Argumenta – Journal of Analytic Philosophy

Rothschild and Spectre (2018b) present a puzzle about knowledge, probability and conditionals. This paper analyzes the puzzle and argues that it is essentially two puzzles in one: a puzzle about knowledge and probability and a puzzle about probability and conditionals. As these two puzzles share a crucial feature, this paper ends with a discussion of the prospects of solving them in a unified way.

Once upon a time, some thought that indicative conditionals could be effectively analyzed as material conditionals. Later on, an alternative theoretical construct has prevailed and received wide acceptance, namely, the conditional probability of the consequent given the antecedent. Partly following critical remarks recently appeared in the literature, we suggest that evidential support—rather than conditional probability alone—is key to understand indicative conditionals. There have been motivated concerns that a theory of evidential conditionals (unlike their more traditional counterparts) cannot generate a sufficiently interesting logical system. Here, we will describe results dispelling…

A unified shared theory of conditionals does not still exist. Some theories seem suitable only for indicative but not for counterfactual ones (or vice versa), while others work well with simple conditionals but not compound ones. Ernest Adams’ approach—one of the most successful theories as far as indicative conditional are concerned—is based on a reformulation of Ramsey’s Test in a probabilistic thesis known as “The Equation”. While the so-called Lewis’ Triviality Results support Adams’ view that conditionals do not express genuine statements, the problem arises whether these results lead inevitably…

We illustrate the notions of compound and iterated conditionals introduced, in recent papers, as suitable conditional random quantities, in the framework of coherence. We motivate our definitions by examining some concrete examples. Our logical operations among conditional events satisfy the basic probabilistic properties valid for unconditional events. We show that some, intuitively acceptable, compound sentences on conditionals can be analyzed in a rigorous way in terms of suitable iterated conditionals. We discuss the Import-Export principle, which is not valid in our approach, by also examining the inference from a material…

The trivalent and functional theory of the truth of conditionals developed by Bruno de Finetti has recently gathered renewed interests, particularly from philosophical logic, psychology and linguistics. It is generally accepted that de Finetti introduced his theory in 1935. However, a reading of his first publications indicates an earlier conception of almost all his theory. We bring to light a manuscript and unknown writings, dating back to 1928 and 1932, detailing de Finetti’s theory. The two concepts of thesis and hypothesis are presented as a cornerstone on which logical connectives…

According to Lewis’ Triviality Results (LTR), conditionals cannot satisfy the equation (E) P(C if A) = P(C | A), except in trivial cases. Ernst Adams (1975), however, provided a probabilistic semantics for the so-called simple conditionals that also satisfies equation (E) and provides a probabilistic counterpart of logical consequence (called p-entailment). Adams’ probabilistic semantics is coextensive to Stalnaker-Thomason’s (1970) and Lewis’ (1973) semantics as far as simple conditionals are concerned. A theorem, proved in McGee 1981, shows that no truth-functional many-valued logic allows a relation of logical consequence coextensive with…

In the middle of the last century, it was common to explain the notion of necessity in linguistic terms. A necessary truth, it was said, is a sentence whose truth is guaranteed by linguistic rules. Quine famously argued that, on this view, de re modal claims do not make sense. “Porcupettes are porcupines” is necessarily true, but it would be a mistake to say of a particular porcupette that it is necessarily a porcupine, or that it is possibly purple. Linguistic theories of necessity fell out of favour with the…

My topic in this paper is the relationships of metaphysical priority which might hold between the different alethic modal statuses—necessity, contingency, possibility and impossibility. In particular, I am interested in exploring the view that the necessity of necessities is ungrounded while the contingency of contingencies is grounded—a scenario I call ‘necessity first’. I will explicate and scrutinize the contrast between necessity first and its ‘contingency first’ contrary, and then compare both views with ‘multimodal’ and ‘amodal’ alternatives, drawing on David Lewis’s modal realism and Barbara Vetter’s potentialism as example cases.…

General consensus has it that contingencies lack the requisite modal umph to serve as explanations for the modal status of necessities. The central aim of this paper is to show that this received opinion is incorrect: contingent necessity-makers are in fact possible. To do so, I identify certain conditions the satisfaction of which entail the possibility of contingent necessity-makers. I then argue for two broad instances where these conditions are satisfied. Consequently, the associated necessities in fact have contingent necessity-makers.