I show that intuitive and logical considerations do not justify introducing Leibniz’s Law of the Indiscernibility of Identicals in more than a limited form, as applying to atomic formulas. Once this is accepted, it follows that Leibniz’s Law generalises to all formulas of the first-order Predicate Calculus but not to modal formulas. Among other things, identity turns out to be logically contingent.

Ben-Yami presents Wittgenstein’s explicit criticism of the Platonic identification of an explanation with a definition and the alternative forms of explanation he employed. He then discusses a few predecessors of Wittgenstein’s criticisms and the Fregean background against which he wrote. Next, the idea of family resemblance is introduced, and objections answered. Wittgenstein’s endorsement of vagueness and the indeterminacy of sense are presented, as well as the open texture of concepts. Common misunderstandings are addressed along the way. Wittgenstein’s ideas, as is (...) then shown, have far-reaching implications for knowledge of meaning and the nature of logic, and with them to the nature of the philosophical project and its possible achievements. (shrink)

Descartes was the first to hold that, when we perceive, the representation need not resemble what it represents but should correspond to it. Descartes developed this ground-breaking, influential conception in his work on analytic geometry and then transferred it to his theory of perception. I trace the development of the idea in Descartes’ early mathematical works; his articulation of it in Rules for the Direction of the Mind; his first suggestions there to apply this kind of representation-by-correspondence in the scientific (...) inquiry of colours; and, finally, the transfer of the idea to the theory of perception in The World. (shrink)

There is currently a theoretical tension between young children’s failure in False Belief Tasks (FBTs) and their success in a variety of other tasks that also seem to require the ability to ascribe false beliefs to agents. We try to explain this tension by the hypothesis that in the FBT, children think they are asked what the agent should do in the circumstances and not what the agent will do. We explain why this hypothesis is plausible. We examined the hypothesis (...) in two experiments, each involving a new task. In the first task, the hypothesised misunderstanding of the question leads to failure without the need to ascribe a false belief, and we show that failure in this new task is correlated with failure in the FBT. In the second task, passing which requires ascribing a false belief to an agent, and for which we have partial yet encouraging results, the children are asked a question which is unlikely to be misunderstood. Children pass this task much more often than they do a standard FBT. The mentioned tension is thus resolved. We conclude that the so-called False Belief Task probably does not check the ability to ascribe false beliefs but rather linguistic development. (shrink)

I explain why model theory is unsatisfactory as a semantic theory and has drawbacks as a tool for proofs on logic systems. I then motivate and develop an alternative, the truth-valuational substitutional approach (TVS), and prove with it the soundness and completeness of the first order Predicate Calculus with identity and of Modal Propositional Calculus. Modal logic is developed without recourse to possible worlds. Along the way I answer a variety of difficulties that have been raised against TVS and show (...) that, as applied to several central questions, model-theoretic semantics can be considered TVS in disguise. The conclusion is that the truth-valuational substitutional approach is an adequate tool for many of our logic inquiries, conceptually preferable over model-theoretic semantics. Another conclusion is that formal logic is independent of semantics, apart from its use of the notion of truth, but that even with respect to it its assumptions are minimal. (shrink)

I introduce some distinctions concerning depiction and show that the checker-shadow phenomenon is not an illusion of the kind it is claimed to be. This might also help to think more clearly about other ‘illusory’ phenomena.

I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of complementary inaccuracy between spatial location and velocity is derived, and its relation to the Uncertainty Principle discussed. In addition, even if the laws of nature are deterministic, the behaviour of systems will be random to some degree. These and other (...) considerations draw classical physics closer to Quantum Mechanics. An arrow of entropy is also derived, given an arrow of time. Lastly, chaos is given an additional, objective meaning. (shrink)

I agree with Nachev and Hacker’s general approach. However, their criticism of claims of covert automaticity can be strengthened. I first say a few words on what voluntary action involves and on the consequent limited relevance of brain research for the determination of voluntariness. I then turn to Nachev and Hacker’s discussion of possible covert automaticity and show why the case for it is weaker than they allow.

An expression of disagreement with the views stated in The New York Declaration on Animal Consciousness.