Abstract
According to Kant, a true judgement can be called a priori in case it can take place absolutely (schlechterdings) independent of experience. Propositions that are knowable in this way are called a priori propositions by him (Kant 1787 B, 3–4). As is well known, the class of those a priori propositions that are synthetic was particularly important for Kant. In contrast to analytic propositions, they are supposed to contain nontrivial information about the world and yet be irrefutable by experience. Not many of his critics were satisfied with Kant’s way of drawing this distinction. Peter Strawson, for example, writes in his commentary on the Critique of Pure Reason:
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Notes
- 1.
As will become explicit below, what Bolzano does is not too different from what Carnap calls “explication,” namely, “the task of making more exact a vague or not quite exact concept used in everyday life or in an earlier stage of scientific or logical development, or rather replacing it by a newly constructed, more exact concept” (Carnap 1956, 7).
- 2.
An exception is Lapointe (2010).
- 3.
I use “the apriori” here as an umbrella term for the concepts of cognition or judgement a priori and of a priori propositions or truths.
- 4.
Since the translation of Bolzanian terminology is not always straightforward, I always add the German terms in brackets. When I quote longer passages from Bolzano, I also quote the German original in a footnote. Unless indicated otherwise, all translations of Bolzano’s texts are my own.
- 5.
In this chapter, I will use the term “matter” (which is a translation of Bolzano’s term “Stoff [eines Urtheils]”) to refer to what is normally called the content of a judgement, i.e., the proposition that the person who judges holds to be true. The reason for this is that the term “content” is used by Bolzano in another sense.
- 6.
Within Bolzano (1969ff./1837) (henceforth WL), Bolzano was reluctant to accept this characterization as a proper definition. In a letter to Franz Exner, however, he considered it to be one (Cf. Bolzano and Exner 2004, 141f.).
- 7.
Note that Bolzano rejects the traditional doctrine that with increasing complexity of a representation the cardinality of its extension decreases (Cf. WL, §120).
- 8.
Two extensionally equivalent representations which are composed out of the same parts can still be different, according to Bolzano. Take, for example, the representations expressed by “24” and “42.” For a criterion of identity for Bolzanian representations, see Morscher (2008), p. 50f.
- 9.
In Bolzano’s times, this thesis was far from trivial. According to the then widespread doctrine that the cardinality of the extension of a representation decreases with increasing complexity of its content, representations whose content has the smallest possible complexity and which yet have only one object as their extension must have seemed to be an impossibility.
- 10.
It has often been noticed that Bolzano’s intuitions bear some resemblance with the logically proper names of the early Russell. Mark Textor has argued that with his concept of an intuition, Bolzano provides a structural characterization of direct reference, which is the function of Russell’s logically proper names (Textor 1996, 89). Bolzano’s doctrine of intuitions has some crucial consequences. Since he seems to assume that intuitions always refer to mental events, namely, sensations, it follows that each representation that refers to a single abstract object must be complex (cf. Textor 1996, 79). Thus, Bolzano is committed to the thesis that number terms like “four” express complex concepts. Conversely, every simple concept has to refer plurally (like the one expressed by “some”) or not at all (like the ones expressed by “has” or “and”). For a critical discussion of Bolzano’s theory of intuition, see also George (1999).
- 11.
“die […] Eintheilung unserer Erkenntnisse in solche, von denen Richtigkeit wir uns (wie man zu sagen pflegt) nur durch Erfahrung allein überzeugen können, und in andere, die keiner Erfahrung bedürfen […]. [D]iese Eintheilung unserer Erkenntnisse [fällt] mit jener der Sätze in Begriffs- und Anschauungssätze beinahe zusammen […]; indem die Wahrheit der meisten Begriffssätze durch bloßes Nachdenken ohne Erfahrung entschieden werden kann, während sich Sätze, die eine Anschauung enthalten, insgemein nur aus Erfahrungen beurteilen lassen” (WL II, 36).
- 12.
Bolzano’s claim that only “most” conceptual propositions can be known without the aid of experience presumably derives from his assumption that there are conceptual propositions that are too complex for human beings to grasp. He mentions moreover that to derive some conceptual propositions, one has to rely on memory, which Bolzano classifies as a kind of experience (cf. WL III, 214).
- 13.
And also to the related distinction between truths of reason and truths of fact in Leibniz. Bolzano cites Xenophanes, Parmenides, the Eleats, Plato, Descartes, and Cudworth as other philosophers who already drew similar distinctions (WL III, 166).
- 14.
- 15.
“Nun däucht mir diese Benennung [i.e. ‘Wahrheiten a priori’, S.R.] nicht so Zweckmäßig, weil sie bloß von der Art, wie wir zur Kenntnis solcher Wahrheiten in den meisten Fällen gelangen, entlehnt ist.”
- 16.
They can take place independently of experience.
- 17.
By using the term “explain” here, I want to emphasize that Bolzano’s explication is supposed to enable him to answer certain why questions, e.g., why do these propositions have such and such epistemic properties?
- 18.
- 19.
“Wenn der gegebene Satz aus bloßen Begriffen besteht […] dann hängt die Wahrheit oder Falschheit desselben bloß von der Beschaffenheit dieser Begriffe ab. […] Wahrheiten dieser Art also (reine Begriffswahrheiten) erkennst du kraft dessen, daß du die Begriffe, aus welchen sie zusammengesetzt sind, kennest.” Note that Frege’s version of the distinction between a priori and a posteriori propositions bears some similarities to Bolzano’s in the sense that Frege, too, grounds the distinction in properties of propositions, i.e., their generality. Cf. Frege (1987/1884), 4. On the relation between Kant, Bolzano, and Frege on analyticity, see also de Jong (2001).
- 20.
“Wenn die Sätze, aus welchen wir ein Urtheil M ableiten, und ebenso auch diejenigen, aus welchen wir zuvor schon jene abgeleitet und so fort bis zu den unmittelbaren Urtheilen hin, durchgängig reine Begriffssätze sind: so kann man M ein Urtheil aus reinen Begriffen, oder rein, a priori nennen; in jedem anderen Falle mag es ein aus der Erfahrung geschöpftes oder ein Urtheil a posteriori heißen.” – Here and in the following, underlined text is spaced in the original.
- 21.
Note that this definition does not exclude that a conceptual proposition may be the matter of a judgement a posteriori. A conceptual truth does not necessarily have to be judged on the basis of other conceptual truths (cf. Sect. 4, below).
- 22.
Note, moreover, that in Bolzano, the analytic/synthetic distinction divides the class of propositions and not the class of sentences.
- 23.
Condition (a) is due to the fact that according to Bolzano’s definition of truth, propositions whose subject is empty are always false. (B-A) is an example of an application of Bolzano’s famous method of variation. The method consists in characterizing properties of propositions (or representations) by considering certain parts of them to be variable. Up to a point, variation is analogous to the familiar method of substitution with respect to linguistic objects. Bolzano uses this method not only to define analyticity but also numerous other logically important concepts – most importantly, (logical) consequence, as well as probability-theoretic and epistemological concepts (for this, see below). Note that when more parts of a given proposition are considered to be variable, one has to assure that variation is executed in a systematic way. For a detailed account, see Morscher (2008). For an extensive discussion of Bolzano’s notion of analytic truth, see also Künne (2008).
- 24.
This is very close to what Quine calls “vacuous occurrence” in his definition of logical truth (as noted by Quine). Cf. Quine (1977a), 88 and 105 and Quine (1977b), 117ff. – the difference being that Quine defines those notions for sentences and not for propositions. Cf. Künne (2008), 290ff. for a discussion of this point.
- 25.
Though of course this does not hold if one analyzes (1) by means of a first-order language (i.e., as “”). Although the proposition is still analytic in Bolzano’s sense, one cannot literally say that its predicate is contained in its subject.
- 26.
Note that the class of logical notions in Bolzano comprises different elements than modern suggestions and that he had a certain pragmatic attitude toward drawing the distinction between logical and nonlogical notions (cf. Künne 2008, 259ff.).
- 27.
Where “A” is a placeholder for representations of all kind and “b” is a placeholder for designators of properties, e. g., “blackness.” Note that b may also collectively refer to particularized qualities (Cf. Betti 2012).
- 28.
For further elaboration, see Künne (2008), 236.
- 29.
- 30.
“Die eigentliche mit schulgerechter Präzision ausgedrückte Aufgabe, auf die alles ankommt, ist also: Wie sind synthetische Sätze a priori möglich?” (Kant 2001/1783, 41). Of course, I take Kant here to be asking not about the possibility of a certain kind of object but rather about how one could justify synthetic propositions a priori and hence know them.
- 31.
Bolzano is clearly alluding to a specific passage of the Critique of Pure Reason here, in which Kant asks how one can come to know synthetic truths a priori, namely, “What is the unknown = X which gives support to the understanding when it believes that it can discover outside the concept A a predicate B foreign to this concept, which it yet at the same time considers to be connected with it?” (“Was ist hier das Unbekannte = X, worauf sich der Verstand stützt, wenn er außer dem Begriff von A ein demselben fremdes Prädikat B aufzufinden glaubt, welches er gleichwohl damit verknüpft zu sein erachtet?”) (Kant 1787 B, 13).
- 32.
“Mir will gerade hier, wo K. eine Schwierigkeit antraf, nichts Unbegreifliches erscheinen. ‘Was den Verstand berechtige, einem Subjecte A ein Prädicat B, welches doch in dem Begriffe von A nicht lieget, beizulegen?’ Nichts Anderes, sage ich, als daß der Verstand die Begriffe A und B beide hat und kennet. Bloß dadurch, daß wir gewisse Begriffe haben, müssen wir (meine ich) auch in dem Stande seyn, über sie zu urtheilen. Denn sagen, daß Jemand gewisse Begriffe A, B, C, … habe, heißt doch wohl sagen, daß er sie kenne und unterscheide. Sagen, daß er sie kenne und unterscheide, heißt aber wieder nur sagen, daß er von dem einen derselben etwas behaupte, was er nicht eben auch so von dem andern behaupten wollte; heißt also sagen, daß er über sie urtheile.”
- 33.
Two remarks on this formulation are in order: First, I take it that by talking about being justified in connecting certain concepts, Bolzano wants to indicate that one has knowledge of the respective truth. Second, as it is immaterial to the problems I will be concerned with later on, I follow Bolzano talking about propositions of the form “A is B,” even though strictly speaking one should talk about propositions of the form “A has b” in Bolzano’s framework.
- 34.
To see that this claim expresses an analytic truth in the first place, one has to recognize that the proposition expressed by “Every bachelor is a man” is identical to the one expressed by “Every man which is unmarried is a man.” (Cf. also de Jong 2001).
- 35.
“den Bedingungen […] denen die Erkenntnis der Wahrheit, besonders bei uns Menschen, unterliegt”.
- 36.
For good overview of the conceptual framework of Bolzano’s epistemology (cf. Siebel 1999).
- 37.
For a recent exposition of this (cf. Konzelmann Ziv 2008).
- 38.
Bolzano actually calls judgements “actions of the mind” (Handlungen des Geistes) (WL I, 155).
- 39.
Cf. WL III, §§270ff. for subjective representations and WL III, §290ff. for judgements.
- 40.
Anita Konzelmann Ziv argues that Bolzano’s picture of the human mind is in many aspects similar to a view that is nowadays known as the modular view of the mind (Cf. Konzelmann Ziv 2008, 4ff.).
- 41.
The translation of Bolzano’s epistemological vocabulary is not easy. A straightforward translation of “Erkenntnis” is also “knowledge.” However, to be able to differentiate both terms, I will use the somewhat odd-sounding “cognition.”
- 42.
“[W]enn wir Jemand ein Wissen, nämlich das Wissen der Wahrheit A beilegen: so wollen wir damit keineswegs sagen, daß er das Urtheil A in eben dem Augenblicke, wo wir ihm diese Beschaffenheit des Wissens zuschreiben, fälle; sondern es genügt uns, wenn er dieß Urtheil nur schon irgend einmal gefällt hat und gegenwärtig nichts als eines äußeren Anlasses bedarf, um es zu wiederholen.”
- 43.
The modern concept of a belief can thus also be defined within the Bolzanian framework. S believes that P iff S is disposed to judge that P. In the following, therefore, I will use the term “belief” in this sense. For an analysis of Bolzano’s account of disposition, dispositions to belief, and belief in the dispositional sense, see Siebel (1999), 70–1 and 75ff.
- 44.
Although, interestingly, some contemporary epistemologists have proposed similar definitions (Cf. e.g. Sartwell 1991).
- 45.
“[W]enn also die Zuversicht, mit der wir dem Urtheile M anhängen, uns als eine solche erscheint, die zu vernichten gegenwärtig nicht mehr in unserer Macht steht, so sage ich, die Wahrheit M sey bei uns zu einem Wissen erhoben.”
- 46.
Mark Siebel argues in Siebel (1999, 83f.) that Bolzano’s explanation of the definition allows for different interpretations. He holds that it is not clear whether Bolzano holds that one is supposed to judge about one’s confidence or about possible other reasons that speak against the judgement that constitutes knowledge. Contrary to Siebel, I opt for the first option, since it is closer to Bolzano’s words. Further, I will show below that the confidence one has in a judgement is determined by the reasons that speak against it. Thus, focusing on the reasons that speak against a judgement is a way of estimating its confidence.
- 47.
Bolzano also indicates that the degree of confidence is additionally determined by the respective degree of confidence S has in all other those beliefs/judgements, but from the way he spells out this idea, it becomes apparent that he in fact only considers the degree of probability of a given proposition with respect to all other propositions the subject holds true (cf. also WL III, 277).
- 48.
- 49.
Bolzano poses several conditions on which variants are admissible. Most important for the present context is that extensionally equivalent variants may be counted only once. Without this constraint, it would be impossible to calculate the probability of any proposition, since for most representations, there are infinitely many extensionally equivalent ones. For this and other constraints, see WL II, 78ff. and Berg (1962), 93.
- 50.
This idea is not completely unproblematic. Since Γ has to be consistent, Bolzano’s definition is not applicable to inconsistent sets of beliefs, which should be an extremely rare phenomenon. One might think that Γ has to be restricted to a consistent set of S’s beliefs, but this chapter is not the place to discuss possible adjustments of Bolzano’s account.
- 51.
A further problem is that, to avoid an infinite regress, Bolzano does not demand that S has to estimate her confidence in the given judgement in such a way that she knows how high it really is (WL III, 276). What is more is that he does not even seem to demand that one has to judge truly about one’s confidence in a judgement. This, however, opens the possibility that S may judge wrongly about her confidence in P in which case the (B-K) is still satisfied – which resembles the problem Gettier famously pointed out with respect to the classical definition of knowledge.
- 52.
It should be mentioned that Bolzano himself has expressed some dissatisfaction with (K-B) after the publication of WL in a letter to Zimmermann (cf. Bolzano 1978/1848, 189). In that letter, he complains that his definition of knowledge runs against the normal use of the word “knowledge” (“ganz gegen den Sprachgebrauche”). According to Bolzano, “we say that someone knows something not if he assumes with perfect confidence, but if he assumes something according to truth.” (“Denn nicht von demjenigen, was jemand mit vollkommener Zuversicht annimmt, sagt man daß er es wisse, sondern von dem was er der Wahrheit gemäß annimmt.”) However, it is not clear to what extent (K-B) actually does fail to respect this aspect of the normal use of “knows,” for Bolzano explicitly restricts the class of propositions that can be known to true propositions.
- 53.
One can even read the first section of WL §321 in which Bolzano introduces the concept of knowledge in such a way that the notion of degree of confidence is entirely absent from Bolzano’s definition of knowledge and only the kind of confidence matters. I take this, however, not to be the best interpretative hypothesis, as virtually the only characteristic of the notion of confidence that Bolzano discusses is its degree.
- 54.
“Soll man in Wahrheit sagen können, daß wir eine gewisse objective Vorstellung, welche nicht einfach, sondern aus mehreren Theilen zusammengesetzt ist, in unser Gemüth aufgefaßt hätten: so müssen alle die einzelnen Theile, in deren Verknüpfung sie besteht, von uns aufgefaßt worden sein. Denn nur aus ebenso vielen und solchen Theilen, als in unserer subjectiven Vorstellung sich finden, besteht die objective, für deren Erscheinung in unserer Seele wir jene ausgeben dürfen.”
- 55.
In this respect, I depart from the interpretation given by Sandra Lapointe, who argues that Bolzano must have had judgements about the essential properties of the objects that fall under the respective concepts in mind: “What properties of concepts are here relevant? The significant feature of concepts Bolzano has in mind here is that we can ‘infer’ from them the properties of the objects to which they refer.” (Lapointe 2010, 276). In the passage from which I extracted (C1) and (C2) and in similar passages (e.g. WL I, 180ff.), Bolzano does only mention properties of concepts and not (essential) properties of the objects that fall under the concepts the respective conceptual truths are composed of.
- 56.
“[es] ist […] doch nicht immer nötig, daß wir uns alles dessen, was wir uns denken deutlich bewußt sind, und es auch anzugeben vermögen.”
- 57.
Both notions are also defined for judgements derivatively (WL III, 116–118).
- 58.
“Denn sagen, daß jemand gewisse Begriffe A, B, C, … habe, heißt doch wohl, sagen, daß er sie kenne und unterscheide.”
- 59.
On another occasion, Bolzano even claims that having a representation is a precondition of knowing it (cf. WL III, 243).
- 60.
Bolzano also has a detailed account of how we acquire subjective representations. He holds that we acquire intuitions as causal effects of certain changes within our mind, caused, e.g., by external objects. The change caused by the smell of a rose causes an intuition that has that change as an object (WL III, 84–7). Pure concepts are acquired when we are engaged in passing a judgement and lack some necessary part of it – for example, the concept expressed by “and” (WL III, 86). Bolzano assumes that the human mind is somehow capable of bringing the respective missing subjective representation about.
- 61.
The second conjunct is needed to prevent representations that fall under representations as the one expressed by “the representation I had between 6 and 6:30 pm 2 days after I was born” from satisfying the definition (WL III, 28).
- 62.
“wenn wir sonach ein der Wahrheit gemäßes Urtheil von folgender Form: “Die Vorstellung A besteht aus den Vorstellungen a, b, c, … in dieser und jener Verbindung,” zu fällen im Stande sind, so dieß eine die Vorstellung A betreffende Kenntniß, die uns in manchen Fällen, besonders aber bei wissenschaftlichen Untersuchungen, wichtige Dienste zu leisten vermag. Gewöhnlich pflegt man, um das Vorhandenseyn dieses Umstandes bei einer Vorstellung anzuzeigen, sie eine deutliche zu nennen.”
- 63.
“Wir sagen, meine ich, daß wir einen Gegenstand kennen, wenn wir so viele, sich auf ihn beziehende, wahre Urtheile zu fällen im Stande sind, alles bei einem Gegenstande dieser Art für uns Menschen überhaupt möglich und nützlich scheint”.
- 64.
And also on other occasions such as WL I, 180f.
- 65.
Note that we are not speaking about knowledge that in the normal sense (the German “Wissen”) but about knowledge of an object (the German “einen Gegenstand kennen”). In the latter case, the talk of degrees of knowledge might seem to be more plausible than in the former.
- 66.
We will discuss some important exceptions to this below in Sect. 4.3.
- 67.
In that passage, Bolzano speaks of coming to know whether the relation of derivability obtains. But in those cases, in which we speak of logical derivability, this amounts to the same as coming to know a logically analytic (conceptual) proposition that states an implication. Now, if these kinds of propositions can be known by knowing their form, then the same surely also holds for tautological conceptual propositions. Note that it is crucial that we speak here of tautological conceptual propositions, since there may very well be tautological propositions in Bolzano’s sense which cannot be known without experience (See WL III, 454 and also Sect. 1.2.2 above.).
- 68.
Note that I do not want to claim that the notion of knowledge in virtue of form is unproblematic; I just take it for granted for the purpose of this chapter.
- 69.
“wenn man uns mit einem Beweise desselben bekannt macht. Denn nun erkennen wir die Wahrheit dieses Satzes in der Art, daß wir versichert sind, es würde uns, selbst wenn wir wollten, nicht gelingen, uns von der Falschheit desselben zu überreden.”
- 70.
“Wir pflegen überhaupt jedes beliebige Etwas, von dem wir uns vorstellen, daß Jemand sich desselben bedienen könnte, um durch die Lenkung der Aufmerksamkeit eines denkenden Wesens auf dasselbe in dem Gemüthe des letzteren ein Urtheil M zu erzeugen, das es bisher entweder noch gar nicht, oder doch nicht mit so hohem Grade der Zuversicht gefällt hatte, einen Beweis […] des Satzes M zu nennen.”
- 71.
As mentioned above, some propositions in Bolzano’s universe might be too complex to grasp for human beings.
- 72.
To give an intuitive example (cf. WL II, §162), coming to know the truth that a well-functioning thermometer stands higher at a certain location l 1 than at a location l 2 is a means to come to know the truth that it is warmer at l 1 than at l 2. Nonetheless, the latter proposition is the ground of the former according to Bolzano, i.e., the latter precedes the former in the objective order of grounding. For discussions of Bolzano’s theory, consider Sebestik (2011), Betti (2010), Tatzel (2002), Buhl (1961), Lapointe (2010), and Centrone (2011).
- 73.
That this assumption is crucial for Bolzano’s account of a priori knowledges seems also to be the hypothesis of Sandra Lapointe. Cf. Lapointe (2010), section 5.
- 74.
It should be emphasized that not every purely conceptual proof needs to be a demonstration. An example for this is Bolzano’s proof (or attempted proof) of the claim that there exist infinitely many truths. He says explicitly that for them to succeed, a reader does not need to know whether the concept of a truth or of a proposition is simple or complex and, if the latter, of which parts it consists. (WL, I 71) The only purpose of the proof is to convince the reader that there are infinitely many truths, not to show why this is the case. Yet, the proof does not make use of any empirical truths.
- 75.
“So oft es sich also in dem Vortrage einer Wissenschaft um die Erreichung einer möglichst hohen Deutlichkeit handelt; sollte man nicht unterlassen, bei jedem Satze, soviel es möglich ist, bemerklich zu machen, aus welchen Theilen derselbe bestehe, und bey jeder Vorstellung zu zeigen, daß sie entweder einfach, oder aus welchen einfachen Vorstellungen sie zusammengesetzt sey. Nicht nur, daß man durch dieses Verfahren dem Leser eine vortreffliche Uibung im Denken verschaffen würde, sondern durch Zergliederungen würde man auch in den Stand gesetzt, den objectiven Zusammenhang, der zwischen den aufgestellten Wahrheiten herrschet, am Richtigsten zu beurtheilen und am Deutlichsten nachzuweisen.”
- 76.
“[Z]ur Beurtheilung der Frage, ob eine gegebene Wahrheit Grund- oder Folgewahrheit sey, und in dem letzteren Falle, aus welchen, anderen Wahrheiten sie erfolge, [ist es sehr nothwendig (S.R.),] die einzelnen Theile zu kennen, aus welchen sie selbst sowohl, als auch die Wahrheiten, die man für ihren Grund ausgeben will, zusammengesetzt sind. Eine Zergliederung des gegebenen Satzes, die sich, sofern wir es vermögen, bis auf dessen einfache Theile erstrecket, wird also wohl unser erstes Geschäft bei dieser Aufgabe seyn müssen.”
- 77.
This is also strongly suggested in WL III, 453ff.
- 78.
I will assume that the suggestion as to how Bolzano’s claim (C) can be applied to such cases I discuss below is also valid for the case of complex fundamental truths (should there be any) and simple non-fundamental truths (should there be any).
- 79.
“Da dieses ganz allgemein gilt, so gilt es auch in dem Falle, wenn diese Begriffe ganz einfach sind” (WL III, 180).
- 80.
Lapointe also refers to Bolzano’s earlier writings in which we find this idea quite explicitly stated. To convince oneself of a fundamental truth (a Grundsatz in the terminology of Bolzano 2004/1810), one proceeds by finding
some generally accepted and unmistakably clear propositions which are however basically nothing but consequences, and even judgements inferred from that axiom [Grundsatz, SR] which we wish to deduce. By making this connection apparent we will become convinced of the truth of the axiom itself. (Bolzano 2004/1810 II, §21, note)
For a discussion of this idea, consider Rusnock (2000), pp. 23, 43, 51ff.
Bibliography
Ayer, A.J. 1946. Language truth and logic, 2nd ed. New York: Dover.
Berg, J. 1962. Bolzano’s logic. Stockholm: Almqvist & Wiksell.
Berg, J. 1987. Einleitung des Herausgebers. In Bernard Bolzano Gesamtausgabe, Reihe 1, Bd. 12,1, ed. J. Berg a.o., 5–62. Stuttgart Bad-Cannstatt: Frommann-Holzboog.
Berg, J. 2003. Bolzano’s heuristics. In Bernard Bolzanos Leistungen in Logik, Mathematik und Physik, ed. E. Morscher, 35–56. Sankt Augustin: Academia Verlag.
Betti, A. 2010. Explanation in metaphysics and Bolzano’s theory of ground and consequence. Logique et Analyse 211(53): 281–316.
Betti, A. 2012. Bolzano’s universe: Truth, logic and metaphysics. In Categories of being: Essays on metaphysics and logic, ed. L. Haaparanta and H.J. Koskinen, 167–190. Oxford: Oxford University Press.
Bolzano, B. 1804. Betrachtungen über einige Gegenstände der Elementargeometrie. Prag: Karl Barth.
Bolzano, B. 1969ff./1837 [WL]. Wissenschaftslehre. In Bernard Bolzano Gesamtausgabe, Reihe 1, Bd. 11–14, ed. J. Berg a.o. Stuttgart Bad-Cannstatt: Frommann-Holzboog.
Bolzano, B. 1975/1833–41. Translated in on the mathematical method and correspondence with Exner, ed. P. Rusnock and R. George. Amsterdam/New York: Rodopi.
Bolzano, B. 1978/1848. Selbstkritik der Wissenschaftslehre. In Bernard Bolzano Gesamtausgabe, Reihe 2A, Bd. 12/2, ed. J. Berg a.o., 187–189. Stuttgart-Bad Canstatt: Frommann-Holzboog.
Bolzano, B. 2004/1810. Contributions to a better-grounded presentation of mathematics. In The mathematical works of Bernard Bolzano, ed. S. Russ, 83–138. Oxford/New York: Oxford University Press.
Bolzano, B., and F. Exner. 2004. Selections from the Bolzano Exner correspondence. In On the mathematical method and correspondence with Exner, ed. P. Rusnock and R. George. Amsterdam/New York: Rodopi.
Buhl, G. 1961. Ableitbarkeit und Abfolge in der Wissenschaftstheorie Bolzanos. Köln: Kölner Universitätsverlag.
Carnap, R. 1956. Meaning and necessity. A study in semantics and modal logic, 2nd ed. Chicago/London: The University of Chicago Press.
Centrone, S. 2011. Begründungen bei Bolzano und beim frühen Husserl. Zeitschrift für Philoso-phische Forschung 65(1): 1–23.
de Jong, W.R. 2001. Bernard Bolzano, analyticity and the Aristotelian model of science. Kant Studien 92(3): 328–349.
Frege, G. 1987/1884. Die Grundlagen der Arithmetik. Stuttgart: Reclam.
George, R. 1999. Anschauungen bei Kant und Bolzano. In Bernard Bolzanos geistiges Erbe für das 21. Jahrhundert, ed. E. Morscher, 129–144. Sankt Augustin: Academia Verlag.
Kant, I. 1787. Kritik der reinen Vernunft. Riga: Hartknoch.
Kant, I. 2001/1783. Prolegomena zu einer jeden künftigen Metaphysik, die als Wissenschaft wird auftreten können. Hamburg: Meiner.
Konzelmann Ziv, A. 2008. Naturalized rationality – A glance at Bolzano’s philosophy of mind. Baltic International Yearbook for Cognition, Logic and Communication, ‘200 Years of Analytical Philosophy’ 4: 1–12.
Künne, W. 2008. Analyticity and logical truth: From Bolzano to Quine. In Versuche über Bolzano, ed. W. Künne, 233–303. Sankt Augustin: Academia Verlag.
Lapointe, S. 2010. Bolzano, a priori knowledge and the classical model of science. Synthese 174: 263–281.
Morscher, E. 2008. Bolzano’s life and work. Sankt Augustin: Academia Verlag.
Proust, J. 1989. Questions of form: Logic and the analytic proposition from Kant to Carnap. Minneapolis: University of Minnesota Press.
Quine, W.V.O. 1977a. Carnap on logical truth. In Ways of Paradox and other essays. Revised and enlarged edition, ed. W.V.O. Quine, 107–132. Harvard: Harvard University Press.
Quine, W.V.O. 1977b. Truth by convention. In Ways of Paradox and other essays. Revised and enlarged edition, ed. W.V.O. Quine. Harvard: Harvard University Press.
Rusnock, P. 2000. Bolzano’s philosophy and the emergence of modern mathematics. Amsterdam: Rodopi.
Sartwell, C. 1991. Knowledge is merely true belief. American Philosophical Quarterly 28: 157–165.
Sebestik, J. 2011. Bolzano’s logic. In The Stanford encyclopedia of philosophy, ed. E. Zalta, winter 2011 edition.
Siebel, M. 1999. Bolzanos Erkenntnistheorie. In Bernard Bolzanos geistiges Erbe für das 21. Jahrhundert, ed. E. Morscher, 59–95. Sankt Augustin: Academia Verlag.
Strawson, P.F. 1966. The bounds of sense. An essay on Kant’s critique of pure reason. London/New York: Routledge.
Tatzel, A. 2002. Bolzano’s theory of ground and consequence. Notre Dame Journal of Symbolic Logic 43: 1–25.
Textor, M. 1996. Bolzanos propositionalismus. Berlin/New York: Walter De Gruyter.
Textor, M. 2001. Logically analytic propositions a posteriori. History of Philosophy Quarterly 19(1): 91–113.
Acknowledgements
This chapter has profited considerably from discussions with Arianna Betti and Iris Loeb. I am also indebted to comments and suggestions from Johan Blok, Anthony Booth, Lieven Decock, Wim de Jong, Sebastian Lutz, Rik Peels, and Herman Philipse and an anonymous referee. Work on this chapter was made possible by ERC Starting Grant TRANH 203194.
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Roski, S. (2013). A Priori Knowledge in Bolzano, Conceptual Truths, and Judgements. In: van der Schaar, M. (eds) Judgement and the Epistemic Foundation of Logic. Logic, Epistemology, and the Unity of Science, vol 31. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5137-8_8
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