Bernard Bolzano (/bɒlˈtsɑːnoʊ/; German: [bɔlˈtsaːno]; born
Bernardus Placidus Johann Nepomuk Bolzano; 5 October 1781 – 18
December 1848) was a Bohemian mathematician, logician,
philosopher, theologian and
Catholic priest of Italian extraction,
also known for his antimilitarist views.
Bolzano wrote in German, his native language. For the most part,
his work came to prominence posthumously.
3 Mathematical work
4 Philosophical work
4.1 Wissenschaftslehre (Theory of Science)
4.1.1 Introduction to Wissenschaftslehre
4.1.3 Satz an Sich (proposition in itself)
4.1.4 Ideas and objects
4.1.5 Sensation and simple ideas
4.1.8 Judgments and cognitions
5 Philosophical legacy
6.1 Translations and compilations
7 See also
7.1 Named after Bolzano
10 Further reading
11 External links
Bolzano was the son of two pious Catholics. His father, Bernard
Pompeius Bolzano, was an Italian who had moved to Prague, where he
married Maria Cecilia Maurer who came from Prague's German-speaking
family Maurer. Only two of their twelve children lived to adulthood.
Bolzano entered the University of
Prague in 1796 and studied
mathematics, philosophy and physics. Starting in 1800, he also began
studying theology, becoming a
Catholic priest in 1804. He was
appointed to the new chair of philosophy of religion at Prague
University in 1805. He proved to be a popular lecturer not only in
religion but also in philosophy, and he was elected Dean of the
Philosophical Faculty in 1818.
Bolzano alienated many faculty and church leaders with his teachings
of the social waste of militarism and the needlessness of war. He
urged a total reform of the educational, social and economic systems
that would direct the nation's interests toward peace rather than
toward armed conflict between nations. Upon his refusal to recant his
beliefs, Bolzano was dismissed from the university in 1819.
His political convictions, which he was inclined to share with others
with some frequency, eventually proved to be too liberal for the
Austrian authorities. He was exiled to the countryside and then
devoted his energies to his writings on social, religious,
philosophical, and mathematical matters.
Although forbidden to publish in mainstream journals as a condition of
his exile, Bolzano continued to develop his ideas and publish them
either on his own or in obscure Eastern European journals. In 1842 he
moved back to Prague, where he died in 1848.
Bolzano made several original contributions to mathematics. His
overall philosophical stance was that, contrary to much of the
prevailing mathematics of the era, it was better not to introduce
intuitive ideas such as time and motion into mathematics (Boyer 1959,
pp. 268–269). To this end, he was one of the earliest
mathematicians to begin instilling rigor into mathematical analysis
with his three chief mathematical works Beyträge zu einer
begründeteren Darstellung der Mathematik (1810), Der binomische
Lehrsatz (1816) and Rein analytischer Beweis (1817). These works
presented "...a sample of a new way of developing analysis", whose
ultimate goal would not be realized until some fifty years later when
they came to the attention of
Karl Weierstrass (O'Connor &
To the foundations of mathematical analysis he contributed the
introduction of a fully rigorous ε–δ definition of a mathematical
limit. Bolzano was the first to recognize the greatest lower bound
property of the real numbers. Like several others of his day, he
was skeptical[dubious – discuss] of the possibility of Gottfried
Leibniz's infinitesimals, that had been the earliest putative
foundation for differential calculus. Bolzano's notion of a limit was
similar to the modern one: that a limit, rather than being a relation
among infinitesimals, must instead be cast in terms of how the
dependent variable approaches a definite quantity as the independent
variable approaches some other definite quantity.
Bolzano also gave the first purely analytic proof of the fundamental
theorem of algebra, which had originally been proven by Gauss from
geometrical considerations. He also gave the first purely analytic
proof of the intermediate value theorem (also known as Bolzano's
theorem). Today he is mostly remembered for the Bolzano–Weierstrass
Karl Weierstrass developed independently and published
years after Bolzano's first proof and which was initially called the
Weierstrass theorem until Bolzano's earlier work was rediscovered
(Boyer & Merzbach 1991, p. 561).
Bolzano's posthumously published work Paradoxien des Unendlichen (The
Paradoxes of the Infinite) (1851) was greatly admired by many of the
eminent logicians who came after him, including Charles Sanders
Peirce, Georg Cantor, and Richard Dedekind. Bolzano's main claim to
fame, however, is his 1837 Wissenschaftslehre (Theory of Science), a
work in four volumes that covered not only philosophy of science in
the modern sense but also logic, epistemology and scientific pedagogy.
The logical theory that Bolzano developed in this work has come to be
acknowledged as ground-breaking. Other works are a four-volume
Lehrbuch der Religionswissenschaft (Textbook of the Science of
Religion) and the metaphysical work Athanasia, a defense of the
immortality of the soul. Bolzano also did valuable work in
mathematics, which remained virtually unknown until Otto Stolz
rediscovered many of his lost journal articles and republished them in
Wissenschaftslehre (Theory of Science)
In his 1837 Wissenschaftslehre Bolzano attempted to provide logical
foundations for all sciences, building on abstractions like
part-relation, abstract objects, attributes, sentence-shapes, ideas
and propositions in themselves, sums and sets, collections,
substances, adherences, subjective ideas, judgments, and
sentence-occurrences. These attempts were basically an extension of
his earlier thoughts in the philosophy of mathematics, for example his
1810 Beiträge where he emphasized the distinction between the
objective relationship between logical consequences and our subjective
recognition of these connections. For Bolzano, it was not enough that
we merely have confirmation of natural or mathematical truths, but
rather it was the proper role of the sciences (both pure and applied)
to seek out justification in terms of the fundamental truths that may
or may not appear to be obvious to our intuitions.
Introduction to Wissenschaftslehre
Bolzano begins his work by explaining what he means by theory of
science, and the relation between our knowledge, truths and sciences.
Human knowledge, he states, is made of all truths (or true
propositions) that men know or have known. This is, however, only a
very small fraction of all the truths that exist, although still too
much for one human being to comprehend. Therefore, our knowledge is
divided into more accessible parts. Such a collection of truths is
what Bolzano calls a science (Wissenschaft). It is important to note
that not all true propositions of a science have to be known to men;
hence, this is how we can make discoveries in a science.
To better understand and comprehend the truths of a science, men have
created textbooks (Lehrbuch), which of course contain only the true
propositions of the science known to men. But how to know where to
divide our knowledge, that is, which truths belong together? Bolzano
explains that we will ultimately know this through some reflection,
but that the resulting rules of how to divide our knowledge into
sciences will be a science in itself. This science, that tells us
which truths belong together and should be explained in a textbook, is
the Theory of Science (Wissenschaftslehre).
In the Wissenschaftslehre, Bolzano is mainly concerned with three
(1) The realm of language, consisting in words and sentences.
(2) The realm of thought, consisting in subjective ideas and
(3) The realm of logic, consisting in objective ideas (or ideas in
themselves) and propositions in themselves.
Bolzano devotes a great part of the Wissenschaftslehre to an
explanation of these realms and their relations.
Two distinctions play a prominent role in his system. Firstly, the
distinction between parts and wholes. For instance, words are parts of
sentences, subjective ideas are parts of judgments, objective ideas
are parts of propositions in themselves. Secondly, all objects divide
into those that exist, which means that they are causally connected
and located in time and/or space, and those that do not exist.
Bolzano's original claim is that the logical realm is populated by
objects of the latter kind.
Satz an Sich (proposition in itself)
Satz an Sich is a basic notion in Bolzano's Wissenschaftslehre. It is
introduced at the very beginning, in section 19. Bolzano first
introduces the notions of proposition (spoken or written or thought or
in itself) and idea (spoken or written or thought or in itself). "The
grass is green" is a proposition (Satz): in this connection of words,
something is said or asserted. "Grass", however, is only an idea
(Vorstellung). Something is represented by it, but it does not assert
anything. Bolzano's notion of proposition is fairly broad: "A
rectangle is round" is a proposition — even though it is false by
virtue of self-contradiction — because it is composed in an
intelligible manner out of intelligible parts.
Bolzano does not give a complete definition of a Satz an Sich (i.e.
proposition in itself) but he gives us just enough information to
understand what he means by it. A proposition in itself (i) has no
existence (that is: it has no position in time or place), (ii) is
either true or false, independent of anyone knowing or thinking that
it is true or false, and (iii) is what is 'grasped' by thinking
beings. So a written sentence ('Socrates has wisdom') grasps a
proposition in itself, namely the proposition [Socrates has wisdom].
The written sentence does have existence (it has a certain location at
a certain time, say it is on your computer screen at this very moment)
and expresses the proposition in itself which is in the realm of in
itself (i.e. an sich). (Bolzano's use of the term an sich differs
greatly from that of Kant; for Kant's use of the term see an
Every proposition in itself is composed out of ideas in themselves
(for simplicity, we will use proposition to mean "proposition in
itself" and idea to refer to an objective idea or idea in itself.
Ideas are negatively defined as those parts of a proposition that are
themselves not propositions. A proposition consists of at least three
ideas, namely: a subject idea, a predicate idea and the copula (i.e.
'has', or another form of to have). (Though there are propositions
which contain propositions, but we won't take them into consideration
Bolzano identifies certain types of ideas. There are simple ideas that
have no parts (as an example Bolzano uses [something]), but there are
also complex ideas that consist of other ideas (Bolzano uses the
example of [nothing], which consists of the ideas [not] and
[something]). Complex ideas can have the same content (i.e. the same
parts) without being the same — because their components are
differently connected. The idea [A black pen with blue ink] is
different from the idea [A blue pen with black ink] though the parts
of both ideas are the same.
Ideas and objects
It is important to understand that an idea does not need to have an
object. Bolzano uses object to denote something that is represented by
an idea. An idea that has an object, represents that object. But an
idea that does not have an object represents nothing. (Don't get
confused here by terminology: an objectless idea is an idea without a
Let's consider, for further explanation, an example used by Bolzano.
The idea [a round square], does not have an object, because the object
that ought to be represented is self-contrary. A different example is
the idea [nothing] which certainly does not have an object. However,
the proposition [the idea of a round square has complexity] has as its
subject-idea [the idea of a round square]. This subject-idea does have
an object, namely the idea [a round square]. But, that idea does not
have an object.
Besides objectless ideas, there are ideas that have only one object,
e.g. the idea [the first man on the moon] represents only one object.
Bolzano calls these ideas 'singular ideas'. Obviously there are also
ideas that have many objects (e.g. [the citizens of Amsterdam]) and
even infinitely many objects (e.g. [a prime number]).
Sensation and simple ideas
Bolzano has a complex theory of how we are able to sense things. He
explains sensation by means of the term intuition, in German called
Anschauung. An intuition is a simple idea, it has only one object
(Einzelvorstellung), but besides that, it is also unique (Bolzano
needs this to explain sensation). Intuitions (Anschauungen) are
objective ideas, they belong to the an sich realm, which means that
they don’t have existence. As said, Bolzano’s argumentation for
intuitions is by an explanation of sensation.
What happens when you sense a real existing object, for instance a
rose, is this: the different aspects of the rose, like its scent and
its color, cause in you a change. That change means that before and
after sensing the rose, your mind is in a different state. So
sensation is in fact a change in your mental state. How is this
related to objects and ideas? Bolzano explains that this change, in
your mind, is essentially a simple idea (Vorstellung), like, ‘this
smell’ (of this particular rose). This idea represents; it has as
its object the change. Besides being simple, this change must also be
unique. This is because literally you can’t have the same experience
twice, nor can two people, who smell the same rose at the same time,
have exactly the same experience of that smell (although they will be
quite alike). So each single sensation causes a single (new) unique
and simple idea with a particular change as its object. Now, this idea
in your mind is a subjective idea, meaning that it is in you at a
particular time. It has existence. But this subjective idea must
correspond to, or has as a content, an objective idea. This is where
Bolzano brings in intuitions (Anschauungen); they are the simple,
unique and objective ideas that correspond to our subjective ideas of
changes caused by sensation. So for each single possible sensation,
there is a corresponding objective idea. Schematically the whole
process is like this: whenever you smell a rose, its scent causes a
change in you. This change is the object of your subjective idea of
that particular smell. That subjective idea corresponds to the
intuition or Anschauung.
According to Bolzano, all propositions are composed out of three
(simple or complex) elements: a subject, a predicate and a copula.
Instead of the more traditional copulative term 'is', Bolzano prefers
'has'. The reason for this is that 'has', unlike 'is', can connect a
concrete term, such as 'Socrates', to an abstract term such as
'baldness'. "Socrates has baldness" is, according to Bolzano,
preferable to "Socrates is bald" because the latter form is less
basic: 'bald' is itself composed of the elements 'something', 'that',
'has' and 'baldness'. Bolzano also reduces existential propositions to
this form: "Socrates exists" would simply become "Socrates has
A major role in Bolzano’s logical theory is played by the notion of
variations: various logical relations are defined in terms of the
changes in truth value that propositions incur when their non-logical
parts are replaced by others. Logically analytical propositions, for
instance, are those in which all the non-logical parts can be replaced
without change of truth value. Two propositions are 'compatible'
(verträglich) with respect to one of their component parts x if there
is at least one term that can be inserted that would make both true. A
proposition Q is 'deducible' (ableitbar) from a proposition P, with
respect to certain of their non-logical parts, if any replacement of
those parts that makes P true also makes Q true. If a proposition is
deducible from another with respect to all its non-logical parts, it
is said to be 'logically deducible'. Besides the relation of
deducibility, Bolzano also has a stricter relation of
'consequentiality' (Abfolge). This is an asymmetric relation that
obtains between true propositions, when one of the propositions is not
only deducible from, but also explained by the other.
Bolzano distinguishes five meanings the words true and truth have in
common usage, all of which Bolzano takes to be unproblematic. The
meanings are listed in order of properness:
I. Abstract objective meaning: Truth signifies an attribute that may
apply to a proposition, primarily to a proposition in itself, namely
the attribute on the basis of which the proposition expresses
something that in reality is as is expressed. Antonyms: falsity,
II. Concrete objective meaning: (a) Truth signifies a proposition that
has the attribute truth in the abstract objective meaning. Antonym:
III. Subjective meaning: (a) Truth signifies a correct judgment.
Antonym: (a) mistake.
IV. Collective meaning: Truth signifies a body or multiplicity true
propositions or judgments (e.g. the biblical truth).
V. Improper meaning: True signifies that some object is in reality
what some denomination states it to be. (e.g. the true God). Antonyms:
false, unreal, illusory.
Bolzano's primary concern is with the concrete objective meaning: with
concrete objective truths or truths in themselves. All truths in
themselves are a kind of propositions in themselves. They do not
exist, i.e. they are not spatiotemporally located as thought and
spoken propositions are. However, certain propositions have the
attribute of being a truth in itself. Being a thought proposition is
not a part of the concept of a truth in itself, notwithstanding the
fact that, given God’s omniscience, all truths in themselves are
also thought truths. The concepts ‘truth in itself’ and ‘thought
truth’ are interchangeable, as they apply to the same objects, but
they are not identical.
Bolzano offers as the correct definition of (abstract objective)
truth: a proposition is true if it expresses something that applies to
its object. The correct definition of a (concrete objective) truth
must thus be: a truth is a proposition that expresses something that
applies to its object. This definition applies to truths in
themselves, rather than to thought or known truths, as none of the
concepts figuring in this definition are subordinate to a concept of
something mental or known.
Bolzano proves in §§31–32 of his Wissenschaftslehre three things:
A There is at least one truth in itself (concrete objective meaning):
1. There are no true propositions (assumption)
2. 1. is a proposition (obvious)
3. 1. is true (assumed) and false (because of 1.)
4. 1. is self-contradictory (because of 3.)
5. 1. is false (because of 4.)
6. There is at least one true proposition (because of 1. and 5.)
B. There is more than one truth in itself:
7. There is only one truth in itself, namely A is B (assumption)
8. A is B is a truth in itself (because of 7.)
9. There are no other truths in themselves apart from A is B (because
10. 9. is a true proposition/ a truth in itself (because of 7.)
11. There are two truths in themselves (because of 8. and 10.)
12. There is more than one truth in itself (because of 11.)
C. There are infinitely many truths in themselves:
13. There are only n truths in themselves, namely A is B .... Y is Z
14. A is B .... Y is Z are n truths in themselves (because of 13.)
15. There are no other truths apart from A is B .... Y is Z (because
16. 15. is a true proposition/ a truth in itself (because of 13.)
17. There are n+1 truths in themselves (because of 14. and 16.)
18. Steps 1 to 5 can be repeated for n+1, which results in n+2 truths
and so on endlessly (because n is a variable)
19. There are infinitely many truths in themselves (because of 18.)
Judgments and cognitions
A known truth has as its parts (Bestandteile) a truth in itself and a
judgment (Bolzano, Wissenschaftslehre §26). A judgment is a thought
which states a true proposition. In judging (at least when the matter
of the judgment is a true proposition), the idea of an object is being
connected in a certain way with the idea of a characteristic (§ 23).
In true judgments, the relation between the idea of the object and the
idea of the characteristic is an actual/existent relation (§28).
Every judgment has as its matter a proposition, which is either true
or false. Every judgment exists, but not "für sich". Judgments,
namely, in contrast with propositions in themselves, are dependent on
subjective mental activity. Not every mental activity, though, has to
be a judgment; recall that all judgments have as matter propositions,
and hence all judgments need to be either true or false. Mere
presentations or thoughts are examples of mental activities which do
not necessarily need to be stated (behaupten), and so are not
judgments (§ 34).
Judgments that have as its matter true propositions can be called
cognitions (§36). Cognitions are also dependent on the subject, and
so, opposed to truths in themselves, cognitions do permit degrees; a
proposition can be more or less known, but it cannot be more or less
true. Every cognition implies necessarily a judgment, but not every
judgment is necessarily cognition, because there are also judgments
that are not true. Bolzano maintains that there are no such things as
false cognitions, only false judgments (§34).
Bolzano came to be surrounded by a circle of friends and pupils who
spread his thoughts about (the so-called Bolzano Circle), but the
effect of his thought on philosophy initially seemed destined to be
His work was rediscovered, however, by Edmund Husserl and Kazimierz
Twardowski, both students of Franz Brentano. Through them, Bolzano
became a formative influence on both phenomenology and analytic
Gesamtausgabe (Collected Works), critical edition edited by Eduard
Winter, Jan Berg (sv), Friedrich Kambartel, Bob van Rootselaar,
Stuttgart: Fromman-Holzboog, 1969 ss. (89 vols. published).
Wissenschaftslehre, 4 vols., 2nd rev. ed. by W. Schultz, Leipzig
I–II 1929, III 1980, IV 1931; Critical Edition edited by Jan Berg:
Bolzano's Gesamtausgabe, vols. 11–14 (1985–2000).
Bernard Bolzano's Grundlegung der Logik. Ausgewählte Paragraphen aus
der Wissenschaftslehre, Vols. 1 and 2, with supplementary text
summaries, an introduction and indices, edited by F. Kambartel,
Hamburg, 1963, 1978².
Bolzano, Bernard (1810), Beyträge zu einer begründeteren Darstellung
der Mathematik. Erste Lieferung (Contributions to a better
grounded presentation of mathematics; Ewald 1996, pp. 174–224
and The Mathematical Works of Bernard Bolzano, 2004,
Bolzano, Bernard (1817), Rein analytischer Beweis des Lehrsatzes, dass
zwischen je zwey Werthen, die ein entgegengesetzes Resultat gewähren,
wenigstens eine reele Wurzel der Gleichung liege, Wilhelm
Engelmann (Purely analytic proof of the theorem that between any
two values which give results of opposite sign, there lies at least
one real root of the equation; Ewald 1996, pp. 225–48.
Franz Prihonsky (1850), Der Neue Anti-Kant, Bautzen (an assessment of
the Critique of Pure Reason by Bolzano, published posthumously by his
friend F. Prihonsky).*Bolzano, Bernard (1851), Paradoxien des
Unendlichen, C.H. Reclam (Paradoxes of the Infinite; Ewald 1996,
pp. 249–92 (excerpt)).
Translations and compilations
Theory of Science (selection edited and translated by Rolf George,
Berkeley and Los Angeles: University of California Press, 1972).
Theory of Science (selection edited, with an introduction, by Jan
Berg. Translated from the German by Burnham Terrell, Dordrecht and
Boston: D. Reidel Publishing Company, 1973).
Theory of Science, first complete English translation in four volumes
by Rolf George and Paul Rusnock, New York: Oxford University Press,
The Mathematical Works of Bernard Bolzano, translated and edited by
Steve Russ, New York: Oxford University Press, 2004 (re-printed 2006).
On the Mathematical Method and Correspondence with Exner, translated
by Rolf George and Paul Rusnock, Amsterdam: Rodopi, 2004.
Selected Writings on Ethics and Politics, translated by Rolf George
and Paul Rusnock, Amsterdam: Rodopi, 2007.
Franz Prihonsky, The New Anti-Kant, edited by Sandra Lapointe and
Clinton Tolley, New York, Palgrave Macmillan, 2014.
List of Roman
Named after Bolzano
Bolzano's theorem, or "intermediate value theorem", a theorem in
Bolzano–Weierstrass theorem, a theorem concerning sequences in real
^ a b
Routledge Encyclopedia of
Philosophy (1998): "Ryle, Gilbert
^ Sandra Lapointe, "Bolzano's Logical Realism", in: Penelope Rush
(ed.), The Metaphysics of Logic, Cambridge University Press, 2014, pp.
^ a b c Morscher, Edgar. "Bernard Bolzano". In Zalta, Edward N.
Stanford Encyclopedia of Philosophy.
^ a b Wolfgang Huemer, "Husserl's critique of psychologism and his
relation to the Brentano school", in: Arkadiusz Chrudzimski and
Wolfgang Huemer (eds.), Phenomenology and Analysis: Essays on Central
European Philosophy, Walter de Gruyter, 2004, p. 205.
^ Sundholm, B. G., "When, and why, did Frege read Bolzano?", LOGICA
Yearbook 1999, 164–174 (2000).
^ a b Maria van der Schaar, Kazimierz Twardowski: A Grammar for
Philosophy, Brill, 2015, p. 53; Peter M. Simons,
Philosophy and Logic
in Central Europe from Bolzano to Tarski: Selected Essays, Springer,
2013, p. 15.
^ a b Šebestik, Jan. "Bolzano's Logic". In Zalta, Edward N. Stanford
Encyclopedia of Philosophy.
^ Robin D. Rollinger, Husserl's Position in the School of Brentano,
Phaenomenologica 150, Dordrecht: Kluwer, 1999, Chap. 4: "Husserl and
Kerry", p. 129.
^ Robin D. Rollinger, Husserl's Position in the School of Brentano,
Phaenomenologica 150, Dordrecht: Kluwer, 1999, Chap. 2: "Husserl and
Bolzano", p. 70.
^ Michael Dummett, Origins of Analytical Philosophy, Bloombury, 2014,
p. xiii; Anat Biletzki, Anat Matarp (eds.), The Story of Analytic
Philosophy: Plot and Heroes, Routledge, 2002, p. 57: "It was Gilbert
Ryle who, [Dummett] says, opened his eyes to this fact in his lectures
on Bolzano, Brentano, Meinong, and Husserl.
^ a b Chisholm, Hugh, ed. (1911). "Bolzano, Bernhard".
Encyclopædia Britannica (11th ed.). Cambridge University Press.
^ O'Hear, Anthony (1999), German
Philosophy Since Kant, Royal
Philosophy Supplements, Royal Institute of Philosophy
London, 44, Cambridge University Press, p. 110, His native
language was German.
^ Raman-Sundström, Manya (August–September 2015). "A Pedagogical
History of Compactness". American Mathematical Monthly. 122 (7):
^ Bolzano, “On the Mathematical Method”, §2
^ Bolzano, “On the Mathematical Method”, §3
^ Bolzano, “On the Mathematical Method”, §4
^ Bolzano, Wissenschaftslehre, §72
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Boyer, Carl B.; Merzbach, Uta C. (1991), A History of Mathematics, New
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the Foundations of Mathematics, 2 volumes, Oxford University
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Veverková, Kamila, "Kleinere Schriften des deutschen Lehrers und
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O'Connor, John J.; Robertson, Edmund F. (2005), "Bolzano", MacTutor
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Edgar Morscher (de) (1972), "Von Bolzano zu Meinong: Zur
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von Sein und Nichtsein: Beiträge zur Meinong-Forschung, Graz, pp.
Wikimedia Commons has media related to Bernard Bolzano.
Morscher, Edgar. "Bernard Bolzano". In Zalta, Edward N. Stanford
Encyclopedia of Philosophy.
Šebestík[cs], Jan. "Bolzano's Logic". In Zalta, Edward N. Stanford
Encyclopedia of Philosophy. CS1 maint: Multiple names: authors
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Philosophy of Mathematical Knowledge entry by Sandra
Lapointe in the Internet Encyclopedia of Philosophy
Philosophy of Bernard Bolzano:
Logic and Ontology
Bernard Bolzano: English Translations and Selected Texts
Annotated Bibliography on the Philosophical Work of Bolzano (First
Part: A - C)
Annotated Bibliography on the Philosophical Work of Bolzano (Second
Part: D - L)
Annotated Bibliography on the Philosophical Work of Bolzano (Third
Part: M - Z)
Bernard Bolzano at the
Mathematics Genealogy Project
Works by or about
Bernard Bolzano at Internet Archive
Digitized Bolzano's works
Volume 1 of Wissenschaftslehre in Google Books
Volume 2 of Wissenschaftslehre in Google Books
Volumes 3–4 of Wissenschaftslehre in Google Books
Volume 1 of Wissenschaftslehre in Archive.org (pages 162 to 243 are
Volume 2 of Wissenschaftslehre in Archive.org
Volume 4 of Wissenschaftslehre in Archive.org
Volume 3 of Wissenschaftslehre in Gallica
Volume 4 of Wissenschaftslehre in Gallica
ISNI: 0000 0001 2277 5147
BNF: cb12027042g (data)