Caterina Sisti

This chapter presents some key concepts of Ramsey’s epistemology. The fundamental notions needed to understand Ramsey’s account of conditionals are here introduced. The chapter focuses on those concepts that appear in Ramsey’s renowned footnote, which served as the source of the Ramsey test(s), and tries to give them a precise characterisation and systematisation in a coherent epistemological framework. Such concepts are ‘degree of belief’, ‘knowledge’, and ‘laws’, and in order to recover and understand them, other notions will be needed, like ‘full belief’ and ‘habits’.The texts here considered were written in different years of Ramsey’s life, and they might sometimes present different positions or be underdeveloped and ambiguous. The main aim is thus to see if it is possible to obtain a coherent picture. The result is, I believe, a convincing epistemological framework that offers a better understanding of Ramsey’s footnote and provides a philosophical background for Ramsey’s account of conditional sentences.

The aim of this chapter is to recover Ramsey’s view on conditionals. The chapter first examines Ramsey’s famous footnote, the inspiration of many Ramsey tests in the literature on conditionals. First, I focus on indicative conditionals and Ramsey’s definition of conditional probability. I claim that, contrary to what is today usually believed, conditional probability cannot express, in Ramsey, the meaning of all types of indicative conditionals. Then, I discuss Ramsey’s account of counterfactuals. By taking into account an overlooked note by Ramsey on the meaning of hypothetical propositions, I show that Ramsey had a well-developed account of counterfactuals. Finally, the chapter ends with a discussion of Ramsey’s perspective on the classification of conditional sentences.

In this chapter, I compare the results of Chaps. 3 and 4 with some contemporary theories of conditionals. First, I suggest a reading of Ramsey’s footnote along the lines of the account outlined in the previous chapter. I propose a Ramsey test for the account of conditionals outlined in Chap. 4 and compare it with other Ramsey tests, when possible, or, more generally, with the guiding principles and consequences of relevant theories. I start with what I call ‘additional premises theories’ (Chisholm, Analysis 15(5):97–105, 1955, Goodman, J Philos 44(5), 113–128, 1947, Rescher, Hypothetical reasoning. Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Company, 1964, Veltman, Amsterdam papers of formal grammar, 1 (pp. 248–281), 1976 and Kratzer, J Philosoph Logic 10(2), 201–216, 1981). Then, I turn to possible-world semantics, as developed by Stalnaker (Studies in logical theory (american philosophical quarterly monographs 2) (pp. 98–112). Blackwell, 1968) and Lewis (Counterfactuals. Blackwell, 1973), varying strict conditionals. Next, I consider probabilistic semantics that focus on indicative conditionals, focusing on Adams’ approach (Inquiry: Interdiscipl J Philos 8(1–4):166–197, 1965). I then discuss belief revision theories and the version of the Ramsey test proposed by Gädenfors (Am Philosoph Quart 18(3):203–211, 1981, Philosoph Rev 95(1):81–93, 1986). Lastly, I briefly discuss some recent developments in trivalent and relevance logics of conditionals, with which the present account shares some intuitions. This chapter shows that the account outlined in this work could be, once fully developed, an alternative to contemporary most attractive solutions, delivering similar results, and covering all types of conditionals.

The aim of this work was, first, to understand and give a precise characterisation of Ramsey’s famous footnote. In order to do so, an exploration of Ramsey’s texts was needed to check if something more on Ramsey’s ideas on conditionals could be found.This work shows that Ramsey had more developed ideas on conditionals than it appears from the footnote. In turn, the footnote itself requires to be re-read, in light of these ideas. Contrary to what is generally believed today, Ramsey holds that in many circumstances, the meaning of a conditional sentence is material, namely it is given by the truth conditions of the material conditional corresponding to the conditional sentence. However, this is not always the case, and often a conditional expresses something more. Ramsey points out that the classical tool is not apt to always grasp the information a speaker conveys in asserting a conditional. The analysis Ramsey offers, then, is not purely semantic, he does not want to develop alternative truth conditions, but he is interested in the epistemology of conditionals.

In Chap. 2, I recovered Ramsey’s account of conditionals. Now, there are two approaches: a probabilistic and an inferential one. The two accounts, the inferential and the probabilistic, seem, at first glance, incompatible.A unified treatment of all types of conditionals is desirable, and this is the aim of this chapter. Here, I will try to stick as much as possible to what I take Ramsey’s ideas to be. I will use Ramsey’s notion of variable hypotheticals, additional and contextual propositions as tools. In doing so, I will not treat conditional sentences as propositions; I will not attach truth values to them. Instead, I will speak of acceptability conditions for conditional sentences. Finally, the chapter informally outlines the requirements that a validity criterion for the present approach should, in principle, satisfy. The account is supposed to cover all types of conditionals, with no distinction concerning the mood of the verbs involved in the sentences.

The aim of this work is twofold. First, it seeks to recover Ramsey’s original account of conditional sentences. Second, it aims to outline a unified epistemological theory of conditionals, drawing inspiration from Ramsey’s recovered account. This work is divided into two parts: Part I is historical and it deals with Ramsey texts and their interpretation; Part II is systematic and devoted to laying down the groundwork for an updated, Ramsey-inspired theory of conditionals. The two parts are different steps of a single path: from an analysis of the notions involved in the famous footnote—like ‘degree of belief’, ‘contradictories (in a sense)’, ‘knowledge’, ‘laws’—to a reconstruction of Ramsey’s view and its modification into a unified account.

Hempel never met Ramsey, but he knew his work. In his 1958 The Theoretician’s Dilemma: a study in the logic of theory construction, Hempel introduces the term Ramsey sentence, referring to Ramsey’s attempt in Theories to get rid of theoretical terms in formal accounts of scientific theories. In this paper, I draw the attention to another connection between Ramsey’s and Hempel’s works. Hempel’s Deductive-Nomological (DN) account of scientific explanation resembles very closely Ramsey’s account of a certain type of conditional sentences. In the first part of the paper, by introducing a fictional story, I highlight the similarities and differences between the two. In the last part of the paper, I claim that the most relevant difference between Ramsey and Hempel can be used to offer original solutions to Hempel’s Raven Paradox. Two possibilities are presented, arguing that the second, which requires a reconsideration of the formalisation of laws, is the most promising.

Analogy has received attention as a form of inductive reasoning in the empirical sciences. Its role in mathematics has, instead, received less consideration. This paper provides a novel account of how an analogy with a more familiar mathematical domain can contribute to the confirmation of a mathematical conjecture. By reference to case-studies, we propose a distinction between an _incremental_ and a _non-incremental_ form of confirmation by mathematical analogy. We offer an account of the former within the popular framework of Bayesian confirmation theory. As for the non-incremental notion, we defend its role in rationally informing the prior credences of mathematicians in those circumstances in which no new mathematical evidence is introduced. The resulting framework captures many important aspects of the use of analogical inference in the domain of pure mathematics.

In this paper, we propose a unified account of conditionals inspired by Frank Ramsey. Most contemporary philosophers agree that Ramsey’s account applies to indicative conditionals only. We observe against this orthodoxy that his account covers subjunctive conditionals as well—including counterfactuals. In light of this observation, we argue that Ramsey’s account of conditionals resembles Robert Stalnaker’s possible worlds semantics supplemented by a model of belief. The resemblance suggests to reinterpret the notion of conditional degree of belief in order to overcome a tension in Ramsey’s account. The result of the reinterpretation is a tenable account of conditionals that covers indicative and subjunctive as well as qualitative and probabilistic conditionals.

In contemporary works on conditionals, the Ramsey test is a procedure for the evaluation of conditional sentences. There are several versions of the test, all inspired by a footnote by the British philosopher and mathematician Frank Ramsey, in his General Propositions and Causality. However, no study on Ramsey's own account of conditionals has been put forth so far. Furthermore, the footnote seems to cover indicative conditionals only, and this has led to the belief that no account of counterfactuals can be found in Ramsey's work. In this paper, I recover Ramsey's account of counterfactuals and show that it is sketched in the footnote too. The result is a well-developed account of counterfactuals that resembles many contemporary ones. But Ramsey uses the same approach also for other types of conditionals, and this casts doubts on the current criteria for the classification of this type of sentences.