Carnap: Philosophy of Logic

In his recent article "Carnapian Frameworks" (Synthese, 2021), Gabriel Broughton criticizes my discussions of Carnap on ontology and puts forward his own interpretation of what Carnap’s external/internal distinction amounts to. I here first argue that Broughton’s main claims about me are based on a misinterpretation. Then I turn to some issues of broader interest. I argue that Broughton’s own, potentially interesting interpretation of Carnap’s external/internal distinction does not work. And in light of Broughton’s discussion I present a sharpened version of (...) what I have earlier said about Carnap’s this distinction. (shrink)

Carnap’s seminal ‘Empiricism, Semantics and Ontology’ makes important use of the notion of a framework and the related distinction between internal and external questions. But what exactly is a framework? And what role does the internal/external distinction play in Carnap’s metaontology? In an influential series of papers, Matti Eklund has recently defended a bracingly straightforward interpretation: A Carnapian framework, Eklund says, is just a natural language. To ask an internal question, then, is just to ask a question in, say, English. (...) To try to ask an external question is to try, absurdly, to ask a question in no language at all. Finding that so trivial an I/e distinction can’t help to explain Carnap’s deflationary metaontology, Eklund is led to attribute to Carnap a view he calls ontological pluralism. In this paper, I show that Eklund misreads Carnap, and I argue that this misreading obscures fundamental features of Carnap’s philosophy. I then defend an account of frameworks as what Carnap called semantical systems, and I place this account in the context of Carnap’s philosophical program of explication. Finally, I discuss the role that frameworks and the I/e distinction play in ESO, showing that ESO provides no reason to attribute the doctrine of ontological pluralism to Carnap. (shrink)

In Der logische Aufbau der Welt, first published in 1928, Carnap aims to rationally reconstruct all objects of cognition by logico-definitional means. As a result, he intends to obtain a fully objective framework in which scientific discourse can take place. This is made possible by the novel method of ‘purely structural definite description’ of all scientifically relevant objects, which is first introduced in the Aufbau. Key to the attainment of this goal is the notion of ‘foundedness’, which Carnap presents as (...) a new basic notion of logic, in order to establish a link between the purely conventional world of logical and mathematical knowledge and the empirical world of knowledge of scientific objects. This idea experienced major criticism by Friedman (1999a,b) since he considers it to lead to the demolition of the boundary between those two worlds. In this essay, we want to defend foundedness against Friedman’s critique by arguing that its introduction is necessary within Carnap’s logicist world of thought to deal with a more fundamental problem: the demarcation of the empirical parts of the Aufbau. In the last section, we will give an outlook on the actual cause for the failure of the Aufbau, the lack of a principle to determine the truth of the instances of the basic relation in the Aufbau, and we will show how this can contribute to the explanation of Carnap’s future philosophical development and retrospective self-evaluation. This essay serves as a dense informal sketch for a later extensive formal treatment of this reading of foundedness and focuses on its implications for the interpretation of Carnap’s post-Aufbau development. (shrink)

Carnap’s result about classical proof-theories not ruling out non-normal valuations of propositional logic formulae has seen renewed philosophical interest in recent years. In this note I contribute some considerations which may be helpful in its philosophical assessment. I suggest a vantage point from which to see the way in which classical proof-theories do, at least to a considerable extent, encode the meanings of the connectives (not by determining a range of admissible valuations, but in their own way), and I demonstrate (...) a kind of converse to Carnap’s result. (shrink)

A brief introduction to the life and key work of Rudolf Carnap with special attention to his work on inductive logic.

In this paper, I defend Rudolf Carnap's Principle of Tolerance from an accusation, due to Michael Friedman, that it is self-defeating by prejudicing any debate towards the logically stronger theory. In particular, Friedman attempts to show that Carnap's reconstruction of the debate between classicists and intuitionists over the foundations of mathematics in his book The Logical Syntax of Language, is biased towards the classical standpoint since the metalanguage he constructs to adjudicate between the rival positions is fully classical. I argue (...) that this criticism is mistaken on two counts: (1) it fails to fully appreciate the freedom with regard to the construction of linguistic frameworks that Carnap intended his Principle to embody, and (2) Friedman's objection underestimates the extent to which the evaluation of a framework is task-relative. I conclude that Tolerance is not self-undermining in the way that Friedman claims it is. While this is a restricted conclusion -- and is not a vindication of Carnap's views on logic and mathematics tout court -- it nonetheless suggests that his tolerant perspective has been dismissed too quickly, even by his supporters. (shrink)

This paper argues that Carnap both did not view and should not have viewed Frege's project in the foundations of mathematics as misguided metaphysics. The reason for this is that Frege's project was to give an explication of number in a very Carnapian sense — something that was not lost on Carnap. Furthermore, Frege gives pragmatic justification for the basic features of his system, especially where there are ontological considerations. It will be argued that even on the question of the (...) independent existence of abstract objects, Frege and Carnap held remarkably similar views. I close with a discussion of why, despite all this, Frege would not accept the principle of tolerance. (shrink)

We characterize those identities and independencies which hold for all probability functions on a unary language satisfying the Principle of Atom Exchangeability. We then show that if this is strengthen to the requirement that Johnson's Sufficientness Principle holds, thus giving Carnap's Continuum of inductive methods for languages with at least two predicates, then new and somewhat inexplicable identities and independencies emerge, the latter even in the case of Carnap's Continuum for the language with just a single predicate.

This article discusses the relation between the early Wittgenstein’s and Carnap’s philosophies of logic, arguing that Carnap’s position in The Logical Syntax of Language is in certain respects much closer to the Tractatus than has been recognized. In Carnapian terms, the Tractatus’ goal is to introduce, by means of quasi-syntactical sentences, syntactical principles and concepts to be used in philosophical clarification in the formal mode. A distinction between the material and formal mode is therefore already part of the Tractatus’ view, (...) and its method for introducing syntactical concepts and principles should be entirely acceptable for Carnap by his own criteria. Moreover, despite the Tractatus’ rejection of syntactical statements, there is an important correspondence between Wittgenstein’s saying-showing distinction and Carnap’s object-language-syntax-language distinction: both constitute a distinction between logico-syntactical determinations concerning language and language as determined or described by those determinations. Wittgenstein’s distinction therefore constitutes a precursor of the object-language syntax-language distinction which the latter in a certain sense affirms, rather than simply contradicting it. The saying-showing distinction agrees with Carnap’s position also in marking logic as something that isn’t true/false about either language or reality, which is a conception that underlies Carnap’s principle of tolerance. (shrink)

The influential proposal that the analytical component of a theory is captured by its ‘Carnap sentence’ is critically scrutinized. A counterexample which makes the suggestion problematic is presented.