What is Carnap's Conventionalism after all?

As is well known, Carnap's conventionalism was a rejection to Kant's view ofmathematics and was fully developed in his Logische Syntax der Sprache.The purpose of this article is to step back to Der Logische Aufbau der Weltto show that the Logical Syntax of Language is an attempt to solve difficultiesfound in the earlier construction. I first clarify the notion of conventionalism, whichplays a central role in the application of mathematics to the reconstruction of empiricalknowledge. By not strictly distinguishing between the intuitive notion and thetopological concept of dimension, Carnap is led to a construction which is highlyquestionable. To illustrate the constructive method developed in the Aufbauand some of its inherent difficulties, I consider the computational aspects of theconstruction of phenomenological space via the mathematical concept of dimension.Contrary to Carnap's conventionalism, a dual nature of mathematical statements isbrought into existence by his logical reconstruction. So, if Carnap wants to retainhis mathematics as devoid of content, he must make a clear-cut distinction betweenanalytic and synthetic statements. Thus the natural follow-up to the Aufbau isthe Logical Syntax of Language.     

A Diagrammatic Reconstruction of Carnap's Quasianalysis

In this paper, I am zeroing in on Carnap's formal method of quasianalysis, arguing against two interpretations of it, offered by Nelson Goodman and Thomas Mormann. In order to overcome their inadequacy, I propose a diagrammatic reconstruction, which takes advantage of the fact that the concept of local sign is no longer ignored. This will give me the opportunity to show that Quine'scriticism of Carnap's constitution of physical space fails, and will allow me to describe QUASIMODOS (QUASIanalytical Machine Oriented Diagrammatic Operation System) – a system designed to construct qualities in continuous domains.     

Probabilities For Two Properties

Let R(X, B) denote the class of probability functions that are defined on algebra X and that represent rationally permissible degrees of certainty for a person whose total relevant background evidence is B. This paper is concerned with characterizing R(X, B) for the case in whichX is an algebra of propositions involving two properties and B is empty. It proposes necessary conditions for a probability function to be in R(X, B), some of which involve the notion of statistical dependence. The class of probability functions that satisfy these conditions, here denoted P_I, includes a class that Carnap once proposed for the same situation. Probability functions in P_I violate Carnap's axiom of analogy but, it is argued, that axiom should be rejected. A derivation of Carnap's model by Hesse has limitations that are not present in the derivation of P_I given here. Various alternative probability models are considered and rejected.     

Predictive probability and analogy by similarity in inductive logic

The-continuum of inductive methods was derived from an assumption, called-condition, which says that the probability of finding an individual having propertyx _j depends only on the number of observed individuals having propertyx _j and on the total number of observed individuals. So, according to that assumption, all individuals with properties which are different fromx _j have equal weight with respect to that probability and, in particular, it does not matter whether any individual was observed having some propertysimilar tox _j (the most complete proof of this result is presented in Carnap, 1980).The problem thus remained open to find some general condition, weaker than the-condition, which would allow for thederivation of probability functions which might be sensitive to similarity. Carnap himself suggested a weakening of the-condition which might allow for similarity sensitive probability functions (Carnap, 1980, p. 45) but he did not find the family of probability functions derivable from that principle. The aim of this paper is to present the family of probability functions derivable from Carnap's suggestion and to show how it is derived.In Section 1 the general problem of analogy by similarity in inductive logic is presented, Section 2 outlines the notation and the conceptual background involved in the proof, Section 3 gives the proof, Section 4 discusses Carnap's principle and the result, Section 5 is a brief review of the solutions which have previously been proposed.     

Linguistically invariant inductive logic

Summary Carnap's early system of inductive logic make degrees of confirmation depend on the languages in which they are expressed. They are sensitive to which predicates are, in the language, taken as primitive. Hence they fail to be linguistically invariant. His later systems, in which prior probabilities are assigned to elements of a model rather than sentences of a language, are sensitive to which properties in the model are called primitive. Critics have often protested against these features of his work. This paper shows how to make his systems independent of any choice of primitive predicates or primitive properties.The solution is related to another criticism of inductive logic. It has been noticed that Carnap's systems are too all-embracing. Hisc(h, e) is defined for all sentencesh ande. Yet for manyh ande, the evidencee does not warrant any assessment of the probability ofh. We need an inductive logic in whichc(h, e) is defined only whene really does bear onh. This paper sketches the measure theory of such a logic, and, within this measure theory, provides relativized versions of Carnap's systems which are linguistically invariant.     

Dimensional Characterization In Finite Quasi-Analysis

The method of Quasi-Analysis used by Carnap in his program of theconstitution of concepts from finite observations has the following twogoals: (1) Given unsharp observations in terms of similarity relations thetrue properties of the observed objects shall be obtained by a suitablelogical construction. (2) From a single relation on a finite domain,different dimensions of qualities shall be reconstructed and identified. Inthis article I show that with a slight modification Quasi-Analysis iscapable of fulfilling the first goal for a single observable dimension. Weobtain a partition of the so-called Quality Classes representing thepairwise disjoint and exhaustive extensions associated to the ``values' ofthe observable. On the other hand, an example demonstrates that the methodfails, as Goodman has pointed out, for a relation expressing similarity withregard to at least one out of many properties.Since it seems to be impossible in general to reconstruct more-dimensionalqualities from a single similarity relation, the constitution of at least asmany similarity relations as there are qualities have to be presumed. Thenit is possible to state adequate sufficient conditions for the dimension ofthe observable space, even if some of the similarity relations might dependon others. The concept of topological dimension cannot be used for thispurpose on finite sets of observations. We replace it by a set-algebraicalcondition on the Quality Classes.     

A RESERVED READING OF CARNAP'S AUFBAU

Abstract:  The two most popular approaches to Carnap's 1928 Aufbau are the empiricist reading of Quine and the neo-Kantian readings of Michael Friedman and Alan Richardson. This paper presents a third "reserved" interpretation that emphasizes Carnap's opposition to traditional philosophy and consequent naturalism. The main consideration presented in favor of the reserved reading is Carnap's work on a physical construction system. I argue that Carnap's construction theory was an empirical scientific discipline and that the basic relations of its construction systems need not be eliminated.     

Every Dogma has its day

This paper is a reexamination of Two Dogmas in the light of Quine's ongoing debate with Carnap over analyticity. It shows, first, that analytic is a technical term within Carnap's epistemology. As such it is intelligible, and Carnap's position can meet Quine's objections. Second, it shows that the core of Quine's objection is that he (Quine) has an alternative epistemology to advance, one which appears to make no room for analyticity. Finally, the paper shows that Quine's alternative epistemology is itself open to very serious objections. Quine is not thereby refuted, but neither can Carnap's analyticity be dismissed as dogma.     

Zur Rolle der Sprache in erkenntnistheoretischer Hinsicht

Ohne ZusammenfassungContribution in honor of Professor Rudolf Carnap's seventieth birthday, received after Vol. XII no. 4 had been published (editor's note).     

Quine, Analyticity and Philosophy of Mathematics

Quine correctly argues that Carnap's distinction between internal and external questions rests on a distinction between analytic and synthetic, which Quine rejects. I argue that Quine needs something like Carnap's distinction to enable him to explain the obviousness of elementary mathematics, while at the same time continuing to maintain as he does that the ultimate ground for holding mathematics to be a body of truths lies in the contribution that mathematics makes to our overall scientific theory of the world. Quine's arguments against the analytic/synthetic distinction, even if fully accepted, still leave room for a notion of pragmatic analyticity sufficient for the indicated purpose.     

Antecedent-Relative Comparative World Similarity

In “Backward Causation and the Stalnaker–Lewis Approach to Counterfactuals,” Analysis 62:191–7, (2002), Michael Tooley argues that if a certain kind of backward causation is possible, then a Stalnaker–Lewis comparative world similarity account of the truth conditions of counterfactuals cannot be sound. In “Tooley on Backward Causation,” Analysis 63:157–62, (2003), Paul Noordhof argues that Tooley’s example can be reconciled with a Stalnaker–Lewis account of counterfactuals if the comparative world similarity relation on which the Stalnaker–Lewis account relies is allowed to be antecedent-relative. In this paper I show that taking comparative world similarity to be antecedent-relative results in a formal semantics which is a comparative world similarity semantics in name only.     

Einige Beiträge Zum Problem Der Teleologie Und Der Analyse Von Systemen Mit Zielgerichteter Organisation

Ohne ZusammenfassungContribution in honor of Professor Rudolf Carnap's seventieth birthday, received after Vol. XII no. 4 had been published (editor's note).     

Partial Resemblance and Property Immanence

Objects partially resemble when they are alike in some way but not entirely alike. Partial resemblance, then, involves similarity in a respect. It has been observed that talk of “respects” appears to be thinly‐veiled talk of properties. So some theorists take similarity in a respect to require property realism. I will go a step further and argue that similarity in intrinsic respects (partial intrinsic resemblance) requires properties to be immanent in objects. For a property to be immanent in an object is roughly for it to be wholly present in that object. (So understood, immanence does not imply repeatability, and thus tropes count as immanent.) If two objects are intrinsically similar in one way but not another, there must be a difference between the two ways. And if the similarity is between the objects as they are in themselves, then this difference, too, must be within the objects. Partial intrinsic resemblance thus requires internal structure. Without it, there can be no distinctions between ways in which things are intrinsically alike and ways in which they aren't. I will argue, further, that distinctions between properties that transcend objects fail to account for the possibility of partial intrinsic resemblance.     

Carnapian inductive logic for Markov chains

Carnap's Inductive Logic, like most philosophical discussions of induction, is designed for the case of independent trials. To take account of periodicities, and more generally of order, the account must be extended. From both a physical and a probabilistic point of view, the first and fundamental step is to extend Carnap's inductive logic to the case of finite Markov chains. Kuipers (1988) and Martin (1967) suggest a natural way in which this can be done. The probabilistic character of Carnapian inductive logic(s) for Markov chains and their relationship to Carnap's inductive logic(s) is discussed at various levels of Bayesian analysis.     

RAWLS AND CARNAP ON DOING PHILOSOPHY WITHOUT METAPHYSICS

Abstract:  Some philosophers, such as Kai Nielsen, view Rawls's rejection of metaphysical claims, encapsulated in his method of avoidance, as being compatible with the "anti-philosophical" stance, the view that metaphysical debates are sterile and should be abandoned to be replaced by practically viable forms of thinking. This paper shows that this reading of the method of avoidance is incorrect and argues that the method of avoidance is in fact comparable to Carnap's higher-order standpoint of neutrality with regards to different frameworks. This sheds new light on Rawlsian theory and situates it within the empiricist tradition.     

Sahlqvist's theorem for boolean algebras with operators with an application to cylindric algebras

For an arbitrary similarity type of Boolean Algebras with Operators we define a class ofSahlqvist identities. Sahlqvist identities have two important properties. First, a Sahlqvist identity is valid in a complex algebra if and only if the underlying relational atom structure satisfies a first-order condition which can be effectively read off from the syntactic form of the identity. Second, and as a consequence of the first property, Sahlqvist identities arecanonical, that is, their validity is preserved under taking canonical embedding algebras. Taken together, these properties imply that results about a Sahlqvist variety V van be obtained by reasoning in the elementary class of canonical structures of algebras in V.We give an example of this strategy in the variety of Cylindric Algebras: we show that an important identity calledHenkin's equation is equivalent to a simpler identity that uses only one variable. We give a conceptually simple proof by showing that the first-order correspondents of these two equations are equivalent over the class of cylindric atom structures.Presented byIstván Németi     

What is global supervenience?

The relation of global supervenience is widely appealed to in philosophy. In slogan form, it is explained as follows: a class of properties A supervenes on a class of properties B if no two worlds differ in the distribution of A-properties without differing in the distribution of B-properties. It turns out, though, that there are several ways to cash out that slogan. Three different proposals have been discussed in the literature. In this paper, I argue that none of them is adequate. Furthermore, I present a puzzle that reveals a tension in our concept of global supervenience.     

Carnap and translational indeterminacy

InWord and Object W. V. Quine argues that there is no uniquely correct way to assign referents to the terms of a language; any claim about the reference of a term is implicitly relative to a manual of translation. To Rudolf Carnap this must have seemed familiar. BeforeWord and Object was written Carnap had been saying the same thing inMeaning and Necessity: under the assumption of the method of the name-relation, any claim about the reference of a term is implicitly relative to what Carnap calls a conception of the name-relation. Yet Carnap is often taken to be a victim of Quine's relativistic notion of reference. Drawing on Carnap's discussion of the name-relation inMeaning and Necessity, it is argued that Carnap's and Quine's views on reference are not so far apart as is usually perceived.I would like to thank the referees who reviewed this paper for their helpful and insightful comments. In addition, I would like to thank Dr. Richard Creath both for his comments on earlier drafts of this paper as well as for conversations (beyond number) on these and many other issues related to the Quine-Carnap debate. Creath's own discussion of this topic entitled Functionalist Theories of Meaning and the Defense of Analyticity, appears in the volumeLanguage, Logic, and the Structure of Scientific Theories: The Carnap-Reichenbach Centennial, edited by W. Salmon and G. Wolters (Pittsburgh: University of Pittsburgh Press, and Konstanz, Germany: University of Konstanz Press, 1994).