1 Chapter One Introduction This book proposes an analysis of the notion of thinking (das Denken) in Gottlob Frege and argues that this notion has not been sufficiently investigated. In fact, the term “thinking” is disregarded so much as to be forgotten: it does not even deserve to be mentioned in the index of Michael Dummett’s Frege: Philosophy of Language and it does not appear in the indexes of the books of some well-known critics of Dummett such as Hans Sluga or Gregory Currie.1 This is not surprising given the influence of the conviction that the study of thinking is psychological and thus of no interest to logic. It is widely believed that Frege did not regard human mental processes as philosophically relevant because of his often declared anti-psychologism. However, this reading does not explain why Frege says so much about thinking both in his earlier writings such as Begriffsschrift (1879) and “On the Scientific Justification for a Conceptual Notation” (1882), and in his later works such as “Der Gedanke” (1918-1919) and “Sources of Knowledge of Mathematics and the Mathematical Natural Sciences” (1924-1925). As a matter of fact, Frege devoted much attention to human mental processes and
Transcript
1
Chapter One Introduction
This book proposes an analysis of the notion of thinking
(das Denken) in Gottlob Frege and argues that this notion has not
been sufficiently investigated. In fact, the term “thinking” is
disregarded so much as to be forgotten: it does not even deserve
to be mentioned in the index of Michael Dummett’s Frege: Philosophy of
Language and it does not appear in the indexes of the books of
some well-known critics of Dummett such as Hans Sluga or Gregory
Currie.1 This is not surprising given the influence of the
conviction that the study of thinking is psychological and thus
of no interest to logic. It is widely believed that Frege did
not regard human mental processes as philosophically relevant
because of his often declared anti-psychologism.
However, this reading does not explain why Frege says so
much about thinking both in his earlier writings such as
Begriffsschrift (1879) and “On the Scientific Justification for a
Conceptual Notation” (1882), and in his later works such as “Der
Gedanke” (1918-1919) and “Sources of Knowledge of Mathematics and
the Mathematical Natural Sciences” (1924-1925). As a matter of
fact, Frege devoted much attention to human mental processes and
2
to their important role in grasping thoughts and in the
construction of an objective science. Focusing on what he says
about thinking provides insight into his views on the roles of
language in expressing thoughts and in fostering the development
of human knowledge. The main goal of this work is to fill the
gap that most secondary literature on Frege has left open by not
paying close enough attention to what Frege says about thinking.
In this book we provide numerous quotes from Frege’s works,
which should convince even the most skeptical critics that Frege
did indeed pay attention to thinking and had some important
things to say about it. Our hope is that this book will convince
these critics that our effort has been worthwhile.
Frege and the Origin of Analytic Philosophy
The quantity and breadth of scholarship on Frege is
remarkable and credit must be given to Dummett’s extensive study
of Frege’s writings for stimulating such widespread interest in
the work of this German mathematician, logician and philosopher.
Dummett’s Frege: Philosophy of Language2 has inspired heated debates
and provoked the reactions of many.3 According to Dummett, Frege
3
rebels against the Cartesian tradition, which takes epistemology
to be the fundamental branch of philosophy, in order to establish
a new analytic tradition where “the first task, in any
philosophical inquiry, is the analysis of meanings.”4 Our main
goal is to bring to light some concerns of Frege’s which so far
have not been given sufficient attention, namely his concern with
different types of thinking, his interest in epistemological
matters, and his views on the relationship between language and
thinking and language and thought, respectively.
The above three themes are worth discussing not only to
obtain a more complete and accurate interpretation of Frege’s
views, but also to assess one of Dummett’s most intriguing
claims, i.e., the tracking of the origin of analytic philosophy
to Frege. In several of his writings, Dummett argues that Frege
was the initiator of analytic philosophy and of the so called
linguistic turn.5 According to Dummett, Frege generated a shift
from a mostly epistemological or Cartesian focus on the
philosophy of thinking, understood as an inquiry concerning the
mental processes of human beings, which is connected with the
philosophy of mind and which is deeply affected by psychological
4
considerations, to the philosophy of thought.6 Frege referred to
the philosophy of thought as ‘logic’ and characterized it by the
concern with “the question what it is to have a thought, and with
the structure of thoughts and their components: what it is for a
thought to be about an object of one or another kind, what it is
to grasp a concept and how a concept can be a component of a
thought. … the philosophy of thought could not emerge as a
distinguishable sector of the subject until it had been
disentangled from the general philosophy of mind.”7 Dummett is
not the first to ascribe to Frege a central role in such an
important theoretical development as the birth of analytic
philosophy. In the Preface to Our Knowledge of the External World,
i.e., a set of lectures published in 1914, Bertrand Russell
claims that “the first complete example” of analytic philosophy,
which he describes as “the logic-analytic method in philosophy,”
“is to be found in the writings of Frege.”8 Thus, Russell would
have agreed with Dummett on Frege’s merit as the initiator of
analytic philosophy. For Russell, Frege is the initiator of the
“logic-analytic method” that relies on the formal features of
reasoning; Russell regarded Wittgenstein, and not Frege, as the
5
initiator of the linguistic turn in philosophy. To properly
understand and evaluate Dummett’s historical reconstruction –
possibly the claim of Dummett’s that has generated widest
controversy9 – we need to consider more closely how Dummett
defines the distinctive features of analytic philosophy and the
philosophy of thought.
In Origins of Analytical Philosophy, Dummett maintains that “what
distinguishes analytical philosophy, in its diverse
manifestations, from other schools is the belief, first, that a
philosophical account of thought can be attained through a
philosophical account of language, and, secondly, that a
comprehensive account can only be so attained.”10 A combined
statement of these same theses which is dubbed “the fundamental
axiom of analytical philosophy,” is stated as the claim that “the
only route to the analysis of thought goes through the analysis
of language.”11 Analogous statements of these theses appear as
the claim that “the analysis of thought both can and must go via
the analysis of its linguistic expression” or as the claim of
“the priority of language over thought in order of
explanation.”12 We take all these formulations of the axiom of
6
analytic philosophy to assert that a core feature of analytic
philosophy is the acceptance of the thesis that a philosophical
account of language is both necessary and sufficient to provide a
philosophical account of thought. In other words, in analytic
philosophy, an account of language is the only way to obtain a
‘comprehensive’ account of thought.
In reading Dummett’s theses, Gérard Bornet stresses the
independence of the account of language and of the account of
thought as crucial in order to understand Dummett’s claim
concerning the linguistic turn at the origin of analytic
philosophy; Bornet also argues that, if we follow Dummett’s
criterion of linking the birth of analytic philosophy to the so
called ‘linguistic turn,’ then we should regard George Boole as
the true initiator of analytic philosophy whereas Frege merely
developed the “technical apparatus” to support the linguistic
turn.13 We do not enter into this last aspect of the debate
concerning the origin of analytic philosophy and we devote a more
extended discussion to Boole’s philosophical views in the next
chapter. We only note that Dummett’s theses as stated in his
1993 book and the comments that directly follow their statement
7
do not suggest a stress on the independence of the two accounts
but rather on their tight interconnection; for Dummett cites
Gareth Evans’ “posthumous book [1982], which essays an account,
independent of language, of what it is to think about an object”
as almost making Evans “no longer an analytic philosopher”
although he still belongs to this tradition only because he
appeals “to certain writers [i.e., Russell, Moore, and Frege]
rather than to certain others.”14 Thus, Bornet seems to be wrong
in ascribing to Dummett the assumption of independence between
the accounts of language and thought: for Dummett, it is exactly
the assumption of their inextricable dependence that
characterized analytic philosophy, its ancestors as well as its
current practitioners. Yet, there is also something intuitively
right in Bornet’s remark on the need for some independence of the
account of language and the account of thought since if they were
not in some way distinct, neither one could provide any insight
into the other. At the end, we believe that our statement of
Dummett’s theses captures Dummett’s position more accurately than
Bornet’s assumption of the independence of thought and language
does.
8
In Origins of Analytical Philosophy, Dummett famously claims that
Frege was “the grandfather of analytical philosophy.”15 The main
motivation for tracing back to Frege the origin of analytic
philosophy did not change significantly for Dummett over time,
although the Origins description of analytic philosophy is more
broadly and rigorously characterized. Yet, Dummett never claims
that Frege explicitly stated the above theses,16 for he is well
aware that Frege often claimed that the subject matter of his
work focused on thoughts, not on sentences,17 and described his
work as a struggle against language.18 Of course, ‘struggling
against language’ may involve a critical reflection on language,
which is at the core of Dummett’s definition of analytic
philosophy. Ludwig Wittgenstein and Gilbert Ryle were often
‘struggling against language’ in their philosophical reflections
but they are usually regarded as analytic philosophers. Yet,
Frege is also critical of the problems ordinary language creates
for logical thinking. So, on what grounds does Dummett retrace
the birth of analytic philosophy to him?
Dummett’s linking of analytic philosophy to Frege is
complex. We have identified three main reasons for Dummett’s
9
claim. First, in Dummett’s view, Frege’s philosophy is
characterized by the above ‘axiom of analytical philosophy.’ We
indirectly discuss this claim especially in chapter two, which is
devoted to Frege’s anti-psychologism, and chapter five, in which
we argue that Frege’s attitude toward language and its relation
to thinking is more nuanced than the above two theses suggest.
Second, in Dummett’s reading, Frege’s work was at the origin of
analytic philosophy because Frege had very limited interest in
epistemological concerns and thus abandoned the historical
philosophical focus on epistemology or the philosophy of thinking
in favor of a philosophy only focused on thought. Others have
already called in question this claim of Dummett’s and pointed
out that, at least with regard to the realm of mathematical and
logical cognition, Frege was deeply aware of, and wrestled with,
core epistemological issues, such as the grasping of abstract
entities.19 In chapter four we provide evidence that Frege
wrestled with some core epistemological issues, that still
dominate debate in contemporary research, and that he had some
novel ideas about them. Finally, one of Dummett’s main reasons
for linking Frege’s philosophical views to the origin of analytic
10
philosophy is Frege’s stern separation of philosophy and
psychology and his imperative to disallow the use of this latter
for any normative or philosophical reflection. It would be
foolhardy to deny that Frege wrote many critical comments on the
appeal to psychology in inquiries on the justification of
mathematical or logical truths. Yet he took human thinking
seriously; he wrote about it more extensively than it is usually
acknowledged; he distinguished thinking from thoughts, he pointed
out the occurrence of distinct forms of thinking, and reflected
on the relationship between thinking and language pretty much
throughout his whole writing career. We bring new attention to
this theme in order to better circumscribe the features of
Frege’s psychologism and to show how it was grounded in a complex
view of different types of human thinking. This discussion is
developed mostly in chapters two and three.
The analysis of language might plausibly be the only way to
attain the analysis of the content of propositions, but it is
much less plausible to say that it is the only way to attain an
analysis of the process of thinking or of the objects of
thinking; unless, of course, some arguable assumptions are made,
11
e.g., that there cannot be any thinking without language. In the
fifth chapter, we show that Frege discussed these very questions
and believes that language plays a role in fostering thinking.
He does not exactly claim that an analysis of language is a
necessary tool for an analysis of thinking but language is said
by him to be a necessary tool for a certain type of thinking,
namely conceptual thinking as human beings carry it out.
The Scope and Structure of This Book.
We cannot claim that Frege was interested in the mental
process of thinking without discussing the objection that our
main thesis conflicts with his deeply seated anti-psychologism.
This is what we do in the second chapter, in which we review
different understandings of the notion of psychologism and argue
that we do not need to deny Frege’s anti-psychologism. The
discussion in our third chapter focuses on Frege’s three distinct
notions of thinking; in particular, we claim that he held that
there is one form of thinking that can grasps thoughts and that
is not the subjective mental process whose content are ideas, but
a process of thinking that, although it cannot be considered
12
either true or false as no act of thinking can, yet has a deep
connection with truth. In this chapter, we present our main
argument in support of the claim that Frege’s belief in the
possibility of an objective human science can be granted only if
we allow for a notion of thinking that is neither merely
psychological nor merely logical. We call this a type of
logical-psychological thinking that aspires to emulate logical or
pure thinking and to transcend psychological thinking, but that
does not equate or collapse in either one of them. In some
passages Frege indicates that strictly speaking we can never be
sure that we grasp the same meaning, the same definition or the
same thoughts and that instead we have to somehow ‘guess’ what
others have in mind. 20 These passages could be taken to imply
that thinking is wholly and only subjective and that there cannot
be any objective component in human thinking. However, Frege’s
trust in a common system of science and in a shared wealth of
thoughts among humans would be utterly unfathomable if there were
no form of thinking that takes us beyond the thoroughly
subjective world of ideas. We devote the fourth chapter to
arguing that Frege’s interest in thinking is supported by the
13
central role that thinking plays in grasping thoughts and in thus
connecting the subjective world of ideas to the objective world
of thoughts. Finally, in the fifth chapter, we argue that
language plays an epistemic role for Frege both in its necessary
role for thinking and in its representational role for the
expression of thoughts.
Some of the most influential scholars of Frege’s work, such
as Dummett, Sluga, and Carl have discussed the notion of thinking
in connection with the historical context in which Frege
developed his philosophical views on logic and especially his
anti-psychologism, namely in scholarly discussion of historical
figures such as Wilhelm Wundt, Hermann Lotze, or Boole, who are
credited for having influenced Frege’s philosophy by providing a
foil for his critique of psychologism. We believe that Frege’s
discussion on thinking is deeply influenced by these thinkers’
concerns; even if he ended up with positions quite different from
theirs, keeping in mind their preoccupations and problems helps
to bring to light the similarity in Frege’s treatment of thinking
in his own discussion.
14
We are not alone in claiming that Frege paid attention to
epistemically significant notions such as thinking. Wolfgang
Carl’s Frege’s Theory of Sense and Reference Its Origins and Scope remains a
lone work with whose perspective we are very sympathetic. Our
reading of Frege owes much to Carl’s reading. Even if we do not
agree on everything Carl wrote, we share his appreciation of
Frege’s interest in the process of human thinking, but our
analysis of Frege’s notion of thinking goes further than Carl’s.
Among the works published in English so far, there has not been
any discussion devoted only to the notion of thinking and to the
role it plays in Frege’s views on the laws of logic, on
objectivity, science and human knowledge;21 furthermore, we
identify different types of thinking in Frege’s discussion and
point out that thinking is a central player in his defense of the
possibility of objective knowledge. Carl seems to be the only
scholar reading some passages in Frege as we do; since his work
is rarely mentioned in the vast collection of secondary
literature on Frege and seems to have been less influential than
Dummett’s, we would like to reiterate and support with new
evidence some points originally made for the first time by Carl.
15
We hope that a side effect of our discussion will be a broader
acknowledgment of Carl’s unique contribution to the
interpretation of Frege’s thought.
As it will be apparent from the very next chapter, we cite
extensively from Frege’s writings.22 This practice seems to be
necessary to anyone who wants to argue that an author had an
interest in a topic that is rarely associated with such an
author’s philosophy. We believe that these extensive quotations
from Frege’s writings enrich and strengthen rather than interrupt
our discussion, although it may not be a dominant practice in the
secondary literature on Frege; many authors provide overviews of
Frege’s views based on his writings but not directly or
explicitly connected with specific passages. In our citations
from Frege’s writings, at times we cite from works that were
composed at different times in his career. We believe that this
is a legitimate practice in Frege’s case, because there is
remarkable continuity on some major themes in his thought. We
are not alone in thinking this: Dummett stresses a certain
consistency in Frege’s work throughout his life. In contrast to
thinkers such as Russell or Wittgenstein, “Frege’s work can be
16
treated as a unity.”23 Moreover, “views expressed in the mature
period must be taken as having more weight than earlier ones with
which they conflict, and later formulations of old views as
having more weight than the earlier formulations;” exactly
because “Frege worked so single-mindedly at the perfection of his
theories, every change ... must be regarded as fully
deliberate.”24 According to Dummett, the main mistake that can
be made is “to interpret what he said in his mature period in the
light of his earlier writings”25 for “it is unhistorical to read
back into Frege ideas which originated only with his
successors.”26 The majority of Frege’s writings supports the
claim that his views on some central matters changed very little
during his life time. Dummett’s principles of exegesis laid out
above seem highly sensible to us and we strive to abide by them
in our discussion. Accordingly, we will make notice of internal
developments in Frege’s views only when appropriate.
This is not a book in the History of Philosophy or in the
History of Analytic Philosophy; its approach is not historical,
we do not look at all that Frege wrote and we do not pay much
attention to the targets of his views with the lone exception of
17
next chapter’s discussion of Boole’s thought. We focus on the
notion of thinking, because Frege’s comments on thinking are
interesting and salient, and we attempt to bring attention to
them as they have not been often mentioned or discussed. We do
not address directly the question of what is analytic philosophy
or who should be recognized as its initiator although we realize
that, by bringing to light Frege’s views on thinking, we may
indirectly affect the plausibility of attributing a linguistic
turn to his philosophical approach. This is a book on Frege’s
philosophy that touches on some features of analytic philosophy;
it is not a book on analytic philosophy that addresses some
aspects of his philosophy.
We do not look at all secondary literature on Frege: it
would be pretentious to try to do so. It is puzzling that so
much secondary literature is produced on the thought of a writer
whose philosophical work has never been so far reaching or
theoretically rich as René Descartes’s or Immanuel Kant’s. It is
indeed surprising that so much critical work is published on
Frege, since he never dealt explicitly or systematically with
tripartite philosophical issues such as moral values, causation,
18
or the nature of reality. The rich production of secondary
literature on Frege’s views suggests that the influence of a
philosopher’s thought should be measured on the basis not only of
what they have written but also of the works that they have
inspired. Frege’s writings have had a much broader effect than
could be expected; Wittgenstein’s thought is another excellent
example of this phenomenon. Our book aims at enriching the
secondary literature on Frege in an area not broadly discussed.
Our focus is on Frege’s views rather than on the plurality of
interpretations that they have generated.
Some may object to the fact that we often discuss Dummett’s
interpretation of Frege’s philosophy and that Dummett’s work is
often the foil against which we characterize our positions. This
may seem an outdated exercise since Dummett’s work has already
been widely criticized. Despite our deep disagreement with some
core points of Dummett’s interpretation of Frege, we think that
his work still provides the best developed, encompassing,
systematic, and articulated effort to reconstruct Frege’s
thought. This is why Dummett is still our main interlocutor in
19
contrast to other more recent and not yet as influential
scholars.
It may also surprise some scholars that we discuss Frege’s
views on thinking independently from an analysis of the whole of
his logic or his views on sense and reference, hence in isolation
from Frege’s logicist project and his philosophy of language.
This will be particularly surprising for scholars who link
Frege’s epistemological views exclusively to his logicist
concerns. We acknowledge that we find it difficult to determine
whether Frege was first interested in the logicist project and
then in thinking or vice versa. It is however a fact that when
the logicist project fails, because of Russell’s discovery of the
contradiction in Frege’s system, Frege does not abandon his
reflections on thinking, but rather continues to develop them
with a clearer epistemological focus rather than merely in
connection with the foundation of logic and mathematics. Frege’s
thinking - if we are successful in showing that there is one such
notion - plays a role in his epistemological views, namely on his
views concerning the grasping of all thoughts. In chapter four,
we argue that, even if Frege’s interest in epistemological issues
20
originally ensued from his logicist project, he was interested in
such issues for their own sake and, interestingly enough, some of
these issues are still alive in contemporary epistemological
debates.
Since the notion of thinking is usually ignored in
discussions of Frege’s philosophy in favor of widespread
attention to the notion of thought (der Gedanke), whenever
possible we discuss thinking in its relation to thoughts.
Thoughts are claimed to play central roles in Frege’s views on
logic, semantics, philosophy of mathematics, and ontology.
Thinking on the other side is centrally mentioned mostly in
discussion of Frege’s anti-psychologism. We do not claim that
thinking replaces the notion of thought or that it plays an
analogously crucial notion as thoughts play in Frege’s logic,
philosophy of mathematics, or semantics. Our aim is not to
attack this widely shared thought-centered reading of Frege;
instead we claim that the current mainstream interpretation of
his work is incomplete because of its neglect of Frege’s many
comments on thinking and thus needs to be integrated by an
interpretation of the role of thinking in his philosophical views
21
on logic, knowledge and language. Indeed, since Frege’s thinking
is never mentioned in connection with some of the major topics of
discussion in his philosophy, it will be no surprise that our
book will only marginally deal with such major topics; we will
not talk about Frege’s logical and symbolic innovations, or about
his seminal distinction between sense and reference, about his
philosophy of mathematics or about his more or less contested
role in the history of analytic philosophy. Many valuable books
have already been written on these topics, but no book has yet
discussed Frege’s notion of thinking in connection to his
philosophy of logic, his epistemology, his views on language, or
the relationship between Frege’s anti-psychologism and Boole’s
alleged psychologism. Perhaps what we say about Frege’s notion
of thinking in connection with these subjects should lead to a
reconsideration of the place of his views in the development of
20th century analytic philosophy, but this is not a topic we can
discuss in earnest in this book.
Finally, it will be clear that we find Frege’s thought
interesting and stimulating; so do many others scholars, witness
the breadth and richness of the secondary literature on Frege.
22
Yet, working on an author does not mean idealizing his views or
accepting them in their entirety. Frege left many questions
unanswered or only partially answered; some will emerge from our
discussion. The fact that we devote time and effort to bringing
to light a side of his views that is usually not discussed does
not mean that we find Frege’s views in general, and in particular
on thinking, perfectly coherent or flawless; neither do we
implicitly believe that his views are always better than the
views of other thinkers we do not discuss. Our goal is to bring
to light something new, i.e., an aspect of his thought that so
far has not been given sufficient attention.
Das Denken and der Gedanke
One reason that might have led to the under-evaluation of
the role of thinking in Frege’s views is the fact that many,
although certainly not all, readers of Frege rely on the English
translations of his main works, which frequently obscure the fact
that he used two distinct German terms for thinking and thoughts,
i.e., das Denken and der Gedanke.
23
The practice of translating ‘das Denken’ as ‘thought’ has
greatly diminished the number of passages in which it is apparent
that Frege discusses thinking and has given unwarranted support
to the claim that he promoted the philosophy of thought in
contrast to the philosophy of thinking.27 More significantly, it
has obscured the presence in Frege of a notion of thinking that
is not of a merely psychological nature. In this book, we have
routinely amended the official translations of Frege, by
replacing ‘thought’ with ‘thinking’ every time in German Frege
used ‘das Denken’ and limited the use of ‘thought’ to those places
where ‘der Gedanke’ occurs in German. Since it is our goal both to
provide textual evidence that Frege discussed das Denken,
i.e.,‘thinking,’ and to reflect his use of das Denken and der
Gedanke more accurately, we italicize the word ‘thinking’ every
time we use it instead of ‘thought’ in variance with standard
translations of his writings.28
In the late 1890’s and in the last years of his life, Frege
explicitly acknowledged a distinction between the notion of
thinking, das Denken, and the notion of thought, or der Gedanke.
However, he did not contrast das Denken and der Gedanke throughout
24
the whole development of his career. Begriffsschrift and the articles
written shortly thereafter, in which Frege defends his conceptual
notation, show that he was interested in thinking before he
developed his notion of thought or der Gedanke. It makes thus
sense to infer that the notion of thinking is philosophically
interesting for Frege and autonomous from the notion of thought,
although after 1892 and the writing of “On Sense and Reference,”
when he did develop his notion of der Gedanke as an objective
abstract entity, this latter notion might have provided Frege
with an appropriate term of contrast for das Denken or the mental
process of thinking.29
Frege wanted to avoid any confusion between thoughts, i.e.,
the content of propositions, and thinking, i.e., the mental
process.30 Moreover, he was deeply aware of the need for a
consistent use of the words der Gedanke and das Denken to denote
thoughts and thinking, respectively:
What if it is objected that I am attaching to the word
‘thought’ [“Gedanke”] a sense that it does not ordinarily
have, and that other people understand by it an act of
thinking [eine Tat des Denkens], which is obviously private
25
and mental? Well, the important thing is that I remain true
to my way of using it; whether this agrees with the ordinary
use is of less importance. It may well be the case that
people sometimes understand by the word ‘thought’ an act of
thinking – in any case this is not always so* – and such an
act cannot be true.31
Here Frege provides an almost stipulative definition of der
Gedanke and declares his intention never to use this term to
denote an act of thinking, which he instead denotes with the term
das Denken. The awareness of the need to keep the use of these
two terms clearly distinct might have increased after the
completion of the first volume of Grundgesetze where Frege
explicitly acknowledges that what he used to call “judgeable
content,” for example in Begriffsschrift, has now split into what he
now calls thought and truth-value. He also plans on being
consistent in using these terms. From this passage, we can glean
that he believed that the use of der Gedanke by other people
created the same problem that the English word “thought” creates
on the part of English speakers: sometimes denoting the content
of propositions and sometimes denoting the mental process of
26
thinking. At the end of the passage, Frege restates his well-
known thesis that thoughts and thinking have different properties
since truth appropriately belongs to thoughts, but not to acts of
thinking.
Most of the times, in translations of Frege’s writings,
there is no ambiguity between thoughts and thinking. Take for
example the following passage in which Frege is clearly talking
about thoughts as propositions: “Let Ω be a group of true
thoughts. Let a thought G follow from one or several of the
thoughts of this group by means of a logical inference such that
apart from the laws of logic, no proposition not belonging to Ω
is used. Let us now form a new group of thoughts by adding the
thought G to the group …”32 In the German original of the passage
just quoted, Frege uses the word der Gedanke throughout, and the
standard translation correctly uses the word “thought(s).” In
contrast, in the German original of the following passage, Frege
uses only das Denken and the standard translation correctly uses
“thinking” throughout: “But isn’t thinking a kind of speaking?
How is it possible for thinking to be engaged in a struggle with
speaking? Wouldn’t that be a struggle in which thinking was at
27
war with itself? Doesn’t this spell the end to the possibility
of thinking?”33
However, sometimes the duplicity of meaning of the English
word “thought” introduces an ambiguity in the translation, which
is not present in the original text. At the beginning of the
last paragraph in “What is a Function?”, Frege writes, “Das
Streben nach Kürze hat viele ungenaue Ausdrücke in die
mathematische Sprache eingefürt, und diese haben rüchwirkend die
Gedanken getrübt and fehlerhafte Definition zuwege gebracht.”34
The standard translation reads, “The endeavour to be brief has
introduced many inexact expressions into mathematical language,
and these have reacted by obscuring thought and producing faulty
definitions.”35 Die Gedanken in the original is correctly
translated with “thought” and not “thinking.” However, in
German, die Gedanken is plural, while in the English translation
“thought” is singular and thus ambiguous, possibly denoting the
content of a proposition or the process of thinking. The result
is that it is possible to read this passage as one in which Frege
is charging the drive for brevity in mathematical language of
having fostered the adoption of imprecise expressions, which are
28
responsible for clouding the process of thinking and generating
faulty definitions. Yet, if Frege is as careful as he claims to
be about the usage of der Gedanke and das Denken, this cannot be the
correct meaning of this sentence. Instead, the whole paragraph
concerns the obscurity and falsehood of thoughts or propositions
generated by a faulty process of definition. A more literal
translation would read, “The endeavour to be brief has introduced
many inexact expressions into mathematical language, and these
have reacted by obscuring [the] thoughts {die Gedanken, or the
contents of propositions} and producing faulty definitions.” It
is the obscurity of the thoughts, not the clouding of the process
of thinking that is a consequence of the excessive brevity of
definitions. What follows this passage renders explicit that
Frege is indeed talking about propositions (die Gedanken) rather
than of thinking (das Denken), for he continues, “Mathematics
ought properly to be a model of logical clarity. In actual fact
there are perhaps no scientific works where you will find more
wrong expressions, and consequently wrong thoughts, than in
mathematical ones.” The terms Frege uses here parallel those he
uses in the first sentence: Ausdrüche and Gedanken, “expressions”
29
and “thoughts:” both are found in mathematical works, both are
labeled as schiefe, i.e., as false, defective, wrong.
Problems arising from this type of ambiguities persist in
recently published research and even among careful scholars who
do not trust the official English translations of Frege’s
writings to express his views faithfully.36 The significance of
these misinterpretations of Frege’s views on thinking and
thoughts may be debatable, but this lack of precision in keeping
separate thoughts and thinking clearly does not match the care
with which Frege distinguished between der Gedanke and das Denken.
Finally, even philosophers who see the occurrences of these two
German terms do not ascribe to them serious philosophical
significance.
Although we cannot point out all the passages we have found
where das Denken has been translated with ‘thought’ and not
‘thinking,’ it is worth mentioning this other passage from
Grundgesetze because in the most recent translation of it, Frege’s
choice of terms has been fortunately more carefully heeded.
Montgomery Furth translated this passage as follows: “[w]e cannot
reject this law – of Identity, for example; we must acknowledge
30
it unless we wish to reduce our thought {unser Denken} to
confusion and finally renounce all judgment whatever.”37 In
Furth’s translation, the singular “thought” suggests the correct
notion of “thinking.” In the new complete translation of
Grundgesetze this passage more explicitly reads: “we cannot
discard this law – of identity, for example – but have to
acknowledge it if we do not want to lead our thinking into
confusion and in the end abandon judgment altogether.”38
The unfortunate use of the English word ‘thought’ to
translate both das Denken and der Gedanke means that if we take into
account only the occurrences of the term “thinking” in the
English translations of Frege, it does seem indeed that he wrote
very little about the mental process of thinking. The problem is
that in the classic English translations of Frege’s writings the
term “thinking” was used with rare exceptions only when it was
obvious that Frege was talking about the psychological and
subjective process of thinking; this was of course an accurate
translation of das Denken because he did use this term to denote
the subjective actual mental processes of thinking and we know
that he believed that these subjective mental processes were of
31
no interest to logic. However, there are also passages in which
Frege used das Denken when he was not discussing specific
individual mental processes, but thinking as a process with
philosophical and logical relevance. This is the main thesis we
defend in this book.
One further note on the translation of das Denken: in several
passages Frege uses the expression “das wirkliche Denken,” which is
often translated in English as “thinking as it actually occurs.”
The German original expression, which can be literally rendered
as “the actual thinking,” leads to an implicit contrast with “das
reine Denken,” or “the pure thinking,” which appears for example –
and quite significantly - in the subtitle of the Begriffsschrift.
This contrast is important to reach a thorough understanding of
Frege’s views on thinking. For Frege, thinking is not always the
subject matter of psychology: specific subjective mental
processes of thinking, or instances of actual thinking, are the
concern of psychology. However, there is also another type of
thinking, which Frege calls pure thinking {reine Denken} and which
is the proper object of the logicians’ and philosophers’
reflection. Thus, translating “das wirkliche Denken” as “actual
32
thinking” in contrast with “das reine Denken” or “pure thinking”
suggests the possibility of different types of thinking, which
the expression “thinking as it actually happens” does not
suggest. We will thus adapt our translations of Frege’s passages
to this further stipulation.
1. Hans Sluga, Gottlob Frege (London: Routledge, 1980); Gregory Currie,
Frege, An Introduction to His Philosophy (Brighton: The Harvester Press, 1982).
Edward Kanterian’s recently published introduction to Frege
uncharacteristically lists in the index “thinking” together with
“thought.” See Kanterian, Frege A Guide for the Perplexed (London and New
York: Continuum, 2012), 248. Although we argue that keeping
“thinking” and “thought” carefully distinct is crucial for a correct
understanding of Frege’s views, it is encouraging to see that Frege’s
“thinking” (no pun intended) is occasionally noticed.
2. Michael Dummett, Frege: Philosophy of Language (London: Duckworth,
1973).
3. See among others Sluga, Frege; Currie, Frege; Wolfgang Carl, Frege’s
Theory of Sense and Reference (Cambridge, UK: Cambridge University Press,
1994).
4. Dummett, Frege: Philosophy of Language, 667.
5. Dummett, Frege: Philosophy of Language, 665-684; The Interpretation of Frege’s
Philosophy (London: Duckworth, 1981a), 39; “Introduction” to the
Italian Edition of Frege, G., Logical Investigations (Milan: Guerini,
1988), 25-37, 35; Origins of Analytical Philosophy (London: Duckworth, 1993),
4-14, 22, 26, 127-128.
6. It may be claimed that Dummett’s representation of the history of
philosophy from Descartes to Frege is a mere caricature of the
development of philosophy in that period. We concede this point, but
a more in depth discussion of the views of Descartes is not our focus
here.
7. Dummett, Origins, 129.
8. See Russell, Our Knowledge of the External World (London: Allen & Unwin,
1926),7.
9. See Sluga, “Frege and the Rise of Analytical Philosophy,” Inquiry
18 (1975): 471-87; “Frege as a Rationalist,” in Studien zu Frege, Volume
I, Logik und Philosophie der Mathematik, ed. Matthias Schirn, Problemata,
no. 42 (Stuttgart and Bad Cannstatt: Frommann-Holzboog 1976), 27-47;
“Frege’s Alleged Realism,” Inquiry 20 (1977): 227-42; Frege, 1-6; Stuart
Shanker, “Review of Michael Dummett ‘Frege: Philosophy of language’”
Dialogue 21 (1982): 565-571; Hans-Johann Glock, “Dummett on the Roots
of Analytical Philosophy,” Mind 98 (1989): 646-49; Johannes Brandl,
“Michael Dummett: Ursprünge der analytischen Philosophie. Ubers. von
Joachim Schulte. Frankfurt .M.: Suhrkamp 1988,” Archiv für Geschichte der
Philosophie 73 (1991): 337-344; Herman Philipse, “Husserl and the
Origins of Analytical Philosophy,” European Journal of Philosophy 2, 2
(1994): 165-184. Gideon Makin denies that Frege was primarily
interested in language, see The Metaphysicians of Meaning: Russell and Frege on
Sense and Denotation (London and New York: Routledge, 2000). Some recent
views on the origins of analytic philosophy contrast with Dummett’s
view, see Peter M. S. Hacker, “Analytic Philosophy: Beyond the
Linguistic Turn and Back Again,” in The Analytic Turn: Analysis in Early Analytic
Philosophy and Phenomenology, ed. Michael Beaney (London: Routledge,
2007): 125-141; Peter Hylton, Russell, Idealism, and the Emergence of Analytic
Philosophy (Oxford: Clarendon Press, 1990); Scott Soames, Philosophical
Analysis in the Twentieth Century, Volume 1 (Princeton, NJ: Princeton University
Press, 2003) and The Analytic Tradition in Philosophy, Vol 1: Founding Giants
(Princeton, NJ: Princeton University Press, 2014).
10. Dummett, Origins of Analytic Philosophy, 4. A more rigorous statement is
given in The Interpretation of Frege’s Philosophy, 39: “The basic tenet of
analytical philosophy … may be expressed as being that the philosophy
of thought is to be equated with the philosophy of language: more
exactly, (i) an account of language does not presuppose an account of
thought, (ii) an account of language yields an account of thought,
and (iii) there is no other adequate means by which an account of
thought may be given.”
11. Dummett, Origins, 128.
12. Dummett, Origins, 134, 148.
13. Gérard Bornet, “George Boole’s Linguistic Turn and the Origins of
Analytical Philosophy,” in The British Tradition in 20th Century Philosophy, eds.
Jaakko Hintikka and Klaus Puhl (Vienna:Verlag Hölder-Pichler-Tempsky,
1995), 236-248, 236.
14. Dummett, Origins, 5-6.
15. Dummett, Origins, 14, 26; this claim was previously stated in the
Introduction to the Italian Edition of Frege’s Logische Untersuchungen
(Milano: Guerini, 1988), 35. Notice that in an essay entitled
“Frege’s Place in the History of Philosophy,” published in the 1973
first edition of Frege Philosophy of Language, Dummett states that “Frege
can ... be considered the father of ‘linguistic philosophy,’” where
this latter is understood as ‘all philosophy which sees the key to
the analysis of concepts as consisting in the study of the means of
their expression.’ Whether or not the debate generated by Dummett’s
ascription of the origin of analytic philosophy to Frege was the
factor that caused the demotion from father to grandfather has never,
to our knowledge, been mentioned in print by Dummett.
16. Bornet also points out this fact: “Astonishingly enough, Dummett
has difficulties making Frege look like an analytic philosopher on
his own characterization.” “George Boole’s Linguistic Turn,” 236.
17. “Frege became more and more insistent that thoughts, and not the
sentences that express them, formed his true subject matter.” See
Dummett, Origins, 5. For an example of a passage in which Frege makes
this point, see Frege “Logic in Mathematics,“ in Posthumous Writings,
transl. Peter Long and Roger White (Basil Blackwell, Oxford, 1979),
206.
18. Dummett, Origins, 6. See Frege, Conceptual Notation and Related Articles
(Oxford: Clarendon Press, 1879), 106; “On the Scientific
Justification,” 83-86; “Sources of Knowledge of Mathematics and the
mathematical natural Sciences”, in Posthumous Writings (Basil Blackwell,
Oxford, 1979), 267-274, 270. For a discussion of Frege’s views on
ordinary language, see Andrew Rein, “Frege and Natural Language”
Philosophy 60, No. 234 (1985): 513-524.
19. See especially David Bell, Frege’s Theory of Judgment (Oxford, UK:
Clarendon Press 1979); Carl, Frege’s Theory; Tyler Burge, “Frege on
Knowing the Third Realm,” Mind 101(1992): 633-650; “Frege on Knowing
the Foundation,” Mind 107 (1998): 305-347; “Frege on Apriority,” in
Building on Frege New Essays on Sense,Content, and Concept, eds. Albert Newen et
al. (Stanford: CSLI. 2001), 53-87; Currie, Frege; Graciela De Pierris,
“Frege and Kant on A Priori Knowledge,” Synthese 77 (1988): 285-319;
Richard Eldridge, “Frege’s Realist Theory of Knowledge,” Review of
Metaphysics 35 (1982): 483-508; Gottfried Gabriel, “Frege’s
Epistemology in Disguise,” in Frege: Importance and Legacy, ed. Matthias
Schirn (Hawthorne, New York: de-Gruyter, 1996), 330-346; Bob Hale and
Crispin Wright, eds. The Reason’s Proper Study: essays towards a neo-Fregean
philosophy of mathematics (Oxford: Clarendon Press, 2001); Philip Kitcher,
“Frege’s Epistemology,” Philosophical Review 88 (1979): 235-262; Wolfgang
Malzkorn, “How Do We ‘Grasp’ a Thought, Mr. Frege?” in Newen, Building
on Frege,329-344; Mark Amadeus Notturno, Objectivity, Rationality and the Third
Realm (Dordrecht: Martinus Nijhoff, 1985); Sluga, Gottlob Frege; Joan
Weiner Frege in Perspective (Ithaca: Cornell University Press, 1990).
20. “In practice ... we do manage to come to an understanding about
the meanings of words. Of course we have to be able to count on a
meeting of minds, on others guessing what we have in mind.” “Logic in
Mathematics,” 207; “[W]e must be able to count on a little good will
and cooperative understanding, even guessing.” “On the Foundations of
Geometry: Second Series.” Translated by Max Black et al. In Collected
Papers on Mathematics, Logic and Philosophy, 293-340 (Oxford: Basil Blackwell,
1984), 300ff.
21. Two exceptions published in German are Markus Stepanians, Frege
und Husserl über Urteilen und Denken (Paderborn: Schöningh 1998) and Wolfgang
Künne, Die Philosophische Logik Gottlob Freges: Ein Kommentar (Frankfurt am Main:
Klostermann 2010).
22. Following a practice now fairly common, in the text we refer to
Begriffsschrift, Grundgesetze, and Grundlagen by their original German
titles. Most of the times we quote from translations of Frege’s
works cited in the endnote and references section. We indicate
explicitly when we modify the translation or provide our translation.
23. Dummett, Origins, 628; Dummett, The Interpretation of Frege’s Philosophy, 6.
24. Dummett, The Interpretation of Frege’s Philosophy, 7.
25. Dummett, The Interpretation of Frege’s Philosophy, 7.
26. Dummett, Frege and Other Philosophers (Oxford, UK: Clarendon Press,
1991), 217. Yet, this is the error that Shanker claims Dummett
committed in Frege and in The Interpretation of Frege’s Philosophy and that is
at the origin of Dummett’s claim that Frege’s philosophy anticipated
the linguistic turn carried out by analytic philosophers; see
Shanker, “Review.”
27. “Frege made a very clear distinction between questions about the
content of thoughts and the meaning of sentences, on the one hand,
and genuinely epistemological questions about, say, the process of
thinking, on the other.” Dummett, Origins, 185. More than ten years
earlier, Dummett also writes, “[T]he agreement of all might be
secured for the adoption, as a neutral designation for that branch of
philosophy which Frege called simply “logic”, of the term ‘the
philosophy of thought’, which, as he would have been the first to
insist, is to be sharply distinguished from a philosophical account
of thinking.” Dummett, The Interpretation of Frege’s Philosophy, 39.
28. In the effort to avoid the ambiguity of using ‘thought’ to
translate both das Denken and der Gedanke in Frege, other authors have
used ‘Thought’ to translate the latter and left ‘thought’ to
translate the former. Although this is a viable solution to the
issue of the ambiguity of the English term ‘thought,’ our proposal
brings to sharper focus the fact that thinking is a mental process.
Because of the importance of psychologism, which we discuss in the
next chapter, we believe our proposal is preferable. See for example
Marcos Barbosa de Oliveira, “Logic and Cognitive Science: Frege’s
