The paper proposes a new reading of the Aufbau, one that contends that Carnap's epistemological project is not, or not only, to identify the conditions under which a system of purely structural definite descriptions can attain objectivity. Rather, the project is more ambitious: to determine the conditions that allow the concomitant attainment of objectivity and understanding. As such, it can, and perhaps should, be regarded as an attempt to refute a view elsewhere called Weylean skepticism, i.e., the view that objectivity (...) and understanding are opposite epistemic ideals of science. (shrink)

This paper discusses the idea that some of the causal factors that are responsible for the production of a natural phenomenon are explanatorily irrelevant and, thus, may be omitted or distorted. It argues against Craig Callender’s suggestion that the standard explanation of phase transitions in statistical mechanics may be considered a causal explanation, in Michael Strevens’ sense, as a distortion that can nevertheless successfully represent causal relations.

This note revisits the debate between Mach and Husserl on thought economy and argues that, to a considerable extent, they talked past each other, insofar as the latter rejected thought economy as a principle of theoretical rationality, whereas the former conceived of it as a principle of practical rationality. This is further supported by their correspondingly different readings of the so-called principle of the permanence of forms.

The idea that scientific objectivity requires a method of concept formation according to which concepts are freely created by the mind was famously propagated by Hermann Weyl. I argue that this idea, which he saw as essentially characterizing what physicists do when they do physics, led him to abandon the phenomenological view on objectivity, more particularly the strong connection between objectivity and evidence (understood in a Husserlian sense as a satisfaction of meaning intentions). The free creation of concepts, that is (...) ultimately their introduction via Hilbert-style axiomatizations, is at the heart of Weyl's account of scientific objectivity, for it allows the introduction of hypothetical elements, without which, on his view, objectivity collapses (at best) into mere intersubjectivity. (shrink)

This paper discusses a novel approach to singularities, based on a recent extension of general relativity that shows why singularities do not constitute a breakdown of physical laws: it is not only the case that physical laws are valid, but they also remain invariant at singularities. The paper describes this kind of invariance, and draws its consequences for our understanding of equivalence in general relativity. In particular, it points out that the difference between the metrics at singularities and those outside (...) of singularities is factual, rather than nomological, and that this justifies the extension of the principle of equivalence to singularities. (shrink)

This paper discusses Weylean invariantism, the view that scientific objectivity requires categoricity, and shows that it may correctly be attributed to Weyl, who took this condition to express a type of theoretical completeness. The condition is satisfied by quantum mechanics, for the Stone-von Neumann theorem can be naturally interpreted as a categoricity result. However, quantum field theory invalidates the theorem due to unitary inequivalence, so either Weylean invariantism is false and should be rejected, or categoricity can be established despite unitary (...) inequivalence. I argue against the latter and point out that one should take non-categoricity more seriously. (shrink)

The paper argues against defending realism about numbers on the basis of realism about instantiated structural universals. After presenting Armstrong’s theory of structural properties as instantiated universals and Lewis’s devastating criticism of it, I argue that several responses to this criticism are unsuccessful, and that one possible construal of structural universals via non-well-founded sets should be resisted by the mathematical realist.

This paper, written in Romanian, explains why the eutaxiological argument - endorsed by scientists like Newton, Einstein, and Weyl - is not a sound one.

It has been contended that it is unjustified to believe, as Weyl did, that formalism's victory against intuitionism entails a defeat of the phenomenological approach to mathematics. The reason for this contention, recently put forth by Paolo Mancosu and Thomas Ryckman, is that, unlike intuitionistic Anschauung, phenomenological intuition could ground classical mathematics. I argue that this indicates a misinterpretation of Weyl's view, for he did not take formalism to prevail over intuitionism with respect to grounding classical mathematics. I also point (...) out that the contention is false: if intuitionism fails, in the way Weyl thought it did, i.e., with respect to supporting scientific objectivity, then one should also reject the phenomenological approach, in the same respect. (shrink)

This paper discusses an intriguing, though rather overlooked case of normative disagreement in the history of philosophy of mathematics: Weyl's criticism of Dedekind’s famous principle that "In science, what is provable ought not to be believed without proof." This criticism, as I see it, challenges not only a logicist norm of belief in mathematics, but also a realist view about whether there is a fact of the matter as to what norms of belief are correct.

This paper criticizes two reconstructions of Carnap's technical procedure of quasianalysis, which were given by Nelson Goodman and Thomas Mormann. It then offers a diagrammatic reconstruction, one that does not ignore the essential role played by Lotze's concept of a local sign, and explains away a point raised by Quine against Carnap's project in the Aufbau.

The paper shows that a particular point raised by Schröder – that Frege's conceptual notation fails to be modelled on the formula language of arithmetic – is based on a misunderstanding. After pointing out what seems to be the most advantageous aspect of Frege's diagrams, it gives a serious reason for their eventual cast-off.