Précis of Uncut

Uncut is a book about two kinds of paradoxes: paradoxes involving truth and its relatives, like the liar paradox, and paradoxes involving vagueness. There are lots of ways to look at these paradoxes, and lots of puzzles generated by them, and Uncut ignores most of this variety to focus on a single issue. That issue: do our words mean what they seem to mean, and if so, how can this be? I claim that our words do mean what they seem to, and yet our language is not undermined by paradox. By developing a distinctive theory of meaning, I show how this can be.

A Tale of Excluding the Middle

he paper discusses a number of interconnected points concerning negation, truth, validity and the liar paradox. In particular, it discusses an argument for the dialetheic nature of the liar sentence which draws on Dummett’s teleological account of truth. Though one way of formulating this fails, a different way succeeds. The paper then discusses the role of the Principle of Excluded Middle in the argument, and of the thought that truth in a model should be a model of truth.

The Liar Without Relativism

Some in the recent literature have claimed that a connection exists between the Liar paradox and semantic relativism: the view that the truth values of certain occurrences of sentences depend on the contexts at which they are assessed. Sagi (Erkenntnis 82(4):913–928, 2017) argues that contextualist accounts of the Liar paradox are committed to relativism, and Rudnicki and Łukowski (Synthese 1–20, 2019) propose a new account that they classify as relativist. I argue that a full understanding of how relativism is conceived within theories of natural language shows that neither of the purported connections can be maintained. There is no reason why a solution to the Liar paradox needs to accept relativism.

The liar paradox in the predictive mind

Most discussions frame the Liar Paradox as a formal logical-linguistic puzzle. Attempts to resolve the paradox have focused very little so far on aspects of cognitive psychology and processing, because semantic and cognitive-psychological issues are generally assumed to be disjunct. I provide a motivation and carry out a cognitive-computational treatment of the liar paradox based on a cognitive-computational model of language and conceptual knowledge within the Predictive Processing (PP) framework. I suggest that the paradox arises as a failure of synchronization between two ways of generating the liar situation in two different (idealized) PP sub-models, one corresponding to language processing and the other to the processing of meaning and world-knowledge. In this way, I put forward the claim that the liar sentence is meaningless but has an air of meaningfulness. I address the possible objection that the proposal violates the Principle of Unrestricted Compositionality, which purportedly regulates the conceptual competence of thinkers.

The Perceptual-cognitive Foundation of the Subject-predicate Structure

This article describes a theoretical attempt to found thesubject predicate structure of declarative sentences on a frameworkof the human perceptual cognitive system. The basis of this studyis the idea that perception and cognition of events in the worldwould form mental representations in the system , a kind of modelsof the events that embody pieces of information about the events.This idea suggests that such models have structures that correspondto grammatical structures of the linguistic expressions thatrepresent the events and express the pieces of informationembodied by the models. The model structure s that correspond tothe subject predicate structure and logical connectives have beenconstructed following the way in which the system should functionto form the models of the events. This construction of thestructures entails propositional logic. Application of the structurest o the liar paradox le ads t o a new solution of this paradox .Keywords:

The Rule of Contradictory Pairs, Insolubles and Validity

The Oxford Calculator Roger Swyneshed put forward three provocative claims in his treatise on insolubles, written in the early 1330s, of which the second states that there is a formally valid inference with true premises and false conclusion. His example deployed the Liar paradox as the conclusion of the inference: ‘The conclusion of this inference is false, so this conclusion is false’. His account of insolubles supported his claim that the conclusion is false, and so the premise, referring to the conclusion, would seem to be true. But what is his account of validity that can allow true premises to lead to a false conclusion? This article considers Roger’s own account, as well as that of Paul of Venice, writing some sixty years later, whose account of the truth and falsehood of insolubles followed Roger’s closely. Paul endorsed Roger’s three claims. But their accounts of validity were different. The question is whether these accounts are coherent and support Paul’s claim in his Logica Magna that he endorsed all the normal rules of inference.

The Logic of the Self-Refutation Argument in Dissoi Logoi 4.6

Dissoi Logoi 4.6 presents a beautiful self-refutation argument, which I analyse here, offering a different assessment of its relation to self-contradiction and the Liar paradox from the only one available in the literature.