Tom 14 (2022): Zeszyt 64 (May 2022)

In this paper, I will discuss accounts to solve the problem of induction by introducing necessary connections. The basic idea is this: if we know that there are necessary connections between properties F and G such that F -ness necessarily brings about G-ness, then we are justified to infer that all, including future or unobserved, F s will be Gs. To solve the problem of induction with ontology has been proposed by David Armstrong and Brian Ellis. In this paper, I will argue that these attempts to solve the problem of induction fail. Necessary connections fail to reliably imply the respective regularities for two main reasons: Firstly, according to an argument originally presented by Helen Beebee, the respective necessary connections might be time-limited, and hence do not warrant inferences about future cases. As I will discuss, arguments against the possibility or explanatory power of time-limited necessary connections fail. Secondly, even time-unlimited necessary connections do not entail strict or non-strict regularities, and nor do they allow inferences about individual cases, which is an important function of inductive reasoning. Moreover, the proposed solution to the problem of induction would only apply to a tiny minority of inductive inferences. I argue that most inductive inferences are not easily reducible to the proposed inference pattern, as the vast majority of everyday inductive inferences do not involve necessary connections between fundamental physical properties or essences.

In this article I introduce constitutive norm accounts of assertion, and then give three arguments for giving up on the constitutive norm project. First I begin with an updated version of MacFarlane’s Boogling argument. My second argument is that the ‘overriding response’ that constitutive norm theorists offer to putative counterexamples is unpersuasive and dialectically risky. Third and finally, I suggest that constitutive norm theorists, in appealing to the analogy of games, actually undermine their case that they can make sense of assertions that fail to follow their putative constitutive norm. These considerations, I suggest, together show that the constitutive norm project founders not because any single norm is not descriptively correct of our assertion practices, but rather, because giving a constitutive norm as the definition of assertion alone is insufficient.

We will formulate some analogous higher-order versions of Skolem’s paradox and assess the generalizability of two solutions for Skolem’s paradox to these paradoxes: the textbook approach and that of Bays (2000). We argue that the textbook approach to handle Skolem’s paradox cannot be generalized to solve the parallel higher-order paradoxes, unless it is augmented by the claim that there is no unique language within which the practice of mathematics can be formalized. Then, we argue that Bays’ solution to the original Skolem’s paradox, unlike the textbook solution, can be generalized to solve the higher-order paradoxes without any implication about the possibility or order of a language in which mathematical practice is to be formalized.

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. ‘Whitehead and Russell wrote Principia Mathematica’), while in others they are not (e.g. ‘Some philosophers wrote Principia Mathematica’). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called ‘discrete plural logic’) is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic—or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system.