Sandra Lapointe

Bolzano a priori knowledge, and the Classical Model of Science

This paper is aimed at understanding one central aspect of Bolzano’s views on deductive knowledge: what it means for a proposition and for a term to be known a priori. I argue that, for Bolzano, a priori knowledge is knowledge by virtue of meaning and that Bolzano has substantial views about meaning and what it is to know the latter. In particular, Bolzano believes that meaning is determined by implicit definition, i.e. the fundamental propositions in a deductive system. I go into some detail in presenting and discussing Bolzano’s views on grounding, a priori knowledge and implicit definition. I explain why other aspects of Bolzano’s theory and, in particular, his peculiar understanding of analyticity and the related notion of Ableitbarkeit might, as it has invariably in the past, mislead one to believe that Bolzano lacks a significant account of a priori knowledge. Throughout the paper, I point out to the ways in which, in this respect, Bolzano’s antagonistic relationship to Kant directly shaped his own views.

Meaning and Analysis

We say of a sentence or a sentence utterance that it is context-sensitive when its truth or falsehood depends on certain elements that only the context of utterance can reveal. Sentence utterances that contain indexical expressions such as ‘here’, ‘now’, ‘yesterday’, ‘she’ or ‘this’ are such that what they mean — and what they refer to — can shift from context to context. What ‘It is windy today’ refers to, that is, the weather on the day it is uttered, at the place it is uttered, will sometimes make it false, sometimes make it true — since it can be uttered on different more or less windy days or in different more or less windy places. By contrast, an utterance of ‘2 + 2 = 4’ is typically considered not to be context-sensitive since it is true no matter what the context in which it is uttered. On Bolzano’s account, context-sensitive sentences are semantically underdetermined: they do not express the proposition that forms their content “completely”. Only sentences that are “eternally” or “immutably” true (or false), that is, only sentences that are not context-sensitive express their content completely in the sense that is relevant to Bolzano. The purpose of analysis in his theory is to reveal the “Sinn” of expressions (cf. 1837, §285, 67).

Bolzano, Kant, and Leibniz

The few decades that extend from the publication of the Critique of Pure Reason (1781) to what some consider the ‘high water mark’ of German Idealism, Hegel’s elaboration of his philosophical system in the Encyclopedia of all philosophical sciences (1817), make for a fascinating period in intellectual history. While it has been extensively studied by scholars of post-Kantian Idealism, this scholarly literature has been, in important respects, one-sided. In contrast to what is often assumed, the history of the influence of Kant’s critical philosophy in the German-speaking world is not merely the story of the development of idealism in the works of Fichte, Schelling, and Hegel.1 It is also the story of the development of logic at the turn of the nineteenth century. While Kant himself is not usually considered to have made a substantial contribution to logic itself, his work was seminal and his influence — both positive and negative — on the logic of his time considerable. There were, on the one hand, those who attempted to devise logics based on the Critique. There was, on the other hand, Bernard Bolzano.2 Bolzano engaged with Kant and the Kantian logicians, sought to determine what is distinctive in their approach and their overall conception of the role of logic in epistemology at large. He also subjected their views to a withering criticism.

Things, Collections and Numbers

While Bolzano’s theory of collections has been compared to set-theory and Lesniewskian-type mereology, it can be reduced to neither.1 His analyses present a vast historical interest and arguably a philosophical one as well — the latter as long as they are considered for what they are: an investigation in the nature of collective entities whose results are put to work in Bolzano’s semantics as well as in his philosophy of mathematics. Bolzano’s collections (Inbegriffe) are neither sets, nor mereological sums, nor classes. What they are follows from the following tentative definition: One very important genus of complex ideas that we encounter everywhere are those in which the idea of collection (Inbegriff) appears. There are many types of the latter […] I must first determine with more precision the concept I associate with the word collection. I use this word in the same sense as it is used in the common usage and thus understand by a collection of certain things exactly the same as what one would express by the words: a combination (Verbindung) or association (Vereinigung) of these things, a gathering (Zusammensein) of the latter, a whole (Ganzes) in which they occur as parts (Teile). Hence the mere idea of a collection does not allow us to determine in which order and sequence the things that are put together appear or, indeed, whether there is or can be such an order. […] A collection, it seems to me, is nothing other than something complex (das Zusammengesetztheit hat). (1837, §82, 393)

A priori Knowledge

What Bolzano had to say about the Kantian conception of a priori knowledge in his early essay on the philosophy of mathematics, the Contributions to a Better Founded Exposition of Mathematics, is valuable on many accounts. In the Appendix to the latter — the title is On the Kantian Doctrine of the Construction of Concepts in Intuition — Bolzano criticises Kant’s doctrine of pure intuition. The views he puts forward in the latter have been discussed in some detail (Laz 1993; Rusnock 2000; Sebestik 1992).1 In fact, commentators tend to rely exclusively on this short text when it comes to assessing Bolzano’s criticism of Kant’s views on a priori knowledge. In 1810, however, Bolzano’s theory remained overall tentative. In particular, Bolzano did not provide a substantial alternative to Kant’s views. By contrast, in the Theory of Science, Bolzano not only offered a thorough and mature criticism that became the basis for the comprehensive assessment of Kant’s philosophy later published under the title The New Anti-Kant (Přihonský 1850) but also developed his own alternative conception of a priori knowledge.

Husserl, Logical Psychologism and the Theory of Knowledge

It is often claimed that Frege was the one to have steered the “early” Husserl away from his presumed psychologism: Frege according to a widespread opinion was the one who prompted Husserl’s criticism of psychologism in the Logical Investigations (cf. Bell 1994; Follesdal 2001). It is clear that there were intellectual connections between Husserl and Frege at the time Husserl was first coming to grips with the issue in the early 1890s (see for instance the Frege-Husserl correpondence, in Bernet et al. 2005, 20–31). But in light of Husserl’s 1896 lectures on logic, it is much clearer that the real impetus behind Husserl’s criticism was Bolzano’s Theory of Science. Husserl’s antipsychologistic position rests on a meta-epistemological reflection that has two aims. The task is to fix the respective domains of the sub-disciplines that belong to the theory of knowledge in order to explain how these sub-disciplines are connected. In this regard, Husserl considerably diverges from Frege whose treatment of metaphilosophical questions of this type is insubstantial. Directly and indirectly — “indirectly” because Twardowski played an important role in Husserl’s rediscovery of Bolzano around 1894 — Husserl is indebted to Bolzano for many of his views on the nature of logic, its relation to psychology and their respective role within the theory of knowledge.

Kant and German Philosophy

In the introduction, I’ve sketched a landscape of the cultural context in which Bolzano’s work evolved. I argued that different sociological factors such as the anti-intellectual spirit of educational policies in Austria partly explain the lack of attention his work received until recently. Because of its broad liberality and emphasis on autonomous thought, Bolzano’s social and political philosophy — which he presented in part in his edifying speeches — was associated in the mind of the Austrian establishment with Kant’s. This led in Bolzano’s early career to a series of vexations. In Austria, being accused of “Kantianism” was not unusual and often served as a pretext to oust detractors of the State — mostly Jesuits and Free-Masons (see Sauer 1982, 267ff.).1 These accusations were, in Bolzano’s case, consequential enough to threaten his academic position. The number of those who were dismissed under the same pretext is significant. It included Lazarus Ben-David from Vienna in 1793, Anton Kreil from Pest in 1795, Stephan Tichy from Kaschau in 1795 and Benedikt Feilmoser from Innsbruck in 1820.

Frege, Meaning and Communication

In Dialogue de connexione inter verba et res, Leibniz was concerned with the question as to what entity should bear the predicate ‘is true’. The discussion pertains to the question whether ‘is true’ should be ascribed to “things” or to “thoughts”. The property of being true, Leibniz observed, cannot be ascribed to thoughts since a truth, for instance, that the surface described by a fixed length on a plane is a circle does not depend on the fact that it be thought. But the predicate ‘is true’ cannot be ascribed to things either. As Leibniz sees it, whatever can be said to be true can also in principle be called false but, according to Leibniz, it does not make sense to say that things are false. Leibniz takes the solution to consist in ascribing truth to neither the former nor the latter but to what he calls propositio or cogitationes possibile (possible thoughts). Notwithstanding certain definitional qualifications,1 it is to this Lebnizian idea -which he also ascribes to the Stoics — that Bolzano appeals when he asserts that he was not the first to have put forward the notion of a Satz and sich (cf. Bolzano 1837, §21, 84, 85).

A Substitutional Theory

Considering later developments in the field, two aspects of Bolzano’s semantics are particularly significant: his definition of Ableitbarkeit and his definition of “logical analyticity”. The first — Bolzano’s attempt at an analysis of statements of the form ‘if…, then…’ — has often been compared to Tarski’s notion of logical consequence, and as we will see in Chapter 6, there are good reasons to maintain the comparison. The second anticipates the Quinean definition of logical truth and will be discussed in some detail in the next chapter. Both notions are common themes in the literature. Yet, important features of both have been neglected. Consequently, their role in Bolzano’s theory has often been misunderstood with the upshot that crucial aspects of Bolzano’s theory as a whole have been completely overlooked. The concern that is at the core of virtually every discussion of Bolzano’s substitutional method is that the latter does not deliver the kind of results one would reasonably expect when it comes to defining analyticity and consequence and, in particular, that it does not account for the kind of epistemic and metaphysical necessity those notions are assumed to carry with them.

Justification and Proof

Bolzano’s theory of objective ground and consequence is part of a general account of a priori knowledge and a theory of demonstration or proof — note here that I do not use the term ‘proof theory’ which Bolzano’s theory is not — that has attracted some attention in recent years. When it comes to explaining the nature of deductive knowledge at large, Bolzano distinguishes between three notions: grounding (Abfolge), objective justification (objective Erkenntnisgrund) and what we may call objective demonstrations or proofs, which Bolzano calls Begrundungen. This tripartite distinction in itself testifies to Bolzano’s refined sense for the differences between logical, epistemological and pragmatic concerns: grounding is a relation between true propositions; objective justification is a relation between beliefs or cognitions (i.e., certain types of epistemic states); and Begrundungen are linguistic objects that are meant, according to Bolzano, to reliably cause in agents objectively justified knowledge of the type we find in a priori sciences such as mathematics. Roughly, the structure of the theory is the following: (i) grounding is a relation that subsists, according to Bolzano, between true propositions independently of epistemic access to them. We may grasp grounding relations and (ii) our grasping the latter is also the condition for our having objective justifications for our beliefs, as opposed to, say, merely subjective or evidential ones.