Die Transplantate vom deutschen Recht für die Reform des Privatrechts in Estland. Am Beispiel des Abstraktionsprinzips

Estonia is one of the few countries where the abstraction principle (Abstraktionsprinzip) is recognised as the basis for title transfer in property law. Derived from the works of Savigny and from Germany’s strong land-register system, it is also among the basic principles of property law in Germany (the foundations of the BGB). In most countries, however, transfer of title is causal. The article describes how Estonia adopted and adapted German legal doctrine and thinking in this important field of law. This path was a long one, even though Estonian law has deep connections to German traditions. Before 1940, Estonia’s most important legal act was the Baltic Private Law Act, wherein the abstraction principle clearly was not recognised and the causal transfer of title formed the grounds in property law. In the Soviet era, though property law was given far less emphasis, the causal approach still served as its basis. When Estonia became independent, in the early 1990s, a new system of property law was urgently needed for purposes of land reform and for implementing the land-register system. German support for preparing the new Law of Property Act along the lines of German law was accepted, and the new law entered into force in 1993. Remarkably, at the beginning of this process it was not certain whether the abstraction principle would get implemented, but it became accepted through almost a decade of case law, and the new laws were later amended such that the principle was – unlike in German law – clearly formulated (in the General Part of the Civil Code). The abstraction principle has been an important part of Estonian property law and legal thinking ever since, firmly established both in legal theory and in case law. This process demonstrates well how a legal transplant from a given legal system can work in another.

Aboutness Paradox

The present work outlines a logical and philosophical conception of propositions in relation to a group of puzzles that arise by quantifying over them: the Russell-Myhill paradox, the Prior-Kaplan paradox, and Prior's Theorem. I begin by motivating an interpretation of Russell-Myhill as depending on aboutness, which constrains the notion of propositional identity. I discuss two formalizations of of the paradox, showing that it does not depend on the syntax of propositional variables. I then extend to propositions a modal predicative response to the paradoxes articulated by an abstraction principle for propositions. On this conception, propositions are “shadows” of the sentences that express them. Modal operators are used to uncover the implicit relation of dependence that characterizes propositions that are about propositions. The benefits of this approach are shown by application to other intensional puzzles. The resulting view is an alternative to the plenitudinous metaphysics of impredicative comprehension principles.

Ordinals by Abstraction

The neo-Fregean programme in the philosophy of mathematics seeks to provide foundations for fundamental mathematical theories in abstraction principles. Ian Rumfitt (2018) proposes to introduce ordinal numbers by means of an abstraction principle, (ORD), which says, roughly, that ‘the ordinal number attaching to one well-ordered series is identical with that attaching to another if, and only if, the two series are isomorphic’. Rumfitt’s proposal poses a sharp and serious challenge to those seeking to advance the neo-Fregean programme, for Rumfitt proposes to save (ORD) from threatening paradox by avoiding dependence on an impredicative comprehension principle. However, such a principle is usually taken to be required by the neo-Fregean account of the cardinal numbers. Thus if neo-Fregean foundations for elementary arithmetic are to be saved, we must explain how we can avoid paradox for (ORD) in another way. In this chapter, the prospects for doing so are explored.

Does Choice Really Imply Excluded Middle? Part I: Regimentation of the Goodman–Myhill Result, and Its Immediate Reception†

ABSTRACT The one-page 1978 informal proof of Goodman and Myhill is regimented in a weak constructive set theory in free logic. The decidability of identities in general ($a\!=\!b\vee\neg a\!=\!b$) is derived; then, of sentences in general ($\psi\vee\neg\psi$). Martin-Löf’s and Bell’s receptions of the latter result are discussed. Regimentation reveals the form of Choice used in deriving Excluded Middle. It also reveals an abstraction principle that the proof employs. It will be argued that the Goodman–Myhill result does not provide the constructive set theorist with a dispositive reason for not adopting (full) Choice.

Neo-Fregeanism and the Burali-Forti Paradox

This chapter considers what form a neo-Fregean account of ordinal numbers might take. It begins by discussing how the natural abstraction principle for ordinals yields a contradiction (the Burali-Forti Paradox) when combined with impredicative second-order logic. It continues by arguing that the fault lies in the use of impredicative logic rather than in the abstraction principle per se. As the focus is on a form of predicative logic which reflects a philosophical diagnosis of the source of the paradox, the chapter considers how far Hale and Wright’s neo-logicist programme in cardinal arithmetic can be carried out in that logic.

Abstraction and the Question of Symmetry

Frege and many thinkers inspired by him defend a symmetric conception of abstraction according to which the two sides of an acceptable abstraction principle provide different “recarvings” of one and the same content. Some defenses of the symmetric conception are criticized: first, a seductive argument based on a generalized notion of identity; then, an argument by Rayo based on the notion of a “just is”-statement. Instead, an asymmetric conception of abstraction is defended according to which the two sides of an acceptable abstraction principle are not on a par with respect to all worldly properties. For example, the parallelism of two lines grounds the existence of their shared direction, but not vice versa.

Predicative vs. Impredicative Abstraction

According to Frege and many of his followers, there is no “metaphysical distance” between the two sides of an acceptable abstraction principle. How should this attractive idea be understood? An analysis is developed in terms of the existence of a translation from the language concerned with the relevant abstract objects to a language not committed to such objects, such that this translation maps one side of the abstraction principle to the other. Next, two different notions of predicativity are distinguished: one pertaining to the background higher-order logic, and another associated with the abstraction principle itself. Finally, it is shown that only abstraction which is predicative in the latter sense satisfies our explication of the attractive idea about no “metaphysical distance”. This provides a reason to favor a conception of abstraction which is predicative in this sense.

In Search of Thin Objects

Are there objects that are “thin” in the sense that their existence does not make a substantial demand on the world? First, some extant approaches to thin objects are surveyed, associated with mathematical structuralism and Fregean abstraction. The philosophical benefits of thin objects are then explained. Next, the idea of thin objects is clarified by articulating some logical and philosophical constraints that any account must satisfy in order to deliver the promised benefits. Finally, it is argued that these constraints favor an asymmetric conception of abstraction, where abstraction on “old” entities gives rise to “new” objects. This asymmetric conception allows the two sides of an abstraction principle to have different ontological commitments.

GENERALIZING BOOLOS’ THEOREM

It’s well known that it’s possible to extract, from Frege’s Grudgesetze, an interpretation of second-order Peano Arithmetic in the theory $H{P^2}$, whose sole axiom is Hume’s principle. What’s less well known is that, in Die Grundlagen Der Arithmetic §82–83 Boolos (2011), George Boolos provided a converse interpretation of $H{P^2}$ in $P{A^2}$. Boolos’ interpretation can be used to show that the Frege’s construction allows for any model of $P{A^2}$ to be recovered from some model of $H{P^2}$. So the space of possible arithmetical universes is precisely characterized by Hume’s principle.In this paper, I show that a large class of second-order theories admit characterization by an abstraction principle in this sense. The proof makes use of structural abstraction principles, a class of abstraction principles of considerable intrinsic interest, and categories of interpretations in the sense of Visser (2003).