This paper presents an enrichment of the Gabbay–Woods schema of Peirce’s 1903 logical form of abduction with illocutionary acts, drawing from logic for pragmatics and its resources to model justified assertions. It analyses the enriched schema and puts it into the perspective of Peirce’s logic and philosophy.

A mathematical model in science can be formulated as a counterfactual conditional, with the model’s assumptions in the antecedent and its predictions in the consequent. Interestingly, some of these models appear to have assumptions that are metaphysically impossible. Consider models in ecology that use differential equations to track the dynamics of some population of organisms. For the math to work, the model must assume that population size is a continuous quantity, despite that many organisms (e.g., rabbits) are necessarily discrete. This means our counterfactual representation of the model can have an impossible antecedent, giving us a counterpossible. Analogous counterpossibles arise in other sciences, as we’ll see. According to a prominent view in counterfactual semantics, the *vacuity thesis*, all counterpossibles are vacuously true, that is, true merely because their antecedents are necessarily false. But some counterpossible formulations of differential equation models in science are not all vacuously true—some are non-vacuously true, and some are false. I go on to show how an alternative semantics, one that employs impossible worlds, can deliver this judgment.

The paper critically discusses two prominent arguments against closure principles for knowledge. The first one is the “argument from aggregation”, claiming that closure under conjunction has the consequence that, if one individually knows *i* premises, one also knows their *i*-fold conjunction—yet, every one of the premises might exhibit interesting positive epistemic properties while the *i*-fold conjunction might fail to do so. The second one is the “argument from concatenation”, claiming that closure under entailment has the consequence that, if one knows a premise, one also knows each of its remote consequences one arrives at—yet, again, the premise might exhibit interesting positive epistemic properties while some of its remote consequences might fail to do so. The paper firstly observes that the ways in which these two arguments try to establish that the relevant closure principle has the relevant problematic consequence are strikingly similar. They both crucially involve showing that, given the features of the case, the relevant closure principle acts in effect as a soritical principle, which is in turn assumed to lead validly to the relevant problematic consequence. There are however nontransitive logics of vagueness (“tolerant logics”, developed elsewhere by the author) where soritical principles do not have any problematic consequence. Assuming that one of these logics is the correct logic of vagueness, the paper secondly observes that both arguments describe situations where knowledge is arguably vague in the relevant respects, so that a tolerant logic should be used in reasoning about it, with the effect that the relevant soritical principle no longer validly leads to the relevant problematic consequence. This shows an interesting respect in which the gap between validity and good inference that arguably arises in a transitive framework can be bridged in a tolerant one, thereby approximating better certain features of our epistemic lives as finite subjects. Moreover, even for those who do not subscribe to tolerant logics, the paper’s two observations jointly indicate that, for all the arguments from aggregation and concatenation show, the status of the relevant closure principles should be no worse than that assigned by one’s favoured theory of vagueness to soritical principles, which only rarely is plain falsity and can indeed get arbitrarily close to full truth.

We describe Peirce’s 1903 system of modal gamma graphs, its transformation rules of inference, and the interpretation of the broken-cut modal operator. We show that Peirce proposed the normality rule in his gamma system. We then show how various normal modal logics arise from Peirce’s assumptions concerning the broken-cut notation. By developing an algebraic semantics we establish the completeness of fifteen modal logics of gamma graphs. We show that, besides logical necessity and possibility, Peirce proposed an epistemic interpretation of the broken-cut modality, and that he was led to analyze constructions of knowledge in the style of epistemic logic.

Joint attention customarily refers to the coordinated focus of attention between two or more individuals on a common object or event, where it is mutually “open” to all attenders that they are so engaged. We identify two broad approaches to analyse joint attention, one in terms of cognitive notions like common knowledge and common awareness, and one according to which joint attention is fundamentally a primitive phenomenon of sensory experience. John Campbell’s relational theory is a prominent representative of the latter approach, and the main focus of this paper. We argue that Campbell’s theory is problematic for a variety of reasons, through which runs a common thread: most of the problems that the theory is faced with arise from the relational view of perception that he endorses, and, more generally, they suggest that perceptual experience is not sufficient for an analysis of joint attention.

It is almost universally accepted that the Frege-Geach Point is necessary for explaining the inferential relations and compositional structure of truth-functionally complex propositions. I argue that this claim rests on a disputable view of propositional structure, which models truth-functionally complex propositions on atomic propositions. I propose an alternative view of propositional structure, based on a certain notion of *simulation*, which accounts for the relevant phenomena without accepting the Frege-Geach Point. The main contention is that truth-functionally complex propositions do not include as their parts truth-evaluable propositions, but their simulations, which are neither forceful nor truth-evaluable. The view makes room for the idea that there is no such thing as the forceless expression of propositional contents and is attractive because it provides the resources for avoiding a fundamental problem generated by the Frege-Geach Point concerning the relation between forceless and forceful expressions of propositional contents. I further argue that the acceptance of the Frege-Geach Point mars Peter Hanks’ and François Recanati’s recent attempts to resist the widespread idea that assertoric force is extrinsic to the expression of propositional contents. Rejecting this idea, I maintain, requires a deeper break with the tradition than Hanks and Recanati have allowed for.