend].”94 In addition, this interpretation is confirmed by the 17 Kernsätze
zur Logik dating from around the same period as the Begriffsschrift (Michael Dummett
even dates them earlier).95 For Frege there already attacks any psychologistic conception
of logic (“17. The laws of logic cannot be justified through psychological investigation”)
and instead in effect already conceives them as laws of truth (“12. Logic only begins with
the conviction that there exists a distinction between truth and untruth”).96 In short,
Frege’s own position in The Basic Laws of Arithmetic was already his own position when
he first revolutionized logic in the Begriffsschrift. It is therefore not unreasonable to
assume that what the former work reveals to us about the intellectual influences on him
and his motives also tells us much about those behind the latter work.
*
As I mentioned earlier, Schlegel and Hegel both championed a thesis that skepticism is
fundamental to philosophy, i.e. essentially involved at its beginning and also as it
continues to develop. In “Does Every Genuine Philosophy Have a Skeptical Side?” I
have defended a version of this thesis. However, the thesis might still seem to run into a
counterexample in the case of formal logic. For was not this part of philosophy at least
both from the start and throughout its development more or less independent of
skepticism?
94
Begriffsschrift und andere Aufsätze, p. ix, my emphasis; cf. p. x.
M. Dummett, “Frege’s Kernsätze zur Logik,” in his Frege and Other Philosophers
(Oxford: Clarendon Press, 1991).
96
G. Frege, Schriften zur Logik und Sprachphilosophie (Hamburg: Felix Meiner, 2001),
p. 24.
95
47
It would not be fatal to the Schlegel-Hegel thesis if logic did turn out to be independent
of skepticism. For from its very inception, it has been disputed whether logic is part of
philosophy (Aristotle and especially the Peripatetics tended to say no, the Stoics in
general said yes).97 And still today, the character of logic’s subject-matter warrants such
doubts: perhaps it should really be classified as part of mathematics, or as one of the
sciences, or as sui generis? However, on balance it does nonetheless seem reasonable to
consider logic to be part of philosophy. And so it would at least strengthen the SchlegelHegel thesis if it could be defended in the case of logic.
I certainly hope that the historical account sketched in this paper has been of some
intrinsic interest. But in addition, it seems to me interesting because it can help towards
defending the Schlegel-Hegel thesis in the area of logic. In fact, Schlegel himself already
performed part of that task. It will be recalled that Kant had held that the logic of his own
day was essentially unchanged since Aristotle. That view was no doubt too simplistic, but
on any plausible account Aristotle was at least one of the main founders of the discipline.
Now, contrary to a fairly widespread and tempting impression that Aristotle founded the
discipline in blissful independence of any concerns about skepticism (say, just with
constructive scientific purposes in mind), Schlegel argues in his 1804-6 Cologne lectures
on philosophy that Aristotle in fact did so largely in response to the Sophists, i.e. in
response to their use of argument for epistemologically subversive, or skeptical, ends.98
This is a very plausible claim. For example, Aristotle’s discussion and defense of the
laws of contradiction and excluded middle in Metaphysics, book gamma is to a large
extent directed against Sophists such as Protagoras who, in Aristotle’s view, had sought
97
98
See Kneale and Kneale, The Development of Logic, esp. p. 139.
KFSA, 12:312, 316; 13:192 ff., 210-11.
48
to subvert them. Moreover, especially when one keeps in mind that Aristotle developed
his logic against the background of a Socratic-Platonic project of both borrowing from
and sharply critiquing epistemologically subversive Sophistic forms of argument (see, for
example, Plato’s Euthydemus), it seems plausible to say, in the general spirit of
Schlegel’s interpretation, that Aristotle’s On Sophistical Refutations and Topics, rather
than being (as it were) merely a tail wagged by the dog of the Prior Analytics (with its
theory of the syllogism) and the Posterior Analytics (with its application of logic for
scientific purposes) are in fact something more like the dog that wags the tail. That is, it
seems plausible to say that the former works’ central project of diagnosing, defusing, and
countering the epistemologically (and otherwise) subversive arguments of the Sophists
was not merely a happy byproduct of the latter works but one of their driving purposes.
The chronological priority of the former works over the latter in the history of Aristotle’s
development speaks in favor of this, for example.
Now Kant was actually mistaken in thinking that the logic of his own time was almost
entirely due to Aristotle, for the Stoics had contributed to it heavily as well.99 (The
importance of their contribution, especially that of Chrysippus, was only really
recognized in the twentieth century.100) However, here again the Schlegel-Hegel thesis
holds up well on reflection. For Stoic logic, which developed largely in independence
from Aristotle, had its origins in the subtle paradox-mongering of the Eleatics,
Parmenides and Zeno, and of the Megarians, especially Eubulides (inventor of the Liar
See Kneale and Kneale, The Development of Logic, pp. 175-6, 355.
For example, Prantl in his Geschichte der Logik im Abendlande (1855-70) still
strikingly fails to recognize it (see esp. 1:408).
99
100
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Paradox, among several others).101 So this strand of logic ultimately leads back to a sort
of skepticism as well.
But our historical investigation in this article has also supplied a further important part
of the answer to the threat to the Schlegel-Hegel thesis that seems to arise in the case of
logic: After the ancient Greeks, the second great revolution in the history of logic, namely
Frege’s development of quantification theory, with its enormous extension of insight into
logical laws and forms of inference, as well as its profound implications for such
disciplines as mathematics and eventually computer science, might again appear at first
sight to have taken place in independence from skepticism. However, I hope that this
article has shown that on the contrary it is very likely that the new awareness of
traditional logic’s lack of adequate epistemological defenses and of its consequent
vulnerability to skepticism, and the resulting program of revolutionizing logic in order
both to exploit and to cure this situation, that emerged with Bardili, Schlegel, and Hegel
at around the turn of the nineteenth century constituted an essential part of the intellectual
background within which Frege’s ultimately much more important revolutionary
endeavors in logic were subsequently able to emerge.
101
Cf. Kneale and Kneale, The Development of Logic, ch. 3.
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