Abstract
My original training as a philosopher, at Uppsala and at Oxford, was ruggedly analytical. Also the notion of an analytic judgement, or ‘proposition’, or ‘sentence’, or ‘statement’, (one did not overly distinguish these notions) was repeatedly treated of by excellent teachers and colleagues. There were aficionados of Quine and experts on Kant among them, but no names, no pack-drill! If there was one central topic in traditional epistemology on which I felt philosophically at ease, it was that of analyticity. In the early 1980s, I entered for the first time a pluralist philosophical environment in the Philosophy Department of the Catholic University at Nijmegen, with ample representation in phenomenology, Hegelian idealism, and (neo)Thomism. To my considerable surprise, I discovered that it could be enjoyable as well as instructive talking to such rare birds in the philosophical aviary. A colleague drew my attention to Thomas Aquinas’ Five Ways, which I had never read, having adopted, from the exposition in Anders Wedberg’s History of Philosophy, the opinion that, like Kant’s transcendental deduction, Aquinas’ demonstrations were ‘worthless’. However, the Summa Theologica was readily available on open shelves in the library at Nijmegen, and my curiosity got the better of me. Upon consultation of its second question, my shock was great. In a discussion of whether the judgement Deus est admits of demonstration, Aquinas introduces the notion of a propositio per se nota, that is, an S is P judgement known in, or—perhaps better—from itself: The explanation offered is that the predicate P is included, or contained, in the notion (= concept) of the subject S. Needless to say, in view of my previous deep and thorough (as I misguidedly thought) exposure to analyticity, I had a powerful déjà lu experience, pertaining to Kant, four centuries later. Clearly, I had been choused. What was the hidden tale behind this, and why had my eminent teachers not told me that the notion of an analytic judgement was known long before Kant?
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Notes
- 1.
The lemmas by Heinrich Schepers on Analytisch and Apriori in the Historisches Wörterbuch der Philosophie were most helpful to me, as was the study of Wolfgang Künne’s Abstrakte Gegenstände (1983, Ch. 5), ‘Verstehen und Evidenz’.
- 2.
Duns Scotus, ‘Concerning Human Knowledge’, Wolter edition, 126. Ex vi terminorum is another notion that has undergone a sense-disturbing meaning shift; already in Garland the Computist do we find this expression. There, however, it is placed against ex vi syllogisticae: In modern terms, the two notions correspond to material, respectively, formal validity. For instance, what terms we use in a syllogism in modus Barbara is immaterial for the correctness of the inference, whereas in the inference
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Socrates is a man.
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Therefore, Socrates is mortal.
its validity is highly dependent on the specific terms man and mortal. See Desmond Paul Henry (1984, 82).
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- 3.
See Summa contra Gentiles, Chapter 10. The edition and German translation offered in Seidl (1986) I have found particularly helpful. His German translation of per se nota as ‘an sich Erkanntes’ seems to me more felicitous than any of the English translations I have seen.
- 4.
An Pr, 24b24.
- 5.
See the fragment called ‘primary propositions’, in Parkinson (1973, 87).
- 6.
Containment, KrdrV (A6, B10), Contradiction (A151, B190).
- 7.
(A7, B11).
- 8.
Kant—if he be the author of these remarks. There is scholarly controversy on the issue—in the Jäsche Logik, §37, notes this regarding ‘tautologies’. Warning: Definition is another term that has changed its meaning. From Frege onwards, a definition consists of a definiendum and definiens joined together by definitional equality:
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Definiendum = df definiens
is the form of a definition, whereas earlier in the tradition,
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definitum = definitio
used to be the form. Thus, in current terminology, the definition is an equation whose right-hand-side definiens used to be called definition.
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- 9.
Aristotle actually formulated his account in terms of ‘belongings’ rather than predications.
- 10.
Pseudo-Duns Scotus cited after Kneale and Kneale (1962, 278).
- 11.
Wissenschaftslehre § 148:3 is the locus classicus for Bolzano’s notion of (logical) analyticity, whereas his notion of (logical) consequence, called deducibility (Ableitbarkeit), is treated of in § 155. His reduction of epistemic notions to alethic, ontological ones can be found in §§34 and 36, whereas the fourth chapter of the Wissenschaftslehre, §§ 223–268, bears the title ‘Of Inferences’ but deals exclusively with the holding of consequences. In Vol. III, Bolzano also gives a treatment of Vermittlungen, that is (what I would call) inferences, namely, mediately grounded (not grounded in Bolzano’s sense though!) acts of judgement, but then rather as a part of individual psychology and not in his usual objectivist terms. For him, objective grounding is a relation not among judgements but among propositions.
- 12.
Künne (2007) treats of the vicissitudes of the variational notion from Bolzano to Quine in lucid detail.
- 13.
§36; Bolzano was aware of a certain tension at this point §314. Adherents of today’s anti-anti-realism tend to make a virtue out of necessity, whence this tension is held to be a defining mark of realism: ‘True but unknowable propositions’ are its hallmark. Here truth and knowability are both applied to propositions. However, propositions are not really what is known. An object of knowledge surely must take the form that a proposition is true. (Know a proposition properly speaking means being familiar with the words, knowing what it says, but not knowledge that it is true.) The surprising impoverishment of current English for epistemological purposes makes itself felt here: Thus, for instance, the fine verb to wit has been jettisoned in contemporary parlance. Fortunately, it(s etymological equivalent) is retained in Germanic languages (e.g. kennen vs. wissen) or in Latin ones (e.g. connaitre vs. savoir). A further consequence of the abolition of to wit is that German Gewissheit has no good equivalent in English. ‘Certainty’, the translation commonly used, for instance, in discussions of Wittgenstein’s final work, properly speaking is the translation of Sicherheit. English philosophy as a consequence tends to ignore Gewissheit that is the objective side of knowing and considers only the psychological dimension of certainty.
- 14.
Grundlagen, §§ 3 and 4, especially footnote 1 on p. 3.
- 15.
Boghossian (1997, 337) and especially footnote 13.
- 16.
As far as I know, the only place where logical truth is even remotely considered by Frege is his final article Gedankengefüge from 1923. It is best seen as a Critical Notice of Wittgenstein’s Tractatus, and it is through reflection on that work that Frege considers assertions of trivial truths such as ‘if A, then A’ or ‘A or not A’.
- 17.
For Quine, see ‘Two dogmas of empiricism’, Quine (1951), in particular §1, where Boghossian’s crucial phrase ‘can be turned into a logical truth by putting synonyms for synonyms’ is to be found.
- 18.
Grundlagen, §3.
- 19.
Cf. my ‘A Garden of Grounding Trees’ (2011, 53–64).
- 20.
I am expressing myself with considerable care here; Wittgenstein’s notion of an elucidation (3.262) is a difficult and much discussed one. One should note though that Satz is used differently by Wittgenstein and Bolzano; for Wittgenstein, a Satz is anchored in language, whereas Bolzano’s Sätze (an sich) is sui generis and serves as the content of linguistic Sätze.
- 21.
I carried out the comparison between Kantian analytic judgements and Tractarian ascriptions of internal properties in some detail in my (1989).
- 22.
I am indebted to my Leiden colleague Jeroen van Rijen for help with the Aristotelian Greek.
- 23.
SuB, 25. Black (1948) translated it; thus,
a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labelled, analytic, while statements of the form a = b often contain valuable extensions of our knowledge and cannot always be established a priori.
The translation of Satz is crucial here. Should it be a Gedanke (‘proposition’) or a sentence? Black uses statement, which is multiply ambiguous, but is the usual equivalent of German Aussage, rather than of Satz. Michael Beaney (1997, 151) retains statement. Feigl (1949, 85) on the other hand opts for sentence as the translation of Frege’s Satz and uses cognitive significance for Erkenntniswert.
Secondly, we note that Frege does not place his identity sentences within quotation marks. Frege, in the final lines of his preface to Grundgesetze der Arithmetik, Vol. I, 1893, is, after all, the source of our current neurotic use of quotation marks and the foremost precursor of Quine’s distinction between use and mention in Mathematical Logic (Quine 1940, § 4). Against this background, his omission is quite remarkable, the more so since quotation marks do get used around the identity sentence in Frege’s footnote on the same page. (Recalling crucial changes with respect to quotation marks in various printings of Russell’s On Denoting, I deemed it wise to check the original Fette Fraktur printing of Frege (1892, 25), and it agrees with the way the quote is given above.) Black and Beaney follow suit in their translations but do not comment upon the matter. Feigl, on the other hand, clearly smelled a rat since he inserted quotation marks where none are found in Frege’s text. Later in the text, for instance, on page 32, Frege uses Satz for Behauptungssatz, that is, declarative sentence. However, he does not use sentence as it is commonly used in current philosophy of language, where a sentence is an ‘expression’, that is, a certain thing (entity, object …) void of meaning. Frege’s sentences, on the other hand, do have thoughts as contents. So it remains a mystery why those quotation marks were left out on his first page.
- 24.
‘Placed within the Kantian tradition’ might be too weak here. The passage may well have a direct Kantian source. The quote from ‘Über Sinn und Bedeutung’ reads as a symbolization of § 37, ‘Tautologische Sätze’, of Kant’s Jäsche Logik. From the Grundlagen der Arithmetik, §12, p. 19, we know that Frege was familiar with this book, whence a direct influence cannot be ruled out.
- 25.
- 26.
The analogy between Kantian analytic judgements, Tractarian predications of internal properties, and type ascriptions in Martin-Löf’s Constructive Type Theory, was the main theme of my (1989) and especially at fn. 21. Martin-Löf treats of parallels between his Type Theory and Kant in his (1994). My (2004) gives a reasonably full description of Constructive Type Theory and spells out relations to a number of traditional epistemological issues, including analyticity. In particular, the significance of Gödel’s theorem is treated of.
- 27.
Martin-Löf notes that all judgments of the form [A true] are synthetic since their explicit form is Proof(A) exists. Kant stressed that every existential judgement is synthetic. Here we go even further: A correct existential judgement is always grounded in an analytic one that instantiates the existence claim in question.
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Acknowledgements
The format of an oral presentation has largely been retained in this written version of my lecture at the Leiden Days of Judgement, and scholarship is confined to footnotes. The theme is one that I have pursued in lectures and seminars at Leiden since the early 1990s and I am grateful to my colleague Maria van der Schaar, as well as to student participants, in particular Giuseppe Primiero and Ansten Klev, for discussion and feedback. To Per Martin-Löf, I owe a debt of gratitude for innumerable conversations on these and other matters. The work on the written version was begun during a visiting professorship in the spring of 2010 at the Archives Poincaré, Nancy, and the material was presented in a colloquium there. I am much indebted to the Archives and my host Gerhard Heinzmann for the generous hospitality I enjoyed.
Wolfgang Künne’s writings on analyticity have long been a source of inspiration, already from a Nijmegen reading group in 1983 on his Abstrakte Gegenstände. In 2004, I furthermore had the privilege to serve as ‘Président de la séance’ at an early Paris presentation of his ‘Analyticity and logical truth: from Bolzano to Quine’ (2007).
Prior commitments prevented me from attending the symposium that honoured him at his retirement from the Hamburg chair. Since Wolfgang has long-standing links to Leiden and was a key speaker, both at the prior Leiden Days of Truth dedicated to his Conceptions of Truth in 2004 and at the present event, and did not protest too much after my lecture, it is a great pleasure to dedicate this chapter to him.
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Dedicated to Wolfgang Künne on the occasion of his retirement
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Sundholm, G. (2013). Containment and Variation; Two Strands in the Development of Analyticity from Aristotle to Martin-Löf. 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_3
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