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Bolzano and Kim on grounding and unification

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Abstract

It is sometimes mentioned that Bernard Bolzano’s work on grounding anticipates many insights of the current debate on metaphysical grounding. The present paper discusses a certain part of Bolzano’s theory of grounding that has thus far not been discussed in the literature. This part does not so much anticipate what are nowadays common assumptions about grounding, but rather goes beyond them. Central to the discussion will be a thesis of Bolzano’s by which he tries to establish a connection between grounding and (deductive) unification. The paper spells out this thesis in detail and discusses the assumptions on which it rests. Next to this mainly historical aim, the paper also presents reasons why philosophers who are not interested in the historical Bolzano should find the thesis interesting by relating it to a certain view on unification and explanation that has been put forward by Kim. A final part of the paper provides a critical evaluation of the thesis against the background of current accounts of grounding.

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Notes

  1. Cf. Tatzel (2002), Lapointe (2010), Betti (2010), Textor (2013), Rumberg (2013), Schnieder (2014), Roski and Rumberg (2016), and Roski (2017). Consider also the Bolzano-inspired account by Poggiolesi (2016).

  2. A minor exception are two texts that are difficult to access, not written in English, and only provide a rather cursory discussion of the relevant passages, namely Buhl (1961, p. 63ff) and Kambartel (1963, pp. L–LII). I will briefly comment on both below. The thesis is also discussed in my (2017, chs. 4.3.7–9), which was still in the making when the present paper was submitted. The present paper extends and complements that discussion in various respects.

  3. ‘WL’ refers to Bolzano’s Wissenschaftslehre (1985ff/1837). I refer to passages of the WL in the following format:<paragraph> [<volume>.<page>]. Unless indicated otherwise, I follow the translation by Rusnock and George (2014).

  4. See Kim (1994).

  5. The term ‘unification’ is not used uniformly in ordinary or philosophical discourse. In the present paper, I follow a certain use of the term that has been popularized by Friedman (1974) and taken up by Kitcher (1989), according to which unification is cashed out (very roughly) in terms of being a minimal deductive base.

  6. For a general overview of Bolzano’s theoretical philosophy, see Lapointe (2011) and Morscher (2014).

  7. This is a natural option for conceptualists about grounding in the sense of Correia (2010). Roughly speaking, conceptualists take grounding to be a relation among propositions or take grounding-claims to be otherwise sensitive to representational features. Conceptualists are opposed to adherents of wordly conceptions of grounding which do not take grounding-claims to be sensitive to any representational features and often construe it as a relation among relatively coarse-grained facts. Conceptualist theories of grounding are defended by Correia (2016), as well as Schnieder (2011). Correia (2016, p. 1) also classifies Fine (2012a) as a conceptualist, and the account of Rosen (2010) can be viewed in this light, too. The account of Audi (2012), on the other hand, is a paradigmatic example for a worldly conception of grounding.

  8. Cf. WL, §203. Bolzanian collections are mereological compounds of various sorts. When I speak of collections of propositions, I will take propositions (rather than their non-propositional parts) to be their atoms. For reasons of simplicity, I will allow the limiting case of a ‘collection’ containing only a single proposition. I will often use set-theoretic notation to express relations among collections.

  9. See Künne (1997) for an in-depth comparison.

  10. This view is strongly suggested by the remarks in WL, §45 [I.206]. That each truth that p grounds the truth that it is true that p is explicitly stated in WL, §205.

  11. For a recent discussion, see Morscher (2014, §3.4).

  12. For more on Bolzano’s notion of substitution (usually called ‘variation’), cf. Morscher (2014) and Morscher (1997).

  13. Cf. e.g., Quine (1970, p. 48ff).

  14. See WL, §155. Note that the definition involves a slight simplification. Bolzano takes deducibility to obtain primarily between collections of premises and collections of conclusions. For the purposes of the present paper, however, there is no need to take this feature of his theory into account.

  15. Note also that deducibility with respect to all ideas that occur in premises and conclusion of a given argument cannot be what Bolzano has in mind when he seems to write about a binary version of deducibility. This notion would be prohibitive in an extreme way: the uniform simultaneous substitution of all ideas that occur in premises and conclusion of a given argument, including logical ideas, will almost always allow for cases in which the premises are true and the conclusion is false; except for limiting cases in which some premise is identical to the conclusion.

  16. See, for instance, WL, §300 [III.124]. Due to his non-standard views on the form of propositions, Bolzano’s list of logical notions does not coincide entirely with the now standard lists of logical notions. When it comes to concrete cases, however, he would classify most arguments as logically valid that are considered logically valid on modern assumptions. See Rusnock and Burke (2010) for a recent discussion of logical notions in Bolzano.

  17. See WL, §177 and cf. Tatzel (2002, p. 3). Cf. Correia and Schnieder (2012, pp. 22–24) on the connection between metaphysical grounding and ‘because’.

  18. Cf. WL, §205 for (a); WL, §§199 and 221.7 for (b); and WL, §198 for (c).

  19. Cf. WL, §§168, 177. For a helpful discussion of this point see Tatzel (2002, p. 3).

  20. Perhaps needless to say, sometimes the ground of a given truth can also serve as evidence for its truth.

  21. For a thorough discussion of the idea see Schnieder (2014). Interestingly, we find a somewhat similar idea in Kitcher (1989, p. 420).

  22. For a comprehensive discussion of Bolzano’s account see Tatzel (2002) and Roski (2017). Cf. also Rumberg (2013), and Roski and Rumberg (2016). Roski (2017, ch. 5) provides a comparison between Bolzano’s account and modern conceptions of metaphysical grounding. Correia and Schnieder (2012) provide a helpful overview of the contemporary debate on grounding, cf. also Bliss and Trogdon (2016).

  23. Note that (i) is, strictly speaking, only a partial immediate consequence of (ii) and (iii). Bolzano assumes that the immediate consequence of every truth and of every collection of truths encompasses more than one truth; cf. WL, §205 [II.358]. This latter assumption won’t play a role in the remainder of this paper, though.

  24. The notation is similar to the one introduced by Fine (2012b). Note, however, that in Fine’s framework, ‘<’ and ‘\(\prec \)’ are sentential connectives that take (lists of) sentences and deliver sentences, whereas here they are predicates that take names for propositions or collections thereof and deliver sentences.

  25. See Rumberg (2013, p. 437) for a precise definition.

  26. With the exception of the more careful remarks by Correia and Schnieder (2012, p. 24) and Schnieder and Steinberg (2016, §2.e–f), it seems to be a consensus in the current debate that grounding is an explanatory relation in some straightforward sense.

  27. Bolzano uses ‘explanation’ (Erklärung) officially as a term for the proper (decompositional) analysis of a given concept. See, however, WL, §500 [IV.213]; WL, §484 [IV.189]; and Bolzano (1981, pp. 132–133).

  28. Cf. WL, §198 [II.341]; WL, §525 [IV.262]; and Bolzano (1841, p. 67). For the distinction in Aristotle see APo, 71\(^{b}\)20–22 and 78\(^{a}\)20ff and the corresponding comments in Barnes (1993, p. 155ff).

  29. Cf. Bromberger (1965). This view is admittedly not obligatory. One may instead adopt a position similar to Lewis’s liberal view on causal explanation. Lewis distinguishes the acts of giving explanations from the information typically communicated by such acts (call the latter ‘explanatory information’). He then claims that any information about the causal history of an event is explanatory information with respect to this event and attempts to account for the (alleged) pragmatic or epistemic factors of explanations in terms of general conditions for successful communication that pertain to the acts of giving explanations; cf. Lewis (1986, §V). Analogously, one could argue that any information about the grounds of a given truth is explanatory and distinguish among good and bad ways to give grounding-based explanations in terms of general conditions for successful communication. However, there are good reasons to resist Lewis’s liberal view on explanatory information; see Ruben (2012, p. 161) and cf. Schnieder and Steinberg (2016, §2.e–f) as well as Schnieder (2015, p. 183).

  30. See Ruben (2012, p. 194) and Kim (1994, p. 56ff), and consider, also Schnieder’s (2010, 2015) work on the semantics of ‘because’.

  31. Cf., e.g., Schaffer (2016) and Audi (2012).

  32. See WL, §512ff. Note that Bolzano’s conception of a proof is thus in one respect different from contemporary notions of proof. A proof in his sense is not merely a valid argument, but also needs to be convincing in a certain sense.

  33. Cf. Roski (2014, p. 350ff) for a discussion of Bolzano’s views on explanatory proofs.

  34. Cf. Textor (2013, pp. 20–22) for more on the historical context. Bolzano’s own remarks in the note to WL, §133 are also helpful in this respect. It should be emphasized that there are numerous differences between the details of each of the aforementioned authors’ accounts. It should also be emphasized that Bolzano does not take conceptual truths to be trivially knowable or self-evident. Nor does the distinction between conceptual and intuitional truths coincide with the analytic/synthetic-distinction. For more on the relation of both distinctions in Bolzano, cf. Textor (2001).

  35. For the record: according to Bolzano, a truth is intuitional iff it contains at least one constituent that is absolutely simple and uniquely picks out exactly one object. A truth is conceptual iff is not intuitional. See WL, §133. Textor (1996) offers a comprehensive study of the distinction. Textor (2013) moreover offers a proposal concerning the motivation of the distinction. Cf. also Textor (2001) and Rusnock (2012).

  36. Cf. WL, §132 [II.29f], §143[II.66], §144 [II.69], and Bolzano (1975/1933ff, §3).

  37. See Textor (2013, p. 15f) for what might have been Bolzano’s motivation to endorse this principle.

  38. Consider Arnauld and Nicole (1996/1683, p. 256): “always to start with the simplest and most general things, to proceed next to the more composite and particular”. Cf. APo 85-6 as well as Descartes (1996, p. 6:20).

  39. Correia (2014, p. 35) and Fine (2012a, p. 58ff) would, for instance, endorse a complexity constraint for the variety of grounding that is often called ‘logical grounding’. Roughly speaking, in the systems they propose, introduction-rules that allow to derive more from less complex propositions are endowed with explanatory import, whereas complexity-reducing elimination-rules for logical connectives are never explanatory. Consider also the remarks by Schnieder on conceptual explanations (2006, p. 406) and the Bolzano-inspired account of grounding by Poggiolesi (2016), which crucially incorporates a complexity constraint. To be clear, that an idea is widely endorsed falls, of course, short of a proof of its viability: it should be stressed that Complexity is a substantial claim rather than a truism about grounding.

  40. Bolzano’s argument is as follows (cf. WL, §221.3). First, note that if there are only finitely many different simple constituents of conceptual truths (Finitude), then for any n, the number of different conceptual truths that have a degree of complexity of at most n must be finite. (This is essentially simple combinatorics: one cannot generate infinitely many different complex items of a finite degree of complexity from a finite stock of atoms.) Now consider any given conceptual truth \(\psi \) of some finite degree of complexity, say of degree n. Call the collection of mediate grounds of \(\psi \) ‘\(G_\psi \)’. From Conceptuality it follows that every truth in \(G_\psi \) is a conceptual truth. From Complexity it moreover follows that every truth in \(G_\psi \) is of a degree of complexity of at most n. But we have seen earlier that there is at most a finite number of those conceptual truths given Finitude. Since mediate grounding is asymmetric and transitive, it follows that \(G_\psi \) must contain fundamental truths. For a more detailed reconstruction of the argument see Roski (2017, pp. 117–120).

  41. Cf. WL, §221.3 [II.386].

  42. The present version of the unification thesis does not include a certain restriction Bolzano makes earlier in the text. Incorporating this distinction at this point, however, makes the discussion of the thesis significantly and unnecessarily more complicated for present purposes. I will briefly turn to the restriction below.

  43. We may do this without loss of generality. Clearly, Bolzano cannot have any stronger notion of order in mind (i.e., a linear order), as this would—absurdly—exclude the order induced by grounding from consideration. We may also safely ignore a weaker notion such as a non-strict partial ordering. The reflexive closure of a strict partial ordering, cannot yield less initial premises than the corresponding strict partial ordering.

  44. See WL, §200. Bolzano’s holds this view apparently merely because of a single purported counterexample that concerns the grounds of a certain ethical truth. The example is not unproblematic; cf. Tatzel (2003) and Betti (2010) for discussion.

  45. It is easy but rather cumbersome to reformulate the thesis in a way that takes such cases into account. See Roski (2017, p. 170) for such a reformulation.

  46. See Friedman (1974, p. 18).

  47. See Friedman (1974, p. 17f). As Kitcher (1976) pointed out, Friedman’s own suggestion of how to solve this problem fails.

  48. Whether the solution works depends, in general, on how one construes the relata of the explanatory relation, on how one understands the pertinent notion of complexity, and of course on the pertinent view of explanation.

  49. Note that the present reconstruction of the unification thesis takes Bolzano’s use of the superlative and the definite description in (U) and (U\(^*\)) (“the smallest”) seriously. According to this reading, the fundamental truths in any collection \(Con_n\) form a unique smallest deductive base for the remaining truths. This entails that there cannot be a collection of truths of the same cardinality as the fundamental truths from which the same number of truths in a given collection \(Con_n\) is I-deducible. This is a strong claim. However, virtually everything I say below would also hold if one were to ascribe to Bolzano merely the weaker claim that the fundamental truths in a given collection \(Con_n\) are a minimal collection from which the remainder is I-deducible (i.e., a claim that results from substituting ‘>’ for ‘\(\geqslant \)’ in the principle above). In particular, all corollaries mentioned in this section would also hold on this weaker reading.

  50. See WL, §148.3 for a definition of this notion and cf. Künne (2008) and Rusnock (2013) for further discussion of Bolzano’s conception of logical analyticity.

  51. See Schnieder (2011, p. 456).

  52. Cf. Buhl (1961, p. 64) and Kambartel (1963, p. LII).

  53. Cf., again, Aristotle (1993, p. 86\(^a\)) as well as Arnauld and Nicole (1996/1683, p. 256). For discussion, consider Betti and de Jong (2010) and Roski (2014, p. 319ff).

  54. Cf. the remarks by Betti and de Jong (2010) on what they call the ‘domain postulate’.

  55. Cf. WL, §483 for both points and Roski (2014, ch. 6.3.2) for further discussion.

  56. See, in particular, Friedman (1974, p. 17f). Another famous advocate of the unification theory of explanation is Kitcher (1989), whose conception of unification is, however, is some respects different from the one that we find in Bolzano’s unification thesis. I will come back to Kitcher’s conception by the end of the paper.

  57. This aspect of the account is often viewed as problematic. It has been argued, in particular, that the unification theory leaves mysterious how agents should ascertain whether the explanation of an individual proposition is successful; cf. e.g., Woodward (2003, p. 369ff) and Kim (1994, p. 64f).

  58. While Bolzano contemplated in passing that grounding may be defined in terms of the property specified by the unification thesis, he ultimately remained sceptical of the prospects of this idea; cf. WL, §221.note [II.388]. Consider Betti (2010) and Roski (2017, ch. 4.6) for further discussion.

  59. Another view that seems to resemble Bolzano’s unification thesis in certain respects is Lewis’s best systems account of laws of nature; cf. Lewis (1994). To explore this connection is, however, a topic for future research.

  60. See, however, Roski (2017, ch. 4.3.9).

  61. Note that there may be different kinds of understanding apart from understanding-why that explanations can give rise to, such as understanding-how. Moreover, it has been argued that one may understand why a fact obtains without being able to construct an explanation for that fact; cf. Lipton (2009) for both points.

  62. Cf. moreover Ruben (2012, pp. 12–13).

  63. Friedman (1974, p. 15). Cf. also Kvanvig (2003, p. 192f).

  64. Note that I take Kim’s talk of ‘simplification’ here as a stylistic variant of ‘unification’. The sense of ‘simplification’ that Kim seems to have in mind here is precisely the sense in which to simplify means to show how various apparently unconnected phenomena can be traced back to a common source.

  65. Similarly to Kim, I will speak of phenomena and events standing in explanation-backing relations. In the case of interest to us, the relata will of course be truths or facts, but for the sake of brevity I will for the moment adjust my terminology to Kim’s.

  66. See footnote 35 for the definition. For an extended discussion of this point see Textor (1996, ch. 5).

  67. The following discussion will thus be relevant mostly for so-called ‘conceptualist’ views of grounding (see footnote 7). To investigate how formulations of the unification thesis for worldly conceptions of grounding would lead too far astray in the context of this paper.

  68. The respective principles are defended by, among others, Fine (2012a), Rosen (2010), Schnieder (2011), and Correia (2014).

  69. Versions of this principle are defended, for instance, in Fine (2012a, p. 59ff), Correia (2014, p. 44ff), and Schnieder (2011, §5.1). As far as I can see, there is no indication that Bolzano would have endorsed the principle.

  70. See footnote 40 above for an argument establishing this.

  71. See Rosen (2010, pp. 119–120).

  72. I am grateful to an anonymous referee for pushing me on this issue.

  73. Bolzano himself might not have shared this assumption given his broadly Leibnizian view of the mental; cf. Chisholm (1991). Be that as it may, the problem obviously does not hinge on this particular view.

  74. See, e.g., Rosen (2010, p. 118) for the entailment assumption. The assumption is not fully uncontroversial, though; cf. Skiles (2015).

  75. Cf. Sider (2011, §1.3). Arguably, this class satisfies Weak Closure.

  76. Note that the present solution to the Entailment Problem is not necessarily wedded to Sider’s particular view about which terms are structural. It is in principle also compatible with the view that structural terms pick out, e.g., mental properties. On such a conception, however, the unification thesis won’t be compatible with physicalism, understood as the view that truths about mental properties are exclusively grounded in truths about physical properties. Otherwise, the Entailment Problem reappears. For, again, truths about mental properties are not in general logically deducible from truths about physical properties alone. Hence, if truths about mental properties are expressible in purely structural terms, some of them have to be fundamental. Another way to circumvent the Entailment Problem is to adopt a conception on which the fundamental truths incorporate certain ‘bridge principles’ that allow to logically deduce truths about mental properties from truths about physical ones. It is unclear, however, whether Complexity\(_K\) still holds when bridge principles are among the fundamental truths. A way get rid of this problem is to think of bridge principles as a sui generis kind of truths, different from fundamental and non-fundamental ones. (See Dasgupta (2014) and deRosset (2013, §5)) for a general discussion of such an idea and of the question to what extent it is compatible with physicalism.) Such a view would, however, require some amendments to the scope of the unification thesis. I will discuss such amendments briefly in the next sub-section.

  77. Cf. e.g., Rosen (2010, p. 131), Audi (2012, p. 693), and, more generally, Wilsch (2015), Dasgupta (2014), and deRosset (2013, §5). Indeed, it seems clear that Bolzano also acknowledged general principles that govern particular cases of grounding; cf. WL, §199.

  78. Note that this modification of the thesis would also suggest a solution to the Entailment Problem mentioned in the previous section: while truths about mental properties may not be logically deducible from truths about physical properties simpliciter, they may well be logically deducible from physical truths against the background of certain laws that connect physical to mental properties.

  79. Schnieder (2016, §3) seems to rely on a related idea.

References

  • Aristotle (1993). Posterior analytics (J. Barnes, Trans.). Oxford: Clarendon Press.

  • Arnauld, A., & Nicole, P. (1996/1683). Logic or the art of thinking. Cambridge, UK: Cambridge University Press.

  • Audi, P. (2012). Grounding: Toward a theory of the in-virtue-of relation. The Journal of Philosophy, 109(12), 685–711.

    Article  Google Scholar 

  • Barnes, J. (1993). Commentary. In J. Barnes (Ed.), Aristotle: Posterior analytics. Oxford: Clarendon Press. pp 81ff.

    Google Scholar 

  • Betti, A. (2010). Explanation in metaphysics and Bolzano’s theory of ground and consequence. Logique et Analyse, 211(53), 281–316.

    Google Scholar 

  • Betti, A., & de Jong, W. R. (2010). The classical model of science. A millenia-old model of scientific rationality. Synthese, 174(2), 185–203.

    Article  Google Scholar 

  • Bliss, R., Trogdon, K. (2016). Metaphysical grounding. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy, winter 2016 edn. http://plato.stanford.edu/archives/sum2012/entries/grounding/.

  • Bolzano, B. (1841). Bolzanos Wissenschaftslehre und Religionswissenschaft in einer beurtheilenden Übersicht (published anonymously). Sulzbach: Seidel.

    Google Scholar 

  • Bolzano, B. (1975/1933ff). Von der mathematischen lehrart. In J. Berg (Ed.), Bernard Bolzano Gesamtausgabe, Reihe 2A, Bd. 7 (pp. 46–97). Stuttgart-Bad Cannstatt: Frommann-Holzboog.

  • Bolzano, B. (1981). Philosophische Tagebücher. In J. Berg (Ed.), Bernard Bolzano Gesamtausgabe, Reihe 2B, Bd. 16/1. Stuttgart-Bad Cannstatt: Frommann-Holzboog.

  • Bolzano, B. (1985ff/1837). Wissenschaftslehre. In J. Berg & E. Winter (Eds.), Bernard Bolzano Gesamtausgabe, Reihe 1, Bd. 11–14. Stuttgart-Bad Cannstatt: Frommann-Holzboog.

  • Bromberger, S. (1965). An approach to explanation. In R. J. Butler (Ed.), Analytical philosophy, 2nd series (pp. 72–105). Oxford: Basil Blackwell.

    Google Scholar 

  • Buhl, G. (1961). Ableitbarkeit und Abfolge in der Wissenschaftstheorie Bolzanos. Cologne: Kölner Universitätsverlag.

    Google Scholar 

  • Chisholm, R. (1991). Bernard Bolzano’s philosophy of mind. Philosophical Topics, 19(2), 205–214.

    Article  Google Scholar 

  • Correia, F. (2010). Grounding and truth-functions. Logique et Analyse, 53(211), 251–79.

    Google Scholar 

  • Correia, F. (2014). Logical grounds. Review of Symbolic Logic, 7(1), 31–59.

    Article  Google Scholar 

  • Correia, F. (2016). An impure logic of representational grounding. Journal of Philosophical Logic, online first, 1–32.

  • Correia, F., & Schnieder, B. (2012). Grounding: An opinionated introduction. In B. Schnieder & F. Correia (Eds.), Metaphysical grounding (pp. 1–36). Cambridge, UK: Cambridge University Press.

    Chapter  Google Scholar 

  • Dasgupta, S. (2014). The possibility of physicalism. The Journal of Philosophy, 111(9), 557–592.

    Article  Google Scholar 

  • deRosset, L. (2013). Grounding explanations. Philosophers’ Imprint, 13(7), 1–26.

    Google Scholar 

  • Descartes, R. (1996). Oeuvres de Descartes. Paris: Librairie Philosophique J. Vrin.

    Google Scholar 

  • Fine, K. (2012a). A guide to ground. In F. Correia & B. Schnieder (Eds.), Metaphysical grounding (pp. 37–80). Cambridge, UK: Cambridge University Press.

  • Fine, K. (2012b). The pure logic of ground. Review of Symbolic Logic, 5(1), 1–25.

  • Friedman, M. (1974). Explanation and scientific understanding. The Journal of Philosophy, 71(1), 5–19.

    Article  Google Scholar 

  • Kambartel, F. (1963). Einleitung des Herausgebers. In F. Kambartel (Ed.), Bernard Bolzanos Grundlegung der Logik. Hamburg: Felix Meiner. I–LXVII.

    Google Scholar 

  • Kim, J. (1994). Explanatory knowledge and metaphysical dependence. Philosophical Issues, 5, 51–69.

    Article  Google Scholar 

  • Kitcher, P. (1976). Explanation, conjunction, and unification. Journal of Philosophy, 73(8), 207–212.

    Article  Google Scholar 

  • Kitcher, P. (1989). Explanatory unification and the causal structure of the world. In P. Kitcher & W. Salmon (Eds.), Scientific explanation (pp. 410–505). Minneapolis: University of Minnesota Press.

    Google Scholar 

  • Künne, W. (1997). Propositions in Bolzano and Frege. Grazer Philosophische Studien, 53, 203–240.

    Google Scholar 

  • Künne, W. (2008). Analyticity and logical truth: From Bolzano to Quine. In W. Künne (Ed.), Versuche über Bolzano (pp. 233–303). Sankt Augustin: Academia Verlag.

    Google Scholar 

  • Kvanvig, J. (2003). The value of knowledge and the pursuit of understanding. Cambridge, UK: Cambridge University Press.

    Book  Google Scholar 

  • Lapointe, S. (2010). Bolzano, a priori knowledge and the classical model of science. Synthese, 174(2), 263–281.

    Article  Google Scholar 

  • Lapointe, S. (2011). Bolzano’s theoretical philosophy. London: Palgrave MacMillan.

    Book  Google Scholar 

  • Lewis, D. (1986). Causal explanation. In D. Lewis (Ed.), Philosophical papers (Vol. II, pp. 214–240). Oxford: Oxford University Press.

    Google Scholar 

  • Lewis, D. (1994). Humean supervenience debugged. Mind, 103(412), 473–490.

    Article  Google Scholar 

  • Lipton, P. (2009). Understanding without explanation. In H. W. de Regt, S. Leonelli, & K. Eigner (Eds.), Scientific understanding: Philosophical perspectives (pp. 43–63). Pittsburgh: University of Pittsburgh Press.

    Chapter  Google Scholar 

  • Morscher, E. (1997). Bolzano’s method of variation: Three puzzles. Grazer Philosophische Studien, 53, 139–165.

    Google Scholar 

  • Morscher, E. (2014). Bernard Bolzano. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy, fall 2014 edn. https://plato.stanford.edu/archives/fall2014/entries/bolzano/.

  • Poggiolesi, F. (2016). On defining the notion of complete and immediate formal grounding. Synthese, 193(10), 3147–3167.

    Article  Google Scholar 

  • Quine, W. V. O. (1970). Philosophy of logic. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Rosen, G. (2010). Metaphysical dependence: Grounding and reduction. In B. Hale & A. Hoffmann (Eds.), Modality: Metaphysics, logic, and epistemology (pp. 109–136). Oxford: Oxford University Press.

    Chapter  Google Scholar 

  • Roski, S. (2014). Bolzano’s notion of grounding and the classical model of science. Ph.D. thesis, Vrije Universiteit, Amsterdam.

  • Roski, S. (2017). Bolzano’s conception of grounding. Frankfurt am Main: Klostermann.

    Google Scholar 

  • Roski, S., & Rumberg, A. (2016). Simplicity and economy in Bolzano’s theory of grounding. Journal of the History of Philosophy, 54(3), 469–496.

    Article  Google Scholar 

  • Ruben, D. H. (2012). Explaining explanation (updated and extended second edition). Boulder: Paradigm Publishers.

    Google Scholar 

  • Rumberg, A. (2013). Bolzano’s concept of grounding (Abfolge) against the background of normal proofs. Review of Symbolic Logic, 6(3), 424–459.

    Article  Google Scholar 

  • Rusnock, P. (2012). Remarks on Bolzano’s conception of necessary truth. British Journal for the History of Philosophy, 20(4), 817–837.

    Article  Google Scholar 

  • Rusnock, P. (2013). Kant and Bolzano on analyticity. Archiv für Geschichte der Philosophie, 95(3), 298–335.

    Article  Google Scholar 

  • Rusnock, P., & Burke, M. (2010). Etchemendy and Bolzano on logical consequence. History and Philosophy of Logic, 31(1), 3–29.

    Article  Google Scholar 

  • Rusnock, P., & George, R. (Eds.). (2014). Bernard Bolzano: Theory of science. Oxford: Oxford University Press.

    Google Scholar 

  • Schaffer, J. (2016). Grounding in the image of causation. Philosophical Studies, 173(1), 49–100.

    Article  Google Scholar 

  • Schnieder, B. (2006). A certain kind of trinity. Philosophical Studies, 129(2), 393–419.

    Article  Google Scholar 

  • Schnieder, B. (2010). A puzzle about ‘because’. Logique et Analyse, 53(211), 317–343.

    Google Scholar 

  • Schnieder, B. (2011). A logic for ‘because’. Review of Symbolic Logic, 4, 445–465.

    Article  Google Scholar 

  • Schnieder, B. (2014). Bolzano on causation and grounding. Journal of the History of Philosophy, 52(2), 309–337.

    Article  Google Scholar 

  • Schnieder, B. (2015). The asymmetry of ‘because’. Grazer Philosophische Studien, 91, 175–208.

    Article  Google Scholar 

  • Schnieder, B. (2016). In defence of a logic for ‘because’. Journal of Applied Non-Classical Logics, 26, 160–171.

    Article  Google Scholar 

  • Schnieder, B., & Steinberg, A. (2016). Without reason? Pacific Philosophical Quarterly, 97(4), 523–541.

    Article  Google Scholar 

  • Sider, T. (2011). Writing the book of the world. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Skiles, A. (2015). Against grounding necessitarianism. Erkenntnis, 80(4), 717–751.

    Article  Google Scholar 

  • Tatzel, A. (2002). Bolzano’s theory of ground and consequence. Notre Dame Journal of Symbolic Logic, 43, 1–25.

    Article  Google Scholar 

  • Tatzel, A. (2003). Bolzano on grounding. In T. Childers & O. Majer (Eds.), The LOGICA yearbook 2002 (pp. 245–258). Prague: Filosofia.

    Google Scholar 

  • Textor, M. (1996). Bolzanos propositionalismus. Berlin: Walter De Gruyter.

    Book  Google Scholar 

  • Textor, M. (2001). Logically analytic propositions a posteriori. History of Philosophy Quarterly, 19(1), 91–113.

    Google Scholar 

  • Textor, M. (2013). Bolzano on conceptual and intuitive truth: The point and purpose of the distinction. Canadian Journal of Philosophy, 43(1), 13–36.

    Article  Google Scholar 

  • Wilsch, T. (2015). The nomological account of ground. Philosophical Studies, 172, 3293–3312.

    Article  Google Scholar 

  • Woodward, J. (2003). Making things happen. Oxford: Oxford University Press.

    Google Scholar 

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Acknowledgements

I whish to thank Michael J. Clark, Miguel Hoeltje, Ansten Klev, Stephan Krämer, and four anonymous referees for Synthese for helpful comments on earlier versions of this paper. Discussions during joint work on related material with Antje Rumberg and Benjamin Schnieder have been crucial in developing the ideas that led to this paper. I wish to thank the both of them. While working on the paper, I received financial support from the Kompetenzzentrum Nachhaltige Universität Hamburg and the Behörde für Wissenschaft und Forschung Hamburg (Grant: Welt der Gründe) for which I am most grateful.

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    Stefan Roski

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Roski, S. Bolzano and Kim on grounding and unification. Synthese 196, 2971–2999 (2019). https://doi.org/10.1007/s11229-017-1593-7

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