Daniel Kodsi

Forcing is a fundamental set-theoretic technique, with which many independence results can be established. A famous example is the independence of the continuum hypothesis in ZFC set theory. Forcing is also well-known to be complex, and therefore difficult to master. Here, we provide a gentle introduction of forcing, by developing forcing for second-order logic. Second-order logic can be interpreted as a rudimentary kind of set theory. Although very limited as a theory of sets, second-order logic is rich enough to capture a form of the continuum hypothesis, as well as the generalized continuum hypothesis, which is slightly easier to state. We develop forcing for second-order logic in the form of possibility semantics, and use this to show that a second-order version of the generalized continuum hypothesis cannot be derived in a standard proof system for second-order logic. Mathematically, the results we obtain in this way are much weaker than standard independence results in set theory. However, as a consequence, we are able to avoid many technical complexities in the presentation of forcing. In this way, we hope that forcing for second-order logic can serve an expository function, of providing an accessible route towards understanding some of the central ideas behind forcing.

Haecceitism is the thesis that some truths are not necessitated by the qualitative truths. In this paper I explore a general argument that purports to establish that haecceitism leads to objectionably 'cheap' violations of determinism. In response to this argument, I develop a novel position that combines considerations from metaphysics and the philosophy of language to secure the compatibility of haecceitism and determinism. This position has important parallels to the way haecceitism has been developed within counterpart theory, but, crucially, it makes no use of counterpart theory itself.

A critique of capitalism, in order to count as such, must identify a problem that is not shared by all other feasible economic systems, for this would amount to little more than a complaint (or kvetch) about the human condition. The distinction between critique and kvetch raises the question of what constitutes a feasible alternative to capitalism. Although it sounds as though this is a pragmatic or technical question, I will argue that it is usually normative. With this clarification in place, I will consider whether Waheed Hussain’s concerns about capitalism amount to a critique or a kvetch.

Talk of ‘defeasible/nondefeasible reasoning’ by some of our leading epistemologists and logicians is misleading. It embodies conceptual confusion about epistemic defeasibility, fallibility, and monotonicity in influential accounts of inferential justification. As argued here, this form of deeply entrenched confusion has blurred the distinction between the concepts of fallibility and defeasibility under the guise of the seemingly benign synonymy between the labels ‘defeasible reasoning’ and ‘nonmonotonic reasoning.’ The careless employment of these labels has had a harmful effect on our understanding of inferential justification. Specifically, it has blurred the fundamental distinction between truth-preservation and justification-preservation in the relevant literature, thus harming the epistemology of reasoning at its core. We have been warned by Timothy Williamson against this kind of confusion, but the warning has gone unheeded. That warning is explained and amplified here on the basis of abundant textual evidence and the discussion of exemplary cases.

(Goodsell, Journal of Philosophical Logic, 51(1), 127-150 2022) establishes the noncontingency of sentences of first-order arithmetic, in a plausible higher-order modal logic. Here, the same result is derived using significantly weaker assumptions. Most notably, the assumption of rigid comprehension—that every property is coextensive with a modally rigid one—is weakened to the assumption that the Boolean algebra of properties under necessitation is countably complete. The results are generalized to extensions of the language of arithmetic, and are applied to answer a question posed by Bacon and Dorr (2024).

Orthodoxy holds that there is a determinate fact of the matter about every arithmetical claim. Little argument has been supplied in favour of orthodoxy, and work of Field, Warren and Waxman, and others suggests that the presumption in its favour is unjustified. This paper supports orthodoxy by establishing the determinacy of arithmetic in a well-motivated modal plural logic. Recasting this result in higher-order logic reveals that even the nominalist who thinks that there are only finitely many things should think that there is some sense in which arithmetic is true and determinate.

kk states that knowing entails knowing that one knows, and K¬K states that not knowing entails knowing that one does not know. In light of the arguments against kk and K¬K⁠, one might consider modally qualified variants of those principles. According to weak kk, knowing entails the possibility of knowing that one knows. And according to weakK¬K⁠, not knowing entails the possibility of knowing that one does not know. This paper shows that weak kk and weakK¬K are much stronger than they initially appear. Jointly, they entail kk and K¬K⁠. And they are susceptible to variants of the standard arguments against kk and K¬K⁠. This has interesting implications for the debate on positive introspection and for deeper issues concerning the structure and limits of knowability.