Abstract
The paper traces nineteenth century devopments in the form of judgement from the traditional ‘S is P’ to the type theoretical \(a\!:\!A\); via Bolzano’s ‘A is true’, Brentano’s a+ \((a-)\), Frege’s P(a) is true, and the Cambridge truth-makers and Heyting’s proof-explanations for the constructive logical constants.
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- 1.
Kant, Kritik der reinen Vernunft, B VII, my translation.
- 2.
See his Wissenschaftslehre. Note the spelling; contrary to an almost universal misapprehension, to which many writers on Bolzano, including myself, have fallen prey, Bolzano’s first name does not contain an ‘h’.
- 3.
For the sake of brevity, in the sequel I take the In-itself qualification as understood.
- 4.
An Idea is Gegenständlich when an object falls under it. Accordingly another equivalent would be [the Idea mortal man is not objectual]. [9] contains a beautiful presentation of Bolzano’s work using Gegenständlichkeit as a key-concept.
- 5.
This is not exactly true; Bolzano imposes some further conditions on his consequences, for instance, that the antecedent propositions be compatible. However, at the level of abstraction at which I want to move, it is more than true enough.
- 6.
Indeed, the version offered by Moore and Russell in their early apostasy from British Hegelianism during the first decade of the twentieth century is much inferior to Bolzano version. The quality of Bolzano’s treatment is enhanced by his arguing primarily against Kant, that is, the foremost exponent of epistemological idealism, whereas Moore and Russell have Bradley and Bosanquet as their target.
- 7.
Consequence is a three-place relation in Bolzano, pertaining to antecedent and consequent propositions, as well as to (a collection of) Ideas occurring in these propositions at which places where the variation takes place, under which truth has to be preserved from antecedent(s) to consequent(s). The consequence holds logically when truth is preserved under all variations with respect to all non-logical Ideas. When variation takes place at fewer place the consequence in question will not be logical. it is a moot point whether Bolzano allows for the natural terminus of preservation of truth from antecedent to consequent with respect to variation in no places. The corresponding consequence relation \(A\Rightarrow B\) between the propositions A and B holds (but, in general, not logically) when the implicational proposition \(A\supset B\) is true (rather than logically true. When this is the case, the consequence holds logically, of course.).
- 8.
Brentano’s use of his \([\alpha+]\) form of judgement is completely parallel to Bolzano’s use of ‘the idea-in-itself V has Gegenständlichkeit’. To my mind, in view of Brentano’s vehement and slightly undignified protestations to the contrary (that were printed by Bergmann [1, pp. 307–08]), a direct influence from Bolzano seems quite likely.
- 9.
The apt truth-maker terminology was introduced in [8].
- 10.
Connoisseurs of the Tractatus are requested to meditate on theses 4.022 and 5.542 at this point.
- 11.
- 12.
- 13.
See [11], i.e. the other half of my Geneva 2002 lecture, deals with this matter in considerable detail.
References
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Acknowledgements
This text is (a part of) an invited lecture at the international workshop ‘Formal Ontology’, Geneva, November 2002. The material was also presented as an ‘Alumni Lecture’ at the Dutch Graduate School in Logic, Amsterdam, March 6, 2003. I am indebted to organisers and participants alike, and to Kevin Mulligan in particular.
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Sundholm, G. (2012). A Double Diamond of Judgement. In: Rahman, S., Primiero, G., Marion, M. (eds) The Realism-Antirealism Debate in the Age of Alternative Logics. Logic, Epistemology, and the Unity of Science, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1923-1_16
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