The past decade has seen notable development of conceptual engineering – a field of analytical philosophy that focuses on the critical evaluation of concepts. Most authors engaged with this area identify Rudolf Carnap’s ideas as its methodological framework and theoretical origin, placing particular emphasis on the philosopher’s method of explication. This article highlights the unquestionable influence Carnap’s thought had on conceptual engineering whilst by no means reducing it to the utilisation and advancement of explication within this field of (...) analytical philosophy: indeed, conceptual engineering has incorporated – and brought to the forefront – much broader tenets of Carnap’s concept. This study draws on a series of the philosopher’s works, as well as his ‘Intellectual Autobiography’, to trace the evolution of his ideas about language and describe the fundamental elements revealing the ‘engineering perspective’ in his reflection. Most clearly, this perspective is evident in his interpretation of logic as a conceptual tool for acquiring and processing knowledge, ‘assembling’ it into a structure and refining the procedures of logic itself. It is shown that the origins of the engineering perspective trace back, on the one hand, to Carnap’s interest in the methodological framework of physics, particularly the measurement problem and its epistemological analysis, and, on the other, his fascination with interpretations of the nature of mathematical theory and the idea of unifying logicism and formalism by introducing the principle of tolerance, which adds a pragmatic dimension to methodology. The article examines in detail the idea of explication and its theoretical origins, which lie, in particular, in Carnap’s intention to exactify the notions expressing the degree of validity and probability. His idea of a link between the results of explication and its goal became the central principle of conceptual engineering, distinguishing it from mere conceptual analysis. It is concluded that, when considered together, Carnap’s two major ideas – explication and the principle of tolerance – can be placed in a broader context of a project seeking a rational reconstruction of the life of society and providing it with knowledge-based underpinnings. (shrink)

Pondering the question of free will in the context of probability allows us to take a fresh look at a number of old problems. We are able to avoid deterministic entrapments and attempt to look at free will as an outcome of the entire decision-making system. In my paper, I will argue that free will should be considered in the context of a complex system of decisions, not individual cases. The proposed system will be probabilistic in character, so it (...) will be embedded in the calculus of probability. To achieve the stated goal, I will refer to two areas of Carnap’s interest: the relationship between free will and determinism, and the probability-based decision-making system. First, I will present Carnap’s compatibilist position. On this basis, I will show how free will can be examined on deterministic grounds. Then I will present Carnap’s probabilistic project—the so-called logical interpretation of probability. In addition to presenting its characteristics and functionality, I will argue for its usefulness in the context of decision analysis and its immunity to problems associated with determinism. Finally, I will show how the two mentioned elements can be combined, as a result of which I will present a concept for a probabilistic analysis of free will. In this context, I will identify free will with the individual characteristics of the system. My main aim is to present the theme of free will in the light of a formal analysis based on probability rather than metaphysical assumptions. (shrink)

"Homage to Rudolph Carnap."--Hempel, C. G. Rudolf Carnap, logical empiricist.--Wedberg, A. How Carnap built the world in 1928.--Eberle, R. A construction of quality classes improved upon the Aufbau.--Carnap, R. Observation language and theoretical language.--Kaplan, D. Significance and analyticity: a comment of some recent proposals of Carnap.--Wójcicki, R. The factual content of empirical theories.--Williams, P. M. On the conservative extensions of semantical systems: a contribution to the problem of analyticity.--Winnie, J. A. Theoretical analyticity.--Wedberg, A. Decision and belief in science.--Bohnert, H. G. (...) Carnap's logicism.--Hintikka, J. Carnap's heritage in logical semantics.--Partee, B. H. The semantics of belief-sentences.--Kasher, A. Pragmatic representations and language-games.--Carnap, R. Notes on probability and induction.--Jeffrey, R. C. Carnap's inductive logic.--Hilpinen, R. Carnap's new system of inductive logic.--Kuipers, T. A. F. A generalization of Carnap's inductive logic. Essler, W. K. Hintikka versus Carnap.--Hintikka, J. Carnap and Essler versus inductive generalization.--Shimony, A. Carnap on entropy, introduction to "Two essays on entropy" by Rudolf Carnap. (shrink)

Common probability theories only allow the deduction of probabilities by using previously known or presupposed probabilities. They do not, however, allow the derivation of probabilities from observed data alone. The question thus arises as to how probabilities in the empirical sciences, especially in medicine, may be arrived at. Carnap hoped to be able to answer this question byhis theory of inductive probabilities. In the first four sections of the present paper the above mentioned problem is discussed in general. After (...) a short presentation of Carnap''s theory it is then shown that this theory cannot claim validity for arbitrary random processes. It is suggested that the theory be only applied to binomial and multinomial experiments. By application of de Finetti''s theorem Carnap''s inductive probabilities are interpreted as consecutive probabilities of the Bayesian kind. Through the introduction of a new axiom the decision parameter can be determined even if no a priori knowledge is given. Finally, it is demonstrated that the fundamental problem of Wald''s decision theory, i.e., the determination of a plausible criterion where no a priori knowledge is available, can be solved for the cases of binomial and multinomial experiments. (shrink)

Is it possible to combine different logics into a coherent system with the goal of applying it to specific problems so that it sheds some light on foundational aspects of those logics? These are two of the most basic issues of combining logics. Paranormal modal logic is a combination of paraconsistent logic and modal logic. In this paper, I propose two further combinatory developments, focusing on each one of these two issues. On the foundational side, I combine paranormal modal logic (...) with normal modal logic, resulting into a paraconsistent and paracomplete multimodal logic dealing with the notions of plausibility and certainty. On the application side, I combine this logic with Reiter’s default logic, resulting into an inductive and consequently nonmonotonic paraconsistent and paracomplete logic able to represent some key inductive principles. (shrink)

Do numbers exist? Carnap (1956 [1950]) famously argues that this question can be understood in an “internal” and in an “external” sense, and calls “external” questions “non-cognitive”. Carnap also says that external questions are raised “only by philosophers” (p. 207), which means that, in his view, philosophers raise ”non-cognitive” questions. However, it is not clear how the internal/external distinction and Carnap’s related views about philosophy should be understood. This paper provides a new interpretation. I draw attention to Carnap’s (...) distinction between purely external statements, which are independent from all frameworks, and pragmatic external statements, which concern which framework one should adopt, and argue that the latter express noncognitive mental states. Specifically, I argue that “frameworks” are systems of rules for the assessment of statements, which are utterances of ordinary language sentences. Pragmatic external statements express noncognitive dispositions to follow only certain rules of assessment. For instance, “numbers exist” understood as a pragmatic external statement expresses a noncognitive disposition to use only rules of assessment according to which numbers do exist. Carnap can thereby be understood as proposing a distinctive form of noncognitivism about ontology that is in some respects analogous to norm-expressivism in metaethics. (shrink)

The running debate between Peter Achinstein and his critics concerning the nature of scientific evidence is misguided as each side attempts to explicate a distinct notion of evidence. Achinstein's approach, however, is valuable in helping to point out a problem with Carnap's statistical relevance model. By claiming an increase in probability to be necessary for evidence, the received view is incapable of accounting for evidence which is statistically irrelevant but explanatorily relevant. A broader view of evidence which can account (...) for pragmatic concerns such as explanation is thereby required. (shrink)

A basic system of inductive logic; An axiomatic foundation for the logic of inductive generalization; A survey of inductive systems; On the condition of partial exchangeability; Representation theorems of the de finetti type; De finetti's generalizations of excahngeability; The structure of probabilities defined on first-order languages; A subjectivit's guide to objective chance.

Tomoji Shogenji is generally assumed to be the first author to have presented a probabilistic measure of coherence. Interestingly, Rudolf Carnap in his Logical Foundations of Probability discussed a function that is based on the very same idea, namely his well-known relevance measure. This function is largely neglected in the coherence literature because it has been proposed as a measure of evidential support and still is widely conceived as such. The aim of this paper is therefore to investigate (...) class='Hi'>Carnap’s measure regarding its plausibility as a candidate for a probabilistic measure of coherence by comparing it to Shogenji’s. It turns out that both measures satisfy and violate the same adequacy constraints, despite not being ordinally equivalent exhibit a strong correlation with each other in a Monte Carlo simulation and perform similarly in a series of test cases for probabilistic coherence measures. (shrink)

In this thesis I defend and pursue that line about the foundations of probability theory which has come to be known as "the logicist view about probability", and, in particular, the shape which it took in Carnap's Inductive Logic. ;Most philosophers who now deal with probability theory claim that Carnap's program of Inductive Logic has failed. The main aim of my thesis is to show that this judgment is based on a fundamental misunderstanding about the nature and (...) the aim of inductive logic. To that end, I follow, in chapter 1, the events in the history of probability, logic and mathematics which led to choosing certain requirements as the requirements which any theory about the foundations of probability must fulfill in order to be acceptable. ;In chapter 2 I explain how Carnap's inductive logic fulfills those requirements and how the method it uses to give foundations to probability theory can also be used to solve another major problem about probability, namely, the problem of statistical inference. ;Chapter 3 shows how the ideas explained in chapter 2 were developed, formally, by Carnap, and how Carnap's program can be continued in a particular case, that of reasoning by analogy. ;Finally, in chapter 4, I attempt to show that subjectivism about probability theory, the rival theory to Carnap's logicism, does not succeed in meeting the most basic requirement for the acceptability of any theory about the foundations of probability. (shrink)

Logical empiricism and pragmatism shared an empiricist orientation, a close interest in the sciences and their methods, and skepticism about propositions which cannot be empirically tested or verified. Both movements came into direct contact in the first half of the 1930s, shortly after the beginning of the so-called public phase of logical empiricism . Around 1930, Schlick and Feigl went to the United States and philosophers in the pragmatist tradition began to pay attention to the new Viennese movement. Only with (...) the rise of this mutual interest did Carnap become acquainted with pragmatism. Contrary to other logical empiricists , there are almost no traces in Carnap’s earlier philosophy of an interest for pragmatism. We will focus here on the historic episode of Carnap’s encounter with pragmatism. This will permit to clear more general claims about the relation of logical empiricism and pragmatism. We can find contradictory claims on this relation in the recent literature on the history of philosophy of science and of analytic philosophy. On the one hand the differences and conflicts between logical empiricism and pragmatism are emphasized and the progressive divergence between these two movements is pointed out.2 On the other hand the literature points out the pragmatic elements in Carnap’s philosophy which facilitated a convergence with pragmatism.3 First, we claim here that in the 1930s it is the convergence between pragmatism and logical empiricism that was prevailing and that it found its expression in Carnap’s support of a “scientific empiricism” as conceived by the pragmatist Charles Morris. The strong impetus for an internationalization of scientific philosophy in the Unity of Science movement placed the project of an alliance of different empiricist movements at the forefront. Secondly we claim that Carnap’s convergence with pragmatism is due to a liberalization of empiricism which took already place in the Vienna Circle, independently of any direct pragmatist influence. With this liberalization of empiricism the convergence with pragmatism became much easier than it would have been with an empiricism as defended in Carnap’s Aufbau. We will show in a first section that Carnap’s encounter with pragmatism was initiated by the pragmatist’s criticism of verificationism and of the empricism of the Aufbau. In a second section we will describe Carnap’s encounter with philosophers of the pragmatist tradition and his attempt to convince them that the pragmatist’s criticism did not apply any more to his new position of the early 1930s . As response some pragmatists proposed models for a convergence of logical empiricism with pragmatism.4 In a final section we will show that in Carnap’s response to the pragmatists, he supported such a convergence. (shrink)

Although we often see references to Carnap’s inductive logic even in modern literatures, seemingly its confusing style has long obstructed its correct understanding. So instead of Carnap, in this paper, I devote myself to its necessary and sufficient commentary. In the beginning part (Sections 2-5), I explain why Carnap began the study of inductive logic and how he related it with our thought on probability (Sections 2-4). Therein, I trace Carnap’s thought back to Wittgenstein’s Tractatus as well (...) (Section 5). In the succeeding sections, I attempt the simplest exhibition of Carnap’s earlier system, where his original thought was thoroughly provided. For this purpose, minor concepts to which researchers have not paid attention are highlighted, for example, m-function (Section 8), in-correlation (Section 10), C-correlate (Section 10), statistical distribution (Section 12), and fitting sequence (Section 17). The climax of this paper is the proof of theorem (56). Through this theorem, we will be able to overview Carnap’s whole system. (shrink)

The classic “self-undermining objection” to the verificationist criterion of meaning states that the criterion does not meet its own standard: since verificationism is not empirically confirmable, analytic, or contradictory, verificationism implies its own meaninglessness. This essay reconstructs and motivates Carnap’s response to this objection. The interpretation presented is contrasted with those of Putnam and Ricketts. I argue that Carnap’s basic move in response to the self-undermining objection is to construe his verificationism as an analytic definition of “meaningfulness” that (...) is meaningful by its own lights. I then discuss possible motivations for this definition. I argue, against Reichenbach, Ayer, and Hempel, that it is not an analysis of the everyday concept of meaning. Instead, I claim, the definition is motivated _pragmatically_: verificationism replaces the ordinary conception of meaning with one that purports to capture all and only the expressions that are pragmatically useful to the scientist. Finally, I consider whether pragmatism faces a self-undermining objection to of its own. I argue that pragmatism is a preference concerning formal languages, and that, since preferences need not apply to themselves, pragmatism is not self- undermining. (shrink)

A basic system of inductive logic; An axiomatic foundation for the logic of inductive generalization; A survey of inductive systems; On the condition of partial exchangeability; Representation theorems of the de finetti type; De finetti's generalizations of excahngeability; The structure of probabilities defined on first-order languages; A subjectivit's guide to objective chance.

According to a popular interpretation, Carnap’s interpretation of probability had evolved from a logical towards a subjective conception. However Carnap himself insisted that his basic philosophical view of probability was always the same. I address this apparent clash between Carnap's self-identification and the subsequent interpretations of his work. Following its original intentions, I reconstruct inductive logic as an explication. The emerging picture is of a versatile linguistic framework, whose main function is not the discovery of objective logical (...) relations in the object language, but the stipulation of conceptual possibilities. Within this representation, I map out the changes that the project went through. Seen from such an explication-based perspective, inductive logic becomes quite hard to categorize using the standard labels. (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.

Stimulating, thought-provoking text by one of the 20th century’s most creative philosophers clearly and discerningly makes accessible such topics as probability, measurement and quantitative language, structure of space, causality and determinism, theoretical laws and concepts and much more. "...the best book available for the intelligent reader who wants to gain some insight into the nature of contemporary philosophy of science."—Choice.

Carnap gives a definition for a comparative concept of confirmation. For it he uses the notation “MC.” His defined notation is intended to be an explicatum for the explicandum: “the hypothesis h is confirmed by the evidence e equally strongly or more strongly than h′ by e′”.

In spite of his tragically short life, Ramsey made extensive contributions in the fields of mathematics, logic, economics and philosophy. In this article we focus on Ramsey's investigations into the notions of belief and judgement, their truth conditions and probability theory. We show that the central role given by Ramsey to belief and action together with his pragmatism allows for a new interpretation of the theories of truth and probability, paving the way for a modern decision theory.

This paper has three interdependent aims. The first is to make Reichenbach’s views on induction and probabilities clearer, especially as they pertain to his pragmatic justification of induction. The second aim is to show how his view of pragmatic justification arises out of his commitment to extensional empiricism and moots the possibility of a non-pragmatic justification of induction. Finally, and most importantly, a formal decision-theoretic account of Reichenbach’s pragmatic justification is offered in terms both of the minimax principle and the (...) dominance principle. (shrink)

Huw Price has sketched a program for a globalized expressivism in support of which he has repeatedly invoked Rudolf Carnap. This paper argues that this is entirely appropriate, as Carnap had something quite similar in mind. However, it also argues that Price’s recent attempts to integrate Robert Brandom’s inferentialism to this program are less successful, and that a more empirically-oriented descriptive pragmatics along Carnapian lines would be a better fit with his original program than Brandom’s explicitly hermeneutical agenda.

This critical editorial introduction summarizes and explicates Frederick Will’s pragmatic realism and his account of the nature, assessment, and revision of cognitive and practical norms in connection with: the development of Will’s pragmatic realism, Hume’s problem of induction, the oscillations between foundationalism and coherentism, the nature of philosophical reflection, Kant’s ‘Refutation of Idealism’, the open texture of empirical concepts, the correspondence conception of truth, Putnam’s ‘internal realism’, the redundancy theory of truth, sociology of knowledge, the governance of practice by norms (...) and the assessment and revision of norms in practice, scientific realism, the alleged independence of reason and tradition, rule-following, legal realism, ethical intuitionism and moral relativism, the regress problem (both in epistemology and in moral theory), the paradox of analysis, and culminating in Will’s account of the philosophical governance of norms. These issues are discussed in close consideration of the views of: William Alston, John Dewey, Descartes, Leibniz, Waismann, Austin, Russell, Schlick, Ayer, Richard Rorty, Michael Williams, Hempel, Carnap, Simon Blackburn, Ramsey, Strawson, Kuhn, Wilfrid Sellars, Wittgenstein, Nozick, Dretske, Quine, Barbara Herman, Hardy Jones, Marcus Singer, and Gerd Buchdahl. (shrink)

Paul Feyerabend once made a remark to the effect that his pragmatic theory of observation can be traced back to proposals put forward by leading Logical Empiricists during the height of the protocol sentence debate. In this paper I want to vindicate the systematic side of Feyerabend’s remark and show that a pragmatic theory of observation can in fact be found in Rudolf Carnap’s writings of 1932. I first proceed to dispel a misunderstanding concerning the term “pragmatic” raised by (...) Thomas Oberdan. Following Morris’ and Carnap’s documented usage, I show that the intended meaning of “pragmatic” refers to a specific semiotic relation between users of a language and their environment describable by empirical means. I reconstruct such a pragmatic theory in terms of a detector model that interprets observation sentences as bodily dispositions indicating physical events in the surroundings of the detector. I then proceed to show how Feyerabend’s later theory of observation picks up central features of Carnap’s account and also shares some of the motivations. I conclude by noting how an empirical theory of observation sentences offers a bootstrapping solution to the “basis problem”. (shrink)

Probability theory promises to deliver an exact and unified foundation for inquiry in epistemology and philosophy of science. But philosophy of religion is also fertile ground for the application of probabilistic thinking. This volume presents original contributions from twelve contemporary researchers, both established and emerging, to offer a representative sample of the work currently being carried out in this potentially rich field of inquiry. Grouped into five parts, the chapters span a broad range of traditional issues in religious epistemology. (...) The first three parts discuss the evidential impact of various considerations that have been brought to bear on the question of the existence of God. These include witness reports of the occurrence of miraculous events, the existence of complex biological adaptations, the apparent 'fine-tuning' for life of various physical constants and the existence of seemingly unnecessary evil. The fourth part addresses a number of issues raised by Pascal's famous pragmatic argument for theistic belief. A final part offers probabilistic perspectives on the rationality of faith and the epistemic significance of religious disagreement. (shrink)

In this paper it is argued that there are relevant similarities of Aristotle's account of definition and Carnap's account of explication. To show this, first, Aristotle's conditions of adequacy for definitions are provided and an outline of the main critique put forward against Aristotle's account of definition is given. Subsequently, Carnap's conditions of adequacy for explications are presented and discussed. It is shown that Aristotle's conditions of extensional correctness can be interpreted against the backdrop of Carnap's condition of similarity once (...) one skips Aristotelian essentialism and takes in a Carnapian and more pragmatic stance. Finally, it is argued that, in general, a complementary rational reconstruction of both approaches allows for resolving problems of interpretational underdetermination. (shrink)

This paper concerns the issue of whether the so-called left wing of the Vienna Circle (Carnap, Neurath, Frank) can be understood as having provided the blueprint for a bipartite metatheory with a formal-logical part (the “logic of science”) supporting and being supported by a naturalistic-empirical part (the “behavioristics of science”). A claim to this effect was recently met by a counterclaim that there was indeed an attempt made to broaden Carnap’s formalist conception of philosophy by the pragmatist Morris, but (...) that this initiative failed and that Carnap showed no interest in it. To defend the original claim this paper provides an analysis of Carnap and Morris on the subject matter of pragmatics in order to show that and how Carnap adopted Morris’s proposals in so far as they agreed with bipartite metatheory conception. (shrink)

Carnap and Reichenbach made extraordinary contributions to our understanding of the foundations of probability.1 Each of them provided a precise logical and mathematical analysis of probability that satisfied the formal calculus of probability. Reichenbach’s theory of probability analysed probability as the limit of relative frequency, while Carnap’s theory of probability explicated probability as a degree of logical connection. Carnap articulated his account of the foundations of probability by insisting that there were (...) two concepts of probability, his own, probability one, and the other, including Reichenbach’s, probability two. Probability one is a logical conception, and the truth of the probability statements is a consequence of the definition of a measure function. Probability two is a factual conception, and the truth of the probability statements is a consequence of the existence of limits of relative frequencies. Explained in this way, the two accounts are not competitive. In fact, there is no inconsistency between the two accounts. They offer us two different interpretations of the calculus of probability. (shrink)

While pragmatic arguments for numerical probability axioms have received much attention, justifications for axioms of qualitative probability have been less discussed. We offer an argument for the requirement that an agent’s qualitative judgments be probabilistically representable, inspired by, but importantly different from, the Money Pump argument for transitivity of preference and Dutch book arguments for quantitative coherence. The argument is supported by a theorem, to the effect that a subject is systematically susceptible to dominance given her preferred acts, (...) if and only if the subject’s comparative judgments preclude representation by a standard probability measure. (shrink)

In section I the notions of logical and inductive probability will be discussed as well as two explicanda, viz. degree of confirmation, the base for inductive probability, and degree of evidential support, Popper's favourite explicandum. In section II it will be argued that Popper's paradox of ideal evidence is no paradox at all; however, it will also be shown that Popper's way out has its own merits.

The faults of logical empiricist accounts of metascientific discourse are examined through a study of the modifications Carnap makes to his version of the program over four decades. As empiricists acquiesced on the distinction between theory and observation, Carnap attempted to retain and insulate an equally suspect sharp distinction between the theoretic and the pragmatic. Carnap's later philosophy was understood as a modification of the program in the direction of pragmatism. But neither the key notion of "external questions" nor an (...) instrumentalist understanding of "pragmatic utility" are genuinely compatible with pragmatism. This underlines the need to clarify what is unique to pragmatic views of cognitive evaluation and normative discourse as they affect scientific reasoning. I conclude by suggesting how pragmatic conceptions of metascientific discourse can work to correct misconceptions about norm generation and governance that are shared in logicist and historicist accounts. (shrink)

In 1959 Carnap published a probability model that was meant to allow forreasoning by analogy involving two independent properties. Maher (2000)derived a generalized version of this model axiomatically and defended themodel''s adequacy. It is thus natural to now consider how the model mightbe extended to the case of more than two properties. A simple extension waspublished by Hess (1964); this paper argues that it is inadequate. Amore sophisticated one was developed jointly by Carnap and Kemeny in theearly 1950s but (...) never published; this paper gives the first published descriptionof Carnap and Kemeny''s model and argues that it too is inadequate. Since noother way of extending the two-property model is currently known, the conclusionof this paper is that a satisfactory extension to multiple properties requires somenew approach. (shrink)

We compare Carnap's and Kuhn's views on science. Although there are important differences between them, the similarities are striking. The basis for the latter is a pragmatically oriented semantic conventionalist picture of science, which suggests that the view that post-positivist philosophy of science constitutes a radical revolution which has no interesting affinities with logical positivism must be seriously mistaken.

In his Anthropology from a Pragmatic Point of View, Kant formulates the idea of the empirical investigation of the human being as a free agent. The notion is puzzling: Does Kant not often claim that, from an empirical point of view, human beings cannot be considered as free? What sense would it make anyway to include the notion of freedom in science? The answer to these questions lies in Kant’s notion of character. While probably all concepts of character are involved (...) in the description and explanation of human action, Kant develops a specific notion of character by distinguishing character as a “mode of thought” (Denkungsart) from character as a “mode of sensing” (Sinnesart). The former notion is distinctively Kantian. Only mode of thought reveals itself in human action such that actions can be seen as linked to an agent’s first-person perspective and the capacity to rationally reflect one’s own intentions and desires. By reference to this concept human actions can be empirically explained qua free actions. The point of this paper is not only to rule out the interpretation that Kant is an incompatibilist concerning the dilemma of freedom and causal determinism. It is also argued that Kant defends a version of soft determinism which is more sophisticated and more adequate for the human sciences than Hume’s. (shrink)

An admirable introduction to inductive logic, this book is both informative and lucidly written. After an excellent introductory chapter comparing deductive with inductive logic, the author presents Hume's problem of induction and several proposed methods for solving or dissolving it, none of which are adequate. Chapter III is devoted to Goodman's paradox about "grue" and the problems it poses for induction. No attempt, however, is made to develop a calculus of projectibility, which is needed to solve this new riddle of (...) induction. The systematic part of inductive logic is presented in the fourth and longest chapter. This chapter begins with a brief account of elementary truth functions which the author then uses to present an updated and rather elegant version of Mill's methods. The rest of the chapter is devoted to the development of the probability calculus in a systematic manner, without, however, any method of assigning initial probabilities. An account of statistics is appended, which is too brief to be of much value. The fifth chapter is devoted to interpretations of the probability calculus. The frequency interpretation of probability is described as an adequate account of descriptive probability. Two interpretations of inductive probability are presented: Carnap's "logic" interpretation and the frequency interpretation of Reichenbach. Both, however, are found lacking in ultimate justification. Though not flawless, this book is of very high quality.—F. S. M. (shrink)

“Probably Peirce’s best-known works are the first two articles in a series of six that originally were collectively entitled Illustrations of the Logic of Science and published in Popular Science Monthly from November 1877 through August 1878. The first is entitled ‘The Fixation of Belief’ and the second is entitled ‘How to Make Our Ideas Clear.’ In the first of these papers Peirce defended, in a manner consistent with not accepting naive realism, the superiority of the scientific method over other (...) methods of overcoming doubt and ‘fixing belief.’” — Robert Burch, “Charles Sanders Peirce,” entry in the Stanford Encyclopedia of Philosophy (2021 revision) -/- “Pragmatist epistemologies often explore how we can carry out inquiries in a self-controlled and fruitful way. (Where much analytic epistemology centres around the concept of knowledge, considered as an idealised end-point of human thought, pragmatist epistemology centres around the concept of inquiry, considered as the process of knowledge-seeking and how we can improve it.) So pragmatists often provide rich accounts of the capacities or virtues that we must possess in order to inquire well, and the rules or guiding principles that we should adopt. A canonical account is Peirce’s classic early paper ‘The Fixation of Belief‘. Here Peirce states that inquiry is a struggle to replace doubt with “settled belief“, and that the only method of inquiry that can make sense of the fact that at least some of us are disturbed by inconsistent beliefs, and will subsequently reflect upon which methods of fixing belief are correct is the Method of Science, which draws on the Pragmatic Maxim described above. This contrasts with three other methods of fixing belief: i) refusing to consider evidence contrary to one’s favored beliefs (the Method of Tenacity), ii) accepting an institution’s dictates (the Method of Authority), iii) developing the most rationally coherent or elegant-seeming belief-set (the A Priori Method).“ — Catherine Legg, “Pragmatism,” entry in the Stanford Encyclopedia of Philosophy (2021 revision). (shrink)

One way of explaining Rudolf Carnap’s mature philosophical view is by drawing an analogy between his technical projects—like his work on inductive logic—with a certain kind of conceptual engineering. After all, there are many mathematical similarities between Carnap’s work in inductive logic and a number of results from contemporary confirmation theory, statistics and mathematical probability theory. However, in stressing these similarities, the conceptual dependence of Carnap’s inductive logic on his work on semantics is downplayed. Yet it (...) is precisely the conceptual resources made available to Carnap from his work on semantics which allows him to understand his work on inductive logic as a kind of conceptual engineering project. The aim of this paper is to elucidate this engineering analogy in light of Carnap’s mature views through the lens of both inductive logic and semantics. (shrink)

This chapter contains sections titled: The Bayesian Orthodoxy Idealization Two Approaches to a Theory of Probability Adjustment for Nonclassical Logics Carnap's Confirmation Theory Proportional Syllogisms Kyburg's Fuzzy Probabilities Levi's Indeterminate Systems Qualitative Theories of Probability The Dynamics of Subjective Probability Probability Theory and Quantum Theory.